A phenomenological model to simulate the two-way shape memory effect (TWSME) in nickel-titanium alloys (NiTi) is proposed. The model is based on the Prandtl–Ishlinksii operator and it is able to simulate the hysteretic behavior of the material in the strain-temperature response. Starting from some experimental measurements of well known thermomechanical characteristics of NiTi alloys, the parameters of the phenomenological model are identified by simple and efficient numerical procedures. The model was developed in the commercial software package SIMULINK® and it is able to simulate the effects of applied stresses on the TWSME as well as partial thermal cycles, which generate incomplete martensitic transformations. A systematic comparison between experimental measurements, carried out under different values of applied stress, and numerical predictions are illustrated for both complete and incomplete phase transformations. The results are considered satisfactory both in accuracy and in computational time; therefore, the method is robust and suitable for use in real-time applications.

1.
Otsuka
,
K.
, and
Ren
,
X.
, 2005, “
Physical Metallurgy of Ti–Ni-Based Shape Memory Alloys
,”
Prog. Mater. Sci.
0079-6425,
50
, pp.
511
678
.
2.
Hamilton
,
R. F.
,
Sehitoglu
,
H.
,
Chumlyakov
,
Y.
,
Maier
, and
H. J.
, 2004, “
Stress Dependence of the Hysteresis in Single Crystal Niti Alloys
,”
Acta Mater.
1359-6454,
52
, pp.
3383
3402
.
3.
Wu Ming
,
H.
, 2002, “
Fabrication of Nitilon Materials and Components
,”
Mater. Sci. Forum
0255-5476,
394–395
, pp.
285
292
.
4.
Schlossmacher
,
P.
,
Haas
,
T.
, and
Shussler
,
A.
, 1997, “
Laser-Welding of a Ni-Rich Tini Shape Memory Alloy: Mechanical Behavior
,”
J. Phys. IV
1155-4339,
7
(
5
), pp.
251
256
.
5.
Tuissi
,
A.
,
Besseghini
,
S.
,
Ranucci
,
T.
,
Squatrito
,
F.
, and
Pozzi
,
M.
, 1999, “
Effect of Nd-YAG Laser Welding on the Functional Properties of the Ni-49.6at.%Ti
,”
Mater. Sci. Eng., A
0921-5093,
273–275
, pp.
813
817
.
6.
Theisen
,
W.
, and
Schuermann
,
A.
, 2004, “
Electro Discharge Machining of Nickel-Titanium Shape Memory Alloys
,”
Mater. Sci. Eng., A
0921-5093,
378
, pp.
200
204
.
7.
Falvo
,
A.
,
Maletta
,
C.
, and
Furgiuele
,
F. M.
, 2005, “
Laser Welding of a Niti Alloy: Mechanical and Shape Memory Behavior
,”
Mater. Sci. Eng., A
0921-5093,
412
, pp.
235
240
.
8.
Falvo
,
A.
,
Maletta
,
C.
, and
Furgiuele
,
F. M.
, 2006, “
Functional Behavior of a Niti Welded Joint: Two-Way Shape Memory Effect
,”
Mater. Sci. Eng., A
0921-5093, in press; doi: 10.1016/j.msea.2006.11.178
9.
Gall
,
K. A.
,
Seitoglu
,
H.
, and
Chumlyakov
,
Y.
, 2000, “
Niti Experiments Versus Modeling: Where Do We Stand?
,”
Proc. SPIE
0277-786X,
3992
, pp.
536
547
.
10.
Paiva
,
A.
, and
Savi
,
M. A.
, 2006, “
An Overview of Constitutive Models for Shape Memory Alloys
,”
Math. Probl. Eng.
1024-123X, art. no. 56876, pp.
1
30
.
11.
Falk
,
F.
, 1980, “
Model Free-Energy, Mechanics and Thermodynamics of Shape Memory Alloys
,”
Acta Metall.
