A Brief Review on Discrete Modelling of Martensitic Phase Transformations

Most materials possess microstructural features at small length scales which are either stationary, such as grains and grain boundaries, phases and phase boundaries, precipitates, inclusions or mobile which tend to evolve during thermomechanical loads, such as cracks, twins or mobile interphase boundaries. The mechanical response of materials depends strongly on these microstructural features. Continuum models are frequently incapable of dealing with the latter microstructural features because they lack information on the evolving microstructure. There is an alternative class of models called Discrete Element Models (DEMs) which are applicable to describe the thermomechanical behaviour of solids, fluids and granular matter (material is modelled as a set of interacting point masses). With their inherent discreteness, DEMs are capable of incorporating the effects of microstructure as well as its evolution on the macroscopic behaviour. The recent development on deriving particle interactions from continuum free energy paves the way for the discrete models to describe complex behaviours like plasticity and phase transformations. This article explains how discrete models can be applied to simulate thermomechanical behaviour and evolving microstructures in martensitically transforming shape memory alloys (SMA). Results of the two dimensional simulations of thermally and stress-induced martensitic transformations for two kinds of martensitic transformation (square to rectangle and square to parallelogram) in SMA single crystal are presented and discussed. Although discrete element models cannot substitute continuum or micromechanics models of thermomechanical functional behaviour of SMAs, they can be successfully applied to investigate various phenomena that are so far poorly understood in SMA research, as for example the role of microstructure evolution or polycrystal grains (size, shape, texture, multiaxial stress) in SMA mechanics.