Proceeding of the NITINOL Heat Engine Conference

NSWC MP 79-44

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Proceedings of the
Heat Engine
Conference

E

INITINOL

EAted by: David M. Goldstein
Leo J. McNamara

26-27 September 1978
Silver SprIng, Maryland

SpoRsored by:
U.S. Naval Surface Weapons Center
U.S. Department of Energy

Is

A

> Approved for publk release, distributon numt ed.
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UNCLASSIFIED
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MP-79-441

RPORTDOCMENTTIO

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INSTRTIN

COMPLETING FORM

T ACESIONBEFORE

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4. TITLE (end ..ble

S.

TYPE OF REPORT A PERIOO. CO)VERED

7.

S.

CONTnACT OR GNAW Ir N~UMBER(s)

_

Proceedings of t~e NITINOL Heat Engine Conference,
26-27 Septemnber 1978, Silver Spring, MD. 5.~eerecvIa*2-7Spebr17
by .S.-Nave-1-Surfee eeponrt-enter eiid-ttS.
6 PERFORMINGOG. REPORT NUMBER
60"0&

Editors:
David M. Goldstein
Leo J. McNamara

DOE-ET-78-I-OL-5919, updatedi
by DOE-DE-AI05-78-0R05919

S. PERFORMING ORGANIZATON NAME AND AOOR LSS

10.

Naval Surface Weapons Center
White Oak

0;AREA A WORK UNIT NIJMBERS
0

Silver Spring,
It.

MOD

PROGRAM ELEMENT, PROJECT. TASK(

20910_________________

CONTROLLING OFFICE NAME AND AOORE1FIS

t2. nepop7 rATE

I3."UM8 EN

TT' MONITOtwiN

ACENrY NAME II ADDRESS(of different fro.n Controlling Office)

U.S. Department of Enero
gyASFE

Ofc. of Assistant Secretary for Fossil Fnergy
1000 Independence Ave., S.W.

OF PAGES

15. SECUR~ITY Ct ASS. (of this ruport)

UCASFE
-Is.--EcL ASSIFICATION/ODOWNGRtAOING

Washington, U.C. 20585

SNOL

IS. DISTRIBUTION STATEMENT rof this Report)

Approved for public release, distribution un'limited.

17.

D.STRIBUTION STATEMENT (of the sbntt~ct entered In block 20. If different fromn Report)

III. SUP06LEMENTARY NOTES

IS. KEY WORDS (Continue m reverse side It noeeeiry and Identify by bloca nuniber)4

Energy Conversionl

NIT INOL

Heat Engines

'

Shape Memory Effect

K hape Memory Alloys
20. ASSYR AC T (Confteewe ae reve-rse aide if nocnedey and Identify by block nuntber)

~Co

erence on NITINOL Heat.Engines was held at !NSWC on 26-201 September
197 .Twelve

technical papers were tape-recorded and reduced to these Pro-,
ceedings. The Conference technical sessions were; Overview of Low Grade
Energy Utilization, NITiNOL Heat Engines, Engine Performance Efficiency
and-Thermodynamics, and NITII40L Alloys.

7

Engine efficiencies were reasonably estimated to range up to 4% absolute,

QO2-L-04.
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30% of Carnot (maximum) efficiency, although some were estimated higher.
Output estimates ranged from a few watts to a kw per kilogram of NITINOL alloy,

>;or

Engine performance data and new designs up to 25 HP were presented during
the sessions. The thermodynamics of NITINOL Heat Engines was examined from
the viewpoints of both theory and application. Tests on NITINOL wire in
imulations of various Heat Engine cycles are reported on, as well as the
trtning' (bi-stable memory) phenomenon. Progress on preparation of NITINOL
alloys by powder metallurgy techniques is discussed, as well as X-ray
diffraction studies of the shape memory transformation.
Separately, inventors displayed 8 different working engines.
of these models was estimated to be under 10 watts for each.

Engine output

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UNCLASSIFIED
SECURITY CLASSIVICATIO4 OF 71413 PAGE(ften Date ZM6*

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Acession Fo"
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MP 79-441

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FOREWORT)

The potential of shape memorv effect (SME) alloys as the workiny element of useful
energy converter.s has excited a great many researchers. NITINOLA has been the alloy
used in most demonstration Heat Engines built to date. It was fitting, therefore, that the
U.S. Naval Surface Weapons Center (NSWC), at which NITINOL was invented, hosted the
first conference 3n this subject. A second conference will be held in Leuven, Belgium in
August 1982, at Katholieke Universiteit.
The U.S. Department of Energy (DOE) provided funds, and NSWC provided technical
assistance, to support development of Heat Engines. Mr. Marvin E. Gunn, Jr. of the
Division of Power 3ystems wa: Program Manager for DOE under Interagency Agreement
DOE ET-7R-I-05-5919, subsequen-ly updated by DOE DE-AI05-78OR05919. Mr. David M.
was Program Manager for NSWC.
The purpose of the Conference was threefold:

iGoldstein

* to review the state of the art,
!,~~~ reerh

nto indicate the direrction of curre.nt and proposed

research, and
*

to provide a forum for the exchaynge of information.

The Conference opened with introductory remarks followed by an Overview of Low
Grade Energy Utilization, Congressional, DOE, and Navy viewpoints on this subject were
given by the respective representatives: for Congress, Dr. John Andelin of the House
Committee on Science and Technology, and Dr. David Claridge of the Office of
Technology Assessment; for DOE, Mt. Marvin Gunn, Jr4 and for Navy, B. Sobers of the
Navy Energy and Natural Resources R&D Office. These presentations are not included in
these Proceedings, which are limited to NITINOL-related technicai material.

INITINOL alloys are based on the compound TiNi. They exhibit a shape memory
phenomenon due to an austenite * "martensite phase transformation. Specifically, if
deformed in the martensite phase, they will recover their prior shape upon reheating into
the austenite temperature range. The increased modulus of the austenite enables useful
work to be done by the warmed alloy, above that used to deform the cold metal. This
shape memory capability is exploited in the NITINOL Heat Engine.

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MP 79-441
Fourteen technical papers were presented. One by Mr. J.T. Gibbs, on StirlinR Cvcle
known
NITINOL Engine, was scheduled but not presented. Neither Dr. H. Mohamed's (now
delivered,
Banks
R.
Mr.
which
Stresaes,
as Dr. H. Mohamed Tawancy) paper on Recovery
designs, is
nor the paper Mr. C. Raymond gave, which contained numerous innovative
included in the Proceedings.
The Conference was organized in much less than the normal workiig time allowance
the option
for a conference at this Center. Due to this short time, the authors were given
in these
publication
for
papers
the
prepare
to
of using their recorded presentations
no peer
been
has
there
clarity,
for
reviewed
were
papers
Proceedings. Although the
own, and are
review for technical accuracy. The data and viewpoints are the authors'
at the
delivery
offered to the community as their best input and not necessarily their oral
Conference.
Eight different prototype engines, all working, were displayed by 7 inventors.
Britain.
Several of these prototypes were subsequently shown on television in the U.S. and
allowed
buffet
social
a
During the intervening evening of the two-day Conference,
advantage.
Conference participants to interchange information to mutual
of
The success of this Conference was in great measure due to the dedicated effort
Schmitz,
George
several people: Mrs. Joy White foremost and Mrs. Deanna Zook, Messrs.
who
Scott Hoover, and Ernie Inman. Our appreciation extends to other NSWC staffers
Reception.
and
participated in the Conference, Engine Demonstrations,
Finally, it is appropriate to recognize the efforts of Mr. David Goldstein in
organizing this Conference.

JACK DIXON
By direction

MP 79-441

PREPACE

Over 2/3 of the thermal energy available in the U.S. is rejected as waste heat.
Creating economically viable Heat Engines--using this low grade (less than 1000 C)
heat energy--would clearly serve the national interest. In recogenition of this, the U.S.
Department of Energy supported research in engine design, construction, and efficiency
determination. D)OE's agreement with the Navy provided for a coordination center,
information interchange, and an enhanced supply of NITINOL alloy for workers in the
Heat Engine field.
The Navy has its own potentially valuable uses for NITINOL engines, for exampl:.
helping to reduce petroleum energy dependence, and providing power sources for remote
locations as well as for emergency use at sea.
Aside from helping to conserve power, any significant increase in NITINOL use will
also benefit the Navy in another way. A larger market for NITINOL will lower its cost
and remove some of the restrictions on its supply. This would enhance its use in ship
construction, where it is now being introduced in tube and pipe couplings. These
couplings--now being evaluated in new Navy destroyers--provide for weld-free,
high-pressure connections, using the same shape memory phenomenon as for Heat
Engines. A joint market in both Heat Engines and couplings is of interest to the Navy,
since it can utilize both devices in large quantities.
In sum, NITINOL's total return on investment to the Navy is potentially very
attractive.
The va,iety of model NITINOL engines constructed in the U.S. and abroad has long
since dissipated the question of whether these engines would work. Their designs
generally suggest that they can be scaled in size to provide greater than I kilowatt of
power. The remaining question is economic: comparing NITINOL engines with other low
temperature regi,'.e energy converters.
We can assume that the energy cost (of waste heat or solar energy) is negligible for
organic Rankine engines, photovoltaics, and NITINOL Heat Engines. A comparison of
their installed costs per kw is

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MP 79-441

Energy Converter Type

C-ost fkw

Rankine

$400-$6001

Photovoltaic

$10,002

NITINOL

$600

For comparison, nuclear power is $1000/kw.
If NITINOL engines can use the low grade heat now being wasted, they will be a
boon to the nation. As shown above, these engines have potential and should be further
investigated. The authors of the following paoers are pioneers in this effort.

lAssumes annual production of 10,000 to 20,000 units. If production is just a few
engines, cost would be about $2000-$4000 per kw. Costs are projected from 1973 data,
allowing 100% for inflation. U.3. Office of Technologzy Assrssment, Application of Solar
Techno~ly to Today's Energy Needs, V. 1, June 1978, pp. 346, 354.
2

Assumes optimal conditions of "noon on a sunny day." AV. Mossbere, "Many ExDerts
Say Solar Electric Cells Too Costly Now, l-ave a Rright Future," Wall Street Journal, 19

Dec 1979.
3

The $600 per kw assumes a power output of 1/2 kw per kilogram (250 watts/lb) oi
NITINOL. The output of NITINOL Heat Engines has been estimated at up to I kw per
kg. Measured values of up to 0.3 kw per kR (10wper Ib) are reported in these
Proceedings. A kg of NITINOL wire of 1/2 mm (0.020 inch) diameter costs about $1200 to
produce in laboratory size lots. In commercial production lots of 10,000 kg per year, $200
per kg is reasonable to expect. NITINOL costs are assumed to be 2/3 of total engine cost.

iv

NSWC MP 79-441

CONTENTS

Page
THE BANKS ENGINE: PAST, PRESENT, AND FUTURE,
R. Banks ............
..............................

.1-1

ONE HORSEPOWER THERMOTURBINE NITINOL ENGINE,
W. S. Ginell, 3. L. McNichols, 3. $. Cory .....................
NITINOL BELT ENGINE,
D. 3. Sandoval. . ..........

..

.

.........................

2-1
3-1

SOME ENGINEERING PARAMETERS FOR A NITINOL ENGINE DESIGN,
P. A. Hochstein . ..
. . . . . . ..
..
. . . . . . . . . ..
. .. .

4-1

AN ANALYSIS OF FACTORS AFFECTING THE EFFICIENCY OF THE
SOLID-STATE ENGINE,
A. A. Golestaneh........
............................

5-1

THERMODYNAMICS OF SME-ENGINES,
P. Wollants, M. DeBonte, L. Delaey, 3. R. Roos ...
- ERMOMECHANICAL BEHAVIOR OF NITINOL,
*. S. Cory ...................

.............
...........

....

6-1

...

7-1

EXPERIMENTAL RESULTS ON A CONTINUOUS-BAND NITINOL ENGINE,
A. D. Johnson . . ..........................

8-1

EFFICIENCY OF ENERGY CONVERSION IN NITINOL,
R. Kopa ........................

.......

9-1

A.D. 3ohnson. . . . . .................

.........

10-1

REPRESENTATION OF MARTENSITIC TRANSFORMATION IN SHAPE
CHANGE SPACE, THE NATURE OF INTERNAL STRESS RETAINED
DURING SM TRANSFORMATION, AND OPERATIONA.. PERFORMANCE
OF A SIMPLE NITINOL ENGINE,
K. H. G. Ashbee, B. Cunningham ......
....................

. ..

HOT ISOSTATICALLY PRESSED POWDER METALLURGV NITINOL WIRE,
M. T. Podub, W. A. Johpson, S. H. Reichman ..................
....

v/vi

11-1
12-1

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NSWC MP 79-441

ILLUSTRATIONS
Chapter I
I
2
3

Page
THE ORIGINAL LAWRENCE BERKELEY LABORATORYPRCTOTYPE NITINOL ENGINE . . . ......
...
THE FIRST CONVERSION OF SOLAR ENERGY TO
MECHANICAL WORK ....................
....
CUTAWAY VIEW OF THE "CAM-TRACK"0 NITINOL
ENGINE ......
......................
....

1-8
1-9
1-10

Chapter 2
I
2
3
4
5

DIFFERENTIAL PULLEY THERMOTURBINE ENGINE
(AFTER JOHNSON) .....
.................
....
GEAR-COUPLED THcERMOTURBINE ENGINE ......
...
NITINOL ENG!NE MODULE - END VIEW SCHEMATIC...
NITINOL ENGINE MODULE .................
....
QUALITATIVE SHAFE OF NITINOL STATE SURFACES . .

2-5
2-6
2-7
2-8
2-9

BASIC NITINOL BELT ENGINE ......
.............
BELT STIMULATION AND TORQUE SYSTEM ..........
ENGINE PERFORMANCE FOR STRAIN WHEELS .......
EFFICIENCY AND POWER FOR 2 STRAIN WHEELS ....

3-5
3-6
3-7
3-8

Chapter 3
I
2
3
4
Chapter 4
I
2
3
4RADIAL
5

ELECTRONIC DYNAMOMETER AND LOAD BANK FOR
NITINOL MOTOR TEST FACILITY........
. ...
BENDINC MODE NITINOL HEAT ENGINE (1975) NOM.
12 W OUTPUT SHOWING SECONDARY MEMORY
(TRAINING) ......
....................
....
PLAN VIEW OF ROTARY THERMAL ENERGY
CONVERTER ........
...................
THERMAL ENERGY CONVERTER SECTION
THRU OUTER RIM - SHOWING CAM DETAIL ....
...
EDGE VIEW OF 'UNROLLED' ROTARY THERMAL
CONVERTER - SHOWING MOTION OF THERMOELASTIC SHAPE MEMORY ELEMENT VANES
THROUGH CYCLICAL STRAINING AND
UNSTRAINING (POWER) CYCLES ............
...

vii

_Jw

4-5
4-6
4-7
4-8

4-9

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NSWC MP 79-441
ILLUSTRATIONS (Cont.)
Chapter 4

Pagi

6

TORSIONAL VANE NITINOL HEAT ENGINE MK I ACTIVE
ELEMENTS: 24 2.0 in x .38 in )f .012 in V4072 TRR
60/80 0 F NITINOL MATL ....
.............
..
TORSIONAL VANE NITINOL HEAT ENGINE - 24
ELEMENT 23 gm V4072 MATERIAL .............
FROPOSED SAFE OPERATING AREA FOR NITINOL
STRESS LIM!TING WITH SPRINGS ............
...
ROTARY THERMAL ENERGY CONVERTER ..........
ROTARY THERMAL ENERGY CONVERTER ..........
ROTARY THERMAL ENERGY CONVERTER ..........
ROTARY THERMAL ENERGY CONVERTER ..........
ROTARY THERMAL ENERGY CONVERTER ..........
ROTARY THERMAL ENERGY CONVERTER ..........
ROTARY THERMAL ENERGY CONVERTER .......
...
ROTARY THERMAL ENERGY CONVERTER ..........
ROTARY THERMAL ENERGY CONVERTER ..........

7
8
9a
9b
9c
9d
9e
9f
9g
9h
9i

4-10
4-11
4-12
4-13
4-14
4-15
4-16
4-17
4-18
4-19
4-20
4-21

Chapter 5
la

SOLID-STATE ENGINE MADE WITH NITINOL WIRES,
OPERTING WITH HOT RESERVOIR (WATER AT
40-75 C AND COLD RESERVOIR (AIR) AT 23 C
.
A UNIT OF THE CRANKING SOLID-STATE ENGINE
MADE WITH l-mm-dia NITINGL WIRE ELEMENTS .
FRACTIONAL SHAPE-RECOVERY OBTAINED
ISOTHERMALLY AT DIFFERE.NT TEMPERATURES .
THE SCHEMATIC STRESS- TEMPERATURE PHASE
DIAGRAM FOR A BINARY NITINOL SM ALLOY . ...
SCHEMATIC REPRESENTATION OF THE M+P
TRANSFORMATION UNDER AN APPLIED STRESS,
ACCORDING TO REACTIONS (3a) to (3c) OF THE
TEXT .......
......................
....
ISOTHERMALLY OBSERVED STRESS-STRAIN (a-)
CURVES FOR NITINOL WIRE SPECIMEN (1 mm dia
x 56 mm) WITH T- Z 33+70 C................
....
PLOTS OF Z VS q EQ. (10), OBTAINED FROM
ISOTHERMAL STRESS-STRAIN DATA ON A NITINOL
WIRE SPECIMEN (1 mm dia x 56 iumi) WITH
TC = 3 3 +70C ............................
...
TRANSIENT STRESS RESPONSE OF A STRAIGHT NITINOL
WIRE SPECIMEN (1mm dia x 56 mm) UNDER A
CONSTANT STRAIN, SUBJECTED TO A SUDDEN
INCREASE IN TEMPERATURE .............
VARIATION OF Z, EQ. (0) WITH ISOTHERMAL TEST
TEMPERATURE FOR FIXED ci = 2.5% XL = TL - TC
AND XH =TH -TC
..................

Ib
2
3
4

5
6

7

8

2_ii

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5-12
5-13
5-14
5-15

5-16
5-17

5-18

5-19
5-20

NSWC MP 79-441
ILLUSTRATIONS (Cont.)
Chapter 5 (Cont.)
9

Emse

TRANSIENT STRESS RESPONSES OF NITINOL WIRE
SPECIMEN (I mm dia x 56 mm) TRAINED IN CURVED
SHAPE WITH SPAN 65 mm AND HEIGHT 13 mm.
FIGURES ON EACH CURVE ARE TEMPERATURES
T AND T AT WHICH THE SR STRESS WAS
MASUREb .......
..................

.....

5-21/22

Chaf)ter 6
I

3

5

6
7
8
9a
9b
9c

SCHEMATIC REPRESENTATION OF THE PARTIAL
DERIVATIVES OF THE CHARACTERISTIC
FUNCTIONS G AND G* .....
..............
....
THREE-DIMENSIONAL SCHEMATIC REPRESENTATION
OF THE CLAPEYRON-LIKE RELATION:
..
dF/dT = -(AS/AL)IM . .. .. .. ...

6-13
6-13

SCHEMATIC REPRESENTATION IN A TS-DIAGRAM
OF THE WORK PERFORMING CYCLE OF A SINGLE
CRYSTAL .......
....................
....
TYPICAL TENSILE CURVE FOR A Cu - 25, 33 AT %
Zn - 9, I AT % Al SINGLE CRYSTAL AS DETERMINED BY VAN HUMBEEKI6 ..................
...
SCHEMATIC REPRESENTATION OF THE o-T
RELATIONShLPS AS DERIVED FROM A NUMBER OF
TENSILE TESTS AT DIFFERENT TEST TEMPERATURES ...............
WORK PER CYCLE AND POWER (FOR VARIOtJS CYCLE
SPEEDS) OF THE CuZnAX SINGLE CRYSTAL AS A
FUNCTION OF ATo (To(o) = 206 K) .....
..........
EFFICIENCY VS. &To DIAGRAM FOR To(o)
TEMPERATURES OF 100 K, 200 K, 300 K and 1100 K
•
SIMPLIFIED QUANTITATIVE TS-DIAGRAM FOR THE
WORK PERFORMING CYCLE AS DiESCRIBED IN THIS
PAPER .........
......................
a-c-DIAGRAM AS PROPOSED BY JOHNSON ...........
...
TS-DIAGRAM AS PROPOSED BY JOHNSON .......
...
TS-DIAGRAM OF THE WORK PERFORMING CYCLE
PROPOSED BY JOHNSON; CORRECTED BY THE
PRESENT AUTHORS ........
................

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6-14
6-14

6-15
6-15
6-16
4-16
6-17
6-17
6-17

Chapter 7
I

5

POSSIBLE THERMODYNAMIC STATES AND PATHS OF
NITINOL .....
.....................
ISOTHERMS AND TRANSITION SURFACE INITIAL
SLOPES ..........
..................
IYo f HERMS OF TRANSITION SU.FA.CES.....7-8
POSSIBLE CONSTANT F, L, and T THERMODYNAMIC
PATHS ON A SINGLE STATE SURFACE ............
NITINOL STATE EQUATIONS ...
.............
...

76

UNIUENESS
SURFACES .
. .7-..itT
NONSTABLE, OF STATE
ISOTHERMAL
THERMODYNAMIC

2
3
4

7-6
7-7
7-9
7-10
7-12

UA

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NSWC MP 79-441
ILLUSTRATIONS (Cont.)
Chapter 7 (Cont.)
8
9

10
11
12

Page
STABLE, CYCLIC, ISOTHERMAL THERMODYNAMIC
PATHS ............
.............
..
THERMODYNAMIC PATHS OF A CONSTANT
TEMPERATURE - CONSTANT LENGTH (TL) NITINOL
ENGINE CYCLE, SOLiD LINES ARE DRAWN ON
UPPER SURFACE - DASHED LINES ON LOWER
....
.....................
SURFACE .......
PERFORMANCE CALCULA TIONS USING
THERMODYNAMIC PATHS
.............
RELATIVE PERFORMANCE OF DIFFERENT CYCLE
TYPES ........
.....................
....
ELEMENT SHAPE AND ALLOY CHARACTERIZATION .

7-13

7-14
7-15
7-16
7-17/18

Chapter 8
1
2
3

CONTINUOUS-BAND NITINOL HEAT ENGINE
INSTRUMENTED FOR EFFICIENCY MEASUREMENTS
DOUBLE REGENERATOR AS USED IN EFFICIENCY
MEASUREMENTS ....
................
NO. 2 TIMET 0.030" WIRE, TRAINED ON ENGINES NO.
10-14 (1974-75) (SEVERAL HOURS ACCUMULATED
RUN TIME) ......
...................
.....

8-6
....

8-7
8-8

Chapter 9
I
2
3
4
5
6
7
8

9
10
11

CYCLE SIMULATOR EXPERIMENTAL SYSTEM .....
.
DESIGN DRAWING OF THE CYCLE SIMULATOR .......
LABORATORY EXPERIMENTAL SET-UP, INCLUDING
CYCLE SIMULATOR, ELECTRONICS AND VIDEO
DATA RECORDING SYSTEM .................
VIDEO RECORD OF A TYPICAL CONSTANT-STRAIN
ISOTHERMAL CYCLE......
.
*...............9-32 •
CONSTANT-STRAIN ISOTHERMAL CYCLE RESULTING
WHEN HEAT IS SUPPLIED BY ELECTRIC PULSE . .
STRESS-LIMITED ISOTHERMAL CYCLE ...........
. ..
CONSTANT-STRESS ISOTHERMAL CYCLE .......
. ..
THERMODYNAMIC EFFICIENCY OF THE ENERGY
CONVERSION IN NITINOL AS THE FUNCTION OF
PEAK STRESSca(a=o 3 ), AND PERCENT ELONGATION E OF THE WIRE ELEMENT .............
....
PEAK RECOVERY STRESS DURING VARIOUS ENGINE
CYCLES AS THE FUNCTION OF TIHE HOT
RESERVOIR TEMPERATURE ..............
USEFUL MECHANICAL WORK PRODUCED BY VARIOUS
CYCLES AS THE FUNCTION OF PEAK RECOVERY
STRESS ........
......................
...
THERMODYNAMIC ENGINE CYCLE EFFICIENCY AS THE
FUNCTION OF THE HOT RESERVOIR TEMPERATURE.

x

9-29
9-30
9-31

9-33
9-34
9-35

9-36
9-37
9-38
9-39

NSWC MP 79-441
ILLUSTRATIONS (Cont.)
Page

Chapter 9 (Cont.)
12

13
14
15
16

17

18

19
20
21
22

RATIO OF THE THERMODYNAMIC ENGINE CYCLE
EFFICIENCY TO THE CARNOT CYCLE EFFICIENCY AS
THE FUNCTION OF THE HOT RESERVOIR
TEMPERATURE ......
..................
...
THERMODYNAMIC ENGINE CYCLE EFFICIENCY AS
THE FUNCTION OF HEAT INPUT ..............
THERMODYNAMIC ENGINE CYCLE EFFICIENCY AS THE
FUNCTION OF PEAK RECOVERY STRESS ......
.
SCHEMATIC DIAGRAM OF THE CONSTANT-STRAIN
ISOTHERMAL CYCLE
...............
DUAL-BEAM OSCILLOSCOPE RECORD OF THE NITINOL
RES!ST!VITY (UPPER TRACE) DURING THE
CONSTANT-STRAIN ISOTHERMAL CYCLE (LOWER
...
......................
TRACE) ........
TOTAL HEAT INPUT AND THE LATENT HEAT OF PHASE
TRANSFORMATION AS THE FUNCTION OF THE
PEAK RECOVERY STRESS DURING THE CONSTANTSTRAIN ISOTHERMAL CYCLE ...............
...
LATENT HEAT OF REVERSE TRANSFORMATION
MARTENSITE + AUSTENITE) AND THE "APPARENT"
LATENT HEAT OF FORWARD TRANSFORMATION
(AUSTENITE+ MARTENSITE) AS THE FUNCTION
OF THE PEAK RECOVERY STRESS ..........
...
SCHEMATIC DIAGRAM OF THE SEMI-ADIABATIC
CYCLE ........
......................
....
DETERMINATION OF THE HEAT INPUT TO THE
NITINOL WIRE DURING THE CONSTANT-STRAIN
ISOTHERMAL CYCLE .....
..............
...
CURRENT AND VOLTAGE PULSES FOR HEATING OF
THE NITINOL WIRE ELEMENT,, JD THE WIRE
CONTPACTION TIMING TRACE .............
...
PEAK RECOVERY STRESS RISE DURING THE ELECTRIC
HEATING PULSE AND THE SUBSEQUENT STRESS DECAY
DUE TO THE HEAT LOSSES FROM THE NITINOL
WIRE ELEMENT .....
.................
.....

9-40
9-41
9-42
9-43

9-44

9-45

4
9-46
9-47
9-48
9-49

9-50

Chapter 10
I
2

3

. . ..
STRESS-STRAIN FIXTURE ...................
FRESHLY - ANNEALED RAYMOND - TIMET WIRE
0.018" x 20" LONG (0.7 gin) ISOTHERMS: STATE
.
....................
SURFACES .......
FRESHLY - ANNEALED RAYMOND - TIMET WIRE
0.018" x 20" LONG (0.7 gin) CONSTANT FORCE CYCLE
FIRST 2 CYCLES.
FRESHLY - ANNEALED RAYMOND - TIMET WIRE
0.018" x 20" LONG (0.7 gin) CONSTANT FORCE CYCLE
CYCLES 3-14 ......
...................
....

10-10
I.10-11
1...................
0-12
10-13

xi

AL

NSWC MP 79-441
ILLUSTRATIONS (Cont.)
Chapter 10 (Cont.)
5
6
7

8

Page

FRESHLY - ANNEALED RAYMOND - TIMET WIRE
0.018" x 20" LONG (0.7 gin) CONSTANT - FORCE
CYCLES: 15-21 ......
..................
...
FRESHLY - ANNEALED RAYMOND - TIMET WIRE
0.018" x 20" LONG (0.7 gin) AFTER 21 CONSTANT FORCE CYCLES, T 50& 95',F = 5N & 35OR 45N .
FRESHLY - ANNEALED RAYMOND - TIMET WIRE
0.018" x 20" LONG (0.7 gin) ISOTHERMS: STATE
SURFACES .........
.
FRESHLY - ANNEALED RAYMOND'- TIMET 0, 1" x 20'"

10-14
10-15

10-16

LONG WIRE (0.7 gin) LOW - HOT - IORCE CYCLE

TCOLD = 2°C THOT> 95 0 C CYCLES 1-14
9

10

......

.

10-17

.

10-18

FRESHLY - ANNEALED RAYMOND - TIME1 WIRE
(1.018" x 20" LONG (9.7 gm) LOW - HOT - FORCE

CYCLE
C THOT> 95C CYCLES 15-21.
RAYMOND - TIMET WIRE 0.018" x 20" LONG (0.7 gm)
AFTER 21 LOW - HOT - FORCE CYCLES

11

ISOTHERMS: STATE SURFACES.........
. ..
RAYMOND - TIMET WIRE 0.018" ,: 20" (0.7 gin) AFTER
ANNEALING & CYCLING 21 TIMES IN LOW-HOTFORCE CYCLE
.................

12

FRESHLY - ANNEALED RAYMOND - TIMET WIRE

13
14
15

0.018" x 18" (0.7 gm) ISOTHERMS: STATE SURFACES.
RAYMOND - TIMET W!RE 0.018" x 20" (0.7 gm) FIXED LENGTH CYCLES 1-12 ....
..................
RAYMOND - TIMET WIRE 0.0IS" x 20" LONG (0.7 gin)
AFTER 12 CONSTANT - LENGTH CYCLES ISOTHERMS:
STATE SURFACES .....................
NO. 2 TIMET 0.030' WIRE, TRAINED ON ENGINES NO.
10-14 (1974-75) (SEVERAL HOURS ACCUMULATED
RUN TIME) 3% ELONGATION RATIO (1.75 gin)

16

17

18

19
20

xii
_______

....

NO. 2 TIMET 0.030" WIRE, TRAINED ON ENGINES NO.
10-14 (1974-75) (SEVERAL HOURS ACCUMULATED
RUN TIME) 3% ELONGATION RATIO (1.75 gm) 3
CONSTANT FORCE CYCLES ...............
...
NO. 2 TIMETn.030" WIRE, TRAINED ON ENGINES 10-14
(1974-75) (SEVERAL HOURS ACCUMULATED RUN
TIME) 3% ELONGATION RATIO (1.75 gin) LENGTH
VS TEMP AT CONSTANT FORCE .....
..........
NO. 2 TIMET 0.030" WIRE, TRAINED ON ENGINES NO.
10-1' (1974-75) (SEVERAL HOURS ACCUMULATED
RUN TIME) 3% ELONGATION RATIO (1.75 gin) LENGTH
VS TEMPERATURE AT CONSTANT FORCE ......
...
RAYMOND - TIMET WIRE .018" x 20" AFTER CYCLE
21 TIMES LOW-hOT-FORCE CYCLE ...........
...
RAYMOND - TIMET WIRE 0.018" x 20" AFTER CYCLE
21 TIMES-IN LOW-HOT-FORCE CYCLE
...

10-19
10-20
10-21
1-22
10-23
10-24

10-25

10-26

10-27
10-28
10-29

I

NSWC MP 79-441
ILLUSTRAT!ONS (Cont.)
Chapter 11
I

3a
3b
4a

4b

5
6

8
9
10
11

11
12
13
14
15

ILLUSTRATING THE GENERAL CASE OF NON-PLANAR
LOOPS OF INTERSECTION BETWEEN A SPHERE IN
THE PARENT PHASE ANI THE ELLIPSOID TO WHICH
IT TRANSFOPMS IN THE MARTENSITE PHASE . ...
THE SPECIAL CASE OF FIGURE I CORRE:SPONDING TO
ONE OF THE PRINCIPAL STRAINS EQUALS ZERO .. .
SPHERE TO ELLIPSOID TRANSFORMATION ..........
PURE SHEAR DEFORMATION ................
....
SHAI Z CHANGE SPACE REPRESENTATION OF
MARTENSITIC TRANSFORMATION BETWEEN CUBIC
AND ORTHORH-OMIC STRUCTURES (a) FOR ONE
PRINCIPAL STRAIN POSITIVE ...............
....
SHAPE CHANGE SPACE REPRESENTATION OF
MARTENSITIC TRANSFORMATION BETWEEN CUBIC
AND ORTHORHOMBIC STRUCTURES (b) FOR
TWO PRINCIPAL STRAIN POSITIVE ...............
SCHEMATIC REPRESENTATION OF TWO TWINS HAVING
THE ORTHORHOMBIC (10+1) PLANE IN COMMON. ..
COHERENT MICROSTRUCTURES FOR THE PRINCIPAL
STRAIN PERPENDICULAR TO THE PAPER EQUAL TO
ZERO ........
.......................
....
SHAPE CHANGE SPACE REPRESENTATION OF
MARTENSITIC TRANSFORMATION BETWEEN CUBIC
AND TE7RAGONAL STRUCTURES FOR (A)
c> alt = a 2 t (B)c <alt = a2t ...
............
...
MICROSTRUCTURE RESULTING FROM A MIXTURE OF
FOUR PSEUDO-TWINS ........
..............
REPRESENTATION OF GEOMETRICAL FORMATION
OF KOSSEL CONICS IN BACK REFLECTION AND
TRANSMISSION CASES ......
...............
SEQUENCE OF KOSSEL PATTERNS SHOWING EFFECTS
OF INCREASING STRESS ................
SCANNING ELECTRON MICROGRAPHS OF A Cu - 14.1
wt% Al - 3.0 wt% Ni ALLOY (A) BEFORE STRESSINDUCED MARTENSITIC TRANSFORMATION .......
SCANNING L.LECTRON MICROGRAPHS OF A Cu - 14.1
wt% Al - 3.0 wt% Ni ALLOY (B) AFTER STRESSINDUCED MARTENSITIC TRANSFORMATION. ....
SCANNINGx ELECTRON MICROGRAPH OF A Cu 14.1
wt% Al - 3.0 wt% Ni AFTER RELEASING THE STRESS.
KOSSEL PATTERN TAKEN FROM AREA SHOWN IN
FIGURE 1' . ......
i*.......................11-24
ANTICIPATED AXIAL RATIO VERSUS TEMPERATURE
RELATIONSHIP FOR AN ORTHORHOMBIC PHASE. . .
A SEQUENCE OF STILLS PRINTED FROM A CINE FILM
TAKEN DURING HALF OF A COMPLETE CYCLE
OF THE ENGINE, FILM SPEED - 24 f.p.s............

xiii

-5

11-9
11-10
11-11
11-12

11-13

11-14
11-15

11-16

11-17
11-IS
11-19
11-20
11-21
11-22
11-23

11-25
11-26

NSWC WP 79-441
ILLUSTRATIONS (Cont.)
Chapter 12
1
2
3
4

Page
SCHEMATIC OF INERT GAS ATOMIZER .............
SCANNING ELECTRON MICROGRAPHS OF NITINOL ASATOMIZED POWDER, HEAT R78245 (55.5 Wt.% Ni - 44.5
. .. .
Wt. 9%Ti) . . . . . . . . . . . . . . . . .
PHOTOMICROZRAPHS OF C/M NITINOL AFTER CONSOLIDATION BY HIP AT f600 F (871 C)/15,000 psi (103MPa)/ 3
hours ...............
.........
.
PHOTOMICROGRAPHS OF LONGITUDINAL (LEFT) AND
TRANSVERSE SECTION (RIGHT) OF P/M NITINOL WIRE
MADE FROM HEAT R78245 (55.5 Wt. % Ni - 44.5

Wt.% TO) .

12-5
12-6

12-7

)................

5

HIGH MAGNIFICATION MICROGRAPH OF P/M'NITINOL
ROD SHOWING FINE DISPERSION OF OXIDES AND/OR
........
CARBIDES ..............

6

PHOTOMICROGRAPHS OF LONGITUDINAL SECTION

7

(LEFT) AND TRANSVERSE SECTION (RIGHT) OF
NITINOL RODS MADE BY RECASTING POWDER
FROM HEAT 178245 (55.5 Wt. % Ni - 44.5 Wt. % Ti)
PHOTOMICROGRAPHS OF TRANSVERSE SECTION AREAS
OF HIP + DRAWN WIRE (LEFT) COMPARED WITH
RECAST POWDER + SWAGED ROD (RIGHT) .........

xiv

12-8
.2-9

12-IC
12-1i

NSWC MP 79-441

TABLES
Chapter 4

I

Page
TORSIONAL VANE NITINOL HEAT ENGINE MK I

.

.

.

4-22

Chapter 6
RESULTS OF A THERMODYNAMIC ANALYSIS OF THE
WORK PERFORMING CYCLE AS DESCRIBED IN THE
TEXT. ...
.......................
RESULTS OF A SIMPLIFIED THERMODYNAMIC
ANALYSIS OF THE WORK PERFORMING CYCLE . . .
DATA FOR THE CALCULATION OF THE WORK
PERFORMING CYCLE OF A CuZuA1 SINGLE
CRYSTAL ........
.....................
...
MEP.S;_!RED AND ESTIM \TED VALUES OF THE PC "ER
...........
GENERATED BY SME ENGINES .....

I
2
3
4

6-18
6-19
6-20
6-21

Chapter 8
I

RESULTS OF EFFICIENCY TEST: NONREGENERATIVE
NITINOL ENGINE ......
.................
RESULT OF EFFICIENCY TEST: NONREGENERATIVE
ENGINE WITH STEEL WIRE ....
.............
...
RESULT OF EFFICIENCY TEST: REGENERATOR ....
TYPICAL RUN PARAMETERS FOR POWER OUTPUT
STUDY ON A CONTINUOUS-BAND NITINOL ENGINE .

2
3
4

8-9
8-10
8-11
8-12

Chapter 12
SCREEN ANALYSIS AND DENSITY RESULTS FOR
.......
NITINOL HEATS R78245 AND R78246
CHEMICAL ANALYSIS OF NITINOL HEATS R78245 AND
R78246 ........
......................
...
CAN FILLING DATA FCR NITINOL SAMPLES ........
...

