Solid state transformations and crack propagation : a phase field study

Diffusional pattern formation processes, which for instance lead to the formation of snowflakes in undercooled watervapor, are doubtless fascinating systems with pretty complex nonlinear behavior. In the accompanying so-called diffusion limited phase transformation kinetics the phase evolution is strongly coupled to the long-range diffusion of latent heat, that is released at the solid liquid interface. For transformations in the solidstate these processes are additionally subjected to nonlocal elastic effects which arise from structural differences between adjacent solid phases. Mathematically, these dynamic systems can be mapped to so-called moving boundary problems, which then, for example, can be treated by the phase field method. To numerically solve the current problem, we develop a phase field model for the simulation of diffusion limited solid-state transformations, that accounts for the coupled influence from both the thermal diffusion of latent heat as well as the elastic lattice strain effects. Then, using basically phase field simulations, we study the kinetics of diffusion limited solid-state transformations. The present investigations provide new insights in the recently discovered mechanism of pattern selection via lattice strain effects. This mechanism turns out to be very effective as indicated by the surprisingly high growth velocities. Also the propagation of cracks can be understood as an elastically driven interfacial pattern formation process. Such a description of dynamic fracture mechanics again leads to a moving boundary problem. In this work we collect the previously gained research results on the behavior of dynamic crack propagation in such models, and reinterpret them in the light of recent findings on the influence of viscous friction in such systems. Finally, to complete the picture about the arising model behavior also supplementing new studies have been performed.