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 grain growth rate model may also be described with topology considerations of microstructure. The size parameter bearing in the model is further discussed both according to the derived model and in another approach with the aid of quantitative relationship between the grain size and the integral mean curvature over grain surface. Both approaches successfully demonstrate that, if the concerned grains can be well approximated by a space-filling convex polyhedra in shape, the grain size parameter bearing in the Hillert-type 3D grain growth model should be a parameter proportional to the mean grain tangent radius.
Based on the two sublattice model of the regular solution,one being metal atom sublattice and another being interstitial atom sublattice,a thermodynamic model for the precipitates of niobium carbonitride,vanadium carbonitride and titanium carbonitride was established to study the starting-temperature of precipitates and the austenite compositions at given temperature in a low carbon steel.The calculation results show that starting-temperature of the precipitation of niobium carbonitride,vanadium carbonitride and titanium carbonitride are 1100℃,920℃ and 1340℃,respectively,the mole fraction of carbonitride precipitates is 8.65×10-4 in the 0.053C-0.0028N-1.28Mn-0.008S-0.031Al-0.046Nb-0.008Ti0.029V-Fe steel.When the N content is from 0.0028% to 0.0056%,the starting-temperature of the precipitation of the titanium carbonitride changes from 1340℃ to 1430℃.And the C content is from 0.053% to 0.07%,the startingtemperature of the precipitation of the titanium carbonitride hardly changes,but the atomic fraction of niobium in the carbonitride obviously increases.
XIANG Song 1,3,LIU Guo-quan 2 (1.School of Materials and Metallurgy,Guizhou University,Guiyang 550003,Guizhou,China
