Phase transformation and incompatibility at grain boundaries in zirconia-based shape memory ceramics: a micromechanics-based simulation study

Zirconia-based shape memory ceramics (SMCs) exhibit anisotropic mechanical response when undergoing elastic deformations as well as during austenite–martensite phase transformation. This behavior results in different types of strain incompatibility at grain boundaries, which we study here using a micromechanical model. A single-crystal model is implemented to provide a full mechanistic three-dimensional description of the anisotropic elastic as well as martensitic transformation stress–strain response, including non-Schmid behavior caused by the significant volume change during martensitic transformation. This model was calibrated to and validated against compression tests of single-crystal zirconia micro-pillars conducted previously, and then used to model bi-crystals. Upon the introduction of a grain boundary, the simulation provides detailed information on the nucleation and evolution of martensite variants and stress distribution at grain boundaries. We identify bi-crystal configurations which result in very large stress concentrations at very low deformations due to elastic incompatibility, as well as others where the elastic incompatibility is relatively low and stress concentrations only occur at large transformation strains. We also show how this approach can be used to explore the misorientation space for quantifying the level of elastic and transformation incompatibility at SMCs grain boundaries. Micromechanics models provide insights on grain boundary elastic and phase transformation strain incompatibility in shape memory zirconia