I
2
3

i

i

xv/ vi

12-12
12-13
12-14

NSWC MP 79-41

THE BANKS ENGINE: PAST, PRESENT, AND FUTURE
Ridgway Banks
Lawrence Berkeley Laboratory
University of California
It is certainly a pleasure to be at this conference which is, among other things, the first
official convocation of NITINOL, engine inventors and developers in history. We are an odd lot,
I suppose, but with certain strong points in common: we're generally stubborn as hell, and tend
to have very patient women, and water-stains on every pair of shoes we own. We a 1so share, I
Lhink, a strong belief in the potential contributions these machines may make to the
development of untapped energy resources, worldwide. I think you will find that, in many
cases, the work on display here today is the product Of individuals working very much on their

own...solving our common problems, and willing to share their solutions in using this amazing
material.
Now, in my case, when I was given my first piece of NITINOL in 1973, I had already been
lobbying for development of a solid-state heat engine for some time, but not one based on
NITINOL, which I had never heard of. I planned to use bimetallic working elements. I knew
the bimetallics would be extremely inefficient. But--when I analyzed the cost of using hightemperature (above the boiling point) thermal energy, which requires concentrating collectors,
and the cost of convc-sion at temperatures you can get pretty cheaply with flat-plate
collectors--I was convinced that the low-temperature regime was the way to go, because I am
just naive enough to believe that getting something is better than getting nothing. What I had
in mind was a little heat engine which could provide a few watts of auxiliary power to pump
water or charge ,atteries for a blackout. i wasn't trying to compete with Con Edison with
these things at all. I knew they would be. small and re.atively inefficient. But at that time
soiar energy was just getting off the ground, in the public sense, and, at the time I became
aware of it, solar energy's main practical impact was confined to oxidizing the finish on
people's cars as they sat out in the parking lot. I felt we could do something more interesting
than that.
When I got my first piece of NITINOL, it came with a printed sheet of instructions from
the Zdmund Scientific Company. It was a littie experimenters' kit. I looked at the wire. I
read the instructions, and I didn't believe them. I just had no place in my thinking for a
material that had these characteristics. I wasn't in a position to go through the annealing
procedures, either, so it was a matter of days before I did the obvious, classical experiment: I
cooled the wire, bent it, and stuck it in the company coffee pot. Now this little experiment
has been repeated on the av2rage a dozen times a day for over five and a half years, and I stil
get excited when it works. Luckily, it always works.
I have a movie which goes back to withir. i, couple hours of the first running of the first
engine, so I think I'll show that now, and just talk as it procedes.

iL

l-A

... . J.. . . ...- ,

'-'T '"7 - - x TJk~T

'-&

k:

'

. :r ' -' "

W ..--

'- '

-1,-t1

'

NSWC MP 79-441
(Film begins)...This is the first Edmund wire, on my first experimental apparatus: a
wooden stick. This shot shows the :rankshaft of the first engine; it is a simple coaxial
eccentric system. In the early days of running this machine, we were aware of only the Shape
Memory response that took place on heating NITINOL wires. So this film doesn't allude to the
fact that we f,,i , after several thousand cycles, that they begin to change shape
automatically .jo cooling as well. Only recently I measured the amount of work the wires in
the original eng, e can do on cooling, and it turns out to be perhaps an additional 20%
compared to the work done on heating.. .This was taken the first day the engine ran. There are
,.wenty loops of NITINOL wire (we doubled the number the following November because--just
at the time of the first press conference--the temperature of the hot-water heaters at LBL
was lowered to conserve energy). (See Fig. 1.)
Query from the audience:
time it ran?

Is this the first time it ran in front of a camera, or the first

RB: This is within two hours oi the first time it ran. Professor McMillan* (who is
incidentally responsible for the name originally given to this machine) came to see it just after
it first ran, and he s'uggested we call the photographers.
This shot shows the engine driving a small generator to light a tiny light bulb.. .Now we
are on the laboratory roof running the engine with a solar collector. It is going to do the same
trick with the light bulb. (Fig. 2.) This took place on an overcast day in November--the sun
didn't come out until about 11:30 a.m .... By 2:00 p.m. the water in this primitive collector
(which is just a black vinyl sheet draped in a styrofoam-lined box, with empty fluorescent light
tubes floating on the surface) got hot enough to run the engine an( light the bulb.
This is engine no. 2, an attempt to boost the power output of NITINOL wires in the
flexural mode sufficiently to impress the funding agencies in Washington. This machine
develops considerable torque (you can't stop it at the hub with your bare hands) but there are
tremendous friction losses, and so on, and a great problem in timing. You see, those are four
synchronized wheels, each of which has to be hung independently from shafts which can't pass
through the journals that support the wheels beneath it. And if it's not properly timed, you
lose all the mechanical advantage on opening and closing. It ran, and it was helpful; it
certainly showed me the limitations of the wheel approach. This is Dave Johnson's first
engine...and this is Dave Johnson. I had the privilege of bringing this machine, and the next
one you'll see, on a coast-to-coast tour which climaxed with some of the top management of
the Foxboro Company watching these things in fascination as the room they were standing in
filled up with water. Executives were literally ankle-deep and didn't complain at all.
This is Dave's Opus 5, otherwise known as the Flintstone Car engine. A differential
pulley mechanism isn't used on this one. Instead, the ratio is supplied by gears, so that the
wheel on one end turns faster than the one on the other end, as you will see...(Film ends.)
Query from the audience: This is not the kind of thing for which you ask for the Carnot
efficiency, is it?

*Edwin M. McMillan, Nobel Laureate, and former Director of Lawrence Berkeley Laboratory
1-2

NSWC MP 79-441
RB: We w(,uld love to say you don't have to, but that is not true. Certainly, the role of
these low-grade heat engines is recovering energy now wasted, but, in any practical
installation, you have to look at the cost ot pumping water, or the cost of solar collectors. So
Carnot efficiencie ; a:e a real issue, to be addressed with respect to competing technologies.
It has taken a long time to develop the experimental approaches that give valid efficiency
figures. You cannot isolate certain aspects of the material and treat others as passive. You
have to calculate the latent heat of transformation (anomalously high in this material) plus
specific heat across th. cycle with respect to stress levels and displacement for a given cycle.
And you never see the optimal work output in a wire that hasn't been in an engine and acquired
pretty complete "training," as we call it. Of course, to get the money to build the engines, you
have to talk about Cat not and the efficiency of the NITINOL conversion, so there is a loop
here.
Now, with my s.:cond engine, I
became pretty convinced that the mechanical
configuxation of the wheel, and maybe also the use of NITINOL wires in the mode of flexure,
was impractical, and I bc.gan looking at wires in tension. The reasoning here is that, if you
have a member in tensicn, the whole cross section is working for you; while if you have a

member in flexure (theor.n'ically, at least), only the outside and the inside of the bend are
putting out maximum wor'<. While this isn't necessarily the case in NITINOL, I accept it on
principle, because thinner wires in tension have produced the highest work output, per unit
mass of NITINOL, so far recorded. And so I proceeded to think about this. I was convinced
(and it has been pretty conclusively shown elsewhere) that the mechanical cycle for wires in
tension had to be something 4i lit :le special. If I simply used a crankshaft as in my first wheeltype engine, with wires in tensi ,n radially disposed from the crank to the outer rim of the
wheel, I was sure they would b eak. The reason is that the kinematics of the crank cycle
makes a lousy match to the way, heat enters and transforms a NITINOL wire. The leverage on
a typical crank (a bicycle pec",i, for instance) increases sinusoidally from zero at top dead
center, to a maximum at 90 de, 7ees. However, when heat enters a NITINOL wire, you have an
exponentially diminishing vo, 'me of material transformed, per unit time, with the greatest
proportion transformed right
'he beginning of the cycle. In fact, in a 20 mil NITINOL wire

in tension, you get an absolutely

azing jolt of force. The instantaneous recovery stresses

are sufficient to permanently deforn, the wire--to introduce irreversible shape change--if the
wires are not free to act on the mechanical system. This problem is compounded by the
effects of shock-loading. To avoid these stress concentrations in the wire, what I needed to do
was somehow find a cycle which somewhat mimicked the behavior of NITINOL wires during
transformation. I essentially needed to let the NITINOL design its own engine cycle (Fig. 3).
This machine is called the "Cam-Track" NITINOL engine. The tracks in question are
these kidney-shaped features that go around the ends of the tank in this cutaway view. The
NITINOL wires are longitudinal, in tension, and they ride between trolleys which, in turn, ride
along the tracks. The "cam" aspect of the tracks means they mostly do not run parallel to
each other. They are supported by standoffs from the ends of the tanks. Varying the lengths
of the standoffs makes it possible to vary the slope of the tracks with respect to the ends of
the tank, and to each other. As the NITINOL wires dip into the semi-cylindrical hot water
tank, the trolleys are at a point whe:e the tracks are just beginning to converge. The pull
exerted by the NITINOL wires as they contract drives the trolleys down along the slope, which
is the power stroke of the engine. Mechanical force is transmitted through a linkage to
advance the next set of NITINOL wires into the hot tank. The "compression" stroke (actually
elongation, in our case) takes place in the cold bath around the outside of the hot tank. There,
force is applied (throvgh the power takeoff linkage) to drive the trolleys forward alonh, the
tracks as they diverge, with a secondary, or resultant, force acting on the NITINOL wires to
deform them axially. The tracks are made of brass, sc that altecing the lengths of the
supporting standoffs made it possible to actually tune them somewhat--to change the slope at
1-3

NSWC MP 79-441
various points in the cycle. By fiddling around with the curve of the tracks, I was able to find
a reproducib'e mechanical cycle--in which the wires could be repeatedly stretched and recover
withoit permanent damage. Lo and behold, it turned out to be a pretty close approximation of
an exponential decay curve. This engine ran, but never up to expectation--I was hoping to see
half a horsepower, and we certainly never got that. It was never fully debugged, either, but it
did give me confidence that wire breakage problems--encountered in other machines using
NITINOL wires in tension-could be overcome. We did, in fact, have some breakage, but only
at the ends of wires, at the holders, where the wires passed around a somewhat tight radius
which probably introduced a complex strain field at that point. But we did not encounter
breakage along the working length of the wi-re elements.
By the time I had figured out what the problem with this machine probably is, and how to
improve its performance, I had already moved ahead in terms of design criteria for a practical
engine. While the Cam Track made me optimistic about being able to use NITINOL wires
efficiently, it still has the basic drawbacks of the original engine prototype in regard to
parasitic losses. Too many moving parts. Too much energy lost in hydrodynamic drag--you are
always moving those wires through water. Incidentally, I believe in using a liquid heat transfer
medium for thermal uniformity, because if a part of a NITINOL wire is in the process of
transforming-or, say, is still cold--it will naturally take up locally the complete load of the
other parts of the wire that hve been transformed. So it is important, in my view, to
maintain thermal uniformity throughout the length of a working element. But I wanted to see
if I could use wires in tension in a simple device--mechanically very simple-and also cut down
on the hydraulic losses. And this is where I went (Slide.)
This is my latest machine, which I call the "Model M." It is simply a reworkir.g of the old
Newcomen "Walking Beam" steam engine. You have the wire elements at the front, with hot
and cold water tanks below. The beams oscillate the wires between hot and cold baths, but
while they are heated and cooled, the wires do not move. Work developed at the wire is also
taken off through the beams. This thing really works. It has probably ten times the power of
the original wheel prototype, with slightly less NITINOL wire in there. Less volume of
NITINOL.
Query from the audience: What is the power of this gadget?
RB:
Don't know.
Haven't measured it.
If you want a "fingertip-dynamometer"
measurement, I would say around 20 watts. Bu. the point is that now, for the first time, I can
see kilowatts. I can see scaling up without more moving parts. This machine, in its rather
quaint embodiment, represents all the moving parts you would need for a very powerful
installation. You just ptug in more wires; make it longer. Size is no problem: in solar, for
example, you have already committed a long low area for your collectors. You could make a
long low machine and stick it behini the collectors. There are 88 wires, 15 inches long, in
tension. Displacement at the wires is very small, but amplified through the lever system.
Between wire and power takeoff motion is very slight--just a slight oscillation. Lots of force,
but not much displacement.
Query from the audience: At what strain levels does that machine run?
RB: This is running at about 3.5 percent strain, which I feel is safe. But recently I am
beginning to feel that maybe 6.5 percent is safe--if you ask nicely.

1-4

".

....- "

NSWC MP 79-441
Th.s thing has just been through preliminary tests, to find out if it works, and I havt seen
it run at about 80 cycles pet minute. The present setup is limited by the fact that heating and
cooling equipment consists of a $19 coffee urn and a 27-year olct refrigerator. So the machine
operates well at the begin.Aing of a run, then the hot and ccld water supplies collapse 3nd
generalized entropy sets in. As I say, what tickles me about this machine is that I think it has
the hydraulic and mechanical losses reduced to a minimum, and allows me to think of an
installation which would work on a practical scale.
I also think realistic efficiency
measurements can be made on it.
Let me say that I hope we will, in the course of these meetings, really confront the issue
of efficiency. I hope anyone who has made measurements will talk about them, even if there
isn't general agreement. You are aware that a big part of the problem we face in this
approach to low-temperature energy conversion is that we are trying to promote a relatively
unresearched 6-year old technology. That's in direct competition with Rankine-cycle turbines
which have been arour.d for decaees--and the competition is way up on the learning curve.
Turbine designs are now relatively sophisticated, while we are still at the level of the devi:es
displayed this noon. Which is absolutely where we shovld be. I have a strong prejudice in
dealing with an unresearched entity--be it an engine or a carrot growing in your garden. You
don't pull a carrot up by the roots every week to find out how it is doing. It has got to have a
little time to develop before it's mature. Same with an engine. I hope we will be se .ing it
mature somewhat before long, but for the time being we are where we ought to be, although
we must confront the efficiency question.
Question: Any idea what Carnot efficiency we should aiir, for? In other words, how far
above and below the transformation temperature should the water baths be?
RB: Okay, that is quite a complex question. Let me treat it superficially first. We
decided, in our program, to simply assign ourselves a goal of minimum coriverrion efficiency.
We picked the number three--whicn we have already exceede6--be ause, in certain lowtemp .rature applications, 3% conversion efficiency is competitive with existing technologies,
particularly in Ocean Thermal Energy Conversion. OTEC plants are being designed with 'arget
efficiencies of 2-3% in mind. OTEC researchers can stijl foresee an economical operation
because there are spinoff., in food production and other bypioducts, in addition to basic energy
conversion. The ocean represents vast solar collector, heat storage, and heat sink systems. So
the n-rmal rather 'ii,t.icost compoiients of the typical solar aray are already present. In
principle all you have to pay for i the pumps. The major probem one has with conversion of
ocean thermal eiiergy is not the efficiency of the process, but the cost and maintenance
requirements of the h.!at exchangers needed in the conven'onal turbine approaches. Vast
areas o' heat c2"changers are not only in contact ,with the sea water but also subject to
corrosion and biotoulir.g on the ocean side and t attack by the working fluid (particularly if it
is ammonia) should it come into contact with water, on the other siJ'e. And heat exchanger
w.,ils have to be kept easunaily tnin, or thermal impedances become so great that systematic
conversion efficiencies are further reduced below an acceptable limit. Now, NITINOL is
noncorrosive, can directly cO,,tact an aggressive env.ronment, and is dynamic. It changes
shape with ever' cycle, so it should be a rotten environment for marine growth. I wouldn't
want to live thet --...cycling up and down 200 C, sixty times a minute, on a moving substrate.
This may eliminate the scaling problem as well.
The more compiicated side of your questiun is this: we don't really know--I certainly
don't know--what NITINOL is yet. I know where it starts, how much force it takes to deform
it, how much energy it puts out, and so on. But I don't know what a fully stabilized piece of
optimized alloy wil'. do, and for how long. In other words, I see a "double" memory developing
in the wires ii the originai engine, and I am able to measure a potential energy output that
1-5

.7'

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NSWC MP 79-441
might be realized from those wire. on cooling...but where is that going to stop? It doesn't
Then, what happens to the
exist at all in a naive wire; there is no double memory.
transformation temperatutvs as a result of cycling...to the thermal hysteresis? Will it get
bigger or smaller? What happens to the wire on the crystalline level? Certain favorablyoriented domans obviously become dominant as you break the wires in. Are they doing all the
work? With the generation of defects there is work hardening, but where are the defects
localized? My unsophisticated observatior is that not oniy do wires not degrade with repeated
cycling in engine! (at least or. the order of twenty-five million cycle3-they in fact improve. I
have seen speed of operation increase about 50% in the original engine at the same temperatures, which does not take into account hydrodynamic losses. So probably the energy output,
per cycle, of the NITINOL has more than doubled in five years of intermittent operation.
Apparently ergines do a certain amount of cold working on these wires that seems to optimize
them. What if you strapped a metallurgist to the engine and let him work on the problem too?
The wire: are extremely history-dependent. Every aspect of their performance changes with
cycling. I don't know.
Question: Where do you get the wire?
RB:

The actual physical wire used in my machines was commercially produced by the

Titanium Metals Corpocation of America, also known as TIMET or TMCA\, which no longer
p.-oduces it. As far as I know, NITINOL wire is not yet quite available, commercially. Well,
maybe some people would disagree.
Question: That means this is the end of this work?
RB: No, it is the beginning of a new way.
Question: Is it available or not, commercially?
David Goldstein: Wire drawn to a specific transition temperature is not commercially
available.
The Naval Surface Weapons Center, which is not a commercial producer, is
NSWC draws wire and provides it to a specific
producing the alloy in 10 pound melts.
transition temperature.
Currently one major commercial firm, TMCA, is accepting orders for the alloy to a
specified composition. TMCA will break ingots down to two inches or some other size, but
does not guarantee transition temperatures. Another firm, Reactive Metals, Inc., can also
produce the alloy.
NSWC has placed orders with both firms for ingots. These materials will be final
processed at NSWC to ensure material uniformity. They will then be supplied as wire or strip
to various people approved by the Department of Energy. In this way the engine builders will
have uniform NITINOLs to work with.
Question

We at MIT would like to experiment.

How would we get the wire--from DOE,

you, or TMCA? How do the three fit together?
DG: You should write directly to NSWC--to me or our NITINOL Technology Center.
Question: Where is TMCA?
DG: Henderson, Nevada. Please call me for the names of the people to contact there.

,

1-6

t-.

NSWC MP 79-441
SL'-stion: If we ask you for some wire or sheets, we don't really have to go to TMCA?
DG: No. I might add: The last talks tomorrow afte, noon will refer to a somewhat new
and possibly successful process of producing NITINOL.
Question: I am still confused about whether the conversion efficiency of these engines is
limited by the transition temper3ture range.
You have to have
That is the Second Law nature of the beast.*
RB: Yes.
The original wheel engine runs on a
a AT, a specified AT, in order to make them run.
temperature difference of 9 0 C between the baths.
To have a high Carnot efficiency, you
would like that way up around incandescence, but, in fact, the heat available for these
purposes is around ambient.
Question: In the applications we're talking about, isn't horsepower more important than
fraction of Carnot efficiency?
RB: Yes, except that the efficiencies will determine how many solar collectors you
need, or how many pumping horsepower you lose in your ocean or geothermal installation. A
really tiny conversion efficiency here couldn't compete with that of organic fluid Rankinecycle turbines. That's the real competition. We really have to beat those costs, and I believe a
reasonable installation's costs can be very competitive. One further point: In solar thermal
electric conversion, the push now is almost entirely to the central-receiver "power tower"
concept. There, focussing mirrors--heliostats--drive the temperatures up, focus them on a
central boiler, and get high efficiencies with a steam turbine. The concept looks good on
paper, but has one serious limitation nobody seems to talk about. When the sun goes down, the
conventional or nuclear plant turns on, because you can't store steam. There is nothing easier
to store than hot water. !t beats batteries. and everything else. A good low-temperature
energy conversion approach--and I don't even care whether it's NITINOL--could be the basis of
solar electricity generating plants that will work 24 hours a day. We suddenly get into base
load territory, whereas before the most optimistic place for solar energy conversion was during
the peak load sunny hours of the day. Very, very serious consideration, I think. Thank you.

II

*Editorial note: From the vantage of six months' tine elapsed sinice the NITINOL Heat Engine
Conference and present struggles with this transcript, I would strongly disqualify my answer
to this question. (RMB)

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ONE HORSEPOWER THERMOTURBINE NITINOL ENGINE
W. S. Ginell, 3. L. McNichols
McDonnell Douglas Astronautics Company
Huntington Beach, CA
3. S. Cory
Cory Laboratories
CA

~Escondido,

The earliest patent on the concept of thermal-to-mechanical energy conversion using
NITINOL was issued to Buehler and Goldstein in 1968 (Reference 1). During the ten years
since the patent was issued, a variety of small model engines of different designs has been
built and operated--engines that demonstrated conclusively the technical feasibility of cyclic
thermal energy conversion using NITINOL. Some engines were built as curiosities--devices
That rotated or oscillated and attracted attention--but little else.
Many of these were
designed empirically, and they operated only because a large enough quantity of NITINOL wes
used to overcome design defects that were unsuspected at that time. Other investigators
designed and built operable engines on the basis of the then-known physical properties of
NITINOL.
These were capable of producing small amounts of power--fractions to tens of
watts.
To our knowledge, operating engines of larger power output have not been
demonstrated at this time.* Such demonstrations are vitally important in furthering the
development of NITINOL heat engine technology to the commercial level.
The NITINOL Heat Engine program at McDonnell Douglas Astronautics Company is
directed toward this goal. The program is sponsored by the Department of Energy with Marvin
Gunn of the Fossil Fuel Utilization Division as the technical program manager. Work on this
effort was initiated officially on September 28, 1978 and therefore we have little in the way of
results that can be presented.
The objectives of the program are: first, to design, construct, and operate a reliable
NITINOL heat engine that will deliver practical amounts of power, about one horsepower; and
second, to demonstrate that engine performance parameters can be predicted. I will describe

Buehler, W. 3. and Goldstein, D. M., "Conversion of Heat to Mechanical Energy," U. S.
Patent 3,403,238, Sept. 1968.
We recognize, however, that the details of such efforts could be considered proprietary
because of the tremendous commercial potential of NITINOL engines. Design i.nd performance
information exchange under these circumstances understandably would be restricted. We hope
that one result of this conference would be enhanced communication among active workers in
the field, primarily in the area of fundamental information, so that progress in our
understanding of the behavior of NITINOL can be accelerated.
*

2-1

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NSWC MP 79-44 1
first the engine type that we have selected and its advantages. This will be followed by a
qualitative description of the engine configuration and the procedure to be used for engine
design.
One class of sma!l model engines that was built and tested extensively is known as the
thermoturbine. Essentially, it is a variation of the well-known differential pulley mechanical
design. The general turbine configuration which uses the thermal expansion and contraction of
an endless, normal-metal belt was patented by Lee in 1967 (Reference 2). A similar engine
design using NITINOL was patented by A. D. 3ohnson in 1977 and is shown schematically in
Figure I (Reference 3).
A continuous loop of NITINOL wire or a NITINOL helix is guided by idlers through cold
and hot water baths and over the differential pulleys which are of different diameters. One
pulley serves as an expander (or turbine) and extracts power from the rotating loop because
tension in the loop on the hot side is greater than tension on the cold side. The expander pulley
is connected mechanically to a compressor (or pump) pulley that does work on the loop.
Because the work performed by the loop on the expander exceeds the work performed by the
compressor on the loop, a net work output results.
Operating NITINOL turbines have also been built by Raymond and by Cory (Reference 4).
A number of engine variations was devised and constructed using NITINOL helixes or wire,
different methods of coupling the expander and compressor pulleys, and variations in heat
source-sink configurations. One engine built by Cory (Figure 2) used a close-wound helix (3mm
OD) , and the expander-compressor pulleys were of the same diameter but were geared to run
at different speeds. The engine, when operated between 343K (70G) and 278K (50C), attained
a speed of 2500 rpm and produced about 0.5 W of power.
The thermoturbine engine configuration using NITINOL in the form of an endless helix
has a number of major advantages: bearing loads are all radial and therefore well-developed,
inexpensive bearings can be used; heat capacity losses (Cp AT) are small because only the
relatively small NITINOL working material mass need be thermally cycled rather than a large
support structure; heating and cooling of the NITINOL helix are uniform and reproducible
because the helix enters and leaves the water reservoirs axially; extremely accurate machining
of the mechanical structure is not required because of the greater compliance of a helix in
torsion relative to that of a wire in tension (limitation of maximum material strain required);
high power densities and high cycle rates possible; and the NITINOL elements cycle
continuously rather than intermittently (as in an oscillating engine).
The thermoturbine engine that will be built in the McDonnell Douglas program will be a
scaled-up version of the small, dual-diameter pulley design. Scale-up to a one horsepower size
will be accomplished through a series-parallel mechanical arrangement of the simple design.
The large and small diameter pulleys will be replaced by large anid small diameter rollers which
will carry 104 helixes in parallel. Each closed helix will cycle through twelve alternate hot and
2 Lee,

L., "Motor," U. S. Patent 3,303,642, Feb. 1967.

3 Johnson,

A. D., "Memory Alloy Heat Engine and Method of Operation "U. S. Patent
4,055,955, Nov. 1977.

4 Cory, 3.

S., "Thermomechanical Behavior of NITINOL," This Conference, Paper
pp. 7-1 through 7-17.

V.

2-2

7ri
NSWC MP 79-441
cold water reservoirs in series before returning to the starting point. Figure 3 shows an end
view of an engine module which consists of two unit cells in series. A unit cell contains one
large and one small diameter roler and one hot and one cold water reservoir. Unit cell rnllers
are coupled to each other mechanically and the total output power appears at a single shaft.
Figure 4 illustrates the parallel arrangement of elements on the rollers. Notice that each
roller has both a large and small diameter end. This corresponds to a direct, mechanical
coupling between the driver (turbine) and driven (pump) roller and results in a zero power
transmission loss. The rollers will have a webbed structure to minimize helix slippage. Water
flow through the troughs will be countercurrent so that the AT over which each parallel helix
operates will be the same.
Initially, an engine module will be built and instrumented to measure cold and hot force.,
hot and cold reservoir temperatures, helix cycle speed, module output speed and torque as
f,nctions of tem'.erature, AT, module speed and number of cycles. The module will be
equipped with only ten helixes, and module performance will be compared with predictions to
establish the existence of synergistic effects. Because helix pro Derties and therefore engine
operating parameters will change with number of operational cycles, helixes will be removed
from the module periodically and their properties measured. This will facilitate correlations
between element property and engine performance.
The full size engine will consist of twelve unit cells in series and 104 NITINOL helixes in
parallel. Present calculations based on NITINOL wire properties (0.020 inches diameter)
indicate that a mass of 1.3 kilograms will be required and the engine speed will be about 480
rpm for a A I'= 60 0 C. NITINOL wire for this program will be supplied by Mr. Goldstein of
NSWC.
Although small NITINOL heat engines have been built and have operated, their
efficiencies, specific power, and total power have been lo',, and attempts to produce engine-s
of practical size have not been succes zul, as yet. Invention of practical machines that use
NITINOL efficiently for thermal to mechanical energy conversion requires first a detailed
knowledge of the engineering thermodynamics of the alloy, ard detailed engine design
equations. Needed are: (1) reliable equation of state data in terms of the variables force,
length, and temperature to identify and provide a quantitative description of possible
thermodynamic paths; and (2) information on heat flow and energy dissipatioa associated with
these paths.

Recently, extensive measurements of the force-length-temperature (FLT) behavior of
NITINOL helixes have been reported (References 4,5,6) from vhich the form of the equation of
state has been deduced. Because of the thermodynamically irreversible nature of the Joule
effect in NITINOL (internal entropy generation), the equation of statc exhibits hysteresis. This
results in a state equation that describes a bounded volume in FLT state space, and all possible

5 Cory, J. S.,

"NiTINOL Thermodynamic State Surfaces," Journal of rEnerg Vol. 2,

No. 5, 1978, pp 257,258.
6 McNichols,

3. L., Jr., and Cory, 3. S., "NITINOL Heat Engines for Economical Conversioi
of Low Graae Thermal Energy," Proc. 13th Lterdisp. Energy Conversion Eng, Conf.,

Aug. 1978, pp 1998-2004.

2-3

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NSWC MP 79-441
thermodynamic paths lie on uniquely defined surfaces within that volume (Reference 5).
Figure 5 illustrates schematically one pair of surfaces and a hypothetical thermoturbine
thermodynamic cycle. Details of NITINOL state surfaces, their properties, and uses will be
found in Reference 4.
To determine the heat flow associated with a given path or cycle, the irr, e. .: ,
thermodynamics for NITINOL pi-,:esses has been formulated and has been used to estimat.
speci..c work and thermodynamic efficiencies for the thermoturbine cycle (Reference 6).
The empirical state equation determination procedure used previously will be used as the
design tool for the one-horsepower thermoturbine engine. State surfaces for the specific
NITINOL alloy to be used will be determined experimentally.
A thermodynamic cycle
optimized for power will be derived on the basis of heat source and sink temperatures, desired
output power and speed and limitations inherent in the specific NITINOL alloy
be used.
These will depend on alloy composition and processing and cycling history. This ,' Urmation
will define the mechanical dimensions of the engine module.
Predictions of module
performance will be made as functions of oa.arating parameters. Iterations on the engine
design will be performed following comparison between engine module performance data and
predictions. The close agreement between the actual small thermoturbine engine performance
and the performance predicted on the basis of experimentally measured state surface data has
given us confidence in this empirical engineering data approach to NITINOL heat engine
design.
In summary, we have undertaken the design, construction, and testing of a one-horsepower
NITINOL engine. The mechanical configuration will be a thermoturbine design with a seriesparallel arrangement of NITIN')L helixes that are cycled through hot and cold water
reservoirs. The engine wili be designed on the basis of an experimentally measured equation of
sta t e for the specific NITINOL alloy supplied by the NSWC NITINOL Technology Center.
Successful completion of the engine tests will provide conclusive evidence of the viability of
the empiric.l engineering data approach to engine design and the technical feasibility of low
temperature energy conversion using practical-sized NITINOL heat engines.

'See footnote 5 on page 2-3.
4

1.e footnote 4 on page 2-2.

6,.
.ee footnote 6 on page 2-3.
2-4
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NSWC MP 79-441

PULE
DUAL DIAMETER

j

OUTPUT SHAFT

CONTINUOUS

PULLEY IN COLD
RESERVOIR
PULLEY IN HOT
RESERVOIR

MOGURE 1 DIFFERENTIAL PULLEY THERMOTURBINE ENGINE (AFTER JOHNSON)

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REFERENCES
1.

Buehler, W. 3. and GoldsteiLj, D. M., "Conversion of Heat to Mechanical Energy," U. S.
Patent 3,403,238, Sept. 1968.

2.

Lee, L., "Motor," U. S. Patent 3,303,642, Feb. 1967.

3.

3ohnson, A. D., "Memory Alloy Heat Engine and Method of Operation, " U. S. Patent
4,055,955, Nov. 1977.

4.

Cory, 3. S., "Thermomechanical Behavior of NITINOL," This Conference, Paper
pp. 7-1 through 7-17.

5.

Cory, 3. S., "NITINOL Thermodynamic State Surfaces," 3ournal of Energy, Vol. 2,
No.5, 1978, pp 257, 258.

6.

McNichols, 3. L., 3r., and Cory, 3. S., "NITINOL Heat Engines for Economical Conversion
of Low Grade Thermal Energy," Proc. 13th Interdisp. Energy Conversion Ens. Conf.,
Aug. 1978, pp 1998-2004.

2-10

NSWC MP 79-441

NITINOL BELT ENGINE
Dante 3. Sandoval

he 55 NITINOL alloy is the active element employed in this engine to convert heat
directly and instantaneously into mechanical energy. This engine of simple construction is
basically comprised of two pulleys of dissimilar diameter and a belt of NITINOL alloy that fits
around such pulleys. Means for heati.ng and cooling the NITINOL belt and for power
transmission are also provided.
Fig. I illustrates the basic NITINOL belt engine. Pulley 14, or "strain wheel," is a free
wheel with a radius that gives the NITINOL belt the selected strain curvature. Pulley 16, or
"power wheel," serves both as heat sink or cooling wheel, and as power transmission wheel by
means of its shaft (17). The power wheel is substantially larger than the strain wheel to
present a large area for heat dissipation, good traction, and small losses from bending the
NITINOL belt around it.
The principle of operation of this engine consists of the work produced by a portion of
the NITINOL belt while trying to recover its original shape when stimulated by heat at the
strain wheel. To produce any work, the NITINOL belt should have a preset shape that is
straight, convex, or with a curvature radius substantially greater than the radius of the strain
wheel.
In operation, the NITINOL belt is pliantly strained around the strain wheel. A heat
source (18)--such as a flame, steam, a hot water jet, or concentrated sun rays--is applied upon
the belt between Points 20 and A. The stimulated portion of the belt between these points will
try to recover its original shape. In doing so, that portion generates a moment of force F
about a fulcrum located at Point 20, which is the last point of contact between the strain
wheel and the belt (Fig. 2).
Such a moment of force has a lever arm with a length equivalent to the straight line (M)
from Point 20 to the last heated point between Points 20 and A, and generates another moment
of force Fr about the center of the strain wheel that is transmitted as a torque to the power
wheel by the belt. This torque sets into motion the NITINOL belt and both the strain and
power wheels, when the heat soojrce is applied. When in motion, any portion of the belt
entering Point A is stimulated by the heat source, becoming itself a part of the lever arm (M).
Any advancement of the belt into Point A withdraws the same amount of belt from Point 20
towards a cooling region at the wheel (16).
A cooling fluid (22), such as water, is placed in a container (24) for faster cooling of the
belt, making it possible to increase the rate of heat application, thus increasing the power
output of the engine. Spokes or gears (26) can be used on the power wheel for transmission of
power.
3-1

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NSWC MP 79-441
The present engine has a gear at the power wheel connected to a fly wheel mechanism to
smooth out the jerking due to hot spots or irregularities in the NITINOL belt and variations in
the heat source. Other physical parameters of this engine are the following:
1.175",
0.875"1
2.656"1
0.875"1
22.000",
.5001,
0.050",
3.5001,
110-140OF

Nylon Strain Wheel Radius
Nylon Strain Wheel Width
Aluminum Power Wheel Radius
Aluminum Power Wheel Width
NITINOL Belt Perimeter
NITINOL Belt Width
NITINOL Belt Thickness
NITINOL Belt Radius
NITINOL Belt TTR
BELT CONSTRUCTION

The belt for this engine was made from a strip of 55-NITINOL alloy, 22"1 long, 0.5" wide,
0.050"1 thick, and TTR I 10-l140 0 F. Both ends were squared, fine ground, and placed in the jaws
of a 3/4"1 band saw welder with a setting for "medium" current.
The welding was done in a regular air atmosphere; the burrs were ground off, and the
weld was annealed in the same machine, as is done with regular band saws after welding. The
belt was then placed for 15 minutes in a kitchen oven heated at 550 0 F, where it adopted a
circular shape, and was then taken out to cool in the air.

1

When cool, the belt was placed in water at 320 F and turned inside out to become a belt
with a convex shape. Then it was installed slightly loose around the strain and power wheels
".

The strain given to the NITINOL belt is expressed as:

S

+

where: v

=

Sb2

+V

***.--

+b2

rb+

belt thickness
r= radius of strain wheel
rb = radius of belt shape curvature
Sp
strain of belt from a straight line to the strain wheel curvature
Sb= strain of belt from its shape curvature to a straight line
Sb= Zero for a belt with a straight shape
Sb= Negative for a belt with a concave shape
Sb= Positive for a belt with a convex shape

3-2

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NSWC MP 79-441

BELT PROBLEMS
The NITINOL belt has a tendency to adopt an outward-channeled shape when subjected to
excessive heat or stress at the strain wheel. This channeling effect causes the edges of the
belt to crack in many places, thus breaking at any point in a very short time.
On the occasions when the belt broke, the original convex shape given to it was
completely lost by adopting a concave shape, sometimes with a curvaturc radius smaller than
its periphery curvature radius. The welded ends of the belt hold very well and break only when
a defective weld is made; otherwise the belt may break at other points.
The most favorable conditions for belt endurance are the use of low temperature steam
and a strain of 2 to 2.5%. The present engine belt has a cumulative time of about 6 hours
without breaking.
ENGINE PERFORMANCE
The engine was tested with two strain wheels of different diameter, keeping all other
parameters constant (Fig. 3).
CONSTANT PARAMETERS
Power Wheel
NITINOL Belt
Cooling Wtr3O

5.312" diam.
22" x 0.5" x 0.050"
32°F

Water

Heat Source
Steam Rate
Fly Wheel Mechanism
Point of Steam Application
NITINOL Belt Return Temperature

200°F Steam Jet 0.125' from Belt
7 Grams per Minute
Cnnected
5 Jrom Point A
70 F

VARIABLES
Strain Wheel
Strain Wheel

2.48" diam.
1.5" diam.

Belt Strain for 2.48" diam. Strain Wheel:
20.050+0,0
Sp = =2 x 1.24
0.050
Sb = 2 x 3.5 + 0.050
S

=

= 0.020
= 0.007

Sp + 5 = 0.020 + 0.007 = 0.027 =2.7%

Belt Strain for 1.5" diam. Strain Wheel:
Sp = 0.032

Sb = 0.007

S= Sp + Sb : 0.032 + 0.007 = 0.039

3.9%
3-3

NSWC MP 79-441
ENGINE EFFICIENCY
It was difficult to measure with reasonable accuracy the net energy input to the
NITINOL belt during operation. Therefore, only to have a reference point, it was assumed that
the power input was the energy required to raise the temperature of the working NITINOL in
one second from 70OF to its upper TTR of 140 0 F.
This assumption introduces the error of
different amounts of heat absorbed by the belt at different speeds. This error was not
accounted for in input calculations.
Specific heat for NITINOL was taken as 0. 111 BTU/Ib/°F., density .234 lb/cu. in. The
power output of this engine was determined from the measured speed-torque developed by the
engine at its power wheel.
i

Fig. 4 graphically represents these parameters.

APPLICATIONS FOR THIS ENGINE
The present engine prototype has been built only to demonstrate the feasibility of using
NITINOL as a solid state energy converter. No effort has been made to optimize its
performance or efficiency.
To simplify its construction and assembly, the engine has no bearings in its wheels, and
the wheel shafts are held only by one end, all of which introduces large friction losses into the
system. Thus, it is reasonable to expect a good deal cf improvement in a well-constructed and
engineered engine of this type.
There are many imillediate and practical applications for this engine, such as:
Solar Tracking Systems
Backup Blower for Heating and Cooling
Waste Heat Recuperators
High Torque Actuators
Heat Motors

3-4

NSWC MP 79-441

STRAIN WHEEL

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NITINOL BELT

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244

FIGURE 1

BASIC NITINOL BELT ENGINE

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BELT STIMULATION AND TORQUE SYSTEM

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Belt Strain

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Power Wheel RPM
FIGURE 3

ENGINE PERFORMANCE FOR STRAIN WHEELS

3-7

NSWC MP 79441

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2.7%

Belt Strain
3.9%

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FIGURE 4

EFFICIENCY AND POWER FOR 2 STRAIN WHEELS

-8

NSWC MP 79-441

SOME ENGINEERING PARAMETERS FOR A NITINOL ENGINE DESIGN
P. A. Hochstein
Quantex Engineering, Incorporated
Warren, MI
INTRODUCTION
The author has been involved in NITINOL Heat Engine (NHE) design since 1974, when the
first rotary vane, bending mode machine was built and tested at the General Motors Technical
Center.

G.M. showea little interest in further NHE development, and work in this area was
terminated until mid 1975, when Quantex Engineering Inc. was formed. The firm is primarily
involved in developing electronic testing systems for the automotive industry, and NHE
development proceeds as finances and time permit.
Liaison with Pringle and Assoc., a Detroit based engineering design company, has allowed
us to design, build, and test various engine designs, while exploring advanced concepts with
computer modeling of motor dynamics and heat exchange mechanisms.

TEST FACILITY
Our NITINOL engine testing facility is designed to supply measured quantities of hot and
cold water to motors under test, while recording engine performance parameters on an
electronic dynamometer (Fig. i) with variable (resistive) loading.
Engine speed, torque, and power are electronically derived from a 4 pole A.C. brushless
generator which is driven by means of a toothed belt.
The dynamo-neter is presently being modified to allow constant speed or constant torque
operation by means of feedback control.
Two 55 gal. insulated drums supply hot and cold media (normally water). Electric heating
(6 KW) temperature controllers and a stirring system permit operation up to 1950F.
2 H.P.
refrigeration compressor allows us to operate the cold water tank down to approx. 35"F. Continuous, rapid agitation of the cold water minimizes ice formation on the evaporator coils.
Separate variable delivery pumps dispense water to the engine through flow reters.
Cavitation in the hot water delivery pumps limits the max. operating temperature to 195 F.
No effort has been made to optimize the thermal efficiency cf any of our NHE models,
and no water recirculation is used.

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NSWC MP 79-44 1
ENGINE DESCRIPTIONS
1.

BENDING MODE TYPE

Our first NHE models were of a "pancake" design (Fig. 2). These motors typically
contained 150 gms. of NITINOL in the form of vanes, attached to an offset central hub.
Operating in simple cantilever bending mode, these engines typically developed 10 to 20 watts
of "ower at a maximum speed of 70 rpm (36 vanes of .03 x .5 x 4 in. NITINOL). While
impressive from an output power/energy density standpoint, these machines consume a
prodigious amount of water which must be carefully aimed at an angle to the vanes.
Separating hot and cold regions is difficult, and water recovery virtually impossible.
In retrospect, these engines are relatively unsophisticated and inefficient. However,
they develop respectable power, very reliably from an extremely simple design at relatively
low strain levels (< 1.5%).
2.

