Polycrystalline shape-memory materials: effect of crystallographic texture

Abstract

A crystal-mechanics-based constitutive model for polycrystalline shape-memory materials has been developed. The model has been implemented in a finite-element program. In our finite-element model of a polycrystal, each element represents one crystal, and a set of crystal orientations which approximate the initial crystallographic texture of the shape-memory alloy are assigned to the elements. The macroscopic stress–strain responses are calculated as volume averages over the entire aggregate. Pseudoelasticity experiments in tension, compression, and shear have been performed on an initially textured polycrystalline Ti–Ni alloy. In order to determine the material parameters for Ti–Ni, the stress–strain results from a finite-element calculation of a polycrystalline aggregate subjected to simple tension have been fit to corresponding results obtained from the physical experiment. Using the material parameters so determined, the predicted pseudoelastic stress–strain curves for simple compression and thin-walled tubular torsion of the initially textured Ti–Ni are shown to be in good accord with the corresponding experiments. Our calculations also show that the crystallographic texture is the main cause for the observed tension–compression asymmetry in the pseudoelastic response of Ti–Ni. The predictive capability of the model for the variation of the pseudoelastic behavior with temperature is shown by comparing the calculated stress–strain response from the model against results from experiments of Shaw and Kyriakides (J. Mech. Phys. Solids 43 (1995) 1243) on Ti–Ni wires at a few different temperatures. By performing numerical experiments, we show that our model is able to qualitatively capture the shape-memory effect by transformation. We have also evaluated the applicability of a simple Taylor-type model for shape-memory materials. Our calculations show that the Taylor model predicts the macroscopic pseudoelastic stress–strain curves in simple tension, simple compression and tubular torsion fairly well. Therefore, it may be used as a relatively inexpensive computational tool for the design of components made from shape-memory materials.