High temperature solid mechanics: Mesoscale computational formulation

A mesoscale phase field formulation for high temperature computational mechanics of polycrystalline solids with voids is developed. The mathematical description includes translation and rotation of crystalline grains, diffusion through the crystals and interfaces, lattice growth at the boundary and grain boundary sliding, elastic stresses and compositional eigenstrains. The formulation connects heterologous continua; solids are represented by the lattice continuum, while the voids/gas are the standard mass continuum viscous (and elastically compressible) fluid. The deformation gradient for solids is consequently a state variable with evolution defined in the Eulerian sense. We consider non-inertial, controlled-temperature processes with vacancy-atom exchange diffusion mechanism and isotropic interface energies. Nevertheless, as discussed in the concluding section, the formulation provides the basis for extensions to the processes with significant heat sources or sinks, diffusion of multiple species and anisotropic interface energies.