TORSIONAL VANE TYPE

More recently, we have concentrated on torsional vane engines with similar flow-through
"pancake" housings.
For the most successful of these designs (Fig. 3), the actual motor has 24 NITINOL strips
rigidly attached to a central hub. The free end of each strip or vane is held in a movable
clamp which can place each strip in torsion along the major (attachment) axis of the element.
The hub and strips are free to rotate about the center shaft, and in doing so, move through four
quadrants. The quadrants being alternately sprayed with hot and cold heat exchange media
(normally water).
As a NITINOL vane moves through a "cold" quadrant, it is cooled below
its Mf temperature, and is concurrently torsionally strained (wound up) by a circumferential
When the strained element moves into the "hot" quadrant, it is now heated above
cam.
its Af temperature and forcibly recovers its unstrained shape. While unstraining, the element
does work on the cam, and is moved along to the next quadrant. Obviously, each NITINOL
element goes through two complete heat exchange cycles per engine revolution.
Fi2. 4 shows the detail of the cam follower mechanism and provisions for lateral motion
Motor housing (5),
of each NITINOL clamp (7) as the element shortens during torsion.
circumferential ring (10), and the hub are fabricated of Celcon AF (a 25% glass-filled acetal
copolymer), which exhibits low thermal conductivity and excellent mechanical properties in a
severe (boiling water) environment.
Fig. 5 diagrams the function of the sinusoidal, circumferential cam and the relationship
of cam amplitude to NITINOL element torsion. Preload and working shear strain for the
elements are naturally a function of cam shape. Cams have been developed for several strain
levels by a numerically controlled milling machine, and are easily changed.
Pertinent engine specifications are outlined in Table 1, along with typical motor
performance values.
These disk shaped motors can obviously be stacked, and the flow-through design
simplifies media separation. Polycarbonate shields separate the quadrants on the test fixture.
Water carry-over between adjacent quadrants at high (>100 rpm) engine speeds precludes
efficient media separation at the output of the motor. An untested design of an air pressure
screen to forcibly shed water from vanes between quadrants may solve this problem.
4-2

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NSWC MP 79-441
As may be determined from the motor performance figures, internal engine friction is
excessively high with respect to net output power. Very high localized cam follower bearing
loads on the cam surface are partly responsible. One early cam was ruined during extende
operation. The primary cause of high running friction is the "scuffing component" of cam
follower bearing motion on the curved cam surface.
Some relatively important conclusions may be drawn from life test data shown in Fig. 6.
When operated at shear strain levels below 0.7% (26 ksi), no long term degradation of the
torsional elements was apparent. At 1% shear strain, which yielded the performance data in
Table 1, one small (1/16") crack developed at the edge of a NITINOL vane after approx. 10
hours of running time (nom. 105 cycles at an average speed of 100 rpm). The vane edges show
excessive roughness, and were installed "as sheared" after a 5 min., 950OF anneal. Proper edge
finishing should extend the "no failure" strain to over 1%.
Fig. 7 shows measured power and torque output for the torsional vane engine described
above.
STRESS LIMITING
Torsional NHE are high compliance low stress machines, therefore desirable from a
machine design standpoint. However, the intrinsic limitation of half the usable energy density
relative to tensile machines has inevitably pointed most NITINOL engine developers to wires or
bands in tension.
A shortage of useful NITINOL material has hampered our work in this area; however,
some preliminary experimental test results will be discL ised.
Ten samples of .015 in. dia. NITINOL wire (V 4547) TTR 180 0 /210°F were tested
conventionally at constant tensile strain. Surprisingly, peak stresses on the order of 75 ksi
were measured at 3.5% strain. Fig. 8 shows a typical work diagram after 15 cycles (adjusting
for strain hysteresis). It seemed impossible to obtain repeatable, consistent results at strain
levels ) 1.5%.
The Lawrence Berkeley Laboratory apparently draws the same conclusions.
Repeated annealing and recycling to "optimal" 4-5% strain levels only caused further
consternation at the excessive creep--- albeit at spectacular recovery stresses. Transient
stresses in excess of 93 ksi were measured when the 10 in. long 0.015 in. dia. wires were
submerged in a 300OF silicone oil bath.
To limit the high peak stresses, we equipped several wires with series helical compression
springs. Obviously, th- - ring allows the NITINOL wire to begin shape recovery at relatively
low stresc
sp.
s compressed the stress level may be controlled by the spring rate
(F=KL). Wot,, is the ..ore stored in the spring.
*..a

While only preliminary experiments have been conducted, it seems that NITINOL exhibits
a "safe operating area" wherein the material may be repeatably cycled to given strain and
stress limits without deg, -,-ion(or property change).

IBanks, R., Hernandez, P., and Nergren, D., "NITINOL Engine Project Test Bed," NSF/
RANN/SE/AG-550/FR-75/2 (1975)

4-3

NSWC MP 79-441
A publication by 3. S. Cory 2 sheds light on this subject, and does much to clarify the
mass of seemingly unrelated NITINOL property data.
The Cory Force Length Temperature (FLT) state surfaces which bound equilibrium FLT
space probably exclude the shaded area shown in Fig. 8. Only at relatively low stresses (on the
MA surface) can the NITINOL exist in equilibrium at relatively high strains. The limiting
stress is the yield stress of about 70 ksi at 1% strain.
ENGINE DESIGN WITH STRESS LIMITING
We have done some preliminary design calculations on a multi-h.p. NITINOL heat engine
using stress-limited wires in tension.
Stress limiting with helical springs offers several advantages:
1.

Equalizes (compensates) for slight variations in element length in a multiwire

engine.

2.

Permits the engine to be stalled --- without overstressing elements.

3.

Allows groups of elements to be used in tandem while sharing loads.

4.

Allows for time delay in reaching transition temperatures in groups of elements.

A schematic design for an engine capable of an estimated 25 h.p. when fully loaded
(104 NITINOL wires 12 in. M"ng x .02 dia.) is shown in Figs. 9a-9i.
Fig. 9i shows the basic NITINOL element/spring stress limiting mechanism. Work is now
under way to effectively cold head the attachment ends (Item 1) onto NIT:NOL wire of 0.0150.030 in. dia. Cold working the complete wire element and annealing "in situ" may offer some
advantage, as early samples show weakness at the flared ends.
The use of master - slave hydraulics (Fig 9d, item I ana rig. 9g, item 1) to translate the
axial motion of the NITINOL wire "packets" into radial motion offers the added advantage of
reduced cam follower loads (Fig. 9g, item 2).
A 5:1 area ratio on the cylinders increases cam displacement proportionately.
Alternate wire carriers (Fig. 9i) communicate with cam follower pistons on either the
upper (3) or lower (4) cam in Fig. 9c.
Each wire "packet" (Fig. 9e, item 5) rotates
circumferentially in its own water tight compartment which commutates through alternate hot
and cold quadrants.
The overall size of a 25 h.p. engine (Figs. 9a, 9b) is expected to be approx. 30 in. in dia.
by 36 in. high.

2Cory, J. S., "Engineering Design Data and Correlations for NITINOL Devices" D.O.E. EC-77X-01-411 1.

4-4

NSWC MP 79-441

0

FIGURE 1

.4

FOR
ELECTRONIC DYNAMOMETER AND LOAD BANK
NITINOL MOTOR TEST FACILITY

4.5

NSWC MP 79-441

o

*

..
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FIGURE 2

do

BENDING MODE NITINOL HEAT ENGINE (1975) NOM. 12 W OUTPUT
SHOWING SECONDARY MEMORY (TRAINING)

4-6

NSWC MP 79-441

IVI

FIGURE 3

PLAN VIEW OF ROTARY THERMAL ENERGY CONVERTER

4-7

NSWC MP 79.441

GREASE-FILL
GREASE RESERVOIR
GLASS- FILLED ACETAL
•-

A.SY LOCKING
BEARING.,&
*
-- SET-SCREW
TEFLON-RULON BUSHING

GLASS-FILLED ACETAL

STATIONARY,,
> MEMBER

CAM FOLLOWER SCREW
ACCESS HOLE
SHC.S.(SS)
SINUSOIDAL CAM
304/316 SS

CAM FOLLOWER AND BEARING

* BEARING LOCATION AT TOP AVOIDS WATER SEEPING INTO BEARING
o REMOVABLE CAM - FOR CHANGING % TORSION OR CHANGING PHASE
0 INDIVIDUALLY ADJUSTABLE CAM FOLLOWERS
FIGURE 4

RADIAL THERMAL ENERGY CONVERTER
SECTION THRU OUTER RIM - SHOWING CAM DETAIL

4-8

NSWC MP 79-441

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NSWC MP 79.4"1

FIGURE 9.

ROTARY THERMAL- ENERGY CONVERTER
4-17

NSWC MP 79441

FIGURE Of

ROTARY THERMAL ENERGY CONVERTER

4-18

NSWC MP 79-441

FIGURE 9g

ROTARY THERMAL ENERGY CONVERTER
4-19

NSWC MP 79-441

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4-20

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NSWC MP 79.441

001

412

NSWC MP 79-441

TABLE I TORSIONAL VANE NITINOL HEAT ENGINE MK I
SPECIFICATIONS
Size: 9.2Y' Dia. x 1.7Y' High

Construction: Glass Filled Acetal Copolymer
Number of Thermal Cycles: 2 Per Revolution

(2 Cycle Sinusoidal Cam)

Active Elements: 24 NITINOL Vanes
V 4072 TTR 60 0 /80 0 F (15o/27oc)
2.00" x . x 0,01211
Total NITINOL Mass: 23 GMS. (0.8 oz)
PERFORMANCE
Cold Water Inlet Temp.: 36°F (2 0 C) Nom. I G PM
Hot Water Inlet Temp.: 195°F (880 C) Nom. 2.2 GPM
Maximum N.L. Engine Speed: 240 RPM
Frictional Power Loss: Nom., 12 Watts (at 240 RPM)
Maximum Engine Output: 7.6 Watts (at 198 RPM)
Nom. Power Density: 300 Watts/Kg

4-22

rI
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NSWC MP 79-441

AN ANALYSIS OF FACTORS AFFECTING THE
EFFICIENCY OF THE SOLID-STATE ENGINE*t
Dr. A. A. Golestaneh
ARGONNE NATIONAL LABORATORY
Argonne, Illinois
ABSTRACT
We discuss the main factors that affect the energy output which accompanies the shape
recovery associated with the martensitic transformation in shape-memory alloys. We describe
an experimental solid-state (SS) engine made with the Ni-Ti (NITINOL) shape-memory alloy,
and discuss the efficiency of such an engine. We also derive and discuss some physical insights
obtained from the thermodynamic treatment of the martensitic transformation, and some
limitations on the efficiency of the SS engine.

*Work supported by the U.S. Department of Energy. The submitted manuscript has been
authored by a contractor of the U.S. Government under contract No. W-31-109-ENG-38.
Accordingly, the U. S. Government retains a nonexclusive, royalty-free license to publish
or reproduce the published form of this contribution, or allow others to do so, for U.S.
Government purposes.
tEditor's Note: There may be some differences of opinion about certain points in this article.

5-1

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NSWC MP 79-441
I.

INTRODUCTION

The shape-recovery phenomenon (SRP), which occurs as a result of certain martensitic
":ansformations in the shape-memory (SM) alloys, has received serious attention from
industry. 1 The main applications of the SRP are in control devices, medical instruments, and
the production of mechanical work from low thermal energy sources (such as industrial waste
heat). The solid-state (S3) engine is a heat-mechanical energy converter based on the SRP, in
which SM elements are subjected to a "cooUng and deforming-heating" cycle. Several
prol type SS engi.,es with various kinematical arrangements have already been reported in the
literture.2 However, these engines are in an early demonstrative stage and are far from
acceptable for industrial or domestic purposes in terms of reproducible performance,
endurance, and efficiency, all of which are related to the mechanism of the martensitic phase
change in SM alloys. Clearly, materials parameters (composition, impurities, grain size and
orientation, etc.) as well as external parameters (such as temperature, applied stress, mode of
material deformation, and cooling and heating rates) play important roles in such a device.
The Carnot efficiency of this engine achieves a maximum of 20% if the temperatures of the
cold reservoir (CR) and hot reservoir (HR) are TL P 20.-24 0 C and TH < I00° , respectively.
The efficiency q, of the shape-recovery (SR) cycle was first estimated by Ahler , who used a
phenomenological approach to deduce a value of r5%.
Later, estimates of 10-16% were
reported by several authors4 - 6 . However, recent experimental and theoretical studies have
shown that the earlier estimate of 5% is, in fact, correct. 7 ,8 Despite this numerical disagreement, the work of these authors shows that n is proportional to the latent heat AH of the
Many authors have studied various aspects of the shape-memory alloys. See, for instance,
Shape Memory Effects in Alloys, edited by 3. Perkins (Plenum Press, New York, 1975),
and New Aspects of Martensitic Transformation, edited by Kobe, supplement to Trans.
Jpn. Inst. Met., Vol. 17 (1976).
2 See, for instaiice,
R. Banks and M. Wahlig, Technical Report LBL-5293, Lawrence
Berkeley Laboratory (1976); and A. D. Johnson, IECEC 75 Record No. 759082, p. 530 (1974).
3

M. Ahler, Scripta Met. 9, 71 (1975).

4H. C. Tong and C. M. Wayman, Met. Trans. 6A, 29 (1975). See also C. M. Wayman and
H. C. Tong, Scripta Met. 9, 737 (1975) and 10, 1129 (1976).
5 B.

Cunningham and K. H. B. Ashbee, Acta Met. 25, 1315 (1977).

6 A. A. Golestaneh,

3. Appl. Phys. 49 ()), 1241 (1978). A somewhat different treatment
was used in this paper, as we will explain in more detail in the present paper.

7P. Wollants, M. DeBonte, L. Delaey, and 3. R. Roos, Z. Metalikde, Part I, p. 147,
Bd 70 (1979) H.3 and Part II, p. 298, Bd 70 (1979) H.5.
8 A. A. Golestaneh,

"Martensitic Phase Transformation in Shape Memory Alloys," Proceedings

of International Conference on Martensitic Transformation (ICOMAT - 79) at Massachusetts
Institute of Technology, Boston, MA, 3une 24, 1979, pp. 679-692.
See also Golestaneh, "Energetic Shape Recovery Associated with Martensitic
Transforration in Shape Memory Alloy," Acta Metallurgica, in press.

5-2

[

NSWC MP 79-44 1
martensitic
reactions in SM alloys.
Mohamed, 9 howeve,-, states that the value
of r increases as AH decreases. This is incorrect, as will be shown subsequently. In fact,
the purpose of the present article is to analyze the essential factors which contribute to, as
well as limit, the energetic SRP and the value of Ti. We also derive some physical insights from
the thermodynamic formalism applied to these martensitic reactions.
II.

BACKGROUND
A.

DESCRIPTION OF THE SR CYCLE

I

We wil first describe the operation of a very small engine we constructed for
laboratory tests. 1 The engine (Figure Ia), has two units fixed side by side on the shaft (a
larger number of units may also be used). Each unit (Figure lb) contains four l-mm-dia wire
elements made of a NITINOL alloy; this number can also be increased. Each element is
"trained" to have a curved shapel I and is fixed by one end to a floating ring (FR), while the
other end is connected to a spoke (or ring) fixed on the engine shaft. The shaft is positioned
horizontally so that about half the elements are in the HR (a water bath wi.h TH =
45-990C) at any given time, while the other elements are in the CR (the air in this case, with
TL S 2 4 0 C). The NITINOL elements used here have the SR critical temperature T c =
33 + 7 0 C; their structure at T < TC is mainly V" martensite, which is a mixture of stressinduced martensite (SIM or 81) and quench-induced martensite (QIM or y').
In the martensite
phase, the wires are soft and thus can be easily deformed. As soon as the elements are heated
in the HR, they undergo SR and push the FR upward and off center; the weight of the FR
deforms the elements which are in the CR. The gravity torque created by the off-center FR
then pushes the shape-recovered elements out of the HR and replaces them by the newly
deformed elements. The rotary unotion continues as long as the HR has TH > TC and the CR
has TL < TC.
Effectively, the SR cycle in any SS engine consists of two stages: In Stage I, the
SM element is deformed to a suitable degree (by tension, compressic=, bending, or torsion),
typically with 2-3% strain, in the CR with temperature TL < TC. Because of the strain energy
input Wi combined with the quenching process, the parent phase-martensite (P- M) -eaction
occurs; the parent phase, or 0, transforms partly to 0' with the release of the latent
heat AHO' and partly to y' with the released AHy'8, or simply AH (Refererce 12). In
Stage 11, the deformed element is rapidly heated to TH> TC in the HR; hence the
M+P transformation takes place and the element recovers its original shape by
absorbing AH and AH$'B from the HR. The SR can be complete or partial, depending
on TH , the resistance stress or and the uniformity of the material structure (which affects
the spread ATc) (Reference 13). !n an SS engine, of course, it is necessary to have a complete
("closed") SR cycle.
9 H.

A. Mohamed,

J. Mater. Sci. 14, 1339 (1979).

The engine described here operates at r40 r/min and generates 5 mW of power.
Engines with different geometries have also been constructed; for instance, see
Reference 5, and the article by R. Banks in Shape Memory Effects in Alloys (Reference 1).
The process of "training" the SM element into a given slape essentially consists of annealing
the element (kept constrained in the desired shape) at a temperature T for a time t. Both
T and t depend on the SM alloy composition and geometry.
A detailed description of the !atent heat AH I and AHB, is in Re ference 8.
1 3 1n the present work we exclude the effects of element geometi y and other material

parameters which affect the heat exchange rate and kinetics of the SRP.

5-3

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77

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NSWC MP 79-441
Experiments show that the most effective SR force is obtained when the SM
elements are subjected to very rapid cooling and heating. Also, even though the martensitic
reaction is massive, under an applied load the reaction period tr is finite and depends on the
engine load and the values of TH- TC and TC- TL (partly because of the heat exchange rates
and partly because of the ATC range'l 4 seen in Figure 2).
B.

EFFICIENCY OF THE CLOSED SR CYCLE

As stated earlier, the efficiency rl of the SR cycle has been evaluated by several
authors3 -7, 9 , but these evaluations have certain shortcomings which are discussed in
Reference 8. We will therefore consider the recent evaluation in Reference 8, -the result of
which is
n =Xah X+(I+ a)h -1,
-where

(la)

a is the fraction of the SIM which, in transforming to the P phase,
causes the SRP;
X = T H - T;

=H
TL;I

the characteristic temperature h is defined as
h - c "1 A H

(lb)

where c is the average specific heat of the M and P phares, and
H isthe latent heat of the stress-Induced M+P transformation;
and

X I -oi/o,
/,

(Ic)

with a'defined by the expression

w i = ,pAH,

(ld)

where p isthe mass per unit volume of the material and Wi
isthe strain energy input required to deform the SM element
in the CR.
In what follows we will analyze the factors that affect the energy output of the SRP and the
efficiency n given by Equation (la). From this analysis we derive .oine physical insights
associated with the martensitic reactions in the SM alloys.
1 4 The kinematics of the

3 See

SRP will be presented in a separate article.

footnote 3 on page 5-2.

4 See footnote 4 on page 5-2.

See footnote 5 on page 5-2.
5 See footnote 6 on page 5-2.
7 See footnote 7 on page
9 See footnote

fo

5-2.

9 on page 5-2.

NSWC MP 79-441
III.

FACTORS THAT AFFECT THE SRP
A.

FEATURES OF THE ENERGETIC SRP

An impottant question is how the SRP in an SM element can produce
mechanical energy. In answering this question, briefly recall several points known
from the previous work:15
1.

The SRP is associated solely with the SIM or B. However,

recent

work

I

showsl 3 ,8 that the QIM or y' plays an important role in producing the SR energy output. We

will discuss this point in more detail below.
2.
The riartensite phase in the SM alloy is essentially an admixture of
y' and 5', denoted by B" and defined as
i3"(A,B) = Ay' + B8',

(2)

where the fractional parameters A and B (with A + B = 1) depend on temperature T
and stress a. Thus, the martensitic transformation takes place as sche, -Itically shown
by the lines TLCD and TLTHD in Figure 3, i.e., via the following channelst

138' * B3

*Ay

I

(3a)
A'

(3b)

(A - A'%8- (A - A'),

(3c)

where (A - A') represents the fraction of the y martensite that, under constant strain and the
combined influence of T and a, is transformed first to 0' and then to 0 as shown schematically
in Figure 4. This fraction (A - A') of y' which transforms via channel (3c) depends not only on T
and a, but also on the geometry of the deformed specimen.
3. The M-*P transformation in SM alloys is an admixture of first- and secondorder transformations and is accompanied by a small fractional volume change, about 0.1%.
This fraction, associated with the y' martensite, is equivalent to a strain C = 0.1% in a uniaxial
specimen.

SA. A. Golestaneh, The Shape-recovery Phenomenon in Shape-memory Alloys, with Particular
Reference to the NITINOL System--Review and Recommendations, Argonne National
Laboratory Special Report (August 1978).
13
See footnote 13 on page

5-3.

See footnote 8 on page 5-2.
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NSWC MP 79-441
4. In an isothermal reaction, there is a temperature TC below which no SR
can occur, and in practice TC is not necessarily equal to the martensitlc transition
temperature TO, since TC increases with the app ied stress. However, for prcaent purposes we
may consider TC t To, and TO may be exp.essed - as
T

v (MS + Mf + As + Af).

(4)

In practice (Figure 2)) both To and T have spreads (± A To and ± A TC ,
respect.vely).
Because of the spread ATo, hiternaliriction, and motion of defects, the martensitic reaction
depends not only on T, a, and c, but also on time1 4 .

I

the Y'

5. The latent heat of the 8' * 8 transformation, AHola, is large,- than that of
I transformation, A Hyl, . In fact, it is found 13 ,7 ,8 that the difference,
6(AH) = AHa'$ - AHy' ,

(5)

is responsible for the mechanical energy output of the SRP. From the evaluation of
the free energy for a closed SR cycle, in accordance with reacL'ions (3a) to (3c), the
factor a in the efficiency formula (1a) has been derived8 as
L= (A- A') 6 (AH)
A

(6)

6. Finally, an important feature of the SM materials (partictila NITINOL
alloys) is that in the absence of residual strain and stress in these alloys, the M structure is
soft and pliable, whereas the P phase exhibits much greater elasticity and strength. 16 In
a uniaxial specimen, the SR strength is defined as&
(TH, TL, A ) =Or(Ta,

r) -aoa (TL,

(7)

ISee footnote "13on page 5-3.
14
See footnote l4on page 5-4.
7

See footnote 7 on page 5-2.

8 See footnote

8 on page 5-2.

16 The

transient stress data are obtained as follows: (a) Strain the specimen, surrounded
by a water bath at temperature TL, to a fixed value; (b) change the water temperature
rapidly from TL to Tlwhiie keeping the specimen constrained under constant strain;
and (c) measure the stress change due to the change TH - TL.

-7 -

NSWC MP 79-441
Here ai is the stress required to proluce a strain ci in a long and thin specimen at temperature
the strain er, at
Ta < TC, and ar is the stress that the specimen can support while recovering
= . From a series of
temperature Ta> TC and A C = Cr - c. For a closed SR, Cr =
isothermal tensile tests such as those in Figure 5, we have deduced the E values shown in
Figure 6. We find that the Z data obtained in this way agree well with those obtained by the
so-called transient stress test shown in Figure 7.(Reference 16).
B.

SR FORCE AND EQUATION OF STATE

Many authors have used an equation of the Clausius-Clapeyron (CC) type to
but
is possible,
This studied
. been
and chas
T, a,matter
parametersThis
of theranges.17
in terms
SR strength
thecertain
express
in detail
and strain
temperature
only within
that the energy
elsewhere; 8 the essential points are described briefly here. We first note
18
as
given
is
W,
by
denoted
engine),
SS
an
output of the SR in an element (or in

is given

Here apA H

(i.e.,

=

(8)

a-r AH + W (TL, C).

W(T,

by Equation

(Id).

Figure 6 shows that for a closed SR

we can write
W$

(9)

W. =a.E

(10)

(where we have neglected the small elastic strain energy terms). In this case the energybalance equation (9) gives
=)&H

(TH , TC)

fcr

A < TH < Af.

(la)

HI

if we assume or = 0 (zero SR), then Eq. (1la) will have the form
T )
L C
Ci
01.= 2A&H-a(TL,

for

Mf < T
f-

M.
S-f

( lb)

Both Eqs. (1la) and (1lb) are identical in form with the CC equations. At a given e, we find
that E z nd oi vary logarithmically or nearly linearly with respect to T, as shown, for instance,

16See footnote 16 on page 5-6.
17A more detailed comment on the work of Reference 9 is given by A. A. Golestaneh,
"Comments on the Thermal Efficiency of an Ideal Shape-Recovery Cycle," Scripta Met., V.: 14,
August, 1980, pp. 845-848.
See ootnote S on page 5-2.
5-7

NSWC MP 79-441
it can be shown
in Figure 8 where the zero point of the stress is taken to be Q(T TC) • Thus,
from
applicable;
is
equation
experimentally that within a certain c and T range the CC
Equations (11) and (1c), we have
TH

FTL

Tc

XH

IXL I(2b

and

I xL I(120)
the c and T ranges within
where XH = TH - T and XL = TL - TC. We note that
of the SM alloy and
nature
the
on
to (12c) are valid depend
which Equations (1
for annealed
instance,
For
stresses.
structural conditions, particularly the internal
to 0.035,
0.015
'P
re
are
ranges
above
the
binary alloys with TC between 30 and 500C,
that
Note
8.
Figure
in
example,
for
XH J 0 to 70, and XL r 0 to -l50C, as seen,
may
and
structural condition,
the magnitudes of Z anJ oi also depend on the material
change with, say, annealing of the specimen.
the material had a sharp
A few points about Equationb (11): First, significantly, if
of Equation (11 a), as seen in
TC value, then Equation (I Ib) would have been acontinuation
between these equations in the range
Figure 8. However, in practice there is a discontinuity
temperature of the specimen is
2 ATc. Second, Or appears rapidly (Figures 7 and 9) as the
of Or - oi. The time required
shifted from TL to TH, and Equation (I la) gives the peak value
impurity content, and structural
to attain the peak value depends on the material composition,
(Figure 9). E is
condition. 1 4 The magnitude of E remains constant as long as TH is constant
AHa' and
between
difference
The
HR.
the
from
Hal$
A
absorbs
element
kept constant, the
that
find
we
(12a),
to
(8)
AH, i.e., 6(A H), depends on or. Making use of Equations
£

(A

A')

(13)

6(AH)

we must take into account the elastic
To obtain a correct result from Equation (13) for c = 0,
(10). This leads to
strain energy terms that were neglected in Equations (9) and
(A-A')6(AH)=-

See footnote

AE e 2e(Ce)

(14)

+ £O(£ ee)

4 on page 5-4.
5-8

...... .....

NSWC MP 79-441
where AE is the change in the Young's modulus
MP reaction, ce is the elastic strain energy, and

e(ce -

I

=

0

ee

of

the

specimen

during

the

for c < ce
for c > C

Another byproduct of our formalism is that by combining Equations (12a) and (1 la),
we obtain a quantity Z defined as
=aH
c
TC -pXH

(I5a)

But according to Figure 8, Z is a linear function of XH; that is, we can write Z kXH in which
k is the slope of the line (EH, T) in Figure 8. Substituting this E expression into Equation (15a)
gives
AH

S=

ke

-

(15b)

which is valid only within the c range in which the CC equation is acceptable. In Reference 7,
the authors stated that Z is a constant. However, as we see from Equation (I 5b), Z is not a
constant, but depends on e.
C.

FACTORS AFFECTING THE SR EFFICIENCY r!

In
The efficiency n depends on four factors: X = TH - TL, h, a, and X.
an economical 5 engine, TH equals TCor and TL equals TC of.
On the ott.er hand, the
maximum efficiency, rm, is found to be7
rmf TC
'Xh+ h
This

expression

indicates that

(16)
in

the

temperature

range

of

interest

(XH

75 and

XL e - 15oC for our NITINOL alloy), nm is nearly independent of X TH - TL. Equation (16)
also shows, the explicit effect of TC on nm.
Note that for X = 1, rIm is the Carnot
efficiency of an engine which works between twotemperaturesTC + h and TC. The influences
of the above parameters are discussed in more detail below.

7

See footnote 7 on page 5-2.
5-9

NSWC MP 79-441
1. The critical temperature TC:
First we recall that the maximum
SR strength E corresponds to a case in which TH > TC and TL < TC, as
can
be
deduced from Figure 9. One can also conclude from Figure 9 that a cycihc SR
with TL > TC cannot have any energy output, particularly if TC
has
large
spread + ATC. These considerations and Equation ( la) indicate that for an effective use of
the SR strength, we must be able to prepare an SM material with a TC which has the smallest
possible spread, defined as 2 A TC = TC +- TC where the upper and lower limits are close to
the As and Af temperatures, respectively. It is known that TC and ATC depend on
the material composition, impurities, crystal defects, etc. In the case of binary NITINOL
alloys, TC is very sensitive to the alloy composition. Better control of TC can apparently be
obtained by introducing a small amount of a third element (Zr, Al, Cu, Fe, etc.) into the
NITINOL alloy. However, at the present time, little quantitative informatio,, exi ts on the
variation of TC with material composition and impurity content.
As iar as the material
structure is concerned, we know that, for instance, in a thin wire specimen with a &iven grain
density, TC varies inversely with the wire diameter d (Figure 2). Figure 2 also shows that the
spread of TC increases with the wire diameter. This may be expected, since tihe degree of
structural uniformity is expected to increase as d is decreased. Another factor that
affects TC is residual stress: In practice, T increases with residual stresses which ran be
produced during the heat treatment or as actesult of incomplete martensitic t:ansformation.
This can be explained from the relationship

T

TC (

+ -

(17)

),

which is obtained by combining Equations (10) and ( 1), and assuming Wi to be the energy
stored in the specimen as a result of internal stresses. Indeed, we have noticed that the TC of
the SM elements in the SS engine increases by a few degrees after a few thousand SR cyclic
operations. To remedy this, these elements must be anneaied occasionally in order to recover
their initial TC.
2. The characteristictemperature h: According to definition (lb), h
is the ratio of AH over c. Since c varies little, h and, in turn. Tim [Equation (15f
depend on AH. For the NITINOL alloy mentioned above, h ZF 20 0 C or AH 9 2 cal/g. Hence to
increase Ti9 it is desirable to find an SM alloy that has a larger h or AH value than the
currently available alloys. This conclusion agrees with the results of all previous studies
except Mohamed. 9 He has stated that the efficiency i increases if AH decreases.
This
is in error because, if it were true, then AH = 0 should lead to maximum efficiency; this is
meaningless, however, since no transformation can occur if AH = 0. The reason for Motamed's
conclusion is that he overlooked the fact that the energy released by the SP is proportional
to A H, as shown at length in Reference 17.
3.
The parameter X: As noted in Section III. B, expressions (10) to (12c) are
derived from the e and T ranges in which the CC equation is valid. For our NITINOL specimen,
It is also
in the temperature range XL = -l°5C to XH = 700C, Equation (12c) gives ) = 0.84.
possible to evaluate X in terms of the SR strength: To do this, we use Equations (7) to (12c),
and write

See footnote 9 on page
1 7 See

Y- I
-2.

footnote 17 on page 5-7.
5-10
I

-

NSWC MP 79-441
where y : orla. We now see that X depends to some degree on the mode of material
deformation,, For instance, according to Figure Ys tensile test data, In the tempe'ature range
of interest and c t 2 to 3%, we find y T 3.5; thus Equation (19) gives X = 0.6.
On the other
'hrnd, for the same specimen in the bending mode (Figure 9) under the same e and T, we find y ,P
7, for which Equation (18) gives 'k$ 0.83 the same value obtained from Equation (12c). It is
difficult at this time to explain why y Is smaller for the SR in the tension mode than for that in
the bending mode. We are now in the process of verifying the.e results by refining the
experimental technique by which the stress and strain values are determined for the uniaxial
wire specirens. In any case, our Investigation indicates that in the above c and T
ranges, X cannot exceed 0.85. We note that in the previous work referred to, with the
exception of References 7 and 8, the authors have neglected the deformationi nergy WI,
Equation (Id), and therefore ) does not appear in their efficiency formulas.
IV.

MAXIMUM EFFICIENCY OF THE SS ENGINE

For most practical purposes, the SS engine must work between an HR with temperature
TH '$ 50-00oC and a CR with TL f 20-24oC. Within this temperature range, the NITIN(.L
SM alloy should have a critical temperature
TC = (TL TH)1/2

(19)

as given in Reference 6, or TC = 1/2(TL + TH). If we assume the latter choice, the maximum
efficiency rrr, of the engine, according to Equation (16), depends on h, )',and TC. For
our NITINOL alloy, TC = 306 + 7 K and h - 20-24; using these data and the maximum ),value of
0.895 given above, Equation 316) gives rim = 5-7%. This is,however, an ideal value. For
TL % 297 K and TH= 360 K and our NITINOL alloy, Equations (1a) and (12) yield i t 4%. We
conclude that to increase flm, we would need a ternary NITINOL Cr other SM alloy
with h > 20-24oC. Of course, if such an alloy is found, its usefulness will depend on such
factors as preparation cost, fatigue endurance, and corrosion resistance in hot water.

I
See footnote 7 on page 5-2.

8See footnote 8 on page 5-2.

I.

-,

f

6See footnote 6 on page 5-2.

5-1l

-

S

NSWC MP 79-44

60

LU C

E u0

Lu 0

.

LUI

a0

u

LA.

5<-12

N

Et

NSWC MP 79-441

aI

LU

LL
LAJ

<aZ
IL
0-E

I-I
U-

5-13

kLu

NSWC MP 79--441

1001

5NITINOL WIRE
SAMPLES X38001
I. 21 mil dia
2. 42 mil dio
3. 62 mil dio
4.83 mil die
1520

FIGURE 2

25
30
TEMPERATURE IN C

35

FRACTIONAL SHAPE-RECOVERY OBTAINED ISOTHERMALLY AT DIFFERENT
TEMPERATURES. THE X-INTERCEPTS OF THE CURVES INDICATE CAND TE.
THE UPPER AND LOWER LIMITS OF THE SR CRITICAL TEMPERATURE TCo
FOR WIRE SPECIMENS WITH DIFFERENT DIAMETERS.

5-14

40

-~~~~~~~~~

mum.

---

-_________

NSWC MP 79-441

am
WMM." -.- mm
-D\

f

T MS TCAS

Af

TIT

THE SCHEMATIC STRESSTEMPERATURE PHASE DIAGRAM FOR A BINARY
NITINOL SW ALLOY. THE DASHED CURVE DEFINES THE LIMIT BEYOND
WHICH THE SRP MAY NOT OCCUR.

FIGURE 3

0---

..

-

NVC MP 7, -*1

j

ELEMENT E ENTERS THE HR.
COLD RESERVOIR,TL
-

-

_

I

] J
l(}
ELEMENT E WITH THE

FIGURE 4

HOT RESERVOIR,TH

I
L (2)

.,-_'.
___-

(3)

-

-

-_
(4)

STRUCTURE ENTERS THE CR.

SCHEMATIC REPRESENTATION OF THE M-O TRANSFORMATION UNDER AN APPLIED
STRESS, ACCORDING TO REACTIONS (3a) TO (3) OF THE TEXT. (1) ELEMENT IS
COMPRESSED BY A STRE$S o i AT TL; (2) AND 13), REACTION (3c) OCCURS AT TH ,
PRIOR TO THE SR; (4) THE TRANSFORMATION AND SR UNDER A RESISTANCE
STRESS or HAVE BEEN (OMPLETED.

5-16

i
'

Fr

"

'

-

NSWC

MP

-~''

79-441

6-

5

C-

2-

TEVRTHI

E0(20
FIGURE~~~~~ 53STEMLYOSRE
TESSRI
WIE 1
PEIMN
m iax 6m)
IT TA

5v-77

0)CREFONTNL
5! 0 C

NSWC MP 79-4"l

TEMP. TH INOC
0 50

TEMP TL 20 C

V5

oi7
a09

C(%

II

~

0.

t~

-

.'

~-",

-..

,

p--

I

1~~-

45u

2

N8WC MP 79-441

6-

5,

T 360 K
f=7%

4TH:363

K
E5.5%

0

-TH:365K

f=:2%/

"2

W36 1K
I0o/

00

TL:294 K

1

2

3

4

5

6

7

8

9

TIME, t (min)
FIGURE 7

TRANSIENT STRESS RESPONSE OF A STRAIGHT NITINOL WIRE SPECIMEN
(1 mm dix 56 mm) UNDER A CONSTANT STRAIN, SUBJECTED TO A
SUDDEN INCREASE IN TEMPERATURE.

NCM MP 73-"l

250-

200150

100-

-0

B

-?0

20

40

60

50
50

FIGURE 8

VARIATION OF L, EQ. (10), WITH ISOTHERMAL TEST TEMPERATURE FOR
FIXED Ci 2,5%. XL TL - TC AND XH TH - TC.

Nsm MP 79-441
0

F-v-

4~.

CCJ

0

FIGURE 9

1)

TRANSIENT STRESS RESPONSES OF NITINOL WIRE SPECIMEN (1 mm dia x 56 mm)
TRAINED IN CURVED SHAPE WITH SPAN 66 mm AND HEIGHT 13 mm. FIGURES
ON EACH CURVE ARE TEMPERATURES TH AND TL AT WHICH THE SR STRESS WAS
MEASURED.

5-21/22

NSWC MP 79-441
REFERENCES
1.

Many authors have studied various aspects of the shape-memory alloys. See, for instance,
Shape Memory Effects in Alloys, edited by 3. Perkins (Plenum Press, New York, 1975),
and New Aspects of Martensitic Transformation, edited by Kobe, supplement to Trans.
3pn. Inst. Met., Vol. 17 (1976).

2.

See, for instance, R. Banks and M. Wahlig, Technical Report LBL-5293, Lawrence
Berkeley Laboratory (1976); and A. D. 3ohnson, IECEC 75 Record No. 759082, p. 530

(1974).
3.

M. Ahler, Scripta Met. 9, 71 (1975).

4.

H. C. Tong and C. M. Wayman, Met. Trans. 6A, 29 (1975). See also C. M. Wayman and
H. C. Tong, Scripta Met. 9, 737 (1975) and 10, 1129 (1976).

5.

B. Cunningham and K. H. B. Ashbee, Acta Met. 25, 1315 (1977).

6.

A. A. Golestaneh, 3. Appl. Phys. 49 (3), 1241 (1978). A somewhat different treatment
was used in this paper, as we will explain in more detail in the present paper.

7.

P. Wollants, M. DeBonte, L. Delaey, and 3. R. Roos, Z. Metallkde, Part I, p. 147,
Bd 70 (1979) H.3 and Part II, p. 298, Bd 70 (1979) H.5.

8.

A. A. Golestaneh, "Martensitic Phase Transformation in Shape Memory Alloys," Proceedings
of International Conference on Martensitic Transformation ICOMAT - 79) at Massachusetts
Institute of Technology, Boston, MA, June 24, 1979, pp. 679-692.
See also A. A. Golestaneh, "Energetic Shape Recovery Associated with Martensitic
Transformation in Shape Memory Alloy," Acta Metallurgica in press.

9.

H. A. Mohamed Tawancy, 3. Mater. Sci. 14, 1339 (1979).

10.

