Phase field modeling of mechanically driven interface propagation in multiphase systems

Computational models based on the phase-field method have become an indispensable tool for modeling the microstructural evolution in material science and physics. The models typically operate on a mesoscopic length scale and provide through describing the interface motion valuable information about structural changes in materials. The specific parametrization method of the model complicates to satisfy the jump conditions and the formulation of the driving forces at the interfaces, since the sharp interface is stretched over a volumetric region. In the present work local homogenization methods of mechanical material parameters are analyzed and a method is presented that guarantee the fulfillment of the mechanical jump conditions and reflects the mechanical configuration forces at diffuse parameterized interfaces. Methods for infinitesimal and for finite deformations are presented and applied to the martensitic phase transformation process. The mechanically driven interface motion also include the propagation and development of cracks. For the study of these processes a multiphase field model is presented to study the crack propagation in polycrystalline materials coupled with a phase transformation process. the model is applied to a polycrystalline material and the influence of a heterogeneous crack resistance and the interfacial energy between the solid phases on the resulting crack path is demonstrated.