Interplay of Fracture and Martensite Transformation in Microstructures: A Coupled Problem

We are witnessing a tremendous transition towards a society powered by net-zero carbon emission energy, with a corresponding escalating reliance on functional materials (FM). In recent years, the application of FM in multiphysics environments has brought new challenges to the mechanics and materials research communities. The underlying mechanism in FM, which governs several fundamental characteristics, is known as martensitic phase transformation (MPT). When it comes to the application of FM in the multiphysics context, a thorough understanding of the interplay between MPT and fracture plays a crucial role in FM design and application. In the present work, a coupled problem of crack nucleation and propagation and multivariant stress-induced MPT in elastic materials is presented using a finite element method based on Khachaturyan's microelasticity theory. The problem is established based on a phase-field (PF) approach, which includes the Ginzburg-Landau equations with advanced thermodynamic potential and the variational formulation of Griffith's theory. Therefore, the model consists of a coupled system of the Ginzburg-Landau equations and the static elasticity equation, and it characterizes evolution of distributions of austenite and two martensitic variants as well as crack growth in terms of corresponding order parameters. The numerical results show that crack growth does not begin until MPT has grown almost completely through the microstructure. Subsequent to the initial formation of the martensite variants, the initial crack propagates in such a way that its path mainly depends on the feature of martensite variant formations, the orientation and direction upon which the martensite plates are aligned, and the stress concentration between martensite plates. In addition, crack propagation behavior and martensite variant evaluations for different lattice orientation angles are presented and discussed in-detail.