The engine described here operates at r40 r/min and generates 5 mW of power.
Engines with different geometries have also been constructed; for instance, see
Reference 5, and the article by R. Banks in Shape Memory Effects in Alloys
(Reference 1).

11.

The process of "training" the SM element into a given shape essentially consists of
annealing the element (kept constrained in the desired shape) at a temperature T for
a time t. Both T and t depend on the SM alloy composition and geometry.

12.

A detailed description of the latent heat A Hy, 0 and AHO, , is in Rference 8.

13.

In the present work we exclude the effects of element geometry and other material
parameters which affect the heat exchange rate and kinetics of the SRP.

14.

The kinematics of the SRP will be presented in a separate article.

15.

A. A. Golestaneh, The Shape-recovery Phenomenon in Shape-memory Alloys, with Particular
Reference to the NITINOL System-Review and Recommendations, Argonne National
Laboratory Special Report (August 1978).
5-23

NSWC MP 79-441

16.

The transient stress data are obtained as follows: (a) Strain the specimen, surrounded
by a water bath at temperature TL, to a fixed value; (b) change the water temperature
rapidly from TL to TL while keeping the specimen constrained under constant strain;
and (c) measure the stress change due to the change TH - TL.

17.

A more detailed comment on the work of Reference 9 is given by A. A. Golestaneh,
"Comments on the Thermal Efficiency of an Ideal Shape-Recovery Cycle," Scripta Met.,
V. 14, August, 1980, pp. 84-848.

5-24

I

,3

NSWC MP 79-441

THERMODYNAMICS OF SME-ENGINES
P. Wollants, M. De Bontet L.. Delaey and 3. R. Roos
(Depar.ment Metaalkunde, Katholieke Universiteit Leuven, Belgium)
ABSTRACT
Recently a number of papers discussed the possibility of using the shape memory effect
and two-way shape memory effect for direct conversion of heat into mechanical energy
through a work performing transformation cycle.I, 2 ,3 , 4 ,5, 6 v7 Some
authors
tried
to
calculate the efficiency of this work performing cycle. However, the results published
were very divergent and even contradictory and consequently caused some serious
misunderstandings. The literature highly overestimated many efficiency values due to the
to the
violation of some basic
data and
wrong
thermodynamic
selection of
A rigourous thermodynamical treatment of the stressthermodynamic principles.
induced martenkitic transformation in a single crystal has been published by P.
The results of this analysis are extremely important for any calculation
Wollants, et al.,
Therefore, this paper
engine.
concerning efficiency or power capacity of a solid state Next
a work performing cycle of
summarizes the most important conclusions of this analysis.

a CuZnAI single crystal is described, and finally efficiency values reported in the literature
are discussed and corrected.

1 Tong,

H. C., and Wayman, C. M., Met. Trans. 6A (1975) 29.

Ahlers, M., Scripta Met. 9 (1975) 71.
3 Wayman,

4 Delaey,
5 Tong,

C. M., and Tong, H. C., Scripta Met. 9 (1975) 757.

L., and Delepeleire, G., Scripta Met. 10 (1976) 959.

H. C., ad Wayman, C. M., Scripta Met. 10 (1976) 1129.

6 ohnson, A.

D., IECEC '75 Record, 759082.

7Cunningham, B., and Ashbee, K. H. G., Acta Met. 25 (1977) 1315.
8Wollants, P,; De Bonte, M.; and Roos, 3. R., accepted for publication in Zeitschr. Metallk.

6-1

..

NSW ' 1P 79-441
1.

A THERMOIDYANIC ANALYSIS OF THE STRgSS-INDUCED MARTENSITIC
TRANSFORMATION IN A SINGLE CRYSTALG

For describing the thermodynamic behavior of the stress-free crystal and the crystal
under stress, the fo!lowing important thermodynamic state functions are defined:
Stress .free crystal

Crystal under stress

H=U+PV

(1)

H*=U +PV -FL

(1)

G=H-TS

(2)

G*zH--TS

(2)'

From thermodynamic standpoint both the stress-free and the stressed crystal may be
considered at closed systems, for which the fundamental equations are expressed as the total
derivatives of their independent thermodynamic variables P and T, and P, F, and T,
respectively.
dG = VdP - SdT

(3)

I

dG* =VdP - LdF - SdT

(3)

It follows that the important partial derivatives of the characteristic functions G and G*
with respect to their independent variables are:
a T'p =

('T

4

(4)

G

(

@Gz. P,F
aT

- S

(5)

(5) = V (-LF"p,T

=V()

(4)'
4)

Fig. I represents these ielations.
From the fundamental equations (3) and (3) ' we obtain immediately the conditions for
thermodynamic equilibrium:
dGT,P = 0

(6)

I

dG,PF

0

(6)

For an isobaric change of state of the stress-free crystal, the heat exchange AQ (o)
equals the enthalpy change AH; and in the same way for an isoforce-isobaric change of state
of the crystal under stress the heat exchange AQ (F) equals AH*, the change of the sta'e
function H*
AH = AQ (o)

(7)

I

AH* z AQ (F)

(7)

Between AH and AH* there exists thus the important relation
AH* = AH- F AL

(8)

8 See footnote 8 on page 6-1.

6-2

NSWC MP 79-441
which explains the work performing capacity associated with the martensitic transformation in
a crystal under stressed conditions. The variation of A H* with thermodynamic equilibrium
(this means changing F and T to maintain thermodynamic equilibrium, P being kept constant) is
given by the equation:
d (AH*)

--- : ACF +
dT

If the value of

AH*

(9)

F

ismuch larger than the value of AC F t follows from equation (9) that

--

&H*
To (F

(10)

constant

From the equilibrium criteria (6) and (6)' the most important Clausius-Clapeyron and
Clausius-Clapeyron-like relations are deduced:
dP ~To(o)AV
AH

(II)

I

dF
?!"

AlIH*

('l)'

or 1A- F .!1L
(1)T
(F).AL

which relate the values of P and T and F and T at thermodynamic equilibrium.
If (10) remains valid over a wider range of temperatures and forces, integration (if
equation ( 1)' becomes very simple:
F = const. AT

(k2)

It must be emphasized that in equation (II)' "F is written instead of "P" and
The reason is that the partial
"A " instead of "A V", and that the minus sign appears.
derivative of the characteristic function "G" of the unstretched crystal . G

V, has the

opposite sign of the analogous derivative of the characteristic function "G*" of the stretched
crystal: a

aP

T
T

- L.

Also, "AV" for thermo-elastic martensites is much smaller than the

transforma aon elongation "AL" due to the formation of stress-induced thermo-elastic
martensite.
Therefore the influence of hydrostatic pressure on the shift in equilibrium
temperature will be much smaller than the influence of an uniaxially applied force.
Fig. 2 illustrates schematically, the Clapeyron-like relation, approaching the G* - T
curves by straight lines. This implies that the transformation entropy remains constant in
Further, if equation (10) is correct, it
the interval of temperature under consideration.
Equation (11) '
follows that G* - T and the G - T lines are parallel to each other.
suggests AH* P+M can be calculated if the F-T relationship and, the transformation
elongation AL are known (e.g. from tensile experiments). It also follows that a linear F-T
relation--which is usually reported--implies a linear a H* - To (F) relation, since AL is constant at first approximation. But since in that case AH*/To (F) is constant, A S also must be
constant.

6-3

NSWC MP 79-441
2.

A THERMODYNAMIC ANALYSIS OF A WORK PERFORMING CYCLE ASSOCIATED
WITH THE MARTENSITIC TRANSFORMATION

Based on the results of the thermodynamic analysis of the stress-induced martensitic
transformation in a single crystal 8 , a work performing cycle of this single crystal has been
analysed thermodynamically. 9 A correct formula for the theoretical attainable efficiency
"r" of this energy conversion system is deduced. The cycle is represented in a TS-diagram.
Assuming some justified approximations, both the efficiency formula and the TS-diagram are
converted into a convenient form.
Let us assume we have at our disposal a rod shaped single crystal showing the shape
memory effects, and trained under compression and tension, such that the shorter shape can be
associated with the martensitic phase and the longer one with the parent phase. We will
describe now the work performing cycle of this crystal between the lower transformation
temperatures Mf(o) and Ms(o) and the transformation temperatures at high stress level
As (a) and Af (a).
In "state " the crystal is stress-free at a temperature Mf (o), which is the temperature
at which the P+M transformation of the unstressed crystal iscompleted. At this temperature
the crystal is reversibly stressed until a compressive stress level a is reached. This is "state 2"
of the crystal. From the temperature Mf (o) the crystal is now reversibly heated at constant
external stress until at the temperature As (a) "state 3" is reached.
As (a) is the temperature at which the M+P transformation starts when the crystal is
under stress a. The transformation is completed at Af (a), reaching "state 4." Next the crystal
is reversibly unloaded at constant temperature, so "state 5" is realised. The stress-free
crystal is then cooled reversibly from Af (a) to Ms (o) ("state 6"), and finally at the temperature Ms (o) the stress-free P.M transformation starts, and is completed at Mf (o). The crystal
is now back in its initial "state 1." The cycle is closed and may be rmpeated.
The results of a rigourous thermodynamic analysis of this work-performing cyclic
process are presented in Table 1, where, for the successive changes of state of the
crystal (1-2; 2+3; 3+4; 4+5; 6+l), the respective changes in T, a, and L of the crystal are given,
as well as the work exchanges, heat exchanges, and changes in entropy involved.
By means of the information in Table 1, various diagrams such as a a-T diagram,
a o-L diagram, a L-T diagram, a a-T-L diagram and a T-S diagram are easily constructed. As
an example, in Fig. 3 a T-S diagram is drawn in a qualitative way.
Concerning Table I the work performing cycle can be simplified substantially by
introducing some justified approximations.
(1) First of all, the elastic deformation work during isothermal loading is approximately
identical to the wok performed during reversible isothermal unloading:

8 See footriote 8 on page 6-1.
9 Wollants,

P.; De Bonte, M.; Delaey, L.; and Roos, J. R., accepted for publication in Zeitschr.
Metallkde.
6-4

g

-

NSWC MP 79-441
a

M

ac e
- -~~*E

Ne
.',.

Therefore,
concerning the
closed
cycle, there is no net to work
performance due to the elastic loading and unloading of the crystal. Even
when ceM 4 Cea then still ce M -c 0 is much smaller than Etr so that no significant
error is introduced by neglecting these work terms.
(2)

It can be shown that the entropy effects due to isothermal elastic loading and unloading
of the crystal are negligibly small. 9

(3)

For a single crystaI in which one martensitic varient is stress-induced, Mf (o) and
Ms (o) are nearly identical. The same holds
for As (o) and Af (o). This is confirmed by
experiments of Salzbrenner
and Cohen 10 on a CuAINi single crystal and by tensile tests
1
of Van Humbeeck I on a Cu-25,33 at % Zn - 9,11 at % Al single crystal (Fig. 4).
Especially in the last case, the hysteresis between Ms (a) and Mf (a) was
remarkably
small. If, however, no hysteresis effects are considered, then Mf (o), Ms (o), As (o) should
coincide. In this case the martensitic transformation is completely described by the
chemical equilibrium temperatures To (o) and To (a).

(4)

Concerning the heat capacity C0 (or CF) it can be shown that it is almost identical
to C (heat capacity of constant pressure) and that its value is extremely insensitive to
evqg large variations in F. 9 So we can replace "C0 " by "Cp". Further we suppose
Co IVto le nearly identical to C P, which is--in view of the usually reported
linear a-T relationship-a good approximation. 1

As a good approximation, Cp can be regarded to be independent of temperature in the Tinterval under consideration, if To (o) is >> T-Debye. If this is not so, Cp can be replaced
by Cp, the mean specific heat for the T-interval.
Taking into account all these approximations, the thermodynamic analysis of the cyclic
process leads to much simpler results (Table 2).
Defining the efficiency of this cyclic process as the ratio of work output to heat added
from the hot reservoir, Table 2 immediately leads us to the following expressions:
W

S=

-FAL

.

x

100%

)

Cp .ATo
To (a)
p = AHTo
9 See

footnote 9 on page 6-4.

10Salzbrenner, R. 3., and Cohen, M. submitted to Acta Met.
"Van Humbeeck, 3.; Delaey, L.; and Deruyttere, A., Z. Metallkde 69 (1978) 575.
ISee footnote I on page 6 -1.
6-5

:1.

.

-i
!

.

.

. .

,

....

t

NSWC MP 79-441
which is identical to:
AHTo(o) x A To

n To(o)[

.
. ATo + AHTo,)

x 100%

(14)

since
AH

=AH-FAL(seeEq. 8)

and

TH

3.

AH

(see Eq. 10).

THE WORK PERFORMING CYCLE OF A CuZnAl SINGLE CRYSTAL' 2

We calculate a work performing cycle for a single crystal of a Cu-25, 33 Zn - 9,11 AI (at
%) alloy. The necessary data are in Table 3 and Fig. 7.
For To (o) = 206 K, work, power, and efficiency have been calculated. Fig. 6 and 7 show
the results as a function of A To. Efficiencies are also calculated (Fig. 7) for To (o) values of
made).
100 K, 300 K, and 400 K (for the lower temperatures, corrections for Cp have been
p1
From Fig. 5 it follows that only for a cold reservoir at about 100°K efficiencies of 10 to
11% may be realised. For To (o) temperatures in the vicinity of room temperature, maximum
efficiencies of 3 to 4% are to be expected.
The TS-diagram is constructqd, u ng the A S-expressioos in Table 2. To (o) is 206 K and
the C value used is 5.7 cal. mole-' K'"123.85 J. mole-I K-1. Fig. 8 represents the result.

p

4.

DISCUSSION
From the foregoing calculations it is obvious that the theoretical maxmum efficiency of

this work-performing cycle of this CuZnAl-single crystal with the low emperature reservoir
at about room temperature is 3 to 4%. Other authors, however, have reported efficiency
values up to 20% (and even higher). A thorough investigation of their published results
revealed:
--

that A Q(o) has always been used instead of A Q(u)
that many times wrong thermodynamic data have been selected
and that some basic thermodynamic principles have been violated.

1 2 Wollants,

P.; De Bonte, M. Delaey, L.; and Roos, 3. R., accepted for publication in Zeitschr.

Metallkde.
6-6

-

..

.

.

:

.

..

;

.

I

I
NSWC MP 79-441
Let us first consider the formula arrived at by Tong and Wayman 1
ATo
,V

in(I+e)
(ApToC

.

(15)

The same AQ has been used both in the numerator and the denominator. In a reply to the
remark of Delaey and Delepeleire 4 that 4Q (o) and AQ (a) should be different in order to
obtain any work at all, Tong and Wayman' nevertheless affirmed that AQ (o) and AQ (o) should
be equal, except for a correction factor which could be neglected. The statement, however, is
based on a wrong interpre'tation of Kirchoff's equation:

AQ

)= AQ (o) +ITO (o) ACp. dT

This

equation

(16)

To (o)

absence of any

should be used only for constant pressure processes in the
t
th
If AC is much smaller than A H*
external load.
To)
isa
AQ (o)%oi valid. Since AQ (a) -4Q (o) = -F. AL it is evident that there

relation AQ (a)
would be no work performance at all it AQ (o) and &Q (a) were equal.

Por a AgCd alloy Tong and Waymani further estimate Cp to bI 4 cal mole- 1 K- 1.
This
value is far too low. A reasonable value for C can be obtained from the Neumann-Kopp rule
which states that Cp (allov'-iENiC i. Using this rule we calculated for Ct (alloy) in the Tinterval 1100 K - A!V0"K
value ofabout 5.46 cal. mole-' K - 1, selecting p - values for Ag
and Cd from HWtgren. I
If Tong and Wayman had used Cp = 5.46 cal. mole

- I K-

= AQ (o)To (a) = 200
and AQ (A)

cal. mole-I instead of AQ (o) = 100 cal. mole - 1, they would have found an efficiency value of
about 12.8%.
This value is still high, but the reason herefore is their extremely low
To (o) value. One can see from Fig. 7 that for To (o) = 100 K we found approximately the same
efficiency value.

See footnote I on page 6- 1.
4

See footnote 4 on page 6-1.
See footnote 5 on page 6-1.

13Hultgren, R.; Desai, P. D.; Hawkins, D. T.; Gleiser, M.; Kelley, K. K.; and Wacman,

P. D.,
Selected Values of the Thermodynamic Properties of the Elements, American Society for
Metals (1973).
6-7

_

_

-

' ...

.. '-

.

_I

I

..._

.-.

n

NSWC MP 79-441
Ahlers 2 calculated the efficiency of a work delivering cycle performed by a Cu-36 at %
Zn - 1.75 at % A l single crystal using the equation:

rl=

YM (A(T 2 - T 1 )- &t)
C(T - T + H
x 100

(17)

and found a value of 4.1% with Y&I = 0.17; dT/dT 0.096 kg mm " 2 K-1, A= 0.5 kg mm - 2 , C = 6
cal mole- ! K-'; AH = 4.45 kg mm 2 Ms (o) = 273 K and ATo = 100 K. Taking into account the
F-T dependence of AH, Ahlers would have arrived at 3.9 5%. Ahlers' result agrees well with
our calculations. Wayman and Tong 3 how'!ver claim that this low value is only due to the use
of unfavourable thermodynamic data. Cootsequently they recalculated nl with another set of-according to them--more accurate values. First of all they "select" for Ms (o) 193 K and put
4 cal mole-I K-1, arguing as follows: ...
Since the Ms temperature is probably 100 K below
the Debyettemperature for the CuZnA'' alloy it is reasonable to take: C = Cp = 2/3 x 6 cal
tinale-L K-' ... ." We prefer to estimate Cn with the Neumann-Kopp rule mentioned above.
Taking CP values for Cu, Zn, and A1 from ifultgren 1 3, we arrive at a (p value for TI 193 K
293K
K I of 5.72 cal mole-' K- 1 .
Furthermore, Ahlers uses the product of sheAr stress and shear strain to calculate the
work performed durint the transformation. As a matter of fact the contribution 9f the normal
to the habit plane is much less and can generally be neglected. Wayman and Tong claim that
the value of dr/dT used by Ahlers is far too small. They derive a value for dr/dT from a figure
published by Pops and Ridley. " 4
This figure, however, shows a a-T relationship and not a T-T relationship.
In so doing,
Wayman and Tong combine a shear strain with a uniaxial tensile stress, which is, of course,
much higher than the resolved shear stress in the habit plane. Therefore, the efficiency value
as calculated by Wayman and Tong (21.3%) is wrong, a better estimate being the one by Ahlers.
The same remarks apply to their calculations made for a CuAINi alloy. 3
The "Carnot
7
Ashbee:

Efficiency of the Marmem Engine" as introduced by Cunningham and

Mf(0*o)

di

in = I -

(8

d f(18)t

Af(G=o) + max--

Sefootnote 2 on page 6-1.
3

See footnote 3 on page 6-1.

13 See footnote 13 on page 6-7.
14

7

Pops, H., and Ridley, M., Met. Trans. 1 (1970) 2653.

See footnote 7 on page 6-1.

6-8
w

-J

NSWC MP 79-441
is not a good indication for the true maximum attainable efficiency of the Marmem
Engine, since it does not take into account the heat capacity of the system. The high

dAf
"max -- values of B-brass and NiTi alloys may indicate the fact that the work.output will
be large. Anyhow, the conclusion of the authors that efficiencies higher than 10t (i.e. at least
half of the Carnot efficiency is realised as useful work) are obtained is not justified by their
arguments.
The work performing cycle as proposed by 3ohnson is shown in a a-c diagram (Fig. 9a) and
in a T-S diagram (Fig. 9b). From state A to state B, the material undergoes a sudden adiabatic
contraction followed by an approach to thermal equilibrium at temperature TH. According
to Johnson6 the entropy effect involved is positive and larger than the entropy effect due to
cooling and transformation. We showed that the entropy change due to isobaric isothermal
stretching of the wire is given by

I

2

QL F
AS = LoF + 2E A

(19)

So, if the wire snaps back isothermally, the entropy change is the negative of this value.
Therefore point B on Fig. 9b should be on the left side of point A. The absolute value of the
entropy chanfe involved, according to formula (19) is of the order of magnitude of 0.1
3. mole-1 . K- . From B to C the wire cools down and simultaneously transforms to the
martensitic phase. Both the entropy elfects involved--first a decrease in entropy due to the
isostress cooling of the wire, and second a decrease in entropy due to the parent to
martensite transformation--are a few orders of magnitude larger than the entropy change
involved in step A.B. 9 Steps C.D, and D...A must be treated in an analogous way as steps
MAB and C-D, respectively. It is now evident that the T-S diagram proposed by 3ohnson is not
correct. Fig. 9c presents a correct T-S diagram. Points A and B are very c!ose to one another.
At B the wire starts cooling and at B1 the parent to martensite transformation is initiated. At
C thT transformation stops and from C to D the material is loaded again isothermally. From D
to D' the wire is heated. At D the martensite to parent transformatlon starts and is
completed at A. Johnson's 6 efficiency formula

(AQAB" AQBB, - AQCD - AQDD )

(20

- AB - AOBB,

apart from being based on a faulty T-S diagram is also wrong. The heat effects AQAB'.... are
associated with the adiabatic (un)loading of the wire. So thjs formula does not take into
account the latent heat of transformation. It has been shown g 99 that
precisely
the
difference between the latent heat of the stress-free transformation and the latent heat of the
SSee footnote 6 on page 6-1.
See footnote 9 on page 6-4.
8 See footnote

8 on page6-1.
6-9

I

NSWC MP 79-441
transformation under stressed conditions is mainly responsible for the work performance.
Further the heat capacity of the system is also neglected.
Cory and Mc Nichols'1 claim that the efficiency of heat engines for low-grade thermal
energy conversion is critically dependent on thermodynamic cycle selection. They select
three cycles for discussion:
a "TA-cycle," consisting of two isotherms and two
adiabatsia "T -cycle," consistin _ of two iso herms and two paths of constant length
diand
a
"
'F-cycle,"
consisting of two paths of constant force and two paths of constant length.
For each of these cycles, the efficiency is calculated for various temperature differences,
and compared to the Carnot efficiercy. For the TA-cycle they calculate a l/rIc value
of
80%. However, since AT in this case is limited to 25 K (with the lower temperature
at P 300 K), true efficiency is restricted to 32j 2 -00 x 80't b.2 %. For the "TI-cycle" and the
"Fl-cycle," lower rl/nc ratios are found, but since in these cases AT can be made larger, true
efficiencies still range from 5..to..3%. The authors' remark that "... With a 150 degree
temperature difference between the heat source and sink, and an engine efficiency of 80
percent of Carnot, the net efficiency of 25 percent is comparable ....
" is in straight
contradiction to their own calculations, since 80 percent of Carnot is only realised for
the "TA-cycle," and for this cycle AT is restricted to about 25 K (if such a cycle can be
reafised at all, considering the two adiabats involved).
Golestaneh 1 6 discusses the efficiency of a solid state engine made from NITINOL
memory material. He defines the thermal energy per cycle which can be converted to
mechanical energy as
W = aMAH - WD

(21)

where W D is the energy required for producing m mass of the martensitic structure by a
deformation process at To; a is the fraction M.P transformation; and A H is the latent heat of
transformation.
This expression assumes the latent heat of transformation may be
entirely converted to mechanical energy if a = I (M-P transformation complete) and
We have shown this is not true at
Wp 0 (low stress-level at zero stress).
It
follows that
al[.
Golestaneh further defines WD = OL' O m A H and (l-a') = 0.
W = a B m A H. This expression is substituted in r=,
T
at

(dT.

where Qa =m

CMdT +z m A H

Taking Cp = CM = C; h = C-I AH and x = Ta - To

at= 3ah 1x+-h 1 _

15

Cory, 3. S., and Mc Nichols, 3. L., IECEC '78 Record.

16

Golestaneh, A.A., 3. Appl. Phys. 49 (3), 1978.

8

aTo

See footnote 8 on page 6-1.

6-10

+

Golestaneh arrives

(22)

H

NSWC MP 79-441
for the efficiency of the solid state engine. However, since the definition of W is wrong, this
formula cannot be correct, and all further arguing of Golestaneh about relations and
Due to the use of an
restrictions between the parameters o, 0. X...is rather irrelevant.
largely exaggerated.
are
again
20%
of
12
to
incorrect formula for in, the estimated efficiencies
Based on measurements on a Ni 55 Ti 45 wire, Baumgartl 7 has calculated a maximum
efficiercy of about 1.5% if only the latent heat of transformation is added. This value seems
very low, but the author says it only roughly estimates a realistic order of magnitude.
From the foregoing discussion it appears that very high efficiencies (.r 20%) for the work
Maximum energy conversion
delivering cycle of an SME-engine are to be excluded.
low temperature reservoir at
with
the
efficiencies for completely transforming single crystals,
about room temperature, of 4 to 5% are to be expected.
If a heat source is available at a very low cost, this low efficiency may not be
objectionable if the generated power per unit mass of working substance is high enough. Table
4 collects both calculated and experimentally determined power-v-lues. Experimentally
determined values are at least an order of magnitude lower than the theoretically calculated
vaiues.
CONCLUSIONS
Based on a rigourous thermodynamical treatment of the stress-induced martensitic
1.
transformation in a single crystal, it has been shown that
-

-

the condition for thermodynamic equilibrium at constant T, P, and F of the stretched
crystal is the minimization of the characteristic function G*= U + PV - FL - TS;
the Clausius-Clapeyron-like equation which describes the influence of F (or a) and T on
the transition temperature To (F) is:
dF

--

- AH
STo(F). AL

and the difference between A H* (a) (- AQ(o)) and .ATi(o) (E AQ(o))
performance during the reverse transformation.

equals

the

work

A work performing cycle for a CuZnAI single crystal has been analysed
2.
thermodynamically. A correct efficiency formula has been derived and a convenient TSdiagram constructed.
With the temperature of the cold reservoir at about 300 K, maximum theoretical
3.
not
does
efficiencies (i) of 3 to 4% are to be expected. Increasing A To above 30 or 40 0 K
influence n markedly, but the power generated increases almost linearly as a function of T.
The available literature concerning TS-diagrams, n and power of the solid state engine is
4.
very confusing, contradictory, and often erroneous. The construction of faulty TS-diagrams
and the selection of incorrect the'modynamic data have been responsible for the appearance in
the literature of too many highly overestimated efficiency values.
17

Baumgart, F., Jorde, 3; and Reiss, H. G., Tuchn. Mitt. Krupp 34 (1976) 1.
6-11

. .. ~.

NSWC MP 79-441
5. Concerning powe onrtion of the solid state engine, theoretical maximumn values of
the order of magnitude o 1.3 att kg-1 are found. Reported values of true existing machines
aemuch lower: 130 Watt kg- , 9 Watt kg , 2.85 Watt kg1 and 0.5 Watt kg- . If one wants
to use the solid state engine for conversion olwgrade thermal energy to mehaIa energy,
values of at least 10' Watt k 4 should be realised.
6.
Direct applications can rather be found where power generation is not the principal aim.
One might think of special devices such as regulation systems, tube fittings ... where a small
but controllable work output is needed or generation of T-controlled stresses is required.
ACKNOWLEDGEMENTS
This work has been supported by the "Gotkoncerteerde Akties van de dienst Programmatic
van het Wetenschapsbeleid" of the Belgian Government.
P. W. is grateful to I.W.O.N.L. (Instituut voor de Aanmoediging van het Wetenschappelijk
Onderzoek In Nljverheid en Landbouw) for a scholarship.

6-12

4

..........

F

FIGURE 1 SCHEMATIC REPRESENTATION OF THE PARTIAL DERIVATIVES OF THE

CHARACTERISTIC FUNCTIONS 0 AND G*.

IIla

FIGURE 2 THREE.OIMENSlONAL SCHEMATIC REPRESENTATION OF ThE CLAPEYROtdLIKE RELATION: dFidT - (ASIAL)P*M.
6-13

iI

3'

1

M#I M54

FIGURE 3

ASMAfM

SCHEMATIC REPRESENTATION IN A TS-DIAGRAM OF THE WORK PERFORMING

CYCLE OF A SINGLE CRYSTALI

2

I

FIGURE 4 TYPICAL TENNILE CURVE FOR A Cu - 2533AT %Zn- 9. 11AT
CRYSTAL AS DETERMINED BY VAN HUMSEECK"s.

Al 51f3l.E

NSWC MP 79-441

dT

2.s MPox1C

IMflos2O3K
M5 14 - 205.2K
?

T
FIGURE 5 SCHEMATIC REPRESENTATION OF THE a-T RELATIONSHIPS AS DERIVED

FROM A NUMBER OF TENSLE TVESTS AT DIFFERENT TEST TEMPERATURES&F
AT THE ZERO STRESS AXIS,*THE EXTRAPOLATED Mf~o). K3(c4. Allo) AND
Aq~o) VALUES ARE FOUND.

Work___

-

Wcttg

-1600-

-1200

__

(,

FIGURE 6 WORK PER CYCLE AND POWER (FOR VARIOUS CYCLE SPEEDS) OF THE
CuZnAI SINGLE CRYSTAL AS A PUNCT"W OF Alo fTnol - 206 K).

NMW MP 79-Mt

ToW a 206 K

TeWw.300K-

FIGURE?

EFIIEC VI. &TO DIAGRAM FOR Tolo) TEMPERATURES OF 100OK. 200 K.
300 K AND 400 K.

a

23.2

AS0

FIGURE 6
r

SIMPLIFIED QUANTITATIVE TS.OAGRAM FOR THlE WORK PIERFORMiNG
CYCLE AS DESCRIBED IN THIS PAPER.

V

r
NW~C W 7g-441
I

In

I
a

3

C
C
U, 4

a

£

ii

r

*1

U.-

w
-S

a!

OL)

in

I

'I

w

*

U

I
a

z
I'

4--

b

ID
4

8

3
U.

6.17

c:
C

-

NSWC MP 794

14
*

I

w0

I1

A

41

X

'

F.,

ba

0

*

a

0

o

00

b

NSWC MP 79-441

HO4

HO

I

0

<)

It.

It-.

u
00

I

0

•

0'

ow
Ci

000
4

08

0

0

U

+

+

+

0

0
-

4

0

~

W.Sdt

A

0

0

00

0

0)
0

0

00

C14

0n

+

+

%a4

4J0J

g

+

~4J 1-41-6

+

+

+

0

0

19
m

0

NSWC MP 7"41j
Table 3:

Data for the calculation of the work performing
cycle of a CuZuAl single crystal.

Alloy composition

Cu-25,33 Zn - 9,11 Al (at %)

calculated
molecular
weight

60,67 mole

calculated density

7,007 kg.

-M-T relation

S

P4M

(1 kg

16,48 mole)

dm-3
7'

aPM - 2,5 T - 513 HPa

(Fig. 4 and 5)
2,5 MPa . K

S
extrapolated stressfree transformation

Mf (o) -203

temperatures (Fig. 5)

A

K; A

(o) = 205,2K

4

(o) = 206,5 K; Af (o) = 210,4 K
If

thermodynamic

equilibrium temperature

A

(o) + M8 (o)

TO (o)

21

2

transformation
elongation

e
= 0,065 %
Cr

AHT 0 (0) as calculated

289,83 J. mole -

from Eq. (11)'
ART

(6)

work per cycle

W = T ()

AT0

power

P - W x n

(n

AHr
effiziency

Y

.

sec

(o) x AT°
x 10,

0

T (o)
0

6-20

cycles

AT
p

+ W o (a)
0
(

NSWC MP 79-44&1

Table 4:
-1

2,85

Measured and estisated values of the power generated
by 8)3 engines.

cycles
se.
kgaterial
0,05

O0s5
9

1 ...

1j3

ref.
CuZnA1

measured

Neys

(20)

NITINOL

measured

Cunninghamf

(7)

NITINOL

meaured

Banks

(19)

130

?NITIN0L

measured

Johnson

(6)

1000

1NITINOL

estimates

Johnson

(6)

2000

?NITINOL

of the ma-

Cory

(10)

1000

0,5

ximal ob-

thi s w,, rk

CuZnA1

tainabl e
work

6-21

NSWC MP 79-441

BIBLIOGRAPHY

M.

_________________
ciaMt

(95

1

Banks, R., "Shape Memory Effects in Alloys," ed. 3. Perkins, Plenum Press, 1975, p. 542.
Baumngart, F.; Jorde, J.; and Reiss, H. G.; Techn. Mitt. Krupp 34 (1976) 1.
Cory, 3. S., and Mc Nichols, 3. L., IECEC '78 Record.
Cunningham, B., and Ashb.ee, K. H. G., Acta Met. 25 (1977) 1315.
Delaey, L., and Delepeleire, G, Scripta Met. 10 (1976) 959.
Golestaneh, A. A., 3. Appi. Phys. _49 (3), 1978.
Hultgren, R.; Desai, P. D.; Hawkins, D. T.; Gleiser, M.: Kelley, K. K.; and Wacman, P. D.,
Selected Values of the Thermodynamic Properties of the Elements, American Society for
Metals (1973).
Johnson, A. D., TECEC '75 Record, 759082.
Kopa, R. D., Presented at the American Section of the International Slar Energy Society, Inc.,
Aug. 28-29, 1978, Denver, Co.
Neys, 3., Energiekonversie steunend op het vormgeheugeneffekt, Eindwerk K. U. Leuven, 1976.
Pops, H., and Ridley, M., Met. Trans. 1 (1970) 2653.
Salzbrenner, R. 3., and Cohen, M., submitted to Acta Met.
Tong, H. C., and Wayman, C. M., Met Trans. 6A (1975) 29.
Tong, H. C., and Wayman, C. M., Scripta Met. 10 (1976) 1129.
Van Humbeeck, J., Delaey, L., and Deruyttere, A., Z. Metalikde 69 (1978) 575.
Wayman, C. M., and Tong, H. C., ScritaMet-. (1975) 757.
Wollants, P.; De Bonte, M.; Delaey, L.; and Roos, 3. R., accepted for publication in Zeitschr.
Metallkde.
Wollants, P.; De Bonte, M.; and J. R. Roos, accepted for publication in Zeitschr. Metallk.
6-22

NSWC MP 79-441

THERMOMECHANICAL BEHAVIOR OF NITINOL
Dr. 3. S. Cory
Cory Laboratories
Escondido, CA

iI
Two hundred fifty years experience with heat engines has taught engineers the
importance of a state equation or state relation for the thermodynamic working material. The
state relation is used in engirse design, for example, to predict the design forces on an
automobile piston and bearings, and the number and size of cylinders required for a given
horsepower. A thermodynamic state re!ation, like PV = nRT, is also used to optimize and
invent new and better heat engines, such as the diesel, the jet engine, and turbines. The entire
engineering history of heat engines has been solidly based on a quantitative understanding of
the relationship between the temperature of the working fluid, and the force and volume of
that fluid.
The importance of a state equation was widely recognized in the 60's by the early
workers in NITINOL. Many measurements were made of stress versus strain as a function of
temperature. State equations were proposed which were analogous to conventional, multiphase
thermodynamic working fluids, such as water. These measurements and equations were vey
useful for initial surveys of the potential of NITINOL Heat Engines (NHEs) but broke Jowr,
completely when applied to operating engines. Also, the experimental results were not
repeatable. At a given temperature and length, for example, at one time a force of one
newton would be measured and then later, with the same wire, a force of ten newtons would be
measured. These measurements and state equations were completely inadequate for engine
design. A wide gap opened between the analytical and hardware engineers.
To close this gap, an exhaustive set of experimental measurements was initiated to find
an empirical state relation between the temperature, length, and force on a NITINOL element.
This empirical state relation was to accurately describe all possible NITINOL behavior,
including stress-strain measurements, engine behavior reported in the literature, and the
results of the ad hoc experiments.
In this experimental program, the first breakthrough occurred when it was realized that
(Fig. 1) all obsecved thermodynamic states and all observed thermodynamic paths occupied a
*
bounded volume in state space.
This behavior is in sharp contrast with conventional
*thermodynamics,
where all possible states occupy a surface, not a volume in Force-LengthTemperature (FLT) space.
This fundamental difference accounts for the confusion and
inaccuracies of the early measurements and state equations: at a single value of temperature
and length, for example, the force on a conventional material would be uniquely determined,
but the force on a NITINOL element could range from 0 to 50 newtons, depending on its
location within the bounded volume.
As usual, the reason for this phenomenon later became obvious: NITINOL is a lossy
material in contrast with even the most complex, multiphase, multicomponent gas or liquid,
here phase and concentration changes are almost exactly reversible.
Non-equilibrium

7-1
trn

NUNN"

NSWC MP 79-441
thermodynamics shows a one-to-one correspondence between internal losses and hysteresis in
the force-length plane. So NITINOL should, as it does, occupy a volume in state space. This
phenomenon explains the inadequacy of the early reversible state equations, and is presently
fairly widely recognized.
The second breakthrough in the experimental program occurred when it was realized that
the location of the boundary surfaces changed as the NITINOL was stressed, strained, or
heated. Thus many of the reported phenomena, such as second memory and creep, could be
described in terms of the migration of the boundary surfaces with cold working. This cold
working effect complicated the problem of determining the empirical relation locating the
state of a NITINOL element within the bounded volume since the location of the bounded
volume changed. Fortunately, the boundary surfaces migration could be eliminated by two
procedures.
First, limiting the cyclic stress, strain, and temperature excursions to small values kept
the boundaries for a large number ol cycles. Reproducible measurements could be made.
Second, preconditioning the NITINOL element for about 20,000 cycles could stabilize even
large FLT excursions. Either procedure was adequate to experimentally isolate boundary
surface migration from the problem of predicting the precise location of the FLT state within
the bounded volume, and also incidentally, to stabilize engine performance.
The final breakthrough occurred with the observation of two phenomena:
First was the observation that reversible paths existed (Fig. 2). In constant force, or
constant length, or constant temperature measurements as shown in Figure 2, specific
conditions existed where reversing the sense of the path would result in an exact retracing of
the path. For example, the lines labled A were formed in the stretching isotherms of Figure 2
by reversing from stret -hing to contraction, for a small excursion, and then reversing again
back to stretching. This behavior strongly constrasts with the normal hysteresis. All these
reversible paths, everywhere within the bounded volume, have nearly the same slope and can
be used to define a set of reversible planes. These planes can be conveniently described by the
new state function, Z(FLT). The utility of these planes is that whenever a change in the
direction of phase conversion occurs, for example the change from creating martensite to
creating parent phase material, the thermodynamic path leaving this starting point is always
initially parallel to the local reversible plane. Thus the initial slope of all paths is determined.
The second phenomenon (Fig. 3) was the observation that all thermodynamic paths
approached one or the other boundary surfaces asymptotically. This was ascertained by
plotting the element length against the force separation between the observed path and the
boundary surface (distance X in the figure) on semi log paper. For all measured paths, this plot
always produced a straight line with the slope independent of the starting point. This behavior
was also observed in constant temperature, constant length, and constant force experiments.
These observations allowed all the published data on NITINOL wire and helices and
engine behavior, and also the ad hoc experiments, to be correlated by a fourfold infinite set of
state surfaces. The state surfaces of each kind--those describing the martensitic and those
describing the austenitic transformation-completely fill the volume between the boundary
surfaces, and allow prediction of the FLT behavior of NITINOL. Examples of predicted
constant force, constant length, and constant temperature thermodynamic paths are shown in
Figure. 4. The projections of these paths onto the corresponding two-dimensional planes are
also illustrated.
These state surfaces can b-= approxiiaated by the equations in Figure 5. In these
equations the reversible surfaces, Z=const and the boundary surfaces, N=const, are flat planes
7-2

NSWC MP 79-441
when the coefficients a through h are constants. The values of these coefficients determine
the location and slope of the planes. The state equations then say that the force differences
between the thermodynamic path and the boundary (FB-F for the martensitic transformation,
and F minus the lowet boundary force for the austenitic transformation) are exponentially
dependent on the tempea,-ire and length excursion from the starting point, which is defined by
the state (FI, L1 , ancd T, or (F 2 , L2 , T2 ).
These state surfaces are an empirical correlation of data, with no theoretical basis, and
are claimed to include all possible thermodynamic behavior.
So a single, measured,
experimental path that does not lie on one of the surfaces, a single counter example, is
sufficient to weaken the correlation. This is a strong (and useful) claim. The immediate
response to such a claim by any self-respecting experimentalists is to try to find a counter
example. Figures 6, 7, and 8 illustrate the efforts so far to find a counter example by
comparing the predictions of the correlation with experimental observations.
The correlation predicts a uniqueness on a single state surface: that is, that the
subsequent behavior or thermodynamic path is uniquely determined by its location on the
surface, regardless of the path used to arrive at that point.
Figure 6 illustrates the
experiments to check this prediction. A single point on a specific state surface was
approached by constant length, constant force, and constant temperature paths. In each case,
the subsequent constant force path leaving the point was the same, within the accuracy of the
experiment. Note that this uniqueness is equivalent to the statement that stress-induced
martensite is energetically (and probably entropically) equivalent to thermally induced
martensite.
A second prediction is the non-uniqueness of a point in state space if that point was
arrived at by paths on two different state surfaces. The experimental verification of this
prediction is illustrated in the isothermal paths in Figure 7. In the top e: .ample, the two
isothermal paths lie on two intersecting state surfaces because the starting points for the two
paths are different (points labled A and B in the figure). As predicted, the subsequent
isothermal paths leaving the common point B in state space are different. This experimental
behavior confirms Wang's conjecture that a single unique energy equation does not exist for
NITINOL. Therefore, the observed thermodynamic paths cannot be simply described as the
minimum of a conventional free energy function, and the phase transformation must involve a
change in the Gibbs free energy.
The consequence of this non-uniqueness fdr closed
thermodynamic cycles is illustrated in the lower set of isotherms of Figure 7. Cycles do not
necessarily retrace themselves, but may drift in length, force, or temperature.
The important consequence of this property of the state surfaces for heat engine design
is illustrated in Figure 8. Any stable, non-drifting closed cycle must lie on a unique pair of
state surfaces, characterized by being symmetrically located between the two boundary
surfaces. Any other cycle will be unstable and will drift (within the constraints of the
experiment or device). This property is used in heat engine design to identify the particular
pair of state surfaces that will contain the operating (stable) thermodynamic cycle.
This state surface correlation is much more complex than a simple PV=nRT, in that it
involves a fourfold infinite set of state surfaces, rather than a single state surface. But,
because of the regularities in the data, this complexity merely means that one additional step
must be added to conventional thermodynamic calculations. This additional step is just
locating the starting point (or extremum of the state function Z) and then using the stability
condition to specify the two particular state functions which must contain all thermodynamic
paths.
From this point, NITINOL thermodynamic calculations follow the familiar, nonequilibrium thermodynamic procedures.
7-3

__

.-.

f1
NSWC MP 79-441
The remainder of this paper describes examples of the use of the state surface
correlation. For instance, the first step in NITINOL heat engine design is to measure
the
coefficients (Fig. 5) a, b, ff g, N, h, and c for the specific NITINOL element to be used in the
heat engine. Then, a lower limit of the Z state function is selected, ZI(F 1 , L 1 , T1 ) and the
cycle stability criteria used to specify Z2(F 2 , L 2 , T2). These conditions define the applicable
pair of state surfaces. The ne;'t step is to locate, on this pair of surfaces, the thermodynamic
paths followed by the heat engine, (Fig. 9). The example illustrates a cycle consisting of the
popular constant length and constant temperature legs.
Note that the paths must be
constructed so that the extreme values of ZI and Z2 are achieved at the corners of the cycle.
This first step is sufficient to specify several critical dimensions of the heat engine, for
example the throw of the crank and the initial length of the NITINOL element for an off-set
crank type machine.

