On the crack onset and growth in martensitic micro-structures; a phase-field approach

In this work, a phase-field approach (PFA) is presented to study crack nucleation and propagation in martensitic micro-structures resulted from multi-variant martensitic phase transformations (MPT) within the framework of a finite element method (FEM). To this end, first, a coupled system of the time-dependent Ginzburg-Landau (TDGL) equation and the equilibrium equation is established based on the micro-elasticity theory, which reveals the nucleation and growth of diffusionless martensitic multi-variants forming a twinned martensitic micro-structure. The Helmholtz free energy used in this work consists of a second-degree polynomial of the phase variable, which leads to a nonlinear dependence on the order parameter in the TGDL equation. Thereafter, the nucleation and propagation of a crack is scrutinized in the obtained martensitic specimen, with and without pre-existing crack, according to three types of martensitic embryos. To do so, a damage variable is introduced to the multi-variant MPT model to study the interactions between the martensitic transformation and fracture. The key contributions of this study are not only to shed light on the evolution of the martensitic variants in the micro-structure with three types of pre-existing martensitic embryos, but also to investigate onset and growth of a crack in the martensitic specimen.