Topology and differential geometry-based three-dimensional characterization of pearlite spheroidization

Abstract

Spheroidized pearlite microstructures in three-dimensions (3D) in a 0.8 mass% C-Fe steel under 700°C static annealing was examined focusing on topology and differential geometry. The topological or differential-geometric features of the microstructures were examined by evaluating the genus and the Gaussian/mean curvatures. 3D visualization demonstrated that the holes intrinsic in cementite lamellae are significant morphological features affecting the kinetics of the initial pearlite spheroidization, due to the mean curvature differences between the hole edge and the adjacent flat surface. The hole coalescence and expansion influence not only the morphological evolution, but also the topological characteristics. The genus per unit volume decreases at an earlier spheroidization time due to a decrease in the number of holes and an increase in independent bodies, but increases at longer coarsening time because of a decrease in independent bodies. The distribution area of nonzero probability of the mean and Gaussian curvature decreases with an increase in spheroidization time, which agrees with the increase in the length scale of the microstructures. © 2012 ISIJ.