*
*

The next step is to evaluate the specific work and thermodynamic efficiency. The
specific work can be easily found (Fig. 10) using the state equations and the integration limits
found in the previous step to evaluate the cyclic intergral of FdL. This specific work is the
amount of heat energy this particular cycle will convert into mechanical work, per unit of
mass of NITINOL cycled. Therefore, when multiplied by the element mass, it is also the
torque contribution of a single element and, when also multiplied by the cycle rate, gives the
output power from a single element. This quantity, easily obtained from the state equations,
therefore indicated the number of elements required to achieve, say, a one kilowatt output.
This calculational procedure has been verified experimentally.
To calculate the thermodynamic efficiency, it is necessary to find the functions dS
and diS, representing the entropy and entropy generation. The entropy as a function of the
FLT state variables can be derived using a procedure similar to the Clausius-Clapeyron
derivation, and the entropy generation evaluated using the equivelance of hysteresis and
energy dissipation.
Because NITINOL is dissipative, non-equilibrium thermodynamics
shows the heat flow to the ,
- must be modified as shown in Figure 10 (for many
cycles diS << dS and can be neg..,.
d).
Then, from the state relations, the known
thermodynamic paths and the derived enLropy and entropy generation, the heat flow for the
particular cycle can 'be calculated and the efficiency evaluated. This evaluation procedure has
not been experimentally verified.
Thus the state equations provide the necessary and sufficient basis for NITINOL device
engineering: designing machines to meet performance requiremvnts.
A second important use of the state surfaces correlation is in parametric studies. Since,
by using the state equations, one can predict the performance of a NITINOL heat engine, the
effect on various performance criteria of new designs, new alloys, new thermodynamic cycles,
and new NITINOL element designs can be evaluated without building the hardware. And, as
engineering experience has shown, analytical parametric studies are much cheaper and more
efficient (but less accurate) than hardware parametric studies. Some of the results of such a
preliminary parametric study of the effect of different types of thermodynamic cycles are
illustrated in Figure 11.
In this study, the two major performance criteria--specific work (which is closely related
to capital costs) and efficiency (which is closely related to operating costs)--are used to
evaluate various thermodynamic cycles. For the cycles studied, it is apparent there is a tradeoff between efficiency and work. Very high efficiencies can be achiev. -1 by a cycle with
constant temperature and adiabatic legs, but at the cost of low specific work. Similary, low
capital costs can be achieved by a cycle with constant temperature and length legs, but such a
cycle has relatively low efficiency. What is desired, and is probably possible, is a cycle in the
upper right hand corner of the graph.
7-4

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.

.........-.......

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rV

NSWC MP 79-441
Figure I I, in isolation, can be misleading, since there are other important performance
criteria besides specific work and efficiency. And there are other possibilities for improving
performance besides selecting the "best" thermodynamic cycle. For example, the element
characteristics can have a large effect on performance as illustrated by the two curves marked
S"TL cycle" in Figure l1. These two curves illustrate the change in performance that can be
achieved by decreasing the hysteresis losses of a helical element. A complete parametric
study would evaluate the effect of all available "improvements" on all significant p-formance
criteria.
The state surface correlation applies to all alloy compositions and element
configurations, so a third important use is in connection with element development. Figure 12
lists the items required to completely characterize a NITINOL element.
The first seven items are the coefficients of the state equations and could be used, for
example, by the NITINOL producers to characterize their product. The engine designer could
then use this information to select a particular alloy that best matches his/her particular mix
of performance requirements. This piocedure is already being followed to some extent in
requesting a specific transition temperature material.
But by using the state surface
correlation, one could specify not only item 7, the transition temperature, but also the other
six items that ultimately determ,ie engine performance.
Another use of the first seven items is in selecting whether to use helices, plates in the
bending mode, wires in tension, or newly invented element configurations. The numerical
values of the first seven items, for different configurations, can be related for a given allly by
mechanics of materials calculations.
So this list provides an interface among element
designers, engine designers, and alloy producers.
The last five items are quantities outside the present state-of-the-art of the state
surfaces correlation.
Item 8, cold working or training, is well known to modify the
thermodynamic oroperties of an element. The first seven items, however, implicitly provide
the outline of an experimental program to evaluate just how training affects performance.
Items 9, 10, and 11 in Figure 12 are concerned with optimization. Obviously the state
surface correlation here applies only over a limited rr.ge in FL T space: Actual behavior is not
described by infinite, exactly parallel planes. Beyond that range the two-boundary surfaces
coalesce and the shape memory effect disappears. Maximum specific work is achieved by
using maximum force, length, and temperature excursions possible, so identifying and
extending the limits is important in device optimization.
This final use of the state surfaces correlation is, perhaps, of the most immediate
importance.
Using this list as an interface, alloy producers, crystallographers, element
designers, inventors, and hardware engineers are provided with a common language for intercommunication.
The state surface correlation is much more complex than I would have preferred. It
requires considerable study to learn and a willingness to discount much of the equilibrium,
reversible thermodynamics we learned in school. In addition, in its present form (flat infinite
surface4) it is obviously only an approximation. Nevertheless, it is sufficiently simple and
accurate to provide a powerful tool for engineering NITINOL thermodynamics. It allows the
engineer to design, shows the inventor what to invent, quantifies tradeoffs for the system
analyst, provides the program manager with priorities, and in short is the powerful engineering
tool that 250 years of heat engine experience had predicted.
7-5

Ii

mpIw
NSWC MP 79.441

I

L

I

I

MA BOUNDARY SUR*FACEI

AM BOUNDARY SURFACE
MA STATE SURFACE1

LII
PHSE
ISO

FIGURE 1 POSSIBLE THERMODYNAMIC STATES AND PATHS OF NITINOL

j

74

NSWC MP 79-l

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WHERE:

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z(FL.T)

aL+bT - F
u

h

F 8 (T,. Li)MA

F B (Ti. Li)AIM CLR - dq/dT) XL

c

FIGURE 5

NITINOL STATE EOUATIONS

710

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NSWC MP 79-441

ZIz

2

4

LU

C-)
u-

LENGTH

FIGURE 6

UNIQUENESS OF STATE SURFACES

7-11

NSWC MP 79-441

Lu

TI0OHR

LENGTH --

FIGURE 7 NON-STABLE, ISOTHERMAL THERMODYNAMIC PATHS

7-12

NSWC MP 79-441

z
LU

30M

7-1-

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0'

CONSTANT]

FIE

THOYNMC AHSO
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ITNOLENINOLI LNE AELRANG
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(Td8-T dS)

HYSTERESIS LOSSES

FIGURE 10 PERFORMANCE CALCULATIONS USING THERMODYNAMIC PATHS
7-15

NSWC MP 79-441

I-L

I:

LU
ILu

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9

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7-16

7-1-

NSWC MP 79-441

a

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-

b

aZfaT)LT

f

a-

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IaFB/aT)LI b

g
c

dq!dT)AL

HYSTERESIS WIDTH

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RELATED TO TRANSITION TEMPERATURE

FB (L -0, T -0)

0

RESPONSE TO "TRAINING"

Qi

MAXIMUM USABLE LENGTH CHANGE (RELATED TO Af, Mf)

G

MAXIMUM USABLE TEMPERATURE DIFFERENCE (RELATED TO Af. Mf)
MAXIMUM USABLE FORCE (RELATED TO Af,Mf)
DEVIATIONS FROM FLAT PLANES APPROXIMATIONS

FIGURE 12

ELEMENT SHAPE AND ALLOY CHARACTERIZATION

7-17/18

.

NSWC MP 79-4,41

EXPERIMENTAL RESULTS ON A CONTINUOUS-BAND
NITINOL ENGINE
Dr. A. D. Johnson
Energy Research Associates
Oakland, CA
ABSTRACT
This report summarizes work done by Energy Research Associates during calendar years
,)75-76. It covers our efforts to obtain ballpark answers to two separate but closely related
questions asked by everyone first seeing these engines. How much power can you get out of
them, and what is the efficiency?
EFFICIENCY STUDIES
The development of solid-state heat engines precipitated several theoretical discussions
of tl,. chievable thermodynamic efficiency of such engines. The problem was misunderstood
by some physicists who considered only the delta-T associated with the phase transition at zero
stre-, and who therefore predicted maximal efficiencies of ten percent or less. Recent works
I
:o agree that the ultimate limit in efficiency is nearly the same for these engines as for
ot. heat engines, namely (TI-T 2 )/T1. For liquid water heat source and sink this sets a
the, -. ical limit of about 25 percent. Actual experimental efficiencies may be expected to be
muc mailer than this.
The prototype continuous-band NITINOL engine is a suitable vehicle for first attempts
at mea iring efficiencies, because the heat source and sink may be thermally isolated and
power output from the working element may be measured directly. For this purpose, a
varia -..
on previous linear-tension engines was constructed and instrumented (Fig. 1). The
methoo for measurement of efficiency was suggested to me by Dr. Jack Cory of Cory
Laboratories, Escondido, California, in August 1975.
Speed was measured with an Elinco Midget dc generator coupled to an Esterline-Angus
strip-chart recorder. Force FH, the force on the hot pulley, was measured by a HamiltonBaldwin load cell energized by a Luchter transducer power supply and read by a Leeds and
Northrup Speedomax recorder. Force FT, the sum of the forces on hot and cold pulleys, was
effected by weights attached to a cable running above the engine. Temperatures in hot and
cold tanks were registered by copper-constantan thermocouples whose emf was recorded by a
Leeds and Northrup Speedomax recorder.
A glass mercury-bulb thermometer made an
auxiliary measurement of the temperature in the hot tank. Weston thermometers monitored
temperatures elsewhere in the system.

I

J. S.
Cory, et al. "NITINOL Heat Engines for Economical Conversion of Low Grade Thermal
Energy," Proceedings of the 13th Intersociety Energy Conversion Engineering Conference,
Vol. Il, San Diego, CA, August 20-25, 1978, Paper #789031, pp. 1998-2004.

8-i

NSWC MP 79-441
Heat input was by a measured volume of water in the insulated hot tank. For heat sink,
cold water was circulated by a pump into the cold tank, and into a vertical water jacket
surrounding the wire as it traveled from the cold tank to the cold drive pulley.
Energy input to the system was inferred from the time rate of change of temperature of
the known volume of water in the hot bath. The heat capacity of the container and the
enclosed idler pulley was negligible compared to that of the water. Heat was rejected into a
cold bath maintained at nearly constant temperature by contact with ice.
Power output of the NITINOL wire, which was the active element (or "working solid") in
this engine, was calculated as the product of torque times angular velocity of the pulley set.
The drive pulleys, which had a 1.03:1.00 diameter ratio, were nominally 10 cm in diameter.
Typical running speed for a 3-gram NITINOL wire 2.2 meters long pulling the generator
was 1000 RPM, corresponding to a linear velocity of the wire of 5.2 m/sec. At this rate the
wire made about 2.5 complete engine cycles/sec. and generated approximately 7 watts with a
weight 133N and FH= 93N. However, at this speed there was considerable loss of water which
It was therefore decided to limit the speed by
spattered from the rapidly-moving parts.
coupling the engine to a synchronous electric motor. Subsequent tests, which form the basis of

~of

this report, were taken with the engine running in this captive mode at a nominal pulley speed
300 RPM.

The thermodynamic efficiency of a solid-state engine will vary with speed, temperature,
elongation ratio (or pulley diameter ratio), a~td force w. Not all these variables have been
ranged in this preliminary study. Rather, a set of conditions was arrived at by trial and error
which gives reasonable power output at a measurable rate of temperature change. Then an
attempt was made to deduce the "energy budget" for the engine in this condition. Obviously
families of curves could be generated by ranging each of the above variables. the values we
have established should be taken as typical rather than definitive. On the other hand, our
engine cycle simulations show that the work output per unit mass per cycle at maximum output
is not more than a factor of two greater than that achieved in the test engine. This engine is
designed by intuitive judgment rather than engineering equations: we feel certain that sizable
improvement is possible.
The "heat budget" for this engine shnuld consist mainly of these contributions:
1) + Heat input, from cooling of water in hot reservoir.
2) - Heat required to cause the phase transition.
3) - Sensible heat to change temperature of the wire.
4) - Heat discarded by the water carried around the circuit by the wire (mixing of hot
and cold fluids)
5)

-

Static heat losses, by conduction and evaporation.

6) - Power output by the wire.
It is important to note that we measure power output by the wire, before friction losses,
etc. This is grossly different from the engine shaft output power, and is a reasonable way to
measure power on a prototype scale model.

8-2

NSWC MP 79-441
Item 1), the caloric input, is determined from the rate of temperature decrease in a
known volume of water.
Items 2) and 3), the heat required for causing the phase
transformation and for sensibly heating, can be estimated from data available in NASA 51102,
although It must be recognized that latent heat is a function of thermodynamic path. Our
method allows a consistency check by measuring these quantities as will be shown below. Item
4) can be estimated by replacing the NITINOL wire with a nearly equal diameter steel wire
(with a 1.0:1.0 drive pulley ratio) and measuring the rate of heat loss. Item 5) is measured by
the rate of temperature decrease for a known volume of water when the engine is standing
still. Item 6) is measured as torque times angular velocity as discussed previously.
Table I gives the numbers obtained, with sizable systematic errors but with overall
consistency of about 10%.
Replacement of the NITINOL wire by a steel wire of approximately the same dimensions
allows measurement of the latent heat required to drive the phase transformation, since all
other parameters of the experiment are approximately the same. Table II shows results of
doing this.
We conclude that at a delta-T of 75 degrees C, losses for the simple NITINOL engine are
almost equally divided into three parts: latent heat; sensible heat; and losses which include
mixing, conduction, and evaporation. Conductive loss itself is only about 10 percent of the
heat budget.

f

I

With this engine, and with presently attainable power output levels, the maximum
achievable efficiency will be about 2.5% after -he obvious losses have been minimized. The
present engine operates at 1.2 percent efficiency, which is less than 10 percent of the
theoretical maximum efficiency. This is due to the largf amount of entropy generated by
heating and cooling the wire by direct immersion in hot and cold baths, which is far from an

equilibrium process.
Several approaches might improve efficiencies. Adiabatic heating and cooling may be
used, but only at relatively low delta-T because adiabatic heating of NITINOL wire by
stretching will pull the wire apart before a temperature difference of 30 degrees C is
achieved.
Increase of the specific power density will increase efficiency directly. There is a good
probability that the present work output of one joule per gram cycle may be increased to 2 or
even 3 joules, with a corresponding increase in efficiency.
Another approach is through the use of a regenerator.
An engine incorporating a
regenerator has been buiit and tested3 , but was not instrumented for calorimetry. We present
here the resut of an experiment using a regenerator which was not operated as an engine.
Conclusions about regenerative engine efficiency should be interpreted with this caveat.
2 C.

M. Jackson et al., "55-NITINOL--the alloy with a memory:
Its Physical
Metallurgy, Properties,and Applications," NASA-SP 5110, National Aeronautics and
Space Administration, Washington, DC, 1972.

3 A. D.

Jo~nson, "NITINOL Heat Engines," Record of the Tenth Intersociety Energy Conversion
Engineering Conference, Newark, DE, August 18-22, 1975, Paper #759082, pp. 530-534.

8-3

NSWC MP 79-441
EFFICIENCY MEASUREMENTS ON A REGENERATOR
In May 1976, preliminary measurements estimated the efficiency improvement in a
regenerator (Fig. 2). This consisted of two sets of pulleys (PIP2) and (P3P4) each reeved about
by a NITINOL wire, all contained in an insulated enclosure. Pulleys PI and P3 were immersed
in hot water, P2 and P4 in cold. If (PIP2) rotate clockwise while (P3P4) rotate counterclockwise, as shown by the arrows in Fig. 2, then, in each of the long narrow passages which
connect the hot and cold baths, heat rejected by the wire leaving PI for P3) is absorbed by the
cold wire leaving P4 (or P2). Thus a temperature gradient was established and maintained
along each of these narrow passages. If the wires pass slowly through a passage, a state of
quasi-equilibrium minimizes entropy generation. Wipers may be placed in each regenerative
passage to reduce water transport through the tubes.
This configuration of NITINOL loops and pulleys could be run as an engine by coupling
(PIP2) and (P3P4) and making P4 and P2 a few percent smaller than P3 and Pl, respectively.
For this study, the machine was not operated as an engine. Instead, losses when the pulleys
were counter-rotated as shown, i.e. in a regenerative mode, were compared with losses when
the pulleys were corotated, i.e. with two wires traveling in the same direction through each
regenerative passage. Table III summarizes the results. The power consumed with counterrotating pulleys (regenerative mode) was approximately 3.6 times less than in a nonregenerative mode. These data were taken at a relatively low speed, so that the calculated
power density is reduced to about .2 watts/gm.
This experiment clearly requires much more work to determine whether this efficiency
can be obtained at higher speeds, and to check on the assumption that latent heat is constant
under load, which is surely only approximately true. However, we feel these results indicate
the regenerator has potential use in situations in which the increased efficiency justifies the
expense of lowered power density.
POWER OUTPUT STUDIES
Power output per unit mass from a continuous-band NITINOL engine is determined by the
cycle rate multiplied by the work output per unit mass per cycle. Maximum cycle rate is
governed by heat transfer rates which depend upon the surface area to volume ratio. Work
output per cycle is a function of temperatures and tensions in the hot and cold segments of the
band. For this study, pow,..r output measured in a simulated engine cycle is compared with the
result of running an actual engine, the same engine used for the above efficiency
measurements (Fig. !.
Engine cycle simulation data (Fig. 3) were taken using the stress-strain fixture employed
for training studies reported at this Conference.
Engine cycle simulation consisted of four phases, indicated by lines on Fig. 3. At
point A the temperature was that of the hot bath TH, and tension SI was at a minimum.
The wire was contracted.
Hot water was valved out and replaced with cold water at
temperature TC from the cold reservoir. The wire relaxed and elongated to length B, still at
minimum tension but now at cold temperature TC. Next, weights were added, increasing
the tension and stretching the wire isothermally to point C, where the temperature
remained TC and the tension was at maximum, S2 . The cold water was then removed and
replaced with water at temperature TH from the hot reservoir.
The NIT!NOL wire
contracted, raising the weight and shortening the wire to elongation D.
Here the
temperature was TH and tension was maximum. The cycle was completed by reducing the
tension to S1 , during which the wire again contracted to elongation A. The Figure shows three
successive cycles at three increasing values of tension S2 .

8-4

NSWC MP 79-41
The work done in this cycle is the area ABCD enclosed in the figure. Segments AB and
CD are straight lines, while BC and DA are curves which depend upon the stress-strain
characteristics of the material. The area within the curve is estimated to be 1.75 joules for a
wire whose mass is 1.75 grams, for a density of one joule/gm cycle.
This result may be compared with data taken with the non-regenerative continuous-band
engine. Table IV shows a typical set of run parameters. The results agree well with the
simulation. It seems reasonable to conclude that power densities approaching one joule/gram
cycle have been achieved in continuous-band engines, and that these bands may be cycled more
than once per second, yielding in excess of a watt per gram of NITINOL.
Power density may be further enhanced at the same stress level by impovements in
design. In the above example (Fig. 1), at least half of the NITINOL wire length is wasted in
traveling from bath to pulley and return. In terms of optimal power density, the most
desirable engine is very long, with pulleys small in relation to the length, and an element
having a large surface to volume ratio such as a flat ribbon or multiple fine wires. Such a
device might cycle 10 or more times per second, with a corresponding power density of 10 or
more watts per gram. Such high speed would, of course, be accompanied by larger viscous
losses.

CONCLUSIONS

I

A non-regenerative continuous-band NITINOL engine operating at liquid water
temperatures has been shown to have an overall efficiency greater than one percent. The
upper limit for this design, due to entropy generation during heating and cooling, is not much
more than 2 or 3 percent. Power density in this design is of order I watt per gram of
NITINOL. Input power is divided among latent heat (approximately 25 watts/gm), sensible heat
(approximately 25 watts/gn), and heat losses (about 25 watts/gm). A regenerator can increase
efficiency by at least a factor of three. Further experimentation is required to determine
what fraction of Carnot efficiency is possible with this configuration.

iI
.t

-5

NSWC MPD 79-441
F + Fc

DRIVE
PULLEY

FT

PRc
H

WEIGHT

",?TACHOMETER

HOTLODCLL
IDLER

ASS'Y4

COLD
IDLER
ASS'Y

CONTINUOUS-BAND
NITINOL HEAT ENGINE
INSTRUMENTED FOR
EFFICIENCY MEASUREMENTS

od=b-LOAD CELL

TORQUE - 1/2 (FM - FC)(rC - rm) -(FH
w/2)(rc - r)
WHERE F. FORCE ON HOT IDLER
FC FORCE ON COLD IDLER
w - FM + Fc - FORCE ON DRIVE PAIR
rHcARE DRIVE PULLEY RADII
POWER - TORQUE x ANGULAR VELOCITY
- (FM - wI2)(rc - rx
RPM x 271760

FIGURE 1

NSWC MP 79-441

tA,.

A

'lip

-'

ccI

w

*z

*-

i

-

A
d

cc

*,

1

l.Z~h.

~.-

w

~

**~~~

4

a
CC

N

IL.
5-.to

8-7A

i

NSWC MPR 79-44l

o

0 Cc

0

LUNLU
LU

6

a1

R@

Z

ILccII

LU

U-

z

4w
EUU)

0N

z

NLU

uU/)
0

INOINiJ
8.8

I--

co

NSWC MP 79-441
TABLE 1 RESULT OF EFFICIENCY TEST: NON-REGENERATIVE NITINOL ENGINE
Specific heat of NITINOL

Cp

.08 ca/gm°C

Latent heat of NITINOL (assumed constant)

Ct

5.8

Temperature in Hot tank

T1

85 to 65 0 C

Temperature in Cold tank

T

5°C

Mass of NITINOL wire

m

3.3 gm

Length of NITINOL wire

cal/gm

2.13 m

Pulley diameter

d

.1 m

Speed 300 RPM

3

Volume of Hot water

V

Rate of temperature change

dT/dt

gm/sec

800 Ml
2.80/min

Power input
Power dissipated as Latent H-eat

+ 164 watts
587watts

Power dissipated as Sensible Heat

-

54 watts

Power lost due to mixing and other losses

-

55 watts

Power output, calculated from speed and torque

-

2

-

5 watts

Balance
Efficiency

power out/power in = 1.2%

.L

8-9

Pa

NSWC MP 79441

TABLE 2 RESULT OF EFFICIENCY TEST: NONREGENERATIVE
ENGINE WITH STEEL WIRE
0

Specific Heat of Steel

Cp

.077

cal/gm C

0.

Latent Heat
Temperature in Hot Tank

T1

Temperature in Cold Tank

T2

5°C

Mass of Steel wire

m

4.8 gm

to ;5
65°C

Length of Steel wire

2.33 m

Pulley diameter

d

.1 m

Speed 300 RPM

3.2 gm/sec

Volume of Hot water

V

Rate of Temperature change

dT/dt

790 ml
2.0 0 /rnin
+ 10 watts

Power input

Power dissipated as Sensible heat
Power lost due to mixing etc (same as TiNi)

-

Power output

67 watts
54 watts
0

Balance

8-10

-

I watt

NSWC MP 79-441

TABLE 3

RESULT OF EFFICIENCY TEST: REGENERATOR

Volume Hot Water
Rate of Temp Change

V

Co-Rotation

Counter-Rotation

650 ml

600 ml

1.6°C/min

dT/dt

.7°C/min @70°C

+ 72 watts

29 watts

Static Losses

- 12 watts

12 watts

Power into Wires

-

60 watts

17 watts

Pulley Diameter

.1 m

.1 m

Linear Speed

.38 m

.38 m/sec

Mass rate (two wires)

1.1 gm/sec

1.1 gm/sec

(Calculated power output
assuming I joule/gn cycle)

1.1 watts

1.1 watts

(Calculated efficiency
assuming constant latent heat)

1.8%

6.5%

Power Input

P

8-11

j

NSWC MP 79-441

TABLE 4 TYPICAL RUN PARAMETERS FOR POWER OUTPUT STUDY
ON A CONTINUOUS-BAND NITINOL ENGINE
Radius of Hot drive Pulley

rh

.0475 meter

Radius of Cold drive Pulley

rc

.0492 meter

Wire length

1

2.13 meter

Wire mass

m

3.3 gm

Mass velocity

v

4.8 gm/sec

Weight = f + f

W

136

newton

Force on Hot Pulley

fh

102

newton

Rotation rate 600 RPM

w

62.8 radians/sec

2
Power output by NITINOL wire = (f h-W/ ) (rh-rc) w

Power density - I watt/gm TiNi
Work output/gm cycle = 3.3/4.8 - .69 joule/gm cycle

_.-12

"

8-12

3.3 watts

NSWC MP 79-441

[, BIBLIOGRAPHY
A. D. 3ohnson, "NITINOL Heat Engines," Record of the Tenth Intersociety Energy Conversion
Engineering Conference, Newark, DE, August 18-22, 1975, Paper #759082, pp. 530-534.
C. M. 3ackson et al., "55-NITINOL--the alloy with a memory: Its Physical Metallurgy,
Properties, and Applications," NASA-SP 5110, National Aeronautics and Space Administration,
Washington, DC, 1972.
3. S. Cory, et al. "NITINOL Heat Engines for Economical Conversion of Low Grade Thermal
Energy," Proceedings of the 13th Intersociety Energy Conversion Engineering Conference, Vol.
III, San Diego, CA, August 20-25, 1978, Paper #789031, pp. 1998-2004.

8/
I

I
'Ii

:I

._.

~

8-13/9-=14

NSWC MP 79-441

t

EFFICIENCY OF ENERGY CONVERSION IN NITINOL
Richard D. Kopa
Lawrence Berkeley Laboratory
University of California, Berkeley
ACKNOWLEDGMENT
This work has been supported mainly by the Division of Fossil Fuel Utilization, Office of
Energy Technology, U.S. Department of Energy, and in part previously by the Solar Heating
and Cooling Research and Development Branch, Office of Conservation and Solar Applications,
D.O.E. under Contract No. W-7405-ENG-48.
The author is grateful to Mr. Mike Wahlig for his support and interest and to all other
Laboratory staff members who directly or indirectly contributed to this investigation,
particularly to Mr. William Worthington, Mr. Jim Hodges, and Mr. Don Calais for careful
fabrication of the mechanical parts of the cycle simulator. The author also wishes to express
his appreciation to Mr. Paul Hernandez for his interest and encouragement and to Mr. Duane
Norgren, whose previous research and interest in the present work have been a source of
inspiration.
ABSTRACT
NITINOL--one of several Shape Memory Effect (SME) alloys--is known to be a suitable
medium for converting heat to usable mechanical work in a "solid state" heat engine. The
present study experimentally investigates the efficiency of the energy conversion in NITINOL.
An electronically controlled Cycle Simulator subjects a single NITINOL wire element tothe stress-strain-temperature cycles corresponding to a specific thermodynamic cycle
(constant-strain isothermal, stress-limited isothermal, constant-stress isothermal, semiadiabatic, etc.), as selected during the investigation. The test parameters, which are varied
singly or in combination, include various stress levels, stress rates, percent of elongation of the
wire, temperature levels, heating and cooling rates, cycling speeds, etc. Efficiency values as a
function of these variables are plotted in graphs, and the factors affecting efficiency are
discussed.
The highest thermodynamic efficiency thus far determined is 1.2 percent
(approximately 6 percent of Carnot efficiency), with a concomitant NITINOL wire life
expectancy on the order of 10
cycles. However, these values are not regarded as the
highest attainable. It is anticipated that higher efficiency as well as life expectancy would be
realized with NITINOL alloys perfected through basic materials research and development.
Nevertheless, the fundamental limitation of the energy conversion efficiency is set by the
inefficient type of thermodynamic cycle-namely, the isothermai cycle-to which the "solid
state" heat engine operation (with presently available SME materials, such as NITINOL) is
restricted. The reasons for this restriction are discussed in pp. 9-12 through 9-22.

9-1

............................
..................

,h".."

~

*2.,,:,

L:

A
NSWC VP 79-441
The simple contant-strain isothermal cycle is analyzed and described in stress-strain
coordinates and in a T-S diagram. An analytic expression for the calculation of the energy
conversion efficiency is presented, along with experimental investigation of the proposed
postulates. A few preliminary investigations of various approaches to efficiency improvement
are reported, and one promising research area is suggested.
Further basic and materials research is needed for better understanding of the energy
conversion process in NITINOL, for the clarification of the extent of validity of the proposed
postulates, and for the determination of a rigorous expression for the efficiency of the
constant-stress isothermal cycle.

N.2'1

9-i

I

NSWC MP 79-441
.

INTRODUCTION

Devices and heat engines which employ Shape Memory effect (SME) alloys (e.g.,
NITINOL) as the energy conversion media have been described in the literature. 1 Since these
engines can work at nearly ambient temperatures and at a relatively small temperature
difference between the hot and cold reservoir, they appear particularly suitable to applications
involving solar flat plate collectors and geothermal and industrial waste heat sources, or for
bottoming cycles of conventonal power plants. Suggested commercial applications include
solar cooling of buildings, agricultural pumping, and decentralized solar power generation.
However, thus far only information on the theoretically estimated efficiencies, anti some
fragmentary information on experimentally determined efficiencies of these devices, have
been published.
This paper describes an experimental parametric study of a NITINOL alloy subjected to a
number of simulated thermodynamic engine cycles, in which the test parameters are
systematically varied so that efficiency values as a function of these parameters are obtained,
and the most efficient type of thermodynamic cycle is identified.
The information derived can serve as a basis for designing a "solid state" heat engine
with the highest attainable efficiency and/or power density, for comparing theoretical and
experimental efficiencies, as well as for providing reference data for further research and
development of thermoelastic materials.
Another objective of the study is the determination of an engine cycle which offers the
lowest progressive degradation, irreversible damage and creep, and therefore the longest life
of the investigated thermoelastic material, which in this study is used in the form of wire
elements subjected to cyclic tension stress.
7.

BACKGROUND

The Shape Memory Effect in alloys has been extensively treated in the literature and
therefore will not be discussed here. For familiarization with the s:' ;ect, Reference 2, and

1W. S. Ginell, 3. L. McNichols and 3. S. Cory, "Low-Grade

Thermal Energy-Conversion
3oule Effect Heat Engines," American Society of Mechanical Engineers, Paper 78-ENAs-7,
July 1978.

2 C.

M. Jackson, H, 3. Wagner and R. J. Wasilewski, "55 NITINOL - the Alloy with a Memory,"

Report NA-.A-SP 5 10, 1972.
9-3

NSWC MP 79-441
for more in-depth study, References 3, 4, 5, and 6 are suggested. Among the alloys exhibiting
SME, NITINOL has been most widely studied and used in various technical applications.
Reference 2 presents a comprehensive overview and an extensive literature survey of research
activity on NITINOL.
More recently, the efficiency of the energy conversion in SME alloys underwent
theoretical study by several investigators. Reference 7 predicted thermodynamic
efficiency of
4.9 percent; References 8-11 calculated efficiencies in the range of 10 percent to over 20
percent. Moreover, some limited information on experimentally determined energy conversion

33. Perkins, "Shape Memory Effects in Alloys," Proc. of the Inter. Symp. on Shape Memory
Effects and Applications, Toronto, Ontario, Canada, May 1975; Plenum Prer -.
, New York.
F. Mohamed, "Martensite Transformation and Shape Memory Effect in Ni-Ti Alloy,"
Report LBL-5112, Lawrence Berkeley Laboratory, University of California, Berkeley, May
1976.

4 H.

5D. S. Lieberman, "Crystal Geometry and Mechanisms of Phase Transformations in Crystalline
Solids," Paper presented at Seminar of Am. Soc. for Met., October 1968.
6 Z.

Nishiyama, Martensitic Transformations, Academic Press, New York, 1978.

7M. Ahlers, "On

the Usefulness of Martensitic Transformations for Energy Conversion," Scripta
Metallurgica, Vol 9 (1975), p. 71.

8 KH.

C. Tong and C. M. Wayman, "Thermodynamic Considerations of 'Solid-State Engines' Based

on Thermoelastic Martensitic Transformations and the Shape Memory Effect," Metallurgical
Transactions A, Vol. 6A, January 1975.
9 C.

M. Wayman and H. C. Tong, "The Efficiency of the Shape Memory Effect for Energy
Conversion," Scripta MetallurRica, Vol. 9 (1975), p. 757.

10 B. Cunningham and K. H. G. Ashbee, "Marmem Engines," Acta MetallurRica, Vol. 25 (1977),
p. 1315.
1 1 A.

A. Golestaneh, "Efficiency of the Solid-State Engine Made with NITINOL Memory

Material," . Apl. Phys., 49 (3), March 1978.

21

9-4

itp

NSWC 'MP79-441
efficiencies in NITINOL has been reported in Reference 2, ranging from 10 percent to 16
percent, and in Reference 12, amounting to 2.7 percent.
These studies were based on
considerably differing assumptions and/or experimental conditions as well as on SME alloys of
substantially different properties.
The previous study at this Laboratoryl2 investigated the thermodynamic efficiency of
the energy conversion process in NITINOL, with particular interest in determining the
repeatability of the results over a large number of work cycles. It was estimated that for
economically feasible technological applications, the life of the SME alloy, before failure due
to fatigue, should extend to over 106 cycles.
3.

EXPERIMENTAL SYSTEM AND METHOD

Briefly, the conversion process of heat to mechanical work during the NITINOL engine
cycle is:
1) The NITINOL wire is cooled by submerging it into the cold bath to a temperature
well below its transformation temperature. Consequently its crystalline structure stabilizes in
a martensitic phase.
2) While in the cold bath, it is easily stretched (NITINOL in the martensitic phase is
highly ductile) by applying a moderate external force and elongated to a predetermined length
(typically 1.0 percent to 5.0 percent strain).
bt,3)
Thereupon the wire--while still elongated--is heated by submerging it into the hot
bath, where it developes high stress (as the result of the reversed martensitic phase
transformation process).
4) Overcoming applied external load, the NITINOL wire contracts with a great force
until it attains its original length. During the contraction, the wire produces useful mechanical
work W equivalent zo the product of the force F times the linear change AL of the wire length
during the contraction (W = F AL).
At the, completion of the wire contraction, a stabilized crystalline structure of the high
temperature phase (austenitic) is again attained. The NITINOL is now ready for the next
cycle, which starts with the cooling of the wire element.
To facilitate an accurate and repeatable execution of the above cycle, at various
parametric conditions, an electronically controlled Cycle Simulator was designed.
Figure I schematically presents the major components of the test apparatus. A test
sample of NITINOL wire N is stretched between arm A1, axially sliding on a rotating shaft, and
arm A2, solidly attached t-o the same shaft. Arm A2 -carries a flexible beam on which is
I

2See footnote 2 on page 9-3.

