A macroscopic constitutive model for shape-memory alloys: Theory and finite-element simulations

Abstract

In this work, we develop a non-local and thermo-mechanically-coupled constitutive model for polycrystalline shape-memory alloys (SMAs) capable of undergoing austenite ↔ martensite phase transformations. The theory is developed in the isotropic metal-plasticity setting using fundamental thermodynamic laws and the principle of micro-force balance [E. Fried, M. Gurtin, Dynamic solid–solid transitions with phase characterized by an order parameter, Physica D 72 (1994) 287–308]. The constitutive model is then implemented in the ABAQUS/Explicit (2007) finite-element program by writing a user-material subroutine. The results from the constitutive model and numerical procedure are then compared to representative physical experiments conducted on a polycrystalline rod Ti–Ni undergoing superelasticity. The constitutive model and the numerical simulations are able to reproduce the stress–strain responses from these physical experiments to good accuracy. Experimental strain–temperature–cycling and shape-memory effect responses have also shown to be qualitatively well-reproduced by the developed constitutive model. With the aid of finite-element simulations we also show that during phase transformation, the dependence of the position i.e. the thickness of the austenite–martensite interface on the mesh density is heavily minimized when a non-local constitutive theory is used.