Thermo-elastic micromechanical modeling of tetragonal ZrO2 with a herringbone microstructure inherited from the cubic phase

The distribution of residual stresses at the crystal scale is investigated in several random polycrystalline aggregates of zirconia. The underlying stochastic model generates tetragonal crystals forming three-dimensional herringbone microstructures, originating from cooling an initial single cubic crystal at high temperatures followed by a solid-state phase transition. The obtained microstructures are constructed following crystallographic constraints in terms of variant selection, as well as twin and band boundary orientations. This stochastic modeling approach allows generating microstructures with twin domains of various aspect ratios, embedded in several Voronoi cells as observed when the phase transition starts simultaneously from different locations in the cubic crystal. Considering the transformation strain and the anisotropic elastic and dilation properties at the crystal scale, these microstructures are solved with the spectral (FFT) full-field method for pure thermal loading (cooling). Thermal dilation has a limited effect on the residual stress field, about one order of magnitude smaller than the transformation strain, even for a cooling of . Normal stresses along the tetragonal crystal axes are in the order of a few GPa and proportional to the tetragonality of the zirconia crystal, except for a specific microstructure where stresses even vanish for infinite aspect ratios.