2
12R. Banks, P. Hernandez and D. Norgren, "NITINOL Engine Project - Test Bed,"

Final Report,
UCID-3739, Lawrence Berkeley Laboratory, University of California, Berkeley, 3uly 31,

1975.
9-5

NSWC MP 79-441
cemented strain gage _, measuring the force exerted by the NITINOL wire N.

motion of arm Al is effected by a lead screw L driven by servomotor Mi. The

The axial

osition of the

arm Al in respect to arm A2 is transmitted 5y means of a potentio-meter readout R to the
oscill-oicope OS as a horizontal deflection of the electron beam. The vertical deflection of the
beam Is effected by an amplified signal from the strain gage S. The stress-strain diagram
displayed on the oscilloscope screen is recorded by means by a video camera and stored on a
video tape.
The NITINOL wire N is transferred back and forth from the hot reservoir H and cold
reservoir C by a 3000 rotation of the shaft driven by the servomotor M2. Two lInear
servoamplners in the electronic control system EC electronically control the-clockwise and
counterclockwise rotation of the shaft as well as oFthe lead screw L. The sequence of events,
of positions, and of the speed of motion is programable to permit simulation of a desired type
of the thermodynamic engine cycle.
Figure 2 shows the actual design drawing of the mechanical part of the apparatus; Figure
3 shows the complete experimental setup.
Since all known NITINOL engines operate on the (constant-strain, stress-limited, or
constant-stress) isothermal cycle, this type of thermodynamic cycle was selected for the first
series of experiments. The isothermal cycle consists of stretching an SME wire element in a
cold bath under constant low temperature (isothermally), and thereupon transferring the
stretched wire into a hot bath where it contracts, while developing strong force, under
constant elevated temperature (isothermally). Typical isothermal work cycles (Figures 4-7)
are discussed below:
isothermal cycle with the
Figure 4 is a sample of a video record of a constant-strain
NITINOL wire No. 1, length of wire

pertinent parametric information (e.g., cycle No. 155,

21.8 in, diameter of wire 0.019 in, temperature of cold reservoir +2.30C and of hot reservoir
+56.30C, elongation &L = 0.29 in, and type of cycle ISOTHERMAL).
The horizontal line at the bottom represents stretching of the wire (from left to right),
under constant temperature; the vertical line represents the rise in stress after transfer of the
wire into the hot bath; and the sloping line from right to left represents the contraction of the
wire in the hot bath (at constant temperature). The area enclosed by these lines represents the
effective work or mechanical energy produced by the wire element during one cycle.
In the following series of tests, the NITINOL wire was heated by an electric pulse,
instead of submerged in a hot bath. Figure 5 shows the resulting record taken by a Polaroid
camera from the oscilloscope screen.
The intensity and duration of the electric pulse (24V, 9A, 350 ms) in Figure 5 were
adjlisted to produce the same peak stress as in Figure 4. This procedure can correlate the
temperature of the hot bath and the heat input to the wire during the phase transformation
which generates the peak stress (see Appendix). The peak stresse.d in this series of tests ranged
from 30Kpsi to 50Kpsi. The elongation (strain) of the wire ranged from 1.3 percent to 1.8
percent.

9-6

.-'-

.. -=.

'-- ....

L_ - "

. ..

, -=..

.=.

,,

"

.

,

NSWC MP 79-441
A noticeable difference exists between the horizontal lines of the records in both
Figures. In Figure 4, the perfectly horizontal line signifies complete absence of stress during
the stretching of the wire. This was attained by subjecting the virgin wire to 1000 training
cycles of heating and cooling with a progressive change of the strain. 3ohnson 13 extensively
By this treatment, a "second memory" effect
investigate training of NITINOL wires.
developed in the wire which consequently caused an elongation of the wire automatically upon
submerging it into the cold bath. In Figure 5, the training did not produce so perfect a result
and only a part of the elongation is stress-free.
Another series of tests investigated a "stress-limited" cycle. Figure 6 presents a typical
result. The NITINOL wire, in this case, was suspended on a preloaded compression spring
attached to the sliding arm Al (Figure 1). As the record indicates, a lower peak stress at
higher elongation (2.7 percent) resulted. The durability of the wire element subjected to this
type of cycle is presently under investigation. This cycle is an intermediate type between the
constant-strain isothermal and the constant-stress isothermal cycle.
Figure 7 shows a typical record of a constant-stress isothermal cycle. The lower
horizontal line and its extension sloping upwards (from left to right) represent the isothermal
stretching of the NITINOL wire at constant temperature in the cold bath. The following short
vertical line results when the strained wire is transferred into the hot bath. The upper
horizontal line represents the contraction of the NITINOL wire (power stroke) at constant
temperature and constant stress (in the hot bath). The following steeply downward sloping line
represents the drop of stress at the end of the wire contraction (end of power stroke).
To execute this cycle, it was necessary to slightly modify the Cycle Simulator apparatus
by attaching one end of the NITINOL wire to a cable (guided over three pulleys) which
transmits a constant force exerted by suspended calibrated weights.
In these tests, the NITINOL wire was initially stretched in the cold bath
(20C) to 8 percent strain, then transferred into the hot bath (80oC) where the wire
contracted under constant stress of 37Kpsi (26.OKg/mm 2 ), lifting a weight of 4.78Kg. After
several cycles, the load was reduced to produce 29Kpsi and the cycle was repeated about 200
times. A stabilized work diagram similar to that in Figure 7 was then recorded in all
successive cycles. The permanent (irreversible) wire elongation amounted to approximately 3
percent of the original strain (portion of the lower horizontal line extending to the left and
outside the area enclosed by stress-strain lines), and the remaining 5 percent constituted the
effective periodic strain of the "stabilized" cycles.

1 3 D.

A. 3ohnson, "Training Phenomena in NITINOL," presented at the NITINOL Heat Engine
Conference, September 1978, Naval Surface Weapons Center, Silver Spring, Maryland
(printed elsewhere in the present volume).

9-7

NSWC .MP79-441
EXPERIMENTAL RESULTS

4.

The efficiency r of the conversion of heat to mechanical work is defined as the ratio of
the useful work W, produced by the NITINOL wire, and of the heat input 2 to the wire element
during every engine cycle.

Th

(I)

The mechanical work is determined by the planinetry of the work ditgrarm (area on the
lines). when
The heat inpv was calculated from
by 2,
theor stress-strain
oscilloscope
experimental screen
data inenclosed
Reference
directly measured
an electric pulse (see Appendix)
supplied heat to the wire.

i

Equation (l) can be written as follows:
(2)

FEaLr8I/L
]=
0.991

Q[s]

where F is the force in Kit exerted by the wire at the peak stress, E is elongation of the wire in
m, 2j] is the total heat input per cycle in Joules per gram of wire element, a is the work
diagram area factor, LjL is the ratio of the length of wire weighing 1.0 ram to the length
of the test wire (for NI INOL wire of D = 0.019 in 0.483 mm, the length LA= 846 mm).
For a constant-strain isothermal cycle a =
cycle a would approach unity.

0.5, and for the theoretically ideal

Equation (2) can further be written as follows:
33 ca/y
Q[g]0.249

(3)

where g is the maximum peak stress in Kpsi, c is strain in percent of elongation, 1 = 0.234
lb/in 3 is the density of NITINOL, and 0.249 is a conversion factor.
Figure 8a graphically represents equation (3) for a typical value of the heat input to the
wire element Q = 50 Joule/g (for full martensitic transformation) and a = 0.5, corresponding
to a typical constant-strain isothermal cycle. Similarly, Figure 79b presents the plot of
Equation (3) for a = 1.0, which would apply to an ideal engine cycle.

2See footnote 2 on page 9-3.
.9-8

Fv

NSWC MP 79-441
Figure 8 indicates the theoretically predicted efficiencies in References 8 to 11
of 10 percent and above are not attainable in any type of themodynamic cycle
involving heat input of the order of 50 Joules (or more) per gram of the SME material. For
example, to obtain efficiency of 10 percent with an ideal engine cycle (a = 1.0), the NITINOL
wire would have to develop a recovery stress over 8OKpsi at 6 percent of elongation. However,
no presently known SME alloy would sustain cyclic (heat-stress-strain) loads at this stress level
for more than a few cycles. Even at considerably lower stress and elongation levels, the
NITINOL wire element would fail after a few cycles because of cumulative permanent
deformation and irreversible damage due to progressive creep.
The following figures present the typical test results obtained in this study. The SME
material used in all tests was NITINOL wire of diameter D = 0.019 in., 50.4 percent atomic Ni,
produced by TIMET. The individual types of engine cycle investigated are:
A

Symbol 0 represents isothermal constant-stress cycle (c
T3 - 750C, with variation ofo_3 from 17.7 to 37.1Kpsi.

B

Symbol V represents isothermal constant-strain cycle
variation of T3 from 450C to 70.40C.

(e = 1.3 percent) with

C

Symbol Q represents isothermal constant-strain cycle (c
variation of T3 from 340C to 840C.

= 0.5 percent) with

D

= 5.0 percent) at constant

Symbol 0 represents isothermal stress-limited cycle (c

0.5

percent)

with

variation of 13 from 370C to 700C.

,*

E

Symbol 0
represents isothermal constant-strain cycle, strain varied in steps:
c = 0.5 percent, c = 1.1 percent, and c - 1.6 percent, at constant D = 5loc.

F

Symbol 0 represents isothermal constant-strain cycle, strain varied in steps:
c = 0.5 percent, e = 1.1 percent, and E = 1.6 percent, at constant T3 = 71 0 C.

G

Symbol A represents isothermal constant-stress cycle (c
=
5.0 percent) and
constant peak stress 03
37.lKpsi, with variation of T3 in steps: 530C, 61oC, and
770C.

Every data point in Figures 9 through 15 represents, on I .., average, several hundreds--and
every curve several thousands--of repeated test cycles. Ev,. series of tests has been started
with a new trained and stabilized wire after at least 500 repeated cycles.

8

See footnote 8 on page 9-4.

9 See

footnote 9 on page 9-4.

1 0 See

footnote 10 on page 9-4.

1 0See

footnote 10 on page 9-4.

11 See footnote I I on page 9-4.
9-9

NSWC MP 79-441
Figure 9 represents the recovery peak stress, resulting during various types of the
isothermal engine cycle, as the function of the hot reservoir temperature T3. The temperature
of the cold reservoir T 1, wasdaintained for all tests between +IOC and +2oC, except for the
stress-limited cycles tcurve ( ), for which it was +250C.
Figure 9 reveals the following:
a) Generally, the peak recovery stresses appear substantially higher than the recovery
stresses reporte in te literature (eW. Reference 14). However, the peak recovery stresses of
the test series
§,
,
, and
for the same c are noticeably different. This could be
due to the nonidentical thermal and mechanical history (resulting during manufacture,"training"
period,
d the test period) of the individual NITINOL wire elements. For example, in test
series
the strain c = 1.3 percent was kept constant, but in M and @ it was varied
from c
0.5 ercenit to. c = 1.6 percent.
b) The peak recovery stresses of the stress-limited cycles (curve (D) are substantially
higher than the recovery stresses of the constant-strain cycles (urv
), although the
strain c = 0.5 percent was maintained the same for both test series. This effect resulted when
the temperature Tj of the cold reservoir for the stress-limited cycles was raised to +250C. In
such case the phiie transformation process is incomplete. Only part of the austenitic phase is
transformed during the ctoling of the NITINOL wire to thermal martensite, while another part
is contributed by the stress-induced martensite during the wire straining. Because of the
substantial stress 22 at the end of straining, a correspondingly higher peak recovery
stress q3 results. Therefore, for Ti = +250 C, the stress-limited operation was necessary to
prevent excessively high peak recovery stresses, which otherwise would rapidly degrade the
wire element.
Figure 10 presents the useful work W produced by the various types of engine cycles as
the function of the peak recovery stress 03. Generally, the useful work increases linearly with

the peak recovery stress. The yield is highest for the constant-st~ss cycle (curve®D ), and is
more than three times as high as the constant-strain cycle (curve (J)
level.

In contrast to this the stress-limited cycle (5

at the same peak stress

produces lower useful work W than the

constant-strain cycle b
when both cycles are performed at the same strain (e.g.,-- = 0.5
percent). This may be explained by the fact that a substantial amount of work has to be

expended for straining of the wire in the cold reservoir at Tj = 250 C,

because

at

this

temperature, the NITINOL has been only partially transformed to the martensitic phase.
Figure I

presents the thermodynamic efficiency _q

of the conversion of heat to

mechanical work in NITINOL as the function of the hot reservoir temperature j:3.
determination of,
the test series

For the

the heat input to the wire element must be known (see Equation (1)). For
and G (broken lines), the heat input QH was calculated as follows: to

the value of the latent heat of transformation AH =5.78 cal/g was added the sensible heat
- T1 ), where Cp = 0.11 cal/g deg (data taken from Reference 2). This represents only a
first ord , roih ap~joximation to tke actual eat input, as will be shown later. For the test
series
, , ) , J , and
nd (K are plotted in Figure 13-the heat input was
--

14 W. B. Cross, A. H. Kariotis and F. J. Stimler, "NITINOL Characterization Study," NASA CR1433, September 1969.
2

See footnote 2 on page 9-3.

9-10

NSWC MP 79-441
measured by the electric pulse method (see Appendix). Thus far no reliable method has been
developed to measure the heat input 2H to the wire element during the constant-stress
isothermal cycle. The electric pulse method cannot be applied, because at high strains (as
employed in contant-stress cycles, e.g., e = 5.0 percent) the wire element cannot be
contracted fast enough during the shape recovery, and therefore the heat losses from the wire
element to the surroundings would introduce a significant error. For the test series G , the
heat input 9H was estimated, assuming for the constant-stress cycles the same relative
difference between the calculated and measured values of Qas was experimentally
determined for the constant-strain cycles.
The highest efficiency was obtained for nost of the test-cycles at hot reservoir
iemperature T3 = 600C, and for the series D at about T3 = 550C. Figure 12 illustrates the
effect of this shift (of the efficiency maximum toward the lower temperature _3) on the ratio
of the engine cycle efficiency n to the Carnot efficiency ri . Particularly pronounced effect
is evident for the stress-limited cycle series D , where it is the consequence of the smallest
temperature difference AT = T3 - TI between the hot and cold reservoir. From Figure 12 it
can be inferred that by a proper selection of the temperature TI, T 3 and of the maximum
stress level o3, a stress-limited or a constant-stress isothermal cycle can be found with a
substantially higher rl/ic ratio than shown. Such a cycle would make the NITINOL heat engine
more competitive with other energy conversion devices where heat sources with small
temperature difference between the hot and cold reservoir (e.g., AT <20 0 C) are available.
Figure 13 shows the thermodynamic efficiency as the function of heat input QH to the
wire element for various types of engine cycles. The superiority of the constant-stress cycle
A and G is apparent.
Figure 14 presents the thermodynamic efficiency as the function of the peak recovery
stress and points out the advantage of the constant-stress cycle A over the constant-strain
cycle C . If, for example, the requirement of the wire durability should dictate the peak
recovery stress limit at 25Kpsi, the efficiency of the constant-stress cycle would be almost
three times higher than that of the constant-strain cycle.
Indeed, the experimental results obtained to date indicate that, for continuous cycling
without noticeable progressive elongation of the NITINOL wire element, the maximum
permissible recovery stress should not exceed 25Kpsi (17.6 Kg/mm 2 ). This limits the strain
(for the tested material) to about 1.0 percent for the constant-strain isothermal cycle, and to
about 5.0 precent for the constant-stress isothermal cycle. At this writing, all tests were
repeated for fewer than 104 cycles, and the durability as well as the cumulative permanent

elongation of the wire element due to creep have not been determined beyond that limit.
Nevertheless, in the case where a perfect "second memory" was established in the
trained wire element (Figure 4), no detectable cumulative permanent elongation was observed
even after several thousand cycles.
Only a small part of the planned research program has been completed thus far.
Therefore the measure efficiency values reported should not be regarded as the highest
attainable. Some improvement of energy conversion efficiency may be possible by thermal and
mechanical pretreatment and by alloying of NITINOL with another metal.

9-11

Mjjjj'A

NSWC MP 79-441
However, results to date clearly indicate the energy conversion efficiency could be
substantially improved only if the required heat input QH to the NITINOL wire during
the engine cycle could be substantially reduced.
5.

ANALYSIS OF THE ISOTHERMAL CYCLE

The isothermal NITINOL heat engine cycle can be described in a stress-strain diagram,
and the flowpath of energy through the cycle can be defined in the corresponding temperatureentropy diagram. Figure ISa presents a simple constant-strain isothermal cycle in the stressstrain coordinates. The cycle starts at point I with straining of the NITINOL wire in the cold
bath (along the isotherm TI) until point 2. Then the wire is transferred into the hot bath and
heated (under constant strain C2) until it attains the temperature 13 (while developing high
recovery stress) at point 3. Thereupon it is allowed to contract at constant temperature
T[3, performing useful work and returning to the inital strain el at point 4. Point 4 does not
lie on the isotherm T3 (as theoretically would be expected for an ideal S-ME material), but on
or near the isotherm TI. This drop in stress is due to non-ideal thermodynamic behaviour of
NITINOL, and the resulting magnitude of irreversible losses depends on the type of cycle used.
It is well known that the change of the thermodynamic state of NITINOL (and other SME
materials) from one point to another in the stress-strain-temperature space continuum depends
on the path by which the new state has been reached. This means that the new state depends
on the previous thermal and mechanical history, and consequently the initial state may not
necessarily be attained by a reversed change of the state parameters. Therefore, the
thermodynamic state parameters (d, c, T, U, H, S) are not uniquely definable in terms of
specific thermodynamic functions.
Figure l5b schematically shows a hypothetical "entropy diagram." The cycle is defined
again by the isotherms T 1 and T3 and by the lines of constant strain el and €_
If we start
the cycle at point I by straining the wire, the exothermic heaf of elastic deformation
21 generated in the NITINOL wire during the straining (because the coefficient of linear
thermal expansion of NITINOL in the transition region is negative 1 5 ) is rejected to the cold
reservoir (point I to point 2). Therefore, the entropy of the NITINOL wire during isothermal
straining decreases; this means that in the entropy diagram, point 2 must lie to the left of
point 1. Conversely, during the wire contraction (point 3 to point 4), the endothermic heat of
elastic recovery QR is absorbed by the wire from the surroundings (i.e., isothermic
contraction in the hot bath), and the entropy increases (point 4 lies to the right of point 3
Figure 15b ).
For isothermal elastic deformation1 6 ,17 (of completely martensitic NITINOL) the heat
2D can be expressed as:

1 5 R.

3. Wasilewski, S. R. Butler, and 3. E. Hanlon, "On the Martensitic Transformation in

TiNi," Metal. Sci 3., Vol. 1 (1967), p. 104.
6M. B.

Bever, D. L. Holt and A. L. Titchener, "The Stored Energy of Cold Work," Progress in

Material Science, Vol. 17, Pergamon Press, Oxford, 1973.
17F. W. Sears, An Introduction to Thermodynamics,

the Kinetic Theory of Gases and

Statistical Mechanics., Addison-Wesley Press Inc., Cambridge, Mass., 1950 (p. 154).

9-12

r.
NSWC MP 79-441
:'

Q~D = (2-"1

(~T
TI(

-

(4)

)T

In this equation, QT is the negative coefficient ot linear thermal expansion o(o)-l] in
transition region, TI is the absolute tem erature of the cold reservoir, (02 -a i) Is the
isothermal change in stress during straining [kg/mA ) is the density of NITINOL [kg/mj and J
is the mechanical equivalent of heat [427.8 mkg/kcalJ.
During the heating of the wire in the hot bath (from point 2 to point 3), the
heat (ZH is absorbed by the NITINOL wire:
:-C P(T
Q

+A
T 1) + A
H(o)j(5
AHM

(5)

where _p is specific hea, of NITINOL 0.11 kcal/kg (nearly constant in the range considered),
H~M+A
and AH(a) is the latent heat of phase transformation (martensite - austenite) in the
(a).M+A
prestrained wire while the recovery stress rises from 2 to 3 (A () to be determined
experimentally).
In Figure 15b, this change is schematically represented by a straight line connecting
points 2 and 3. In reality, this would be an integral curve indicating the progressive entropy
increase of the NITINOL during the reverse phase transformation, as the wire element is
heated from TI to :3. Moreover, during the cooling of the wire in the cold bath (point 4 to
point 1), the progressive decrease in entropy would in reality be indicated by a similar curve of
a reverse trend.
During the wire contraction (point 3 to point 4), the endothemic heat of shape recovery
QR is absorbed by the NITINOL (assuming no phase transformation occurs during the
contraction):
aT

(6)

QR = (03 c4 )T3 -

where 03 -04 is the isothermal change in stress during the shape recovery (point 3 to
point 4).
Finally, during cooling of the wire in the cold bath (point 4 to point I), the
heat QC is rejected
QC = Cp(T 3 - T I ) + AH (0)

where AH(o)M (to be determined experimentally) is the latent heat of transformation of
austenite to martensite in relaxed NITINOL wire (zero external force).

9-13

NSWC MP 79-441
.A
AAM
Note that AH (a) and A H (o) are not equal; the Lechatelier principle demands
•M 1A
A PM
> AH
that A
Their difference is:

(a)

(o)

(a)-

(0)

= QH

QC(8)

Similarly, QR and QDare not equal and their difference is:

(9)

Ar =QR-QD
The sum
Aq

(10)

Ah + Ar =W

represents the total amount of heat which theoretically could be converted into mechanical
work during the isothermal cycle. The major part of the total heat, namely the sensible heat
Cp(T3 - TI) and the latent heat of phase transformation at zero external force AH (o)

(and

the heat of elastic deformation QD), is wasted--i.e., is transferred from the hot to the cold
reservoir.
The theoretical energy conversion efficiency of any type of thermodynamic cycle can be
expressed as:
W

Qin
-

Qout

Qin

Qout

(11)

Qin

where Qin is the total heat absorbed by the SME wire element in the hot reservoir,
and Qout is the heat rejected from the wire to the cold reservoir. For the constant-strain
isothermal cycle employing SME material, chis becomes:
TI

QC + QD
QH + QR

(2

Substituting Eqs. (4), (5), (6), and (7) in (12) yields for the efficiency of the constant-strain
isothermal cycle:
rn =

CP(T 3 - TI) + AH (0)
(o!+-2 - ll T
HMA

=
T4L

or substituting Eqs. (8) and (9) in (12) gives:

9-14

(13)

NSWC 'MP 79-441
Q 0
r- Ah
IZ H++ Ar

Aq
QH*+QR

____=__

(14)

Equation (14) proposes the theoretical limit of the efficiency of energy conversion in
NITINOL subjected to a constant-strain isothermal cycle.
From equation (13) it is evident that the efficiency n will increase with increasing peak
MAA
recovery stress 23, since both terms &H (,) and (03 - 04) increase with p., Peak recovery
stress 3, however, is the function of 02 (and of h T = T3 - Ti), and furthermore,
function of the effective strain e = £2 - C1,

the

S2 is

The size of the area 1-2-3-4 in Figure 15b (which indicates the cycle efficiency)
increases with c = £2 - cl (i.e., increases with the distance between point 3 and 4).
Conversely, if'the strain c is reduced (in the limiting case) to zero, the elficiency a becomes
zero, because Ar = 0, Ah-= 0. Consequently by definition:
A. M+A

(a)

HM4A

(o)
(o=0)

(15)

AHAoM

(o)

For this case, the area 1-2-3-4 in Figure lSb reduces to a single curve between points I and 4,
which then represents a simple strain-free thermal cycling of the (free, unrestrained) NITINOL
wire between the temperatures TI and T3.
The

present

transformation

analysis

AHM-A before

(a)

assumes

the

NITINOL

the contraction

absorbs

the

latent

heat

of

of the wire begins (before point 3 in

Although this assumption conflicts with the theorems of other
Figure 15b is reached).
investigators 8 y1 8 , it is nevertheless supported by the experimental evidence presented by
Figure 16 shows a dual-beam
Melton and Mercierl 9 and by the following observation.
oscilloscope record of the constant-strain isothermal cycle taken from the test series F
The electrical resistivity (higher beam) of the NITINOL wire during the engine cycle is
recorded above the stress-strain diagram (lower beam). As indicated, the maximum change in
resistivity occurs upon submerging the wire in the hot bath (from point 2 to point 3), and the
resistivity subsequently remains nearly constant during the contraction of the wire element

8 See footnote 8 on page 9-4.
1 8 L.

Delaey and G. de Lepeliere, "The Temperature-Entropy Diagram of Solid State Engines

and Solid State Heat Pumping Systems with Shape Memory Alloys," Scripta Metallurgica,
Vol. 10 (1976), p. 959.
19K. N.

Melton and 0. Mercier, "The Effect of Opposing Stress on Shape Memory and
Martensitic Reversion," Scripta Metallurgica, Vol. 12 (1978), p. 5.
9-15

NSWC MP 79-44,1
(point 3 to point 4). It has been well established 20 that the resistivity of NITINOL is distinctly
different for the austenitic and for the martensitic phase. Moreover, the diagram in Figure 16
can be nearly duplicated when the heat input QH is effected by an electric pulse (Figure 20 in
the Appendix). The pulse can be timed to be completed before the wire element begins to
contract. Consequently, positively no external heat is supplied to the wire element during the
shape recovery process.
On the basis of the above experimental evidence, it is proposed that, during the constantstrain isothermal cycle, the constrained NITINOL wire absorbs the latent heat of phase
the contraction, which implies that the phase
transformation before the beginning of
may occur before the shape recovery event.
transformation (martensite -+ austenite)

In the case of the constant-stress isothermal cycle, the experimental results to date are
HM+A isabsorbed during
inconclusive. Further investigation isplanned to identify the way AH
this type of cycle.
Returning now to Equations (12) and (13), we may first calculate QD, QR, and
QC. For a trained NITINOL wire with fully developed "second memory," no stress rise results
during stretching of the wire in the cold reservoir, i.e., 02 - l = 0 and QD = 0. Taking the
value of the coefficient of thermal expansion from Reference 15 gives us;
aT = 33 x 10 6 /QC
r

and the other material properties from Reference 2:
y =6.45 x 10

kg/m 3 , AH =5.78 cal/g

and setting (03 - 04) = 30Kpsi, and T3 = 343 0 K in Equation (6) gives:

1-3
= Q8654
R= 6.54 x 10 cal/g = 0.363 Joule/g
Furthermore,

approximationt

A+M
assuming A H (0)

AH in

Equation (7) yields for QC

as

the

first

QC = 0.11 x 70 + 5.78 = 13.48 cal/g = 55.4 Joule/g

2 0 F. E. Wang, B. F. DeSavage, and W. J. Buehler, "The

Irreversible Critical Range in the TiNi
Transition," Jour. of AppL. Phys., Vol. 39 (1968), P. 2166.
See footnote 15 on page 9-12.
t -M

9-16

.. t V " '

1 '

NSWC MP 79-441
is relatively small and significantly contributes to the
In comparison to QC,the value of 2
efficiency of the constant-strain isothermal cycle only if p is comparable to the difference
between QH and QC (Equation 12).

For the calculation of 2H, the value of
(o) has to be determined. Tong and
Wayman 2 l concluded there will be only a small correction factor when calculating the
difference between A H (o) and A (o) " Several investigators derived expressions for
AH

)A

Clausius-Clapeyron relation. 2 2- 2 3
based on the W)

Furthermore,

Salzbrenner
and
uA+M

Cohen26 pointed out the difference between the chemical and elastic component of AHA)
oovr
as the function of recovery
Thus far, however, no calculated or measured values of AHM+A astefucin
stress have been published for NITINOL. Therefore, this study attempted to determine
experimentally the effect of stress on the latent heat of phase transformation.
In the test series ®)and (®),the total heat input FH was determined as follows: the
constant-strain isothermal cycle was repeated (atleast one hundred times for every
data point) at c = 0.5 percent, 1.1 percent, and 1.6 percent elongation with Ti = +loC and
T3 = 51oC held'constant (test series ®); the cycles for each c setting were duplicated when
the heat 2H was supplied by an electric pulse instead of the hot bath (see Appendix); the

21 H.

C. Tong and C. M. Wayman, "On Carnot Cycles, Transformation Temperatures, and
Latent Heats Under an A pplied Stress, as Related to the Shape Memory Effect," Scripta
Metallurstica, Vol. 10 (1976), p. 1129.

22 K. Otsuka, C.

M. Wayman, K. Nakai, H. Sakamoto and K. Shimizu, "Superelasticity Effects
and Stress-Induced Martensitic Transformations in Cu-AI-Ni Alloys," Acta Metallurgica, Vol.
24 (1976), p. 207.

2 3 C. Rodriguez

and L. C. Brown, "The Thermodynam its of Stress-Induced Martensites in CuAI-Ni Alloys," Metallurgical Transactions A, Vol. 7A (1976), p. 1459.

2 4R.

Smoluchowski, "Phase Transformation In Solids," in Phase Transition and Critical
Phenomena, edited by H. Stanley (Chapter 8), Oxford University Press, New York, 1971.
3. W. Allen, "Stress Dependence and the Latent Heat of the Morin Transition in Fe203,"
Physical Review B, Vol. 8, No. 7 (1973), p. 3224.

2 6 R.

3. Salzbrenner and M. Cohen, "On the Thermodynamics of Thermoelastic Martensitic
Transformations," Acta Metallurgica, Vol, 27 (1979), p. 739.
9-17

I

.

LA

NSWC MP 79-441
voltage level of the pulse was adjusted so that the same peak recovery stress 23 was obtained
as when the wire was heated in the hot bath; the product of voltage, current, and time interval
of the pulse expressed in 3oules/g is plotted in Figure 17a; also plotted are the data from the
second test series
run at the same parameter settings, except for the hot bath
temperature which was maintained at 7 1C. When the sensible heat (CpA T) was subtracted,
the data points from both test series fell on one curve (Figure 17b). For comparison, the value
AH = 5.78 cal/g = 24.2 Joule/g, from Reference 2, is indicated by a cross (near the vertical

S

scale).

On the basis of these tests, the latent heat of transformation A rM1(

appears

strongly influenced by the magnitude of the peak recovery stress.
to 03

The curve () and (2)is replotted
again on a larger scale in Figure 18 and extralpolated
0 which should theoretically yield:
AAM

(o)

-

A MA
^

(=0)

:
..A+M
If this value could be taken as the true AH ()

,

then the energy conversion efficiency as

calculated by Equation (13) should indeed be high, approaching the Carnot efficiency in

A-*M is,
isothermal cycles with peak recovery stress of about 32 Kpsi. The real value of A H (o)
however, quite different if defined in accordance with the law of conservation of energy: No
energy can be lost during the entire cycle, and therefore the latent heat of
transformation AHAM (austenite+ martensite) during the cooling period must include all
(o)
the "unused" heat energy which, by definition, is the difference between the energy absorbed
by the NITINOL (as the latent, heat of transformation: martensite - austenite) during the
heating period and the amount of heat that was converted to the useful mechanical work
(neglecting Ar).
Based on the above definition, the latent heat

AH AoM

(o)

can be calculated from

Equations (8) and (10), substituting for Ah the mechanical work W, which has been determined
by the planimetry of the stress-strain diagram (for each data point). Figure 18 shows thel
AM
(Neh
A M
plotted results as the curve A (o)
(o)
as derived by the calculation
appears not as a constant value, but as a function of o)
Similar curves of the latent heat of
,,A+M
transformation (AIuM+A
H (CF)
and AH
(o))
can be experimentally derived for other types of
engine cycles, such as the constant-stress isothermal and the semi-adiabatic cycle.
At present, an attempt is being made to define the fundamental causes of energy
degradation during the SME energy conversion process and to determine whether a correlation
exists between these causes and the characteristic trend of the latent heat of transformation
(A

)I0A
and A H (o)

) as the function of the peak recovery stress. Among the causes Of the

energy degradation, the following are being considered:

2

See footnote 2 on page 9-3.
9-18

NSWC MP 79-411
1) Internal friction in the lattice which causes dissipation of the elastic strain energy.
This occurs particularly when stress and strain changes are not in phase. 2 6

6.

2)

The irreversibility of spontaneous thermodynamic processes, such as spontaneous
martensitic transformation. (The reversible processes are never spontaneous and
require careful guidance from outside their boundaries 2 7

3)

The residual internal stress fields in the lattice which contribute to hysteresis and
the loss of the pseudo-elasticity. 28

PRELIMINARY INVESTIGATIONS OF VARIOUS APPROACHES TO EFFICIENCY
IMPROVEMENT

Besides the studies discussed above, a few nreliminary investigations have aimed to
improve the energy conversion efficiency in NITINOL. These investigations deal with: a)
Favorable orientation of martensite variants. b) Adiabatic engine cycles. c) Engine cycles
with heat recuperation.
a)

FAVORABLE ORIENTATION OF MARTENSITE VARIANTS

During the martensitic phase tranformation in a stress-free NITINOL wire,
theoretically 24 random oriented martensite variants develop in the parent (austenitic) lattice
structure. Upon subsequent heating of the wire above the transition temperature, the
martensite variants transform to the parent phase (austenite). However, when the martensitic
(forward) transformation takes place under the action of stress (e.g., resulting from external
force acting on the wire element in the direction of the wire centerline), only some
preferentially oriented variants of martensite are likely to form, while the formation of others
will be suppressed. 2 9
If it can be assumed that upon heating (reversed transformation) these
preferentially oriented variants are those which most effectively contribute to the magnitude
of the resulting recovery stress, then a way should be sought to assure such preferential
orientation of the martensite variants also under the conditions of the actual engine cycle
operation.

I
26

See footnote 26 on page 9-17.

7F. H. Crawford and W. D. VanVorst, Thermodyamics for EnRineers, Harcourt, Brace and
World, Inc., New York, 1968, p. 225.
28S. Mendelson, "Mechanisms for Martensite Formation and the Shape Memory Effect," in
Shape Memory Effect in Alloys, edited by 3. Perkins, Plenum Press, New York, 1975 p. 487.
29

R. 3. Wasilewski, "The Shape Memory Effect in TiNi: One Aspect of Stress-Assisted
Martensitic Transformation," in Shape Memory Effect in Alloys, edited by 3. Perkins,
Plenum Press, New York, 1975, p. 266.

9-19

NSWC MP 7 9-411
Unfortunately, in the practical case of relatively rapid cooling of NITINOL during the
engine cycle (after contraction and relaxation of the wire element has been completed), the
orientation of the variants may rather follow the direction of the resulting internal (thermal)
stresses which are generally oriented perpendicularly to the centerline of the wire element.
Thus far, it has not been ascertained whether or not all these variants reorient themselves in
the more favorable direction during the subsequent straining of the NITINOL wire. Perhaps it
can be argued that a complete reorientation of all martensitic variants would generate
additional lattice dislocations, resulting in increased hysteresis and decreased life of the wire
element28 , 3 0 and also decreased engine cycle efficiency. On the other hand, if a method
could be devised to orient the martensitic variants in the more favorable direction during the
rapid cooling of the NITINOL wire, perhaps a larger recovery force could be produced upon
heating of the wire element, resulting in a larger amount of mechanical work during the engine
cycle.
Preliminary test results of isothermal constant-strain cycles with very slow cooling rate
of the wire element indicate the cycle efficiency improves by a factor of 2.0. This is
interpreted as the consequence ot more favorable orientation of the martensite variants due to
the absence of thermal stresses during very slow cooling of the wire element in air (as
compared to the fast cooling by submerging the wire in a liquid bath).
The most favorable orientation of the martensite could be expected if the isothermal
engine cycle is performed entirely in the austenitic region (at a cold reservoir temperature
above 50oC). Reference 31 suggested this. In such a case, only the stress-induced martensite
would be generated during the straining of the wire, with the favorable orientation of the
variants. However, the disadvantage of such a cycle is the inherently high recovery stress
level and consequently short life of the NITINOL wire element.
b)

ADIABATIC ENGINE CYCLES

For the highest possible thermodynamic efficiency, the NITINOL engine cycle should
ideally closely approximate the Carnot cycle. The Carnot cycle consists of two adiabatic and
two isothermal changes of the thermodynamic state. The heat from the hot reservoir must be
supplied during the engine cycle only at the highest cycle temperature T3 (isothermally), and
the rejected heat must be transferred to the cold reservoir only at the lowest cycle
temperature TI (isothermally). In contrast to the previously discussed isothermal engine cycle
(Figure 15), no heat is exchaned with the surrroundings at any temperature intermediate
between T3 and TI (Reference 2). The necessary heating of the NITINOL wire from TI to
T3 mu-stbe accomplished by the adiabatic heating resulting from rapid straining of the wire
28"See footnote 28 on page 9-19.
3 0 M.

Ahlers,

R. Rapacioli,

and

W. Arneodo,

"The

Martensitic

Transiormation

in 8Brass and the Shape Memory Effect," in Shape Memory Effect in Alloys, edited by 3.
Perkins, Plenum Press, New York, 1975, p. 379.

310. Weres, "On the Thermodynamics of the Shape Memory Alloys," Report LBL-3297,
Lawrence Berkeley Laboratory, University of California, Berkeley, November 1975.
3 2 E.

A. Guggenheim, Thermodynamics, North-Holland Publishing Comparky, Amsterdam, Third

Edition, 1957, p. 94.

9-20

V
NSWC MP 79-441
element. Similarly, the adiabatic cooling of the wire element should be attained by rapid
contraction of the wire. Unfortunately, this type of cycle does not appear realizable with SME
polycrystalline materials, 'ecause the phase transformation process can be accomplished (i.e.,
the latent heat of transformation can be absorbed) over only a definite span of the
temperature range (e.g., 50oC). This means that, in the strict sense of the definition, the
condition of a total heat input at the highest cycle temperature cannot be satisfied.
A part-way approach to the Carnot cycle can be attained by a semi-adiabatic cycle.
Such a cycle is schematically shown in Figure 19a in the stress.-strain coordinates and in Figure
l9b in the T-S coordinates. The cycle starts with the removal of the NITINOL wire from the
cold bath and adiabatic rapid straining of the wire in air (point I to point 2), while the stress
rises from al to a2, and the temperature from TI to T2. Thereafter, the wire is instantly
submerged Irn the lot bath (hot reservoir) which i maintained at the temperature T3. Here the
wire absorbs the latent heat of transformation and the sensible heat Cp(T3 - T2),- while the
stress rises to o_3.

At this point, the wire is removed from the hot bath and allowed to rapidly

At the
contract (point 3 to point 4), while the stress drops to 04 and the temperature to T4.
end of this interval, the original length of the wire is recovered and the power-stroke
completed. Finally the wire is transferred back into the cold bath (point 1), where it is cooled
to temperature Ti while rejecting the latent heat of transformation and the sensible heat
Cp(TI - T4).
Experience shows that the temperature Ti must be adjusted so that only a partial
martensitic transformation takes place in the cold bath. If a complete transformation is
allowed, the NITINOL wire becomes too ductile and the temperature will not rise during the
subsequent rapid straining (point 1 to point 2).
The major difficulty in realization of the semi-adiabatic cycles, aside from the necessity
of accurate timing of all cycle events, is the requirement for rapid straining of the NITINOL
wire. If the straining time is more than one-half second, much of the heat (which was
generated by straining the wire) is lost by convection to the surrounding air, and the adiabatic
temperature rise (point I to point 2) is reduced. Rapid straining, however, may cause
nonuniform stress and temperature distribution in the wire. This in turn may increase internal
friction in the lattice, leading to a decrease of the efficiency and life of the wire element.
The adiabatic temperature rise that can be accomplished by rapid straining of the
presently available NITINOL wire is quite limited. This is because the strain-temperature
coefficient of adiabatic heating (resulting in the heat of elastic deformation) is small. As the
first approximation, ATn can be calculated from Equation (4) dividing the heat of elastic
deformation QID by the specific heat of NITINOL:
CpCldT
y Jl(6T 1
D = ~'(2 AT=

(16)

cpY
Simultaneously, an additional temperature rise ATM is effected by the exothermic
latent heat of transformation, originating from the stress-induced martensite which grows
during the stressing of the wire element. ATM can be calculated only if the amount of the
known:.AIM
stress-induced martensite (%)M is
W
ATM =

M

AH A)-(
C
p

(17)
9-21

NSWC MP 79-441
(where Cp is taken as the average value). The total temperature rise is then:

(T 2 - T)= ATD+

ATM

(18)

Preliminary tests were conducted to determine the total temperature rise
(T2 - TI) experimentally. For 1.0 percent strain effected in 65 ms (starting at Ti =
240C), the total temperature rise was about 40C. The method employed in these tests will be
published later.
The present result is tentative, and additional tests employing other
measurement methods are in preparation.
The efficiency of the semi-adiabatic cycle can be written as:

n

Qc

Q Cp(T

"qH

Cp(T 3

4-

Tl) +

A+M

A19

T2 )+ AH )

Comparing Equation (19) to (13), and assuming all other factors the same, we see that an
efficiency improvement over the isothermal cycle can be expected only if the reduction of the
sensible heat Cp(T 3
T2) and Cp(T 4 - T 1 ) relative to C (T 3 - T 1 ) is substantial.
This, of
and the
course, depencrs on the magnitude of the adiabatic ?emperature rise (T2 -TI)
temperature drop (T4 - T3 ), respectively.
Preliminary tests of the semi-adiabatic cycle have been conducted; however, no data
indicating a substantial efficiency improvement were obtained to date.
c)

ENGINE CYCLES WITH HEAT RECUPERATION

One evident approach to efficiency improvement is based on the principle of heat
recuperation during the engine cycle. The objective is to transfer the heat available from a
NITINOL wire element which has just completed the engine cycle (end of power stroke) to
another wire element which has been strained and is ready to be heated and to start the power
stroke. However, because of the relatively low heat conductivity of NITINOL and the small
temperature gradient between the wires in a (counterflow) heat exchanging relationship, the
heat transfer rate is low, limiting the potential efficiency improvement. Depending on the
sophistication and type cf the engine design concept, an efficiency improvement by a factor of
1.5 to 2.5 appears feasible.
7.

