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A new 3-dimensional front tracking model for grain boundaries (GBs) has been developed. It allows to efficiently simulate the motion of GBs in interaction with other GBs or particles of secondary phases. The model fully accounts for the dependence of the grain boundary energy on the local orientation of the boundary plane, in the sense that any functional dependence can be chosen. In principle, this model allows to study grain growth or recrystallisation considering any realistic description of the GB energy. The present paper describes the deri- vation of the mathematical concept from basic mechanics, in particular the consideration of the Herring torque, and some implementation details. The model is verified by comparison with analytical models. For some heuristic GB energy dependences, the equilibrium shape of a singular grain with a fixed volume embedded in another grain is calculated and discussed. As a first application, the Zener drag for realistic arrangements of about 1350 particles has been derived from simulations.