Quantitative evaluation of the non-uniformity of inclusion distribution in free cutting steel using the Delaunay triangulation method

Delaunay triangulation converts two-dimensional scatter images into statistical data. Parameters derived from the triangulation—such as triangle area, edge length, neighboring triangle area, and neighbor distance—are all related to particle distribution uniformity. In this work, Delaunay triangulation is applied to simulated scatter plots with varying densities and non-uniformity levels to identify an indicator that accurately reflects distribution non-uniformity. Statistical results show that the coefficient of variation of the Delaunay edge lengths ( v d ) sensitively captures differences in non-uniformity while being minimally influenced by areal density, establishing it as a reliable single-value indicator. For MnS inclusions in free-cutting steel, v d exhibits a significant positive correlation between cutting resistance. This a quantitative microstructure-property link, enabling prediction of machining performance from inclusion distribution features.