DISCUSSION AND CONCLUSION

The studies here experimentally investigated the efficiency of converting heat to useful
mechanical work in a "solid state" NITINOL heat engine. Various thermodynamic engine cycles
were performed on a specially designed cycle-simulator apparatus. Each test series covered a
specific range of test parameters, and repeated each specific setting of the test parameters
over several hundreds of cycles.
The highest thermodynamic efficiency on the order of 1.2 percent (approximately 6
percent of Carnot efficiency) has been demonstrated, with NITINOL wire life expectancy of
about 104 cycles. At more conservative stress and strain levels, lower thermodynamic
efficiency resulted (about 0.5 percent); however, the wire life expectancy could be estimated
to exceed 106 cycles.
9-22

NSWC MP 79-401
These experimentally determined efficiencies do not agree with the theoretical
calculations in References 8-11. The reason for this discrepancy might be as follows: The
referenced :z2!culations presume that the chemical free energy difference between the
martersitic and the austenitic phase represents the maximum energy theoretically available
for conversion to useful mechanical work. Although the chemical free energy difference
constitutes the "driving force" for the phase transformation, it does not present a sufficient
basis for the analytical determination of the energy conversion efficiency.
Determinir,,, the efficiency of any thermodynamic cyclic process requires adequately
defining the sequence of events and the mode of energy transaction during each event of the
specific type of thermodynamic cycle under consideration. This study's analysis of the
constant-strain isothermal cycle is an example of such a procedure. To define the mode of
energy transaction during the individual events of the isothermal cycle, several models have
been cry -idered and subjected to experimental verification. As a result, the following
postulat , were proposed:
1)

The effective useful work obtainable during the (constant-strain) isothermal
cycle equals
the
difference
between
the
latent heat of
reverse
transformation A H (a)
(during increasing stress) and the latent heat of forward
transformation A

(o)

(during "stress-free" state:

04

= 0). An additional small

contribution comes from the difference between the heat of elastic
deformation QD (during the straining of the SME element) and the heat of elastic
recovery QR (during the contraction of the SME element).
2)

During the constant-strain isothermal cycle (the simplest NITINOL engine cycle),
the latent heat of reverse transformation A (a) (martensite - austenite) is
absorbed by the SME material before the shape recovery (contraction of the wire
element) takes place.

3)

The magnitude of the latent heat of reverse transformation AH MA
austenite) is a strong funciton of the peak recovery stress.
(a)

(martensite

31
See footnote 8 on page 9-4.

9See footnote 9 on page 9-4.
1 0 See footnote 10 on page
11

9-4.

See footnote II on page 9-4.
9-23

NSWC MP 79-441
4)

The magnitude of the (apparent) latent heat of forward transformation AHAM

(o)
(austenite + martensite) under the zero external force condition (after the
contraction of the wire element) is not constant, as would be expected for an ideal
SME material. Becuase of the nonideal behavior of the SME material (NITINOL), the
magnitude of the (apparent) latent heat of forward transformation increases with
the increasing peak recovery stress. This increase is presently interpreted as the
consequence of the energy degradation in the NITINOL lattice during the engine
cycle.

I

In accordance with the above postulates, Equations (13) and (14) yield efficiency values
consistent with the experimental results reported here. It is evident that extensive basic and
materials research is needed for a better understanding of the energy conversion process in
NITINOL. An important advancement in this direction is presented in Reference 26, which
elucidates the effect of the grain boundaries in a polycrystalline (versus single crystal) Cu-A lNi alloy on the internal frictional resistance, on the stored elastic strain energy in the lattice,
and on the temperature range of the martensitic phase transformation. Phase transformation
stuides of a single crystal NITINOL alloy have been suggested and are in preparation. 3 3
In summary, the following conclusions can be drawn:
a)

Generally, only the heat engines operating on adiabatic thermodynamic cycles can
theoretically approach the Carnot cycle efficiency.

b)

Because of the very limited temperature rise during the wire straining and the relatively
large temperature range of the NITINOL phase transformation, the NITINOL heat engine
can't operate on an adiabatic cycle and therefore is restricted (for all practical purposes)
to the isothermal cycle.

c)

The isothermal cycle is inherently (thermodynamically) inefficient, no matter whether
fluids or solid-state materials are employed as the working medium.

d)

The

magnitude

of

the

latent

heat

of

reverse

transformation

of

NM+A
NITINOL AH (a) substantially increases with increasing peak recovery stress. As
the consequence of this increase of heat which is absorbed during the engine
cycle, the efficiency is further lowered.
The potential engine efficiency a is ultimately limited by the requirement of an
acceptable life of the NITINOL wire element. The capacity of NITINOL to perform
mechanical work cannot be utilized beyond the limits of the peak stress and strain set by
this requirement.

e)

26

See footnote 26 on page 9-17.

3 3 C.

M. Gilmore, Private Communication. (This research was suggested and is in preparation
by Professor Gilmore, George Washington University, School of Engineering and Applied
%ciences,Washington, D.C.).
9-24

NSWC MP 79-44
)

Any improvement of the NITINOL material in respect to the strength and durability
would extend the permissible peak stress and strain limits and therefore result in an
improvement of the thermodynamic engine efficiency r (Figure 8).

g)

In planning future research, perhaps the most promising direction would be toward
developing new NITINOL alloys with a very narrow temperature range of the
phase transformation.
Such alloys would permit engine operation at a small
temperature difference between the hot and cold reservoir, with the result
of a higher /ri/c ratio, This would greatly enhance the potential usefulness of the
NITINOL heat engine in application to heat sources with a very small temperature
gradient.

J

ii

-

---.---.-

*-'.~--

9-25/9-26

NSWC MP 79-44t1

APPENDIX
DE1 ERMINATION OF THE HEAT INPUT Q14
TO THE NITINOL WIRE DURING THE ENGINE CYCLE

4

The heat is supplied to the NITINOL wire element during the engine cycle at the instant
when the wire is submerged in the liquid of the hot reservoir. It would be very difficult to
attempt to measure directly (with any accuracy) the amount of heat which the wire absorbs.
Therefore, this study employed the following two-step method of wire heating and heat input
measurement:
1)

First, the wire is subjected to the constant-strain isothermal cycles (in Accordance
with the chosen test parameters) on the Cycle Simulator, while it is hea.-d in the
standard way by submerging it in the hot bath. The stress-strain diagram (lower
trace) and the wire ohmic resistance (upper trace) are recorded on the screen of a
dual-beam oscilloscope (Figure 20).

2)

Then (while the cycling is continued) the hot bath is removed and the wire is heated
(while in air) by an electric pulse at the proper instant during each of the following
cycles. All other test parameters are kept unchanged. The DC current of the
electric pulse is timed and the voltage is adjusted so that the same peak recovery
stress is obtained as when the wire has been heated in the hot bati. Now the stressstrain diagram is again recorded. The product of the current, voltage, and time
interval of the electric pulse yields the total heat input Ou in Watt-sec (= 3oule) to
the wire element. The electric pulse record is shown in ligure 21.

The final record (Figure 20) consists of the traces of a number of repeated cycles with
heating of the wire by an electric pulse, which are superimposed over the traces of a number
of repeated cycles when the wire has been heated in the hot bath. (Record in Figure 20 was
obtained on Tektronix 7623A storage oscilloscope.)

--

Part of the stress-strain diagram--namely, the lines which slope downward from right to
left--represents
contraction of the wire element after heating. The slightly convex line
resulted when thethe
wire
pulse.
resulted when the wire was
This slightly
was heated
heated byin the
theelectric
hot bath,
and the
difference
concave
line (lower
is partially
due toline)
the
fact that when the NITINOL wire element is heated in the hot bath, it is also allowed to
contract in the hot bath. Consequently it absorbs an additional small amount of heat
during the wire contraction.
This additional heat--the heat of the elastic shape
ro.overy QR (see text)-contributes a modest amount of energy to the engine cycle, which is
also partially converted to useful mechanical work. As a result, the area of the stress-strain
diagram under the convex line is slightly larger (about 10 percent).

9-27
t

'

NSWC MP,79-441
Figurc 20 also presents the following information: cold reservoir temperature
TI= +20C, hot reservoir temperature T3 = +520C, cyclic elongationa AL = 6 mm of the wire
element corresponding to 1.6 percent strain. The difference in the ohmic resistance of the
NITINOL wire (upper trace) between the martensitic (lower line) and the austenitic (upper line)
phase is 0.27 ohms. (The distance between the short horizontal calibration mark and the lower
line indicates 0.1 ohms.) This corresponds to about 15 percent change in the absolute
resistance of the NITINOL wire element.
The upper trace in Figure 21 represents the current pulse, the middle trace and the
voltage pulse, and the lowest trace the time interval of the wire contraction. The duration of
the heating pulse and of the wire contraction is about 350 ms each. Between the end of the
heating pulse and the start of the wire contraction is a small time overlap--about 40 ms--which
was determined experimentally for the optimal utilization of the pulse energy. The current
was read across a calibrated shunt and the voltage across the terminals of the NITINOL wire
element. The signal for the wire contraction was monitored directly from the electronic pulse
control system of the Cycle Simulator.
The heat losses from the NITINOL wire element during the heating pulse and during the
wire contraction period were determined as follows: During one test cycle the wire element
was not allowed to contract, but was held constrained after the completion of the electric
heating pulse. The peak recovery stress a3 was displayed on the oscilloscope screen with the
horizontal sweep of the beam adjusted to 200 ms per cm. The rise of the recovery stress
during the heating pulse and the subsequent decay of stress due to the heat losses to the
surrounding air as the function of time are shown in Figure 22.
The heat losses were calculated from the slope of the asymptotic stress decay curve.
For the total period of the electric pulse and the subsequent wire contraction period (700 ms),
the heat losses amounted to approximately 5 percent of the pulse energy.

-i9-2

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9-31

NSWC MP 79-441

FIGURE 4

VIDEO RECORD OF A TYPICAL CONSTANT-STRAIN ISOTHERMAL CYCLE.

9-32

NSWC MP 79-441

1:

II

'II

IL

FIGURE5

CONSTANT-STRAIN ISOTHERMAL CYCLE RESULTING WHEN HEAT IS SUPPLIED
BY ELECTRIC PULSE.

9-33

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NSWYC MP 79-441

FIGURE 6

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CYCLE. HEAT SUPPLiED BY ELECTRIC
STRESS-LIMITED ISOTHERMAL

9-34

PULSE.

NSWC MP 79-441

FIGURE 7

CONSTANT-STRESS ISOTHERMAL CYCLE.

9-35

NSWC MP 79-"l

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NSWC MP 79441

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Nswc AV' 70.441

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NSWC MP 79-441

FIGURE 16 DUAL-BEAM OSCILLOSCOPE RECORD OF THE NITINOL RESISTIVITY (UPPER TRACE)
DURING THE CONSTANT-STRAIN ISOTHERMAL CYCLE (LOWER TRACE).

9-44

NSWC MP 79441

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z

nail

ON-

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NSWC MP 79-441

FIGURE 20

WIRE DURING THE
DETERMINATION OF THE HEAT INPUT TO THE NITINOL
CYCLE.
CONSTANT-STRAIN ISOTHERMAL

9-48

SE

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NSWC MP 79-441

FIGURE 21

CURRENT AND VOLTAGE PULSES FOR HEATING OF THE NITINOL WIRE ELEMENT,
AND THE WIRE CONTRACTION TIMING TRACE.

9-49

NSWC MP 79-441

THE ELECTRIC HEATING PULSE AND THE
FIGURE 22 PEAK RECOVERY S'RESS RISE DURING
LOSSES FROM THE NITiNOL
SUBSEQUENT STRESS DECAY DUE 'O THE HEAT
WIRE ELEMENT.

9-50

NSWC MP 79-441
9.

REFERENCES

1.

W. S. Ginell, 3. L. McNichols and 3. S. Cory, "Low-Grade Thermal Energy-Conversion
Joule Effect Heat Engines," American Socierty of Mechanical Engineers, Paper 78-ENAs7, July 1978.

2.

C. M. Jackson, H. 3. Wagner and R. 3. Wasilewski, "55 NITINOL - the Alloy with a
Memory," Report NASA-SP 51 10, 1972.

3.

3. Perkins, "Shape Memory Effects in Alloys," Proc. of the Inter. Symp. on Shape
Memory Effects and Applications, Toronto, Ontario, Canada, May 1975; Plenum Press,
New York.

4.

H. F. Mohamed, "Martensite Transformation and Shape Memory Effect in Ni-Ti Alloy,"
Report LBL-5112, Lawrence Berkeley Laboratory, Univiersity of California, Ber'keley,
May 1976.

5.

D. S. Lieberman, "Crystal Geometry and Mechanisms of Phase Transformations in
Crystalline Solids," Paper presented at Seminar of Am. Soc. for Met., October 1968.

6.

Z. Nishiyama, Martensitic Transformations, Academic Press, New York, 1978.

7.

M. Ahlers, "On the Usefulness of Martensitic Transformations for Energy Conversion,"
Scripta Metallurgica, Vol 9 (1975), p. 71.

8.

H. C. Tong and C. M. Wayman, "Thermodynamic Considerations of 'Solid-State Engines'
Based on Thermoelastic Martensitic Transformations and the Shape Memory Effect,"
Metallurgical Transactions A, Vol. 6A, January 1975.

9.

C. M. Wayman and H. C. Tong, "The Efficiency of the Shape Memory Effect for Energy
Conversion," Scripta Metallurgica, Vol. 9 (1975), p. 757.

10.

B. Cunningham and K. H. G. Ashbee, "Marmem Engines," Acta Metallurgica, Vol. 25

(1977), p. 1315.
11.

A. A. Golestaneh, "Efficiency of the Solid-State Engine Made with NITINOL Memory
Material," 3. Appl. Phys., 49 (3), March 1978.

12.

R. Banks, P. Hernandez and D. Norgren, "NITINOL Engine Project - Test Bed," Final
Report, UCID-3739, Lawrence Berkeley Laboratory, University of California, Berkeley,
July 31, 1975.

13.

D. A. Johnson, "Training Phenomena in NITINOL," presented at the NITINOL Heat Engine
Conference, September 1978, Naval Surface Weapons Center, Silver Spring, Maryland
(printed elsewhere in the present volumel.

14.

W. B. Cross, A. H. Kariotis and F. 3. Stimler, "NITINOL Characterization Study," NASA
CR-1433, September 1969.

15.

R. 3. Wasilewski, S. R. Butler, and 3. E. Hanlon, "On the Martensitic Transformation in
TiNi," Metal. Sci 3., Vol, 1, (1967), p. 104.

9-51

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'

'

'

'

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NSWC MP 79-441
16.

M. B. Bever, D. L. Holt and A. L. Titchener, "The Stored Energy of Cold Work," Progress
in Material Science, Vol. 17, Pergamon Press, Oxford, 1973.

17.

F. W. Sears, An Introduction to Thermodynamics, the Kinetic Theory of Gases and
Statistical Mechanics, Addison-Wesley Press Inc., Cambridge, Mass., 1950 (p. 154).

18.

L. Delaey and G. de Lepeliere, "The Temperature-Entropy Diagram of Solid State
Engines and Solid State Heat Pumping Systems with Shape Memory Alloys," Scripta
Metallurgica, Vol. 10 (1976), p., 959.

19.

K. N. Melton and 0. Mercier, "The Effect of Opposing Stress on Shape Memory and
Martensitic Reversion," Scripta Metallurgica, Vol. 12 (1978), p. 5.

20.

F. E. Wang, B. F. DeSavage, and W. 3. Buehler, "The Irreversible Critical Range in the
TiNi Transition," 3our. of App. Phys., Vol. 39 (1968), P. 2166.

21.

H. C. Tong and C. M. Wayman, "On Carsot Cycles, Transformation Temperatures, and
Latent Heats Under an Applied Stress, as Related to the Shape Memory Effect," Scripta
Metallurgica, Vol. 10 (1976), P. 11429.

22.

K. Otsuka, C. M. Wayman, K. Nakai, H. Sakamoto and K. Shimizu, "Superelasticity
Effects and Stress-Induced Martensitic Transformations in Cu-Al-Ni Alloys," Acta
Metallurgica, Vol. 24 (1976), p. 207.

23.

C. Rodriguez and L. C. Brown, "The Thermodynamcis of Stress-Induced Martensites in
Cu-Al-Ni Alloys," Metallurgical Transactions A, Vol. 7A (1976), p. 1459.

24.

R. Smoluchowski, "Phase Transformation in Solids," in Phase Transition and Critical
Phenomena, edited by H. Stanley (Chapter 8), Oxford University Press, New York, 1971.

25.

3. W. Allen, "Stress Dependence and the Latent Heat of the Morin Transition in Fe203,"
Physical Review B, Vol. 8, No. 7 (1973), p. 3224.

26.

R. 3. Salzbrenner and M. Cohen, "On the Thermodynamics of Thermoelastic Martensitic
Transformations," Acta Metallurgica, Vol, 27 (1979), p. 739.

27.

F. H. Crawford and W. D. VanVorst, The.modyamics for Engineers, Harcourt, Brace and
World, Inc., New York, 1968, p. 225.

28.

S.Mendelson, "Mechanisms for Martensite Formation and the Shape Memory Effect," in
Shape Memory Effet in Alloys, edited by 3. Perkins, Plenum Press, New York, 1975 p.
487.

29.

R. 3. Wasilewski, "The Shape Memory Effect in TiNi: One Aspect of Stress-Assisted
Maretensitic Transformation," in Shape Memory Effect in Alloys, edited by 3. Perkins,
Plenum Press, New York, 1975, p. 266.

30.

M. Ahlers, R. Rapacioll, and W. Arneodo, "The Martensitic Transformation in
B-Brass and the Shape Memory Effect," in Shape Memory Effect in Alloys, edited by
3. Perkins, Plenum Press, New York, 1975, p. 379.

9-52

NSWC 'MP79-441
31.

0. Weres, "On the Thermodynamics of the Shape Memory Alloys," Report LBL-3297,
Lawrence Berkeley Laboratory, University of California, Berkeley, November 1975.

32.

E. A. Guggenheim, Thermodynamics, North-Holland Publishing Company, Amsterdam,
Third Edition, 1957, p. 94.

33.

C. M. Gilmore, Private Communication.
(This research was suggested ard is in
preparation by Professor Gilmore, George Wai'hington University, School of Engineering
and Applied Sciences, Washington, D.C.).

9[1

-

"

NSWC MP 79-441
NOMENCLATURE

8.
C

specific heat of NITINOL [0. 11 cal/g°C]

p

E

elongation of NITINOL wire after straining (mm)

F

force extracted by NITINOL wire At peak stress a3 kg

H

enthalpy

AH

latent heat of phase transformation of undeformed (unstretched) and unrestrained
NITINOL wire[5.73 cal/g]
A-M

AHATM external
latent heat
of after
forward
phase transformation
* martensite) at zero
force,
contraction
(shape recovery)(austenite
of the NITINOL
wire
AH MA latent heat of reversed phase transformation (martensite * austenite) of a
(a)
prestrained NITINOL
wire during the rise of a recovery stress 03
J

mechanical equivalent of heat [427.8 mkg/kcal]

L

length of the NITINOL wire [mm]

L9

length of NITINOL wire per I gram weight

AL

linear change of the wire length during the contraction (AL = E)

Q

total heat input to the NITINOL wire during one engine cycle
heat rejected by the wire in the cold bath (cold reservoir)
exothermic heat of elastic deformation (stretching) of the NITINOL wire at constant
temperature
total heat input per I gram of NITINOL
heat absorbed by the NITINOL wire in the hot bath (hot reservoir)

QH

endothermic heat of shape recovery, absorbed by the NITINOL wire during the
elastic contraction at constant temperature

j

S

entropy

T1

temperature of the cold bath

T3

temperature of the hot bath

AT

= T3 - TI

&TD

adiabatic temperature rise due to the heat of elastic deformation in rapidly strained
NITINOL wire

1

-

- . . .

NSWC N P 79-44l
A TM

adiabatic temperature rise due to the latent heat of phase transformation
(austenite - martensite) in rapidly strained NITINOL wire

U

internal energy

W

useful mechanical work produced by NITINOL wire during the engine cycle [mkg]

C&
T

work diagram factor (ratio of acutal diagram area to the ideal diagram area)
coefficient of linear thermal expansion of NITINOL in the transition region r°C t1

y

density of NITINOL

!A

C2

3

0.234 lb/in

I effective strain of the NITINOL wire in percent

£1

initial strain

C2

final strain

rTi

thermodynamic engine cycle efficiency

cI

Carnot cycle efficiency
at

initial stress [kpsi]

02

str-ss at the end of the straining period

03

maximum peak recovery stress

04

residual stress after the contraction (shape recovery) of the NITINOL wire

9-56

NSWC MP 79-441

"TRAINING" PHENOMENA IN NITINOL
Dr. A. D. Johnson
Energy Research Associates
Oakland, CA
ABSTRACT
It is common experience that NITINOL will not generally repeat the same cycle if it is
deformed very much in a stress-strain-temperature cycle. Clearly some of this conditioning is
due to work-hardening. But NITINOL also can develop two-way sh&pe memory under some
conditions. The loss due to hysteresis may decrease with repeated cycling, contrary to what
one would expect from ordinary work-hardening. These material changes affect engine
function, either beneficially or harmfully, and it is important to understand these phenomena
in order to engineer better engine elements.
This discussion attempts to distinguish between the various modes in which NITINOL has
been observed to condition. Experimental data will be shown from naive and "trained"
NITINOL wire. A tentative model for the "training" process will be outlined. An attempt w*Ill
be made to outline the questions which remain to be answered, and some experiments
suggested for a more general understanding of the phenomena involved.

10-1

I
NSWC MP 79-441

OVERVIEW
This report is based on a set of experiments with NITINOL wire in linear tension. Figure
I depicts the apparatus constructed for these experiments.
Figures 2, 3, 4, 5, and 6 show a sequence of operations on a NITINOL wire. Figure 2 is a
set of isotherms taken when the wire was naive. Figures 3 and 4 show successive stress-straintemperature cycles in which the tension in the wire is held constant during shape-memory
recovery. Figure 5 demonstrates that the wire length is stab!e under reduced load. Figure 6
shows that the isotherms characterizing this wire have been drastically altered; the wire has
been permanently deformed more than 5 percent and the horizontal plastic isotherms in Figure
2 have been rotated, resulting in a two-way shape memory.
Figures 7, 8, 9, and 10 are analogous, but with a significantly altered thermodynamic
cycle. In figures 3, 4, and 5, the wire did external work during shape recovery, while in Figures
8 and 9 it does no external work. Comparison of Figures 6 and 10 shows that permanent
deformation and rotation of isotherms do not result from this low-recovery-force cycle, while
Figure i I shows that the wire has not been stabilized.
Figures 12, 13, 14 show a different sequence. In Figure 13, the wire is held at constant
length during heating so that the shape recovery takes place after heating. Figure 14 shows
that this cycle does not result in rotation of the isotherms, but does induce some permanent
deformation. I inler that these are independently modifiable characteristics of NITINOL.
Figure 15 shows a set of isotherms for a wire which was first trained by running on a
continuous-band engine. There is a pronounced two-way shape memory, and -the cold isotherms
are very steeply !otated. The simulated engine cycle in Figure 16 yields a specific work output
in excess of one joule per gram per cycle.
Figures 17, 18, 19, and 20 are traces of tension versus length at constant force as
temperature is cycled. They demonstrate that the hysteresis of a NITINOL wire depends on
the thermodynamic cycle history.
From these experiments I infer that the stress-strain-temperature characteristics of
NITINOL wire in tension are critically dependent on the history of the wire sample. Three
separate effects are observed: a permanent deformation, rotation of the isotherms, and
reduction of hysteresis.

10-2

NSWC MP 79-441

INTRODUCTION AND DISCUSSION
One of the most remarkable properties of NITINOL, and another reason for our keen
interest in it as an engine element, is its behavior under "conditioning." By conditioning, I
mean any repeated stress-strain-temperature cycling which changes the physical
characteristics of the material. Most materials, when subjected to stress-strain cycling (such
as bending) which plastically deforms them, undergo some work-hardening and embrittlement.
Normally the hysteresis, that is the difference between the paths for ikicreasing and decreasing
stress and strain, increases due to piling up of dislocations in the crystal structure. This
eventually leads to fatigue and failure. Repeated bending of a copper or soft iron wire
exemplify this behavior.
NITINOL Aso undergoes work-hardening and embrittlement under conditioning, and in
some stres-strain-temperature cycles this is the most conspicuous result. For example, in the
wobble-plate test-bed built at Lawrence Berkeley Laboratory in 1975, the wires were observed
to "creep" in length until they reached a maximum. This "creep" was followed by failure
(breakage). In this case the work output per cycle diminished with each cycle.
However, NITINOL also exhibits a second behavior under certain conditions. If the
maximum stress (tension) is held below some limit, and is constant during the heating phase of
the stress-strain-temperature cycle, and if the temperature excursion goes well above and
below the unstrained TTR, then the alloy develops a second memory and the hysteresis
decreases significantly. By second memory we mean the alloy has two normal shapes: one to
which it returns when heated; a second to which it goes when cooled. It will now do significant
work when either heated or cooled, although the work done during cooling is only about 10
percent of that available during heating. The fact that the hysteresis decreases indicates that
fatigue, in the ordinary sense, is eliminated. This means NITINOL subjected to an appropriate
conditioning cycle will repeat that cycle indefinitely. Furthermore, the amount of work
available per cycle may be significantly increased compared to that of the naive sample.
These characteristics are of extreme importance in engine design.
This behavior was observed accidentally in early continuous-band engines anj in the
Banks engine. In these engines, performance improved as the NITINOL wire "learned" under
repeated cycling; therefore we gave this the name "training." It appeared that the wire in
these engines always adapted to the cycle given it, as if it were capable of modifying its own
behavior. We now realize this adaptation takes place only under limited and not completely
understood conditions. We now prefer to reserve the word "training" for a conditioning
program which results in a) a pronounced second memory, b) stability, so that a given cycle
may be repeated indefinitely, and c) reduced hysteresis, so that the work output per cyc~e is
comparable to or greater than that for a naive wire. Thus a trained wire is suitable for
designing a NITINOL engine, since it has known characteristics which may be expected to
repeat, and which are desirable for optimization of design.
10-3

II

NSWC MP 79-441

This definition specifically excludes processes which in sum lead to a non-repeatable
cycle behavior and/or in which the ability of the NITINOL is seriously impaired.
This phenomenon has been made clearer by the research of Cory 1 , who started in 1975 to
make x-y plots of complete stress-strain cycles. He observed that the flat region of the
stress-strain curve of naive (freshly-annealed) wire develops a slope as the material is cycled.
He interpreted this as being due to development of internal stresses through work-hardening.
Rotation of the stress-strain curves can result in negative external forces (stresses), which is a
way of characterizing the second memory. At the same time the hysteresis--the distance
between increasing and decreasing isotherms--is diminished. That contradicts the theory that
these internal stresses are simply due to accumulation of dislocations in the crystal structure.
It now appears that at least two separate phenomena are at work in the training of
NITINOL. The first is normal work-hardening, or creep, or fatigue. Th-s second is more
subtle, and probably closely associated with the memory property of NITINOL itself. We have
tried to visualize a model for this process in terms of the martensite-austenite transition. This
model seems to account for all the observed phenomena and makes some predictions which can
be tested.
The behavior of a real sample of NITINOL is a complicated function of its cycle history.
First, recovery, even of small deformations, is imperfect, at least in freshly annealed alloy.
Second, the NITINOL in a wire helix which is repeatedly cooled, stretched, heated, and allowed
to contract adapts to the cycle to some extent. After several thousand cycles, the helix
elongates when cooled even in the absence of external force. Such a "trained" wire will not
quite recover to its annealed length, but has now two natural or unconstrained lengths: one for
each of its two phases, hot and cold.
The mechanism for this two-way shape memory is not well understood. I have speculated
tha ,. . results from martensitic platelets which are trapped during the transition to the hightemperature phase, and release some of their trapped energy when most of the wire transforms
to the martensitic form. This very tentative explanation requires introduction of the concept
of stress-induced martensite.
We have referred to the phase transition as if it took place at a specific temperature.
Actually, even when there are no external forces, the transition is gradual over a temperature
range of as large as 30 degrees C. This is explainable as due to the inhomogeneous nature of
the crystal structure. NITINOL does not exist as single large crystals. It Is a mass of more or
less randomly oriented crystal domains of a few micrometers in extent.

For any particular

deformation, only a small fraction of the martensite platelets are favorably oriented to
accommodate the deformation by the migration of twinning boundaries,
Those not so
favorably oriented distort or move so as to minimize the total energy. A wire swaged and
drawn from a billet will have large intcrnai stresses not completely :elieved by annealing.
These stresses may exhibit themselves, when total energy is minimized, by creating domains
which are not truly of the same phase as the majority of the sample. There may be islands of
martensite in the high-temperature phase, and vice-versa. Another way to say this is that

13. S. Cory, "NITINOL Thermodynamic State .urfaces," 3ournal of Energy, Vol. II, No. 5,
September-October 1978, pp. 257-258.
Full report is National Technical Information
Service #N78-31206, "Engineering Data and Correlations," Springfield, VA.

10-4

""~~

~ ,,,r, ~_

'

AM

NSWC MP 79-441
NITINOL, between certain temperature limits, always exists as a mixture of the two phases.
rurthermore, it is possible to generate or to enlarge these foreign domains through stress.
When parent or high-temperature phase NITINOL is stressed, the islands of martensite created
the energy-minimization process are called
eby stress-induced martensite. This is partially a
misnomer, since there is o intrinsic difference between these platelets which
appear as a
result of stress and those which result from the phase transformation except for a preferred
orientation. In fact, it is not possible to separate the external forces from the internal. ' he
forces exerted upon a given domain in the interior of a sample of NITINOL are the sum of
internal and, to a lesser extent, external forces. And these internal forces may be a function
of temperature, as the phase change takes place.
It is necessary to consider all the thermodynamic variables, in this case stress, strain,
and temperature, in describing the state of a sample of NITINOL. This was not appreciated by
some early critics of the NITINOL engine effort, who argued that the transition takes place
over a limited temperature range, that this is the only range which contributes to work output,
and thus that the Carnot efficiency is extremly small. One may see the folly of this argument
by applying it to the steam engine. Since the boiling point of water is exactly 100 degrees C,
such an engine must have zero Carnot efficiency. The flaw in the argument is that there is no
fixed traasition temperature for water: The vaporization temperature is a function of pressure
and temperature. The same is true for NITINOL, but the variables are stress and temperature,
and the NITNIOL is also inhomogeneous so there is a spread in transition temperature (a
mixture of high-temperature phase and martensite phase) at any given stress level.
The analogy to the steam engine is useful in describing the stress-strain-temperature
cycle in the NITINOL engine. In a clor'd-cycle liquid-vapor heat engine, the working fluid is
allowed to expand at constant pressure during which it takes in heat. Then it is cooled at
constant volume so that the pressure is reduced.
Next, it is further cooled so that it
condenses, and the volume greatly reduces. Finally, it is heated at constant volume so that the
pressure increases. As this cycle is repeated, the area traced out is the useful work done by
the system. In the NITINOL engine, the role of the working fluid is assumed by the NITINOL,
pressure is replaced by stress cn the NITINOL, and volume of fluid becomes strain in the
NITINOL. With these substitutions, the NITINOL cycle is: Heat the NITINOL wire so it
contracts and does work externally; reduce the stress at this temperature; cool the wire under
constant tension; stretch the wire under constant temperature and stress; increase the stress
so the strain increases further. Then repeat the cycle. Both these cycles are, of course, highly
idealized cases and could not be achieved precisely in practice. But they serve to illustrate
the excursion in temperature and stress to which the NITINOL working material is subjected.
Figures 3-5 show examples of this cycle.
What happens internally as the NITINOL is subjected to this cycle? As it is cooled at
constant stress, and consequently elongates, new martensite plates grow from the "seed"
martensite which exists because the metal is a mixture. The growth is preferential in a
direction which most easily accommodates the elongation.
This is required by the
minimization of energy. At the end of the constant-stress part of the cycle, the wire is mostly
martensite, and the martensite platelets have a preferential orientation. When the plastic
deformation is complete, the strain increases further as the stress increases further to the
point in the cycle where there is maximum stress and maximum strain. As heat is applied,
parent or high-temperature phase grows, again preferentially. Some of the more favorably
oriented martensite platelets remain in the matrix of parent phase.

10-5
'

lO-

I"

NSWC MP 79-441
At the point in the cycle where contraction at constant stress ceases, some platelets thus
remain, the ones oriented favorably to elongation of the wire. Next the stress is decreased.
The matrix of parent phase tightens around these platelets, but some will remain because they
cannot deform so as to become parent phase. These become distorted by forces exerted by the
parent phase. One may visualize them as tiny bubbles which have become trapped and cannct
escape, but are compressed, and hence have internal stored energy. They cannot relax because
they are bound by the constraining matrix of parent phase. However, when the wire is cooled,
martensite is allowed to form, and it forms again preferentially beginning with these trapped
"seed" platelets, as the wire converts to mostly martensite. But the martensite no longer binds
the compressed bubbles or compressed martensite platelets: Their energy now may be released
by motion of twinning boundaries. These trapped platelets are oriented to be intheir lowest
energy state when the wire is elongated. Therefore they push out along the wire and cause it
to elongate. This seems to explain how a "trained" wire may have a second memory, and how
it reverts to the cold shape without application of external forces. The cold memory is a
response to internal rather than external forces.
quantNext, I shall describe an experimental program to test some of these ideas, and to get
quantitative information on the first few training cycles.
EXPERIMENTAL PROGRAM
Before one can design an optimal NITINOL engine, one clearly needs detailed knowledge
of the characteristics of the material to be used.
Data taken on naive wire are not
satisfactory, for it has been the ex:perience of everyone that NITINOL changes character as it

iscycled. One should therefore measure the properties of NITINOL after it is trained so that a
cycle is repeatable. But how can one best achieve a repeatable cycle? It is necessary to start
at the beginning, with naive NITINOL, and develop some data as it is cycled.
For this study, I chose wire in tension, since in this form one should see the effects of
training in purest form because all elements of the wire cross-section are deformed equally.
Three distinctly different cycles were selected for this exploratory work. First is
a cycle which closely approximates that of the thermo-turbine or continuous-bantd engine
(Fig. 16). In this cycle the wire contracts as it is heated at constant force. We designate this
the constant-force cycle. Second, a cycle in which contraction is against very small force so
that the wire does minima' work while being heated. This we call the low-hot-force cycle (Fig.
8). Third is a cycle inwhich the wire is constrained at a fixed length while itisheated. This
we call a fixed-length cycle (Fig. 13).
The experimental stress-strain fixture (Fig. 1) was constructed to take the necessary
measurements. A NITINOL wire is suspended inside an insulated tube through which water is
circulated. Two pumps and two reservoir3 permit switching from hot to cold baths by means of
valves. Tension in the wire is measured by a load cell and used as input to the y-axis of a
Mosely two-axis recorder. Length change is determined by a lead screw attached to a
potentiometer, the variable voltage is used as x-axis input. Alternatively, the lead screw may
be disengaged and wire elongation measured by a potentiometer coupled to a pulley over which
a cable runs from the NITINOL wire to a weight. This arrangement is used for fixed-force
measurements.

10-6

NSWC MP 79-441
A sample of NITINOL wire may be characterized by a set of stress-strain isotherms
which lie on state surfaces as defined by Cory. 1 Isothermal state surface measurements are
shown in Figures 2, 6. 7, 10, 12, 14, 15. Differences between these measurements are due to
the differences in conditioning. All except Fig. 15 were taken fron, a single piece of wire
after annealing In an air oven for about one-half hour at 570-580 degrees C.
First consider freshly-annealed samples of wire measured in Figures 2, 7, and 12. These
were taken from Timet heat V-4609 and obtained from Charles Raymond. Starting at zero
force, with the wire pre-heated to 90-95 degrees C, each isotherm is drawn by increasing the
elongation in stages of about one-quarter percent with pauses of a few seconds after each step.
This results in vertical dips as the wire sags due to a slow component of the transformation.
This phenomenon seems not to have been observed by other researchers who elongated at a
constant rate. I believe it significant that the bottoms of these dips or sags lie on an almost
perfectly horizontal line, indicating nearly perfect plastic deformation.

f

The first isotherm, at 6 degrees, is located at considerably greater stress than the
second, at 10 degrees. This has been observed by other researchers., It
is
of
interest,
however, that after stretchin&Lthe wire in the first pull at 6 degrees, this cycle cannot be
repeated (see pulls numbered % in Fig. 2, OZ in Fig. 7). Even one pull on the naive wire has
partially conditioned it.
Figures 3 and 4 record the first 14 constant-force cycles to which this naive wire was
next subjected. After an initial stretching of more than 5 percent, which the wire retains as a
permanent deformation, the cycle approaches a repeatable cycle asymptotically.
For the next set of data, the maximum force was reduced from 45 to 35 Newtons. Fig. 5
records cycles 15 through 21. The irregular variation along the rigit-hand side, where the
force is applied in three steps by adding weights, results from very small variations )n coldreservoir temperatures. The remainder of the cycle is seen to be very nearly repeated,
indicating this wire had been stabilized at this stress-strain-temperature cycle. This is an
important result. It demonstrates that NITINOL may be pre-conditioned for use in a specified
engine cycle.
Fig. 6 shows the isotherms measured on this wire after these 21 cycles. A two-way shape
memory of about 3/4 percent has developed, and the isotherms have been rotated so that they
are no longer horizontal. The alloy characteristics are dramatically modified.
Figures 7-10 show similar curves for a sample taken from the same annealed wire, but
subjected to a low-hot-force cycling. Fig. 10 is particularly interesting compared to Fig. 6.
They aredearly very different, and 10 is similar to that for the naive wire. I conclude that
the two-way shape memory and rotation of isotherms, which I associate with training, do not
occur unless the wire does work while it is being transformed. Fig. 11 shows this sample has
not been stabilzed.
The sequence of Figures 12-14 shows what happens to a wire under constant-length
cycling. Fig. 13 demonstrates that this wire, initially stretched to 4 percent and then heated
at constant length, does considerably less work on the twelfth cycle than on the first. This
corroborates data taken by Hernandez et al. 2 Fig. 14 shows this wire has not been trained by
this fixed-: ngth cycle.
ISee footnote I on page 10-4.
2 H.

P. Hernandez, R. M. Banks, D. Norgren, "NITINOL Test Bed Engine" Lawrence Berkeley

Laboratory, Berkeley, CA (1975).

