Numerical modeling of stress induced martensitic phase transformations in shape memory alloys

Abstract

Phenomenological models of shape memory behavior are based on either continuum hypothesis (macroscopic) or on volume averages over a representative volume element consisting of several grains. These constitutive models attempt to model the shape memory behavior using macro/micromechanics and thermodynamics. In general, these models share a common feature. They describe the martensitic phase transformation by a parameter representing the martensite volume fraction, and formulae an evolution law for the martensite volume fraction. Exploiting the similarity of these models to elastoplasticity, we describe a finite element formulation of a micromechanics based constitutive model. Several other models can be formulated in a similar way, and the present work can be seen as a testbed approach to study and evaluate the constitutive models on a common platform. We present numerical results for Au-47.5at%Cd and Ti-50.6at%Ni to validate the finite element formulation.