Application of the Betti number to prior austenite grain size analysis of repeatedly quenched steel based on the Homology method

摘要

Grain refinement has a strong influence on material strength. Therefore, the automatic evaluation method of the grain refinement level is useful. In order to develop a grain size analysis system, we applied the homology theory to prior austenite grain analysis. We prepared repeatedly quenched high-carbon high-chromium steel samples (JIS-SUJ2) and evaluated their microstructures in order to investigate the relation between the Betti numbers (b_0 and b_1) and prior austenite grains. We found that the Betti number (b_1) is strongly correlated to the number of grains.