Phase field mechanics of residually stressed ceramic composites

A phase field theory for crystalline solids accounting for thermoelasticity, fracture, twinning, and limited slip is presented. Residual stresses are incorporated via referencing thermoelastic strain to a reference state that is not always stress-free. Rate dependence, dissipated energy, and residual strain energy (possibly degraded by local fracture) are included in the theory, with physically valid predictions first verified for homogeneous stress states. A variational form of the model is implemented in finite element (FE) calculations of three-dimensional (3-D) polycrystalline aggregates consisting of up to two different crystal constituents and a binding matrix along grain and phase boundaries. Model specifics correspond to constituents of boron carbide-titanium diboride (B4C-TiB2) ceramic composites. Effects of thermal-residual stresses incurred during processing, as well as other local microstructure properties and physical features, on deformation and failure mechanisms are revealed. Peak aggregate strengths observed for different boundary conditions demonstrate a pressure-dependent failure surface.