Phase Field Modeling of Crack Propagation in Shape Memory Ceramics: Application to Zirconia

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Shape memory ceramics (SMCs) are promising candidates for actuators in extreme environments such as high temperature and corrosive applications. Despite outstanding energy dissipation, compared to metallic shape memory materials, SMCs suffer from a sudden brittle fracture. While the interaction of crack propagation and phase transformation in SMCs have been subject of several experimental and theoretical studies, mainly at the macroscale, the fundamental understanding of the dynamic interaction of crack propagation and martensitic transformation is poorly understood. In this work, we use the phase field framework to fully couple the martensitic transformation to the variational formulation of brittle fracture. The model is parameterized for single crystal zirconia which experiences tetragonal to monoclinic transformation during crack propagation. For the mode I of fracture, the opening mode, crack shows an unusual propagation path that is in good agreement with the experiments and indicates the significant role of phase transformation on the crack propagation path. The investigation on the effect of lattice orientation on crack propagation shows that the lattice orientation has a significant influence not only on the crack propagation path but also on the magnitude of the transformation toughening. In a constrained crystal the maximum (minimum) toughening, under mode I loading, occurs when the crystal lattice orientation makes the angle of 50 (90) degrees with the crack surface.