Thermomechanical representation of the multiaxial behavior of shape memory alloys

A thermomechanically consistent material model representing the multiaxial behavior of shape memory alloys is proposed in this article. The constitutive equations describe the one-way and two-way shape memory effect as well as pseudoelasticity, pseudoplasticity and the transition range between pseudoelasticity and pseudoplasticity. The material model is based on a free energy function as well as evolution equations for internal variables. In detail, the free energy function is introduced in order to describe the energy storage during thermoelastic processes, the energy difference between the regarded phases (austenite and martensite) as well as the energy storage due to the evolution of the residual stresses. In contrast to this, the evolution equations for the internal variables represent the observed inelastic behavior of shape memory alloys as well as the related thermomechanical coupling effects. Due to the description of the energy storage and release during the martensitic phase transitions by means of a mixture theory, one internal variable is the fraction of martensite. Others are the inelastic strain tensor and internal variables describing residual stresses. The viscous material behavior of NiTi shape memory alloys, which is experimentally observed, is represented by an inelastic multiplier of Perzyna-type. Numerical solutions of the developed constitutive equations for isothermal and non-isothermal strain and stress processes demonstrate that the material model represents the main effects of shape memory alloys. Additionally, the material model is able to depict the multiaxial material behavior as observed. Numerical solutions are compared with uniaxial and in particular biaxial experimental observations on NiTi shape memory alloys.

[1]  Ferdinando Auricchio,et al.  Shape-memory alloys: modelling and numerical simulations of the finite-strain superelastic behavior , 1997 .

[2]  E. N. Mamiya,et al.  Three-dimensional model for solids undergoing stress-induced phase transformations , 1998 .

[3]  H. Tobushi,et al.  Phenomenological analysis on subloops and cyclic behavior in shape memory alloys under mechanical and/or thermal loads , 1995 .

[4]  Kevin Barraclough,et al.  I and i , 2001, BMJ : British Medical Journal.

[5]  Dimitris C. Lagoudas,et al.  Thermomechanical modeling of polycrystalline SMAs under cyclic loading, Part III: evolution of plastic strains and two-way shape memory effect , 1999 .

[6]  A. Bertram.  Thermo-mechanical constitutive equations for the description of shape memory effects in alloys , 1983 .

[7]  Tony Owen.  Shape Memory Alloys edited by Hiroyasu Funakubo, translated from the Japanese by J.B. Kennedy Gordon and Breach Science Publishers, New York, 1986 (Price $135.00, circa £75.00) , 1988, Robotica.

[8]  David L. McDowell,et al.  Path Dependence of Shape Memory Alloys during Cyclic Loading , 1995 .

[9]  Hisaaki Tobushi,et al.  Transformation start lines in TiNi and Fe-based shape memory alloys after incomplete transformations induced by mechanical and/or thermal loads , 1995 .

[10]  J. Shaw,et al.  Thermomechanical aspects of NiTi , 1995 .

[11]  Dirk Helm,et al.  Thermomechanical behavior of shape memory alloys , 2001, SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring.

[12]  Dirk Helm,et al.  Shape memory alloys: thermomechanical modeling and finite element simulations at finite strains , 2000, Smart Structures.

[13]  L. Bocher,et al.  Experimental study of pseudoelastic behaviour of a Cu Zn AI polycrystalline shape memory alloy under tension-torsion proportional and non-proportional loading tests , 1996 .

[14]  G. Bourbon,et al.  Thermodynamical model of cyclic behaviour of TiNi and CuZnAl shape memory alloys under isothermal undulated tensile tests , 1996 .