Phase field modeling of current density distribution and effective electrical conductivity in complex microstructures

Phase field model is developed to simulate local current density distribution and macroscopic effective electrical conductivity in complex microstructures. Heterogeneous conductivity tensor in multi-grain and/or multi-phase microstructures is explicitly described by phase field variables without direct tracking of interfaces or boundaries. Microscopic anisotropic Ohm's law is solved efficiently using Fourier transform technique. These advantageous features allow this model to seamlessly integrate with other phase field models of microstructure evolutions. Application examples are presented to demonstrate the model's capability and potential, including polycrystals, solder joints, and two-phase alloys.