The Polycrystalline materials grain boundary structure, crystalline texture and grain surface morphology, each plays an important role in interface transport. Among the different surface evolution phenomenas, the objective of the current work is to study the kinetics of grooving by surface diffusion only. Most of the existing theoretical and computational models use two dimensional grooving with one dimensional surface evolution. Hackl, et al.  have presented a novel variational model of surface motion using a thermodynamic extremum principle for grooving and wetting under diffusion. This model is further extended to a three dimensional grain structure using two dimensional surface evolution .In this paper, the kinetics of grooving for a periodic polycrystalline aggregate is studied. An ansatz function for grain boundary energy is defined as a functional of grain orientation and boundary inclination. For such orientation dependent grain boundary energy, Herring's relation must be satisfied locally at each triple point of intersecting boundaries thus we have four equations at each node in a representative volume element(RVE). Such an overdetermined system is solved using a non‐linear optimization method with weak constraints for the grain boundary energies. The evolution of surface grooves is studied with isotropic surface energy and mobility. The effect of line mobility on surface evolution is also studied for the chosen RVE. A comparison is made between orientation dependent grain boundary energies and isotropic grain boundary energies. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Proceedings in Applied Mathematics & Mechanics – Wiley
Published: Jan 1, 2017
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