Constitutive equations for martensitic reorientation and detwinning in shape-memory alloys

Abstract

A crystal-inelasticity-based constitutive model for martensitic reorientation and detwinning in shape-memory alloys (SMAs) has been developed from basic thermodynamics principles. The model has been implemented in a finite-element program by writing a user-material subroutine. We perform two sets of finite-element simulations to model the behavior of polycrystalline SMAs: (1) The full finite-element model where each finite element represents a collection of martensitic microstructures which originated from within an austenite single crystal, chosen from a set of crystal orientations that approximates the initial austentic crystallographic texture. The macroscopic stress–strain responses are calculated as volume averages over the entire aggregate: (2) The Taylor model (J. Inst. Metals 62 (1938) 32) where an integration point in a finite element represents a material point which consist of sets of martensitic microstructures which originated from within respective austenite single-crystals. Here the macroscopic stress–strain responses are calculated through a homogenization scheme. Experiments in tension and compression were conducted on textured polycrystalline Ti–Ni rod initially in the martensitic phase by Xie et al (Acta Mater. 46 (1998) 1989). The material parameters for the constitutive model were calibrated by fitting the tensile stress–strain response from a full finite-element calculation of a polycrystalline aggregate to the simple tension experiment. With the material parameters calibrated the predicted stress–strain curve for simple compression is in very good accord with the corresponding experiment. By comparing the simulated stress–strain response in simple tension and simple compression it is shown that the constitutive model is able to predict the observed tension–compression asymmetry exhibited by polycrystalline Ti–Ni to good accuracy. Furthermore, our calculations also show that the macroscopic stress–strain response depends strongly on the initial martensitic microstructure and crystallographic texture of the material. We also show that the Taylor model predicts the macroscopic stress–strain curves in simple tension and simple compression reasonably well. Therefore, it may be used as a relatively inexpensive computational tool for the design of components made from shape-memory materials.