A multiphase phase-field study of three-dimensional martensitic twinned microstructures at large strains

TL;DR

This paper develops a multiphase phase-field model to simulate complex three-dimensional martensitic twinned microstructures at large strains, incorporating thermodynamic consistency and detailed interface energies.

Contribution

It introduces a thermodynamically consistent multiphase phase-field approach with multiple order parameters for modeling nanoscale martensitic transformations under large strains.

Findings

Successful simulation of 3D twins within twins microstructures

Validation of the model against crystallographic solutions

Demonstration of large-strain effects on microstructure evolution

Abstract

A thermodynamically consistent multiphase phase-field approach for stress and temperature-induced martensitic phase transformation at the nanoscale and under large strains is developed. A total of N independent order parameters are considered for materials with N variants, where one of the order parameters describes A <-> M transformations and the remaining N-1 independent order parameters describe the transformations between the variants. A non-contradictory gradient energy is used within the free energy of the system to account for the energies of the interfaces. In addition, a non-contradictory kinetic relationships for the rate of the order parameters versus thermodynamic driving forces is suggested. As a result, a system of consistent coupled Ginzburg-Landau equations for the order parameters are derived. The crystallographic solution for twins within twins is presented for the cubic to tetragonal transformations. A 3D complex twins within twins microstructure is simulated using the developed phase-field approach and a large-strain-based nonlinear finite element method. A comparative study between the crystallographic solution and the simulation result is presented.