An Extended Three-Dimensional Finite Strain Constitutive Model for Shape Memory Alloys

Abstract

A 3D finite-strain constitutive model for shape memory alloys (SMAs) is proposed. The model can efficiently describe reversible phase transformation from austenite to self-accommodated and/or oriented martensite, (re)orientation of martensite variants, minor loops, latent heat effects, and tension–compression asymmetry based on the Eulerian logarithmic strain and the corotational logarithmic objective rate. It further accounts for smooth thermomechanical response; temperature dependence of the critical force required for (re)orientation, temperature, and load dependence of the hysteresis width; and asymmetry between forward and reverse phase transformation, and it is flexible enough to address the deformation response in the concurrent presence of several phases, i.e., when austenite, self-accommodated, and oriented martensite co-exist in the microstructure. The ability of the proposed model to describe the aforementioned deformation response characteristics of SMAs under multiaxial, thermomechanical, and nonproportional loading relies on the set of three independent internal variables, i.e., the average volume fraction of martensite variants, their preferred direction, and the magnitude of the induced inelastic strain, which further allow for an implicit description of a fourth internal variable, the volume fraction of oriented as opposed to self-accommodated martensite. The calibration of the model and its numerical implementation in an efficient scheme are presented. The model is validated against experimental results associated with complex thermomechanical paths, including tension/compression/torsion experiments, and the efficiency of its numerical implementation is verified with simulations of the response of a biomedical superelastic SMA stent and an SMA spring actuator.