Multi-axial behavior of shape-memory alloys undergoing martensitic reorientation and detwinning

Abstract

Recently, a rate-independent, finite-deformation-based crystal mechanics constitutive model for martensitic reorientation and detwinning in shape-memory alloys has been developed by Thamburaja [Thamburaja, P., 2005. Constitutive equations for martensitic reorientation and detwinning in shape-memory alloys. Journal of the Mechanics and Physics of Solids 53, 825–856] and implemented in the ABAQUS/Explicit [Abaqus reference manuals. 2005. Providence, RI] finite-element program. In this work, we show that the aforementioned model is able to quantitatively predict the experimental response of an initially textured and martensitic polycrystalline Ti–Ni rod under a variety of uniaxial and multi-axial stress states. By fitting the material parameters in the model to the stress–strain response in simple tension, the constitutive model predicts the stress–strain curves for experiments conducted under simple compression, torsion, proportional-loading tension–torsion, and path-change tension–torsion loading conditions to good accord. Furthermore the constitutive model also reproduces the force–displacement response for an indentation experiment to reasonable accuracy.

Introduction

Shape-memory alloys are finding increasing use in the biomedical (e.g. arterial stents etc.) and force actuation (e.g. clampers etc.) industries.¹ Components which are formed out of these materials are typically subjected to multi-axial stress-states during their operation. Therefore suitable three-dimensional constitutive models are needed to accurately predict the mechanical response of these components under a variety of multi-axial loading conditions.

Depending on temperature, shape-memory alloys exhibit two technologically important types of behavior when stressed: (1) Superelasticity (or pseudo-elasticity) at temperatures above the austenitic finish temperature, θ_af, and (2) martensitic reorientation and detwinning at temperatures below the martensitic finish temperature, θ_mf. For examples of work regarding the constitutive modelling of shape-memory alloys undergoing superelasticity see Boyd and Lagoudas, 1996, Gall and Sehitoglu, 1999, Lim and McDowell, 1999, Tokuda et al., 1999 among others. Of particular note, the works of Lim and McDowell, 1999, Tokuda et al., 1999 deal with the modelling of multi-axial behavior in shape-memory alloys.

Several constitutive models to study the martensitic reorientation in shape-memory alloys have been proposed by various researchers (e.g. Buisson et al., 1991, Marketz and Fischer, 1996, Fang et al., 1999, Tokuda et al., 1999, Sittner and Novak, 2000 etc.). Both the works of Buisson et al., 1991, Marketz and Fischer, 1996 do not provide experimental verification of their models. The constitutive models of Fang et al., 1999, Tokuda et al., 1999, Sittner and Novak, 2000 have experimental verification, but these models were formulated using small-strain theory which do not take into account finite-rotations at a material point. Recently, Thamburaja (2005) has developed a rate-independent, finite-deformation-based crystal mechanics constitutive model² for shape-memory alloys deforming by martensitic reorientation and lattice correspondence variant (lcv) detwinning (to be explained later). This model was modified to include the effect of austenite–martensite phase transformations to study martensitic reorientation and the one-way shape-memory effect exhibited by polycrystalline Ti–Ni sheets (Thamburaja et al., 2005).

To study martensitic reorientation and detwinning in shape-memory alloys under complex loading conditions, we conducted experiments under a variety of uniaxial and multi-axial stress-states (simple tension, simple compression, torsion, proportional-loading tension–torsion, path-change tension–torsion and instrumented indentation) on an initially textured polycrystalline rod initially in the martensitic state. Therefore the main purpose of this work is to quantitatively predict the martensitic reorientation and detwinning response for this set of experiments using the constitutive model developed by Thamburaja (2005).

The plan of this paper is as follows: In Section 2, we summarize the rate-independent, finite-deformation-based crystal-mechanics constitutive model formulated by Thamburaja (2005). Here we also modify the constitutive model of Thamburaja (2005) to include the plasticity in martensite due to dislocation motion. In Section 3, the results of our newly conducted experiments are presented along with the predictions from the corresponding finite-element simulations. The numerical simulations are shown to be in good accord with the physical experiments. We conclude and give directions for future research work in Section 4.