10-7

I

I_

_

NSWC MP 79-441
Finally, as an example of a more fully-trained wire, Figures 15 and 16 show the
isothermal state surfaces measurement and constant-force cvcle for a wire which was run on
an engine for several thousand cycles during which it was elongated 3 percent each cycle.
Temperatures and forces were not recorded, however. This wire shows a two-way shape
memory of nearly 3 percent, and extremely rotated isotherms. In fact, the ascending curves at
low temperatures (traces at 2, 6, and 10 degrees C) are nearly as steep as the hightemperature curves at 60 to 90 degrees. One might describe this sample as having two elastic
regions, at high and low temperatures, and two corresponding unconstrained lengths.
Fig. 16 shows that this wire is stabilized up to a force of 100 Newtons (25 KN/cm 2 ),
at this stress level is capable of doing at least a joule per gram per cycle of work.

and

For us to look at the state surfaces in the temperature versus length projection, a
thermocouple measured the temperature, recorded as displacement instead of force. Figures
17 through 20 measure temperature versus length at constant force. The first two plots are
taken from the highly-trained wire whose isotherms are shown in Fig. 15. Figs. 19 and 20 are
for the nearly-naive wire whose isotherms are in Fig. 12. The state-surface boundaries are
separated by approximately 18 degrees C for the trained wire, and by more than 30 degrees for
the untrained wire. From this I conclude that training decreases the hysteresis of NITINOL
wire n tension.

CONCLUSIONS FROM THE EXPERIMENTAL RESULT
1. Anything done to NITINOL conditions it. It is virgin only once.
2. NITINOL can be trained, i.e. given a two-way shape memory, a stable and repeatable
cycle, and reduced hysteresis, in a few cycles.
3. Rapid training does not occur under certain conditions, for example, in a cycle which
does no external work.
4. A slow (several seconds) component of deformation, especially at low temperatures,
diminishes with nearly all kinds of conditioning.
5. Work available from a naive cycle may be larger than for a trained cycle. 3ut since
no wire remains naive in an engine cycle, it is more relevant to study trained wires. These
have been shown capable of doing a joule per gram per cycle of external work.
6. Although some questions regarding training of NITINOL wire in tension have been

resolved, a number remain.

Needed are studies which range over the variables:

force,

elongation, temperature, and number of cycles of a particular type. So far we have neglected
consequences of differing metallurgy. This study has established only a few points in the
continuum of each variable. It would be useful to measure stress versus strain at negative
external force in order to better characterize the two-way memory.
7. The picture of training given by the concept of trapped martenisites seems compatible
with all the observations. This theory predicts other consequences which should be decided by
experiments.

10-8

V
g. I differ with Cory's conclusion in that training is strictly a matter of maximum
deformation. In particular, stress-strain isotherms for a highly-trained wire are not simply
rotations of those for a naive wire. And the hysteresis for a trained wire is less than that for a
nave wire, indicating that some process takes place besides simple work-hardening.

19

I

10-9

NSWC MP 79-441

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NSWC MP 79-441

FRESHLY - ANNEALED RAYMOND - IMET WIRE 0.018" x 20" LONG (0.7 9mn)
CONSTANT - FORCE CYCLES: 16-211
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BIBLIOGRAPHY

H. P. Hernandez, R. M. Banks, D. Norgren, "NITINOL Test Bed Engine" Lawrence Berkeley
Laboratory, Berkeley, CA, (1975).
3. S. Cory, "NITINOL Thermodynamic State Surfaces," 3ournal of Energy, Vol. II, No. 5,
September-October 1978, pp. 257-258. Full report is National Technical Information Service
#N78-31206, "Engineering Data and Correlations," Springfield, VA.

II
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I
NSWC MP 79-441

REPRESENTATION OF MARTENSITIC TRANSFORMATION IN SHAPE
CHANGE SPACE, THE NATURE OF INTERNAL STRESS RETAINED DURING
SM TRANSFORMATION, AND OPERATIONAL PERFORMANCE OF A
SIMPLE NITINOL ENGINE
K.H.G. Ashbez and B. Cunningham
University of bristol (England)
H.H. Wills Physics Laboratory
ABSTRACT
Martensitic transformations can be described geometrically in space defined by the
principal strains. The condition for coherence between matrix and product phases, and details
of microstructures can all be stated in geometrical terms. The case of transformation from
cubic to orthorhombic or tetragon crysta structure features in most shape memory
transformations and is described in detail. Retention of internal stre! during transformation
gives rise to features characteristic of shape memory behaviour. The nature of this internal
stress, including differentiation between stress associated with elastic and that associated with
plastic deformation, ',as been studied for one shape memory alloy by using Kossel X-ray
diffraction in a scanning electron microsope. Operational experience, including measurements
of power to weight ratio, is described for a simple NITINOL engine.
1.

INTRODUCTION

For all known shape memory (SM) alloys, the transformation is from low crystal
symmetry at low temperature to higher crystal symmetry above the transformation
temperature range, the low symmetry phase consist of Laves pseudo-twins 1 , and application of
mechanical constraint at temperatures below the transformation is accommodated by
redistribution of the relative proportions of the different twin orientations permitted by the
crystal symmetry. After the deformed low temperature phase is heated, transformation to the
high symmetry crystal structure first requires reversal of the redistribution of the relative
proportions of different twin orientations. Recovery of the original shape, i.e., the shape
memory phenomenon, accompanies this reversal. Martensitic transformations are conveniently
analysed using the concept of shape change space. To illustrate one application of this
concept, the commonly occurring shape memory cases of partial transformation of a cubic
crystal to a crystal having orthohombic crystal structure and to a crystal having tetragonal
crystal structure are presented here.
InL, ial stress is believed responsible for the reverse shape memory effect exhibited by
some alloys and for the apparent dependence on sign of externally applied stress of changes in
transformation temperature.
Scanning electron microscopy with in situ Kossel X-ray

1 Laves,

F. Acta. Met. 14 (1966) 58.

NSWC MP 79-441
diffraction offers a direct method for investigating elastic and plastic strain during stress and
temperature cycling, and is used here to study a single crystal of Cu - 14.1 wt% Al - 3.0 wt%

Ni.
Several inventors have exploited the SM effect to transform low grade heat into useful
mechanical work. One of the simplest, built by Frank and Ashbee, 2 consists of an inch of leafspring, an inch of NiTi wire, a three-inch rod, another inch of NiTi wire, and another inch of
leaf-spring in the same plane as the first and joined in a straight line. This assembly is bent
into an S-shape and outer ends of the leaf-springs are fixed into slots in two pieces of metal
mounted four inches apart on the axle. The axle rests across a dish of hot water. When either
NiTi bend dips into the water, it stiffens and straightens a little. This increases the bend of
the other and displaces the centre of gravity of the whole assembly, so that it rocks over and
second so long as the water is above the transformation temperature (-600C). Various versions
of this engine have been given a work load and measurements of work done are presented here.
2.

TRANSFORMATION OF A SINGLE CRYSTAL BY A HOMOGENEOUS STRAIN

The martensites associated with shape memory are all cube-related martensites. For
algebraic simplicity, we confine our attention to these, although the principles presented here
are quite general and apply equally well to monoclinic martensites. Since the martensite is
cube-related, the axes of the ellipsoid of deformaton are parallel to the crystal axes of the
(orthorhombic or tetragonal) product phase.
2.1 THE CONDITION FOR COHERENCY

A sphere in the parent phase transforms to an ellipscid in the product phase. The lines of
intersection between these two figures are two non-planar closed loops (Figure 1). Radii from
the origin to the loops represent directions of identical length in parent and product. In the
general case no plane through the origin, and intersecting the loops, contains three non-parallel
constant length directions. Hence, in general, there can be no plane of coherence between
parent and product. To comply with the theorem that a plane of coherence (twinning plane in
the case of orientation twins, habit plane in the case of transformation of austenite to
martensite) contains three non-parallel constant length directions, it is necessary and
sufficient for one principal strain to be zero. The lines of intersection between sphere and
ellipsoid are then circles (Figure 2), and define two orientations for the plane of coherence.
In the general case, and in the special case of one principal strain equal to zero, the lines
of intersection (non-planar loops and circles, respectively) define the orientations of constant
length directions in the ellipsoid. These same constant length directions come from other radii
in the sphere.
Rayleigh defined shear (meaning pure shear) as deformation at constant volume and with
one principal strain equal to zero. For the sphere to ellipsoid transformation sketched in
Figure 3 (a), the "no volume change" condition locates the constant length directions in the
sphere; the two discs of radii, angle 6 apart in the ellipsoid, were formerly the two discs of
radii, angle 0 apart in the sphere, 0 = e and transformation between locations in the sphere and
locations in the ellipsoid is by way of "scissors" action (Figure 3(b)), hence the name "shear."
The martensite coherency criterion is evidently more general than the criterion for pure shear
since 0 k .
2Frank, F. C. and Ashbee, K. H. G. Spectrum 132 (1975) 1.

11-2

NSWC MP 79-441
2.2 GEOMETRICAL REPRESENTATION OF MARTENSITIC TRANSFORMATION
This problem is conveniently analysed geometrically by using F.C. Frank's concept of
shape change space 3 ,4 , i.e., space defined by the principal strains El, 2, E3.
Consider the
general case. The strain tensor can be rotated to the principal axes, giving rise to three
principal strains and hence to 31, i.e. six, different orientations for the shape change. Six
points, each representing the state of strain coresponding to one of the iix alternatives, define
the apeces of a polygon. The polygon has cubic symmetry only if the unit cell diagonals for
both parent (austenite) and product of transformation (martensite) are < I I(0> directions.
Consider transformation of the cubic lattice parameters al, a2, a 3 to the ortnohombic
lattice parameters a, b, c. If al transforms to a, a 2 can transform to either b or c and
a3 to either c or b. This gives rise to three different orientations for the product phase, i.e. to
three different sets of lamellations. On the other hand, al could transform to either b or c
arid, when the combinations for these alternatives are considered, six different orientations
exist.The principal strains corresponding to the transformation a, - a, a
C1 =..

a

E2

S-aa

= b - a

E

C

a

c

= c

£3

c,

b, a3

c are

- a C

C~a

ac

c

where ac (=al =a 2 =a3) is the lattice parameter of the parent cubic phase. Let these principal
strains be denoted A B C after the lower case letters a b c in the respective numerators. The
full complement of six sets of principal strains corresponding to the six different orientations
is then
ABC, ACB, BCA, BAC, CAB, CBA
In -1 E2 E3 - space, the points defined by these co-ordinates occur in pairs on a plane parallel
to the (11) plane and are the apeces of a hexagon with trigonal symmetry, the orientation of
which depends on whether one or two of the principal strains is positive (Figures 4(a) and (b)).
The height of the hexagon above the origin is a measure of the volume change. If there is no
volume change (the case of mechanical twinning) the hexagon passes through the origin.
The principal strain, £

= a - ac

a

=

c

c

a
a

-1

c

a aa
The corresponding true strain, c

da =log (a T
a
c

-

since loge (+x)

3 FrAnk, F. C. Rev. Geophys. 3 (1965) 485.
4 Cunningham, B. and Ashbee, K. H. G. Acta. Met. 25 (1977) 1315.
11-3

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NSWC MP 79-441
The dilationAis the sum of the principal strains
) since the sum of the logarithms is equal to the
2 + 3 = ,loge (
logarithm of the product. Thi- is the equation to a plane which F. C. Frank calls the
A-plane. The net strain is defined by a vector c from the origin which just touches the
A-plane. t completely describes the shape change
=E

+

_ loge (U + 1) + Loge ( + £2) + loge (1 + £3)
loge (1 + c) (1 + £2) ( + £3)
The volume change associated with the transformation is c_.e, where e is unit vector (1,1,1,).
Perfect shape memory behaviour demands that the transformation be truly elastic.
Otherwise, accumulation of emissary dislocations accompanies repeated transformation, and
this in turn eventually gives rise to fatigue. Truly elastic transformaton implies coherency
between matrix (parent) and product. Although orientation twins of each other, the differently
oriented alternatives the product phase are not twin-related to the matrix. However, the fact
that by virtue of coherency they bear a special geometrical relationship with the matrix
prompted Lavesi to call them pseudo-twins.
Vectors to the corners of the hexagon in Figure 4 (a), for example, represent shape
changes brought about by transformation to a single pseudo-twin. Vectors to points on any line
connecting two apeces of the hexagon represent shape changes brought about by a combination
of two pseudo-twin orientations, e.g. combinations of ABC and CBA for points on the line
between these two corners. These two twins have identical principal strain parallel to the
orthorhombic b - axis, i.e. they have the orthorhombic (10 + 1) plane in common as sketched in
Figure 5. One principal strain identical is the condition for so-called normal twinning, i.e.
coincidence of composition plane and twinning plane. Note also the special points labelled of
which there are three sets of four. For each such point, one principal strain equals zero, i.e.
coherence exists with the parent. All points other than these special points represent shape
changes for which no twin is coherent with the parent. For each principal strain equal to zero,
two such special points give rise to the two alternative coherent microstructures sketched in
Figure 6.
For some shape memory alloys, the transformation is from cubic to tetragonal.
Transformation of the cubic lattice parameters al, a2, a3 to the tetragonal lattice parameters
alt, a2t, c can be accomplished in only three different ways. The triangle defined by the
corresponding three sets of co-ordinates is, for c>alt = a2t, differently oriented with respect
to the A-triangle from the way it is for c<alt = a2t (Figure 7). By the same token, there are
two cases for the special points (o).

*

In Figure 4 (a), again, for the two points labelled P one principal strain equals zero. Each
may be realised by a combination of any two points labelled x and, since each of the latter is
realised by a mixture of two special points (o), it follows that a point P represents a shape
Figure 8 sketches the resulting
c-hange achieved by a mixture of four pseudo-twins.
microstructure. Mixtures of all six pseudo-twins are also possible.
Finally, the origin in Figure 4 (a) represents the cubic parent phase. Points lying within
the pyramid formed between the origin and the hexagon represent shape changes that involve
mixtures of untransformed and transformed material.
ISee footnote 1 on page I1-.

11-4

NSWC MP 79-441
3..

NATURE OF THE TRANSFORMATION:
Application of scanninR electron microscopy with in situ Kossel X-ray diffraction
If the transformation is reversible, the effect of stress on transformation temperature

t

A~cI

~aT
ac

=AS

..................

where Ac and AS, respectively, are the associated strain and entropy changes. aT
is
expected to be independent of sign of the applied stress. The fact that, for at least five
3T

-_ t~nsile
alloys, 80

aT

(Table I in ref. 4) is cause for concern.
si
cm
compressive

Another unexpected feature is the so-called reverse shape memory effect.
Phenomenologically, the shape memory effect is characterised by the existence of a preferred
shape above the transformation temperature. However, some alloys exhibit a preferred cold
shape as well as a preferred hot shape, giving rise to reverse shape-memory behaviour. The
preferred told shape is attributed to retention of internal strain. If, for some microstructural
reason, internal strain complements externally applied stress of one sign, it might also be
possible to account for the anomalous difference between the effects on transformation
temperature of tension and compression tests.
3.1 ELASTIC AND PLASTIC DEFORMATION DETECTED IN KOSSEL X-RAY
DIFFRACTION PATTERNS
The SME in several alloys has been examined using a conventional scanning electron
microsope, with situ Kossel X-ray diffraction facilities. The incident electron beam is focused
onto the specimen and generates KC, X-radiation characteristic of the alloy. These are Braggreflected into a photographic plate positioned for back reflection. Intersection of the X-ray
cones with the film results in Kossel lines shown schematically in Figure 9. Precision ball
bearinigs located between the specimen and film cause sharp elliptical shadows to be cast
on the film, intersection between the major axes of which defines the film centre after
which only simple geometry is needed to determine the specimen-to-film distance.5
Subsequent measurement of the co-ordinates of the Kossel lines permits lattice spacings to be
calculated with an accuracy of 1 in 104
A homogeneous elastic strain, such as might be
produced by thermal expansion, manifests itself as a change in lattice parameters and is
readily detected if greater than 0.1%. Inhomogeneous elastic strain, such as that which would
accompany a distribution of dislocations, amounts to the presence of local variations in lattice
parameters anc causes broadening of Kossel lines.
Stress-induced martensitic transformation has been studied in a scanning electron
microscope using a disc-shaped single crystal of Cu - 14.1 wt %, Al - 3.0 wt% Ni (characteristic temperatures MS- 30C, MF - I OC, AS- 15°C, AF 20 0 C) stressed in situ by axially
loading whilst supported at its rim. The sequence of Kossel photographs in Figure 10 shows the
effect on the Kossel pattern of increasing the applied load. The numbers quoted for axial
Biggin, S. and Dingley, D. J. J. AppL. Cryst. 10 (1977) 376.
4 See

footnote 4 on page 11-3.

11-5

NSWC MP 79-441

I!
stress and strain corresponding to the known values of axial load were calculated using A.E.H.
Love's formula 6 for deformation of an indented plate, and are strictly applicable only while the
alloy is undergoing Hookean elastic deformation. When non-linearity (pseudoelasticity) sets in,
the numbers are only a guide to the magnitudes of axial stress and strain. The sequence of five
Kossel patterns clearly demonstrates the progressive break-up of a triple intersection between
two (I10)Cu and one ( 2 00 )Cu diffraction lines.
At 2% axial strain, the point of triple
intersection has changed to three points of intersection. At 3% axial strain, the individual
lines have obviously broadened. They disappear completely at 4% axial strain, and reappear as
diffuse lines (not nf cubic phase but of the product of transformation) at 6% strain. This
sequence is interpreted as direct evidence of lowering of the crystal symmetry whilst
accommodating elastic deformation in the range 02% axial strain, followed by generation of
emissary dislocations the presence of which gives rise to the line broadening and subsequent
masking of Bragg diffraction, and then partial recovery of low dislocation density crystal at
the time of transformation. Figure II (a) and 11 (b) show scanning electron micrographs of the
surface before and stressinduced martensitic transformation. When the stress is released
(Figure 12), the crystal does not exactly revert to the original microstructure. Figure 13 is a
Kossel pattern taken from the cubic phase after removing the stress. Some line broadening
and therefore residual plastic strain is present. This residual strain is believed to be the origin
of the reverse shape memory.
4.

THE FRANK-ASHBEE ENGINE

Frank and Ashbee 2 demonstrated that the shape memory effect can be used to displace a
rigid beam which, under the action of gravity, causes a useful mechanical displacement. That
is reversed either as the result of a pendulum action in the case of a single element engine or
as the consequence of an opposite displacement in the case of a two element engine. If an
analogy can be drawn between this engine and the beam engine of Newcomen, efficiencies of
about 2% are expected.
Several different variations of the basic rocking engine have been built. One incorporates
a valve-less water pump and this has pumped 1.8 kg water per hour through a height of 5 cm,
i.e. it does 0.88 joules of useful work per hour. The two strips of NITINOL working element in
this engine weigh a total of 0.318 gm, so the power to weight ratio is 0.8 watts per kg. By
mounting in bearings the common axle of a group of four basic engines, a rotary version has
been developed which, when coupled to a generator, delivers sufficient electricity to barely
illuminate a light emitting diode rated at 50 mA, 1.5V. The NITINOL elements of this engine
weigh 13.51 gm and the power to weight ratio is a little under 9 watts per kg.
4.1 EFFICIENCIES
It is difficult to quote effiriencies. The Carnot efficiency is
= Af (a)-

Mf (a-'o)
Af(a)

GLove, A. F. H. "The Mathematical Theory of Elasticity" 4th ed.
Cambridge University Press (1959) 475.
2See footnote 2 on page 11-2.
11-6

I
J

NSWC MP 79-441
where Af and Mf, respectively, denote the temperatures for finish of transformatioR to the
high temperature phase (austenite) and to the low temperature phase (martensite).
Af ()

A (a= o) +odAf

dor
and re-writing Equation I using this new notation shows

dAf

A

do

ES

Ae and AS are both measurable quantities. However, there exist the possibility of precursory
effects and hence the possibiiity of smearing of experimental measurements. There is no
possibility of precursory effects on A c in the cubic phase. However, in say an orthohombic
product phase, a range is possible of orthorhombic axial ratio, as might arise in a polygranular
material from differently oriented crystals being differently stressed. Figure 14 sketches the
anticipated axial ratio versus temperature relationship. AS precursories are possible in both
phases.
In the absence of reliable A e and AS data, it is necessary to resort to experimental
measurement of the slopes of transformation temperature versus stress relationships. This has
been done for several shape memoty alloys and, taking cognizance of the fact that there is a
maximum useful value of a beyond which perfect shape memory behaviour is destroyed, Carnot
efficiencies approaching 20% are predicted.4
The efficiency realized in practice is also difficult to measure. This is because the heat
input is not known with any accuracy.
The specific-heat anomaly associated with the
transformation suffers from the same precursory effects described above for the entropy
change. Superimposed on this, there appears to be a latent heat of transformation, i.e. shape
memory behaviour appears to involve a combination of first and second order
transformations. 7 Delaey 8 and co-workers claim to have reproducibly measured tha
thermodyaamic parameters involved in the transformation of Cu - based alloys and find that
the useful efficiency is about 3%.
4.2 OPERATIONAL CHARACTERISTICS
Since the axis of rotation is above the water level (hot source), the working elements
spend more than half of the period (T) of oscillation (or rotation) cooling down. Forced
cooling, by blowing cold air across the cooling elements, markedly reduces T. The use of oil

4 See

footnote 4 on page 11-3.

7

Cunningham, B. Ph.D. Thesis. Univ. of Bristol (1979)

8

loc. cit.
11-7

NSWC MP 79-441
instead of water as the heat source increases T, presumably because evaporation no longer
assists the cooling. Small increase in section of the working elements has little effect on T or,
for that matter, on the output energy. All of these observations point to the importance of
heat transfer.
The heating time (t) for a cross-section of wire is
2
tr

Lwhere r = radius of wire anda = thermal diffuscivity. a is given by:
a= k
pc
where k = thermal inductivicity, p = density and c = specific heat capacity. Inserting published
values of the above parameters gives a heating time of 2Ysecond for NITINOL wire of 1 mm
radius. One engine, a reciprocating version of the Frank-Ashbee engine, has been studied with
slow motion replays of cine films taken whilst working under various operating conditions. A
sequence of eight stills is reproduced in Figure 15, from which it is evident that a time lag
of -Y secondl. exists between entry into the water bath and transformation of the heated
element. Since t is proportional to r 2 , consideration of heat transfer is evidently important
when scaling up.
If the temperature of the water is above Af (amax), the energy input will include heat
absorbed by the high temperature (parent) phase over and above that absorbed by
untransformed parent. It has not been possible to estimate either of these quantities.
Development of working models of the Frank-Ashbee engine has revealed the very large
advantage of using roller bearings in preference to fixed bearings. It has also proved to be
worth exploiting the fact that the basic engine rocks at its natural frequency.
This work was supported by a British Gas Research Scholarship awarded to one of us
(B.C.). The Cu-AI-Ni SM crystal was kindly provided by Mr. Larry Shepard, Army Materials
and Mechanics Research Center, Watertown, Massachusetts 02172, U.S.A.
The authors acknowledge technical assistance from H.N. Young who built the engines.

11-8

i

I

NSWC MP 79-441

"%

i

/1

FIGURE 1

LOOPS OF INTERSECTION
ILLUSTRATING THE GENERAL CASE OF NON-PLANAR
TO WHICH IT
ELLIPSOID
THE
AND
BETWEEN A SPHERE IN THE PARENT PHASE
PHASE
TRANSFORMS IN THE MARTENSITE
11-9

NSWC MP 79-441

'001I
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FIGURE 2

TO ONE OF
THE SPECIAL CASE OF FIGURE I CORRESPONDiNG
STRAINS EQUALS ZEcRO

THE PRINCIPAL

NSWC MP 79-441

FIGURE 3 (A)

SPHERE TO ELLIPSOID TRANSFORMATION

NSWC MP 79-441

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NSWC MP 79-441

ElI
EINCREASING FROM ZERO

AC13

ABC/

ElINCREASING FROM ZERO

/E2

E3

EINCREASING FROM ZERO

FIGURE, 4

SHAPE CHANGE SPACE REPRESENTATION or MARTENSITIC TRANSFORMATION BETWEEN
CUBIC AND ORTHORHOMB31C STRUCTURES (A) FOR ONE PRINCIPAL STRAIN POSITIVE

11-13

NSWC MP 79-441

El1

ICEAIN
ZERO
FROEAIN

ZER

WOBCf
ACM

CABC

BCAA

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FIGRE

INCREASING FROM ZERO

SHPCA*1
ERSNAINO

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CUBIC AND ORTHORHOMBIC STRUCTURES (B) FOR TWO PRINCIPAL STRAIN POSITIVE

11-14

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NSW- MP 79-441

101

FIGUE 5

OF TWO
CHEMATIC REPRESENTATION
PLANE IN COMMON

TWINS HAVING THE ORTHORHOBIC

(10 ~1

NSWC MP 79-441

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MICROSTRUCTURE RESULTING FROM A MIXTURE OF FOUR PSEUDO-TWINS

11-18

NOWC MP 79-441

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NSWC MP 79-441

(110)cu

(200)

2% STRAIN

0% STRAIN

44
Ak
4% STRAIN
3% STRAIN

6% STRAIN

FIGURE 10

SEQUENCE OF KOSSEL PATTERNS SHOWING EFFECTS OF INCREASING STRESS

11-20

i

NSWC MP 79-441

50$

FIGURE 11

N
OF A Cu - 14.1 wt%/ Al - 3.0 wt%
MICROGRAPHS
ELECTRON
SCANNING
TRANSFORMATION
TRESANDUCED MARTENSITIC
(A)BEFXE

r

;

11-21

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NSWC MP 79-441

50JA

FIGURE 11

SCANNING ELECTRON MICROGRAPHS OF A Cu - 14.1 wt% Al - 3.0 wt% Ni ALLOY
(B) AFTER STRESS-INDUCED MARTENSITIC TRANSFORMATION

11-22

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NSWC MP 79-441

FIGURE 13

KOSSEL PATTERN TAKEN FROM

11-24

AREA SHOWN IN FIGURE 12

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NSWC MP 79-441

References
(1)

Laves, F. Acta. Met. 14 (1966) 58.

(2)

Frank, F. C. and Ashbee, K. H. G. Spectrum 132 (1975) 1.

(3)

Frank, F. C. Rev. Geophys. 3 (1965) 485.

(4)

Cunningham, B. and Ashbee, K. H. G. Acta. Met. 25 (1977) 1315.

(5)

Biggin, S. and Dingley, D. 3. 3. Appi. Cryst. 10 (1977) 376.

(6)

Love, A. E. H. "The Mathematical Theory of Elasticity" 4th ed.
CAmbridge University Press (1959) 475.

(7)

Cunningham, B. Ph.D. Thesis. Univ. of Bristol (1979)

(8)

loc. cit.

11-27111-28

NSWC MP 79-441

HOT ISOSTATICALLY PRESSED POWDER METALLURGY NITINOL WIRE
M. T. Podob
Consolidated Metallurgical Industries
Farmington Hills, MI
W. A. Johnson
Special Metals Corporation
New Hartford, NY

~S.
~Special
i

H. Reichman
Metals Corporation
New Hartford, NY

INTRODUCTION
A range of compositions in the binary nickel-titanium alloy system possesses a rather
unusual property - shape memory. The series of alloys, discovered by the Naval Ordnance
Laboratory (now Naval Surface Weapons Center) in the early 1960's, was lesignated NITINOL.
Forming a sample of the alloys in the 55 weight percent nickel range-he they wire, rod, or
sheet--into a desired shape above the martensitic transformation temperature, imparts the
sample with a "memory" to return to that shape. If the sample is cooled and the configuration
altered after cooling, reheating above the transition temperature will cause reversion to the
"memorized" shape.
The temperature to which the material must be heated to cause shape transformation
depends principally upon the alloy's composition. NITINOL demonstrates a shape memory
response for compositions on the order of 53 to 57 weight percent nickel (the
intermetallic compound compositional range).
Transition temperature range varies from
approximately -60OF (-500 C) to 300OF (1660C)l*, increasing with decreasing nickel content.
During the material transformation, NITINOL experiences large deflections, which can be
translated into mechanical forces.
One problem of NITINOL wire for any commercial application is the difficulty in
producing a chemically homogeneous ingot for wire drawing, hence wire with a consistent,
precise, and predictable shape memory response. It is felt that with the use of a powder
metallurgical (P/M) approach towards NITINOL manufacture, a homogeneous ingot can be
obtained by subsequently hot isostatically pressing (HIP'ing) prealloyed powders into billet and

13ackson,
S

C. M.; Wagner, H. 3.; Wasilewski, R. 3.: 55-NITINOL -- The Alloy With A Memory:
Its Physical Metallurgy, Properties, and Applications, NASA-SPSI 10, Battelle Memorial
Institute, 1972.

*Editors' Note: 120 0 C is more commonly accepted today.

12-1

NSWC MP 79-441
drawing into wire. This consolidated produ.t will have the compositional uniformity necessary
to tighten the broad transition temperature range to a narrow band and allow the development
of a P/M NITINOL wire for a wide range of commercial applications, all incorporating the
shape memory response.
This report describes a series of experiments conducted to
accomplish that goal.
EXPERIMENTAL PROCEDURE
ATOMIZATION. Inert (argon) gas atomization of all heats of material evaluated was
accomplished in the Udimet Powder Division Research Center atomizer in Ann Arbor,
Michigan. This unit is capable of a 200-pound conventional nickel-base superalloy pour. The
furnace was modified to accommodate a graphite core, limiting its capacity to 40 pounds of
NITINOL. All furnace parts and pour cups in contact with molten NITINOL were fabricated
from AT) Graphite.
Atomization is accomplished by pouring molten metal into a cup-tip-nozzle arrangement
and allowing argon gas to impinge the molten stream, breaking the metal into fine droplets.
Figure 1 is a schematic of a typical inert gas atomizer.
Two 40-pound NITINOL heats were atomized, the heats designated R78245-R78246.
Charge for R78245 consisted of loose nickel shot (Ni-99) and titanium chips (Ti-99) with an aim
chemistry of 55.5 wt % Ni. To provide better homogenization of the charge and minimze
carbon pickup during melting, loose nickel shot and titanium chips were placed in a rolled and
welded nickel-200 container and lid, with a nickel-200 evacuation tube TIG welded in place.
The entire assembly was evacuated and the evacuation tube crimped and TIG welded closed.
The can was then hot isostatically pressed (HIP'ed) at 1600OF (871 0 C)/15 Ksi (103 Mpa)/3 hours
to allow for some diffusion bonding of the charge. Aim chemistry of this billet was 55.0% Ni.
This was subsequently melted in the atomizer and atomized to powder.
Post-atomization processing consisted of transferring the powder from the collection
vessel to a gloved dry box for screening. All powder handling was either under a vacuum or
argon blanket to minimize oxidation. As-atomized product was screened to -40 mesh. Yield
after screening wes approximately 15-1/2 pounds of R78245 and 26 pounds of R78246.
POWDER CHARACTERIZATION. Microexamination of loose powder samples mounted in
bakelite revealed most powder particles were homogeneous and single phased. Several random
particles did show fine dispersion of a secondary phase which was light reflective, suggesting
TiC.
Scanning electron microscope examination of the powder (Figure 2) revealed spherical
powder with relatively little flake present. Few satellite particles were observed. In general,
the appearance of the as-atomized NITINOL powder was typical of nickel-base superalloy
product atomized in the Ann Arbor facility.
SCREEN ANALYSIS AND DENSITY. Screen analysis (Table I) of 100 gram samples of
powder revealed R78245 was coarser than R78246. The corresponding apparent and tap
densities of R78245 were greater than its counterpart.
These somewhat unusual results
suggest sampling rather than a materials problem.

12-2

NSWC MP 79-441
CHEMISTRY. Difficulty exists in the precise analytical technique for major element
determination of NITINOL. For a nominal NITINOL composition of 55 weight percent nickel,
the literature indicatesl a compositional measurement uncertainty of + 0.3 weight percent

titanium. Table 11 chemically analyzes heats R78245 and R78246 performed in Princeton using
atomic absorption. Wet chemical analysis was not performed.
HIP CONSOLIDATION.

Six 0.75 inch (0.905 cm) O.D. X 0.049 inch (0.124 cm) wall 304L

stainless steel tubes were cleaned utilizing Scotchbrite and acetone, crimped on one end, and
TIG welded closed. Three tubes were filled with powder from heats R78245 and R78246. Five
additional tubes were similarly filled. Table III gives can filiing data.

All containerized materials (including melt stock) were HIP'ed in the HIP unit at the
Udimet Powder Division in Ann Arbor. This unit, designed and built by Autoclave Engineering,
Erie, PA, has a graphite element furnace. Working zone, temperature, and pressure
capability of the unit are 9.5 inches (24.1 cm) outside diameter by 18 inches in height;

2300OF (1260 0 C), and 15,000 psi (103 MPa), respectively.
medium.

Argon gas is the pressurizing

Microstructural examination of consolidated material samples revealed a uniform, single
phase, recrystallized structure, interspersed with grain boundary and matrix carbonitrides and
nickel-titanium oxides (Figure 3). Grain size was on the order of ASTM 9-10, with no evidence
of prior powder particle boundaries. The overall microstructure is accicular, the basket-weave
structure being more pronounced than the typical hot swaged NITINOL alloy.
WIRE DRAWING. Cylinders 1/4-inch (0.64cm) in diameter were machined from samples
of each heat and submitted to the Nayal Surface Weapons Center for wire drawing. The
samples were hot swaged at 1560 F (850 C) to a finished diameter of 1/8 inch (0.318 cm).
Observed reductions were on the order of 10% per pass. Attempts to draw the swaged rods
into wire at room temperature resulted in brittle failure. Visual and SEM examination of the
fracture surfaces revealed no evidence of cracking through prior particle boundaries.
Microexamination of longitudinal and transverse sections from the swaged rods revealed
a fine grained microstructure, interspersed with carbonitrides and oxide particles (Figures 4
and 5).
SUMMARY AND DISCUSSION

The preliminary experimental results are encouraging. This program demonstrated that
HIP consolidated into billet.
the resulting powder
andbillet
atomized
be successfully
NITINOL
into a useful shape which
can be hot swaged
that the
revealed
Subsequentcanexperiments
demonstrated 100 percent shape recall. Microstructural analysis of samples from this product
showed a uniform structure free from the gross segregation present in conventionally
fabricated material. Results, and the literature, indicate that when the transition temperature
of the two heats is greater than 20 C (room temperature), wire drawing can be accomplished
utilizing existing NITINOL wire production technology. An experiment was conducted by
Naval Research Laboratory to determine whether P/M NITINOL wire behaves differently from
material cast from the same composition. A sample of heat R78245 was HIP consolidated and
then vacuum arc remelted by the Navy. The button produced was then hot swaged. Attempts

1See footnote

I on page 12-1.

12-3

I
NSWC MP 79-441
! ltf

to
draw thetemperature
swaged rod similar
into wire
resistivity
measurements
revealed
it had a
transition
to failed;
the original
HlP'ed
P/M NITINOLonofthethebarsame
composition.
Microstructural analysis (Figures 6 and 7) of the recast bar revealed that, with the exception
of a slightly larger grain size, the microstructure was similar to the HIP P/M bar, indicating
the key reason for the low transition temperatures lies with the composition of the material,
not the process which produced it.
CONCLUSIONS
1.

NITINOL can be successfully inert gas (argon) atomized into a spherical powder.

2.

Conventional canning, outgassing, and HIP'ing techniques can be utilized to compact
NITINOL powder into a fully dense material.

3.

HIP P/M NITINOL is uniform in composition and relatively free from the segregation
present in conventional NITINOL composition billets utilized for wire drawing.

4.

The HIP product can be hot swaged into bars which demonstrate a 100 percent shape
memory response. The chemistry of the heats utilized for the experiments produced
shape memory transition temperatures below room temperature, preventing the
drawing of the HIP NITINOL billets into wire.

FUTURE PLANS
Experimental results reveal that a powder metallurgical approach towards NITINOL wire

fabrication is a practical technique to produce a homogeneous material.

Conclusion--P/M

NITINOL behaves no differently from cast NITINOL. Fabrication of wire with a precise
narrow band of shape memory transition temperature will require greater chemistry control
and chemistry predictability. This goal will be accomplished by atomizing four heats of
powder. Nickel contents of the 3owders will be 56.0 weight percent nickel.
An incremental approach is undertaken to produce a powder with a usable transition
temperatut e range. A second task will ue to study the use of double-VAR forged material for
atomization stock. The use of a fairly homogeneous, low carbon starting material should
enhance the cleanliness of the powder metallurgy product.

14

1.

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12-4
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NSWC MP 79-441

FIGURE 1. Schematic of inert gas atomizer

12-5

NSWC MP 79-441

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FIGURE

S.

High
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magnification
showing

micrograph
fine

dispersion

1% HF,

12% HN0

of
of

P/M

oxides

Nitinol
and/or

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Etchant:

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_______________________________________________
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NSWC MP 79-441

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TABLE I SCREEN ANALYSIS AND DENSITY
RESULTS FOR NITINOL HEATS R78245 AND R78246

Mesh

Percent Retained in Screen
R78246
R78245

+40

0

0

-40+60
-80+100
-100+120
-120+1407.57
-140+170
-170+200
-200+230

15.2
8.3
6.4

4.7
4.6
5.4

7.2
6.9
3.9

7.1
7.3
4.8

-270+325
-325+400
-400+500
-500 (Pan)

7.0
3.2
7.4
9.5

12.2
4.2
14.2
17.3

Apparent Density

3.1 g/cc

3.9 g/ccJ

Tap Density

4.2 g/cc

4.7 g/cc:

Theoretical Density 2

(Consolidated)

-230+270

5.8

4.6

12-12

----

6.47 g/cc

.

NSWC MP 79 -441

DISTRIBUTION
Copies
Library of Congress
Attn: Gift & Exchange Division
Washington, DC 20540
fi

"

4

Defense
Documentation Center
Cameron Station
Alexandria, VA 22314

12

Office of Advanced Conservation
Technologies
Attn: Mr. Marvin Gunn
Department of Energy
1000Independence Ave. S.W.

I

Washington, DC 20585

Naval Civil Engineering Laboratory
Naval Construction Battallion Center

Attn:
Dr. Larry
HallangerI
Port Hueneme,
CAW.93043
Attn:

X-10

oBuilding 4500 North
Attn- H. Arnold
Oak
P.O. Ridge
Box YNational Laboratory
Oak Ridge, TN 37830
Attn:. Y -12
P.O. Box Y
c/o Building 9204-1

Attnry. Michel
Oak Ridge National Laboratory
Oak Ridge, TN 37830
ii

Library
Oak
Ridge National Laboratory
Oak Ridge, TN 37830

I

NSWC MP 79-441

TABLE 2 CHEMICAL ANALYSIS
OF NITINOL HEATS R78245 AND R78246

tTi

R78245
(wt.%)

R78246
(Wt.%)

56.5

56.4

43.8

44.4

C

0.06

0.09

02

858ppm

848ppm

N2

7ppm

14ppm

ELEMENT
Ni

12-13

NSWC MP 79-44 1

TABLE 3 CAN FILLING DATA FOR NITINOL SAMPLES

Number

Number

Filling
(microns)

Vacuum
(microns)

Static
(microns)

Leak Up
(microns/3 min.)

R78245

8

200

3x10 6

I
4.5
3.5

2R78245

7

120

4x10O6

R78245

5

250

4x106

R78246

10

200

WO16

5R78246

8

400

4x106

2.5

6

R78246

7

300

4x10-6

I

2A

R78245

9

80

Unavailable

3A

R78245

9

200

Unavailable

4A

R78246

8

250

Unavailable

5A

R78246

5

35

Unavailable

6A

R78246

5

85

Unavailable

<10

<500

3
4

UPD Standard5
Practice:.

<1x10 5

12-14

<9

NSWC MP 79-441

BIBLIOGRAPK-Y

Jackson, C. M.; Wagner, K. 3.; Wasilewski, R. 3.:. 55-NITINOL
The Alloy With A Memory:
Its Physical Metallurgy, Properties, and Applications, NASA-SP5I 10, Battelle Memorial
Institute, 1972.
--

12-15/12-16