A coupled kinetic Monte Carlo–finite element mesoscale model for thermoelastic martensitic phase transformations in shape memory alloys

Abstract

A mesoscale modeling framework integrating thermodynamics, kinetic Monte Carlo (KMC) and finite element mechanics (FEM) is developed to simulate displacive thermoelastic transformations between austenite and martensite in shape memory alloys (SMAs). The model is based on a transition state approximation for the energy landscape of the two phases under loading or cooling, which leads to the activation energy and rate for transformation domains incorporating local stress states. The evolved stress state after each domain transformation event is calculated by FEM, and is subsequently used in the stochastic KMC algorithm to determine the next domain to transform. The model captures transformation stochasticity, and predicts internal phase and stress distributions and evolution throughout the entire incubation, nucleation and growth process. It also relates the critical transformation stresses or temperatures to internal activation energies. It therefore enables quantitative exploration of transformation dynamics and transformation–microstructure interactions. The model is used to simulate superelasticity (mechanically induced transformation) under both load control and strain control in single-crystal SMAs under uniaxial tension.