Phase Field Modeling of Crack Growth in Shape Memory Ceramics
Authors: Moshkelgosha Ehsan 
Published: August 2021

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 has been the 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. This dissertation attempts to provide a mathematical model for crack propagation in transformable zirconia to address the shortage of classical methods. This dissertation uses the phase field framework to fully couple the martensitic transformation to the variational formulation of brittle fracture.

Firstly, the model is parameterized for single crystal zirconia, which experiences tetragonal to monoclinic transformation during crack propagation. For 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.

Secondly, 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 were 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 the a-axis in the 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.

Finally, 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.