Secondary phase distribution analysis via finite body tessellation

The concept of a Dirichlet tessellation has been extended to that of a ‘finite body’ tessellation to provide a more meaningful description of the spatial distribution of non‐spherical secondary phase bodies on two‐dimensional sections. A finite body tessellation consists of a network of cells constructed from the interfaces of each individual secondary phase body such that every point within a cell is closer to the corresponding body than to any other. Spatial distribution related cell characteristics derived from Dirichlet tessellations have been extended to finite body tessellations. Quantitative comparisons between the two methods indicate that finite body tessellation measurements are more physically representative as well as more sensitive to local distribution characteristics of secondary phases. To reflect the potential application of finite body tessellations, a methodology is described for analysing the effects of particle distribution and morphology on short crack behaviour in particulate reinforced metal matrix composites.