Derivation of Hillert-type 3D grain growth rate model with topological considerations and discussion on its grain size parameter

Guoquan Liu; Haibo Yu;Xiaoyan Song;Xangge Qin;Chao Wang Materials Science and Engineering School, University of Science and Technology Beijing, Beijing 100083, China School of Materials Science and Engineering, Beijing University of Technology, Beijing 100022, China

摘 要：<正> A Hillert-type three-dimensional grain growth rate model was derived through the grain topology-size correlation model,combined with a topology-dependent grain growth rate equation in three dimensions. It shows clearly that the Hillert-type 3D graingrowth rate model may also be described with topology considerations of microstructure. The size parameter bearing in the model isfurther discussed both according to the derived model and in another approach with the aid of quantitative relationship between thegrain size and the integral mean curvature over grain surface. Both approaches successfully demonstrate that, if the concerned grainscan be well approximated by a space-filling convex polyhedra in shape, the grain size parameter bearing in the Hillert-type 3D graingrowth model should be a parameter proportional to the mean grain tangent radius.

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