Author(s)

J. W. Leggoe

Abstract

Material failure is typically a complex multi-scale process, in which macroscale failure properties are strongly influenced by heterogeneity in the spatial distribution of the microscale flaws and secondary phases responsible for failure initiation. The Deviation Ratio, representing the ratio of the distance to the Nth-nearest neighbor in the real material to the distance expected for an equilibrium (random) ensemble of particles, offers a method by which the deviation of particle distribution from an equilibrium spatial distribution can be qualitatively and quantitatively characterized. Previous investigations have identified the importance of using Nth-nearest neighbor statistics derived from ensembles of impenetrable spheres rather than point processes to calculate the deviation ratio, with statistics derived from slices through three-dimensional ensembles being preferred when considering data extracted from micrographs. In the current investigation, it has been found that polydispersity in the particle distribution can significantly affect the mean distance to the Nth-nearest neighbor in equilibrium ensembles of disks and spheres. The mean distances to the Nth-nearest neighbor for polydisperse particle populations exceed those for monodisperse populations for all values of N for two-dimensional ensembles, three-dimensional ensembles, and slices through three-dimensional ensembles. The effect is directly attributable to the decrease in population intensity associated with polydispersity for a given particle volume fraction and mean particle diameter. Continuing investigations will explore the effect of standard deviation, particle volume fraction and the form of the particle size distribution on mean Nth-nearest neighbor distances. 1 Introduction Material failure is typically a complex multi-scale process, in which macroscale failure properties are strongly influenced by heterogeneity in the spatial

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