Polycrystalline shape-memory materials: effect of crystallographic texture

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. (C) 2001 Elsevier Science Ltd. All rights reserved.