0001-6160,
28
(
12
), pp.
1773
1780
.
12.
Falk
,
F.
, 1983, “
One-Dimensional Model of Shape Memory Alloys
,”
Arch. Mech.
0373-2029,
35
(
1
), pp.
63
84
.
13.
Tanaka
,
K.
, and
Nagaki
,
S.
, 1982, “
Thermomechanical Description of Materials With Internal Variables in the Process of Phase Transitions
,”
Ing.-Arch.
0020-1154,
51
, pp.
287
299
.
14.
Liang
,
C.
, and
Rogers
,
C. A.
, 1990, “
One-Dimensional Thermomechanical Constitutive Relations for Shape Memory Materials
,”
J. Intell. Mater. Syst. Struct.
1045-389X,
1
, pp.
207
234
.
15.
Brinson
,
L. C.
, 1993, “
One Dimensional Constitutive Behavior of Shape Memory Alloys: Themomechanical Derivation With Non-Constant Material Functions and Redefined Martensite Internal Variable
,”
J. Intell. Mater. Syst. Struct.
1045-389X,
4
, pp.
229
242
.
16.
Bertran
,
A.
, 1982, “
Thermomechanical Constitutive Equations for the Description of Shape Memory Effects in Alloys
,”
Nucl. Eng. Des.
0029-5493,
74
(
2
), pp.
173
182
.
17.
Souza
,
A. C.
,
Mamiya
,
E.
, and
Zouain
,
N.
, 1998, “
Three-Dimensional Model for Solids Undergoing Stressinduced Phase Transformations
,”
Eur. J. Mech. A/Solids
0997-7538,
17
(
5
), pp.
789
806
.
18.
Auricchio
,
F.
, and
Lubliner
,
J.
, 1997, “
A Uniaxial Model for Shape Memory Alloys
,”
Int. J. Solids Struct.
0020-7683,
34
(
27
), pp.
3601
3618
.
19.
Auricchio
,
F.
, and
Sacco
,
E.
, 1997, “
A One-Dimensional Model for Superelastic Shape Memory Alloys With Different Elastic Properties Between Austenite and Martensite
,”
Int. J. Non-Linear Mech.
0020-7462,
32
(
6
), pp.
1101
1114
.
20.
Auricchio
,
F.
,
Taylor
,
R. L.
, and
Lubliner
,
J.
, 1997, “
Shape-Memory Alloys: Macromodelling and Numerical Simulations of the Superelastic Behavior
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
146
(
3–4
), pp.
281
312
.
21.
Marfia
,
S.
,
Sacco
,
E.
, and
Reddy
,
J. N.
, 2003, “
Superelastic and Shape Memory Effects in Laminated Shape-Memory-Alloy Beams
,”
AIAA J.
0001-1452,
41
, pp.
100
109
.
22.
Ge
,
P.
, and
Jouaneh
,
M.
, 1997, “
Generalized Preisach Model for Hysteresis Nonlinearity of Piezoceramic Actuators
,”
Precis. Eng.
0141-6359,
20
, pp.
99
111
.
23.
Krejci
,
P.
, and
Kuhnen
,
K.
, 2001, “
Inverse Control of Systems With Hysteresis and Creep
,”
IEE Proc.: Control Theory Appl.
1350-2379,
148
(
3
), pp.
185
192
.
24.
Kuhnen
,
K.
, and
Janocha
,
H.
, 2001, “
Inverse Feedforward Controller for Complex Hysteretic Nonlinearities in Smart Material Systems
,”
Control Intell. Syst.
1480-1752,
29
(
3
), pp.
74
83
.
25.
Falvo
,
A.
,
Maletta
,
C.
, and
Furgiuele
,
F. M.
, 2007, “
Two-Way Shape Memory Effect of a Ti Rich Niti Alloy: Experimental Measurements and Numerical Simulations
,”
Smart Mater. Struct.
0964-1726,
16
, pp.
771
778
.
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