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

The nanoscalemultiphase phase-fieldmodel for stress and temperature-induced multivariantmartensitic transformation under large strains developed by the authors in Basak and Levitas (J Mech Phys Solids 113:162-196, 2018) is revisited, the issues related to the gradient energy and coupled kinetic equations for the order parameters are resolved, and a thermodynamically consistent non-contradictory model for the same purpose is developed in this paper. The model considers N + 1 order parameters to describe austenite and N martensitic variants. One of the order parameters describes austenite <-> martensite transformations, and the remaining N order parameters, whose summation is constrained to the unity, 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 kinetic relationship for the rate of the order parameters versus thermodynamic driving forces is suggested, which leads to a system of consistent coupled Ginzburg-Landau equations for the order parameters. An approximate general crystallographic solution for twins within twins is presented, and the explicit solution for the cubic to tetragonal transformations is derived. A large strain-based finite element method is developed for solving the coupled Ginzburg-Landau and elasticity equations, and it is used to simulate a 3D complex twins within twins microstructure. A comparative study between the crystallographic solution and the simulation results is presented.

Automated summary

This paper revisits the nanoscale multiphase phase-field model for stress and temperature-induced multivariant martensitic transformation under large strains developed by the authors. It resolves the issues related to the gradient energy and coupled kinetic equations and develops a thermodynamically consistent model. The model considers N + 1 order parameters to describe austenite and N martensitic variants, taking into account the energies of the interfaces and a kinetic relationship for the rate of the order parameters. A large strain-based finite element method is used to simulate a 3D complex twins within twins microstructure, and a comparative study is presented.