Three-Dimensional Phase Field Modeling of Fracture in Shape Memory Ceramics

Despite the vast applications of transformable ceramics, such as zirconia-based ceramics, in different areas from biomedical to aerospace, the fundamental knowledge about their mechanical degradation procedure is limited. The interaction of the phase transformation and crack growth is crucial as the essential underlying mechanism in fracture of these transformable ceramics, also known as shape memory ceramics. This study develops a three-dimensional (3D) multiphysics model that couples the variational formulation of brittle crack growth to the Ginzburg-Landau equations of martensitic transformation. We parameterized the model for the 3D single crystal zirconia, which experienced stress- and thermal-induced tetragonal to monoclinic transformation. The developed 3D model considers all 12 monoclinic variants, making it possible to acquire realistic microstructures. Surface uplifting, self-accommodated martensite pairs formation, and transformed zone fragmentation were observed by the model, which agrees with the experimental observations. The influence of the crystal lattice orientation is investigated in this study, which reveals its profound effects on the transformation toughening and crack propagation path.