Review of the Constitutive Modeling of Shape Memory Alloy Material

Kamal M. Bajoria(1*), Surajit Das(2)

(1) Department of Civil Engineering, Indian Institute of Technology Bombay, India
(2) Department of Civil Engineering, Indian Institute of Technology Bombay, India
(*) Corresponding author

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A review of Shape Memory alloy characteristics and constitutive laws for describing the stress-strain behavior and its future possible extension of researches is presented.  First, an overview of SMA characteristics is presented. The modeling aspect of SMA stress-strain relationship is discussed. Three commonly used representative constitutive models predicting quasistatic SMA behavior – Tanaka, Liang and Rogers and Brinson are examined and a comparative study is presented. Differences between the definitions of material constants in these models are pointed out. The necessity for incorporating the strain rate and non-isothermal effects in these models is discussed. In addition to the detailed review of the three constitutive laws the Brinson model is verified through a corresponding algorithm. It is shown that the model can simulate both the stress and temperature induced martensite transformation.
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Smart Structures; Shape Memory Alloy; Solid-Solid Phase Transformation; Austenite; Martensite; Martensite Fraction; Twinned Martensite; Detwinned Martensite; Hysteresis Loop

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H. Funakubo, Shape Memory Alloys (Gordon and Breach Science Publishers, Newyork, USA, 1987).

K. Otsuka and C. M. Wayman, Shape Memory Materials (Cambridge University Press, UK, 1998).

K. Otsuka and X. Ren, Recent Developments in the Research of Shape Memory Alloys, Intermetallics, Vol. 7:511-528, 1999.

K. Bhattacharya, Self-accommodation in Martensite, Arch. Rational Mech. Anal, Vol.120: 201-244, 1992.

R. D. James and K. F. Hane, Martensitic transformations and shape-memory materials, Acta. Mater., Vol.48(Issue1):197-222, 2000.

J. A. Shaw and S. Kyriakides, Thermomechanical Aspects of NiTi, J. Mech. Phys. Solids, Vol. 43(Issue 8): 1243–1281, 1995.

K. Tanaka, A thermomechanical sketch of shape memory effect: One-dimensional tensile behavior, Res. Mech., Vol. 18: 251–263, 1986.

K. Seelekce, Modeling the Dynamic Behavior of shape memory alloys, Int. J. Non-Linear Mech., Vol. 37: 1363-1374, 2002.

S. Aizawa, T. Kakizawa and M. Higashino, Case Studies of Smart Materials for Civil Structures, Smart Mater. Struct., Vol. 7(Issue 5): 617-626,1998.

K. Wilde, P. Gardoni and Y. Fujino, Base Isolation System with Shape Memory Alloy Device for Elevated Highway Bridges, Engg. Struct., Vol. 22: 222-229, 2000.

R. DesRoches and M. Delemont, Seismic retrofit of simply supported bridges using shape memory alloys, Engg. Struct., Vol. 24: 325-332, 2002.

J. M. Hollerbach, I. W. Hunter and J. Ballantyne, A Comparative analysis of Actuator Technologies for Robotics, MIT Press, Vol. 2: 299-342, 1992.

V. Birman, Review of mechanics of shape memory alloy structures, Appl. Mech. Rev., Vol. 50(Issue 11):629-645, 1997.

T. M. Duerig, A. Pelton and D. Stöckel, An overview of Nitinol medical applications, Mater. Sci. Eng. A, Vol. 273-275:149-160, 1999.

D. C. Lagoudas, O. K. Rediniotis and M. M. Khan, Applications of shape memory alloys to bioengineering and biomedical technology 4th. international workshop on mathematical methods in scattering theory and biomedical technology, Perdika, Greece, 1999.

L. G. Machado, M. A. Savi, Medical Applications of Shape Memory Alloys, Braz J. Med. Biol. Res., Vol36(Issue 6):683-691, 2003.

M. Achenbach, I. Müller, Simulation of material behavior of alloys with shape memory, Arch. Mech., Vol37(Issue 6):573-585, 1985.

M. Achenbach, T. Atanackovic and I. Müller, A model for memory alloy in plain strain, Int. J. Solids Struct, Vol22(Issue 2):171-193, 1986.

M. Achenbach, A model for an alloy with shape memory Int. J. Plast., Vol 5:371-395, 1989.

K. Tanaka, S. Nagaki, A thermomechanical description of materials with internal variables in the process of phase transition, Ingenieur Archiv Arch Appl Mech, Vol.51:287-293, 1982.

K. Tanaka, S. Kobayashi and Y. Sato, Thermomechanics of transformation, pseudoelasticity and shape memory effect in alloys, Int. J. Plast., Vol.2:59-72, 1986.

C. Liang, C. A. Rogers, One-dimensional thermomechanical constitutive relations for shape memory materials, J. Intell. Mater. Syst. Struct., Vol.1:207-234, 1990.

H. Tobushi, S. Yamada, T. Hachisuka, A. Ikai and K. Tanaka, Thermomechanical Properties due to Martensitic and R-phase Transformations of TiNi Shape Memory Alloy Subjected to Cyclic Loadings, Journal of Smart Materials and Structures, Vol.5:788-795, 1996.

H. Prahlad, I. Chopra, Experimental characterization of Ni–Ti shape memory alloy wires under uniaxial loading conditions Journal of Intelligent Materials Systems and Structures: Special Issue – ARO Workshop on Smart Structures, Vol.11(Issue 4):272-283, 2000.

