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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.
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 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 demonstrated 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.