ASTM grain-size model and related random tessellation

Abstract Three random tessellation models, the Poisson-Voronoi model, the homogeneous Johnson-Mehl model with constant nucleation intensity and constant grain growth rate, and the nonhomogeneous Johnson-Mel model with time-dependent nucleation intensity and constant growth rate, were investigated together with the grain-size model used in ASTM E 112-82. For each model, the corresponding physical backgrounds are outlined, and the expressions for basic characteristics of spatial and planar structure with space-filling grains of a single phase are introduced. The internal relationships among tessellations are derived and analyzed.