Concurrent modeling of martensitic transformation and crack growth in polycrystalline shape memory ceramics

Mechanical degradation of shape memory materials (SMM) has been a long-lasting challenge that has prevented the wider range of high-cycle applications of SMM. The core of the challenge is the limited current knowledge of how crack growth and martensitic transformation (MT) interact concurrently. In this paper, we study the dynamic interaction of MT and crack propagation in polycrystalline shape memory ceramics. We construct a multiphysics phase-field model that couples the Ginzburg-Landau theory of MT to the variational formulation of brittle fracture. The model is parameterized for tetragonal polycrystalline zirconia, and the experimental data from literature were used to validate the model. The model predicts the three dominant crack propagation patterns which was observed experimentally including the secondary crack initiation, crack branching, and grain bridging. The model shows the critical role of texture engineering in toughening enhancement. Polycrystalline zirconia samples with grains that make low angles between a -axis in tetragonal phase and the crack plane, show higher transformation toughening, due to maximum hydrostatic strain release perpendicular to the crack tip. The model also shows the grain boundary engineering as a way to enhance the transformation toughening. The maximum fracture toughness occurs at a specific grain size, and further coarsening or refinement reduces the fracture toughness. This optimum grain size is the consequence of the competition between the toughening enhancement and MT suppression with grain refinement.