Characterizing Spatial Heterogeneity In
Polydisperse Particle Distributions
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
Keywords
Related Book
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