Finite element simulations of dynamics of multivariant martensitic phase transitions based on Ginzburg-Landau theory

A finite element approach is suggested for the modeling of multivariant stress-induced martensitic phase transitions (PTs) in elastic materials at the nanoscale for the 2-D and 3-D cases, for quasi-static and dynamic formulations. The approach is based on the phase-field theory, which includes the Ginzburg-Landau equations with an advanced thermodynamic potential that captures the main features of macroscopic stress-strain curves. The model consists of a coupled system of the Ginzburg-Landau equations and the static or dynamic elasticity equations, and it describes evolution of distributions of austenite and different martensitic variants in terms of corresponding order parameters. The suggested explicit finite element algorithm allows decoupling of the Ginzburg-Landau and elasticity equations for small time increments. Based on the developed phase-field approach, the simulation of the microstructure evolution for cubic-tetragonal martensitic PT in a NiAl alloy is presented for quasi-statics (i.e.; without inertial forces) and dynamic formulations in the 2-D and 3-D cases. The numerical results show the significant influence of inertial effects on microstructure evolution in single- and polycrystalline samples, even for the traditional problem of relaxation of initial perturbations to stationary microstructure.