Phase-field simulation of stress-induced martensitic phase transformations at large strains

A complete system of coupled phase-field and mechanical equations for the simulation of multivariant martensitic phase transformations at large strains is formulated. The finite-element approach and an algorithm for the solution of corresponding problems are developed and implemented in a code FIDESYS. Cubic to tetragonal phase transformation in NiAl is studied. Various problems on stress-induced nucleation and evolution of martensitic variants in nanosize samples are solved, including a rectangular sample with single and multiple circular or elliptical nanovoids (with and without surface tension), as well as nanotube and beam. Importance of finite strain formulation is demonstrated. In particular, for the case when structural instability (buckling) of a beam is caused by phase transformation, for a geometrically linear formulation, phase transformation is suppressed. This is because finite rotation increases the energy of the system, while in a geometrically nonlinear theory energy is independent of rotation. Similar phase field and numerical approaches can be applied for twinning, dislocations, and reconstructive transformations.