L. C. Brinson, One-dimensional constitutive behavior of shape memory alloys: Thermomechanical derivation with non-constant material functions and redefined martensite internal variable, J. Intell. Mater. Syst. Struct., Vol.4:229-242, 1993.

A. Bekker, L. C. Brinson, Temperature-induced phase transformation in a shape memory alloy: Phase diagram based kinetics approach, J. Mech. Phys. Solids., Vol.45(Issue 6):949-988, 1997.

J. G. Boyd, D. C. Lagoudas, A thermodynamic constitutive model for the shape memory materials part I. The monolithic shape memory alloys International Journal of Plasticity, Vol.6:805-842, 1998.

Z. K. Lu, and G. J. Weng, Martensitic transformation and stress-strain relations of shape-memory alloys, J. Mech. Phys. Solids., Vol.45(Issue 11/12):1905-1928, 1997.

Z. K. Lu, and G. J. Weng, A self-consistent model for the stress-strain behavior of shape-memory alloy polycrystals, Acta Mater., Vol.46(Issue 15):5423-5433, 1998.

M. Huang, L. C. Brinson, A multivariant model for single crystal shape memory alloy behavior, J. Mech. Phys. Solids, Vol.46(Issue 8):1379-1409, 1998.

M. Huang, X. Gao, L. C. Brinson, A multivariant micromechanical model for SMAs, Part 2: Polycrystal model, Int. J. Plast., Vol.16:1371-1399, 2000.

B. C. Goo, C. Lexcellent, Micromechanics-based modeling of two-way shape memory effect of a single crystalline shape memory alloy, Acta Mater., Vol.45(Issue 2):727-737, 1998.

A. Vivet, C. Lexcellent, Micromechanical modeling for tension-compression pseudoelastic behavior of AuCd single crystals, Eur. Phys. J.: Appl. Phys., Vol.4:125-132, 1997.

B. Peultier, T. Ben Zineb and E. Patoor, A simplified micromechanical constitutive law adapted to the design of shape memory applications by finite element methods, Materials Science and Engineering A, Vol.481-482:384-388, 2008.

Y. Ivshin, T. J. Pence, A constitutive model for hysteretic phase transition behavior, Int. J. Eng. Sci., Vol.32:681-704, 1994.

Y. Ivshin, T. J. Pence, A thermomechanical model for a one variant shape memory material, J. Intell. Mater. Syst. Struct., Vol.5:455-474, 1994.

A. Sadjadpour, K. Bhattacharya, A Micromechanics Inspired Constitutive Model for Shape-Memory Alloys: The One-dimensional Case, Smart Materials and Structures, Vol.16:S51-S62, 2007.

J. M. McNaney, V. Imbeni, Y. Jung, P. Papadopoulos, and R. O. Ritchie, An Experimental Study of the Superelastic E_ect in a Shape-Memory Nitinol Alloy under Biaxial Loading, Mechanics of Materials, Vol.35:969-986, 2003.

S. Nemat-Nasser, J. Y. Choi, W. G. Guo, J. B. Isaacs and M. Taya, High Strain- Rate, Small Strain Response of a NiTi Shape-Memory Alloy, Journal of Engineering Materials and Technology, Vol.127:83-89, 2005.

S. Sun, R. K. N. D. Rajapakse, Simulation of Pseudoelastic Behaviour of SMA under Cyclic Loading, Computational Materials Science, Vol.28:663-674, 2003.

L. Hui, M. Chen-Xi and O. Jin-Ping, Strain Self-Sensing Property and Strain Rate Dependent Constitutive Model of Austenitic Shape Memory Alloy: Experiment and Theory, Journal of Materials in Civil Engineering, Vol.17(Issue 6):676-685, 2005.

E. Stein, G. Sagar, Theory and Finite Element Computation of Cyclic Martensitic Phase Transformation at Finite Strain, International Journal of Numerical Methods in Engineering, Vol.74(Issue 1):1-31, 2007.

P. Popov, D. C. Lagoudas, A 3-D Constitutive Model for Shape Memory Alloys Incorporating Pseudoelasticity and Detwinning of Self-Accommodated Martensite, International Journal of Plusticity, Vol.23:1679-1720, 2007.

P. Thamburaja, N. Nikabdullah, A macroscopic constitutive model for shape-memory alloys: Theory and finite-element simulations, Comput. Methods Appl. Mech. Engrg, Vol.198:1074-1086, 2009.

C. Liang, C. A. Rogers, A Multi-Dimensional Constitutive Model for Shape Memory Alloys, Journal of Engineering Mathematics, Vol.26:429-443, 1992.

V. R. Buravalla, A. Khandelwal, Differential and integrated form consistency in 1-D phenomenological models for shape memory alloy constitutive behavior, Int. J. Solids Structures, Vol.44:4369-4381, 2007.

L. C. Brinson, M. Panico, Comments to the paper “Differential and integrated form consistency in 1-D phenomenological models for shape memory alloy constitutive behavior” by V. R. Buravalla, A. Khandelwal [Int. J. Solids and Struct., 44(2007)4369-4381], Int. J. Solids Structures, Vol.46:217-220, 2009.

L. C. Brinson, R. Lammering, Finite Element Analysis of the Behavior of Shape Memory Alloys and Their Applications, Int. J. Solids Structures, Vol.30(Issue 23):3261-3280, 1993.


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