Persistent Homology Analysis of the Microstructure of Laser-Powder-Bed-Fused Al–12Si Alloy

The laser powder bed fusion (L-PBF) process provides the cellular microstructure (primary α phase surrounded by a eutectic Si network) inside hypo-eutectic Al–Si alloys. The microstructure changes to the particle-dispersed microstructure with heat treatments at around 500 °C. The microstructural change leads to a significant reduction in the tensile strength. However, the microstructural descriptors representing the cellular and particle-dispersed microstructures have not been established, resulting in difficulty in terms of discussion regarding the structure–property relationship. In this study, an attempt was made to analyze the microstructure in L-PBF-built and subsequently heat-treated Al–12Si (mass%) alloys using the persistent homology, which can analyze the spatial distributions and connections of secondary phases. The zero-dimensional persistent homology revealed that the spacing between adjacent Si particles was independent of Si particle size in the as-built alloy, whereas fewer Si particles existed near large Si particles in the heat-treated alloy. Furthermore, the first principal component of a one-dimensional persistent homology diagram would represent the microstructural characteristics from cellular to particle-dispersed morphology. These microstructural descriptors were strongly correlated with the tensile and yield strengths. This study provides a new insight into the microstructural indices describing unique microstructures in L-PBF-built alloys.