Characterizing Heterogeneity in the Distribution of Particles in Multiphase Materials
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Characterizing Heterogeneity in the Distribution of Particles in Multiphase Materials Jeremy W. Leggoe Chemical Engineering Department, Texas Tech University Box 43121, Lubbock, Texas, 79409 ABSTRACT Advances in the development of multiscale failure models are dependent on the development of techniques for accurately characterizing the nature of spatial heterogeneity. Nth-nearest neighbor statistics offer a means of quantitatively and qualitatively characterizing deviation from complete spatial randomness (CSR). This investigation has determined the mean distances to the Nthnearest neighbor for CSR dispersions of monodisperse spheres in 2D and 3D for N up to 200. To evaluate data obtained from micrographs, mean Nth-nearest neighbor distances have also been collected for planar slices through 3D arrays of monodisperse spheres. Results are presented for a volume fraction of 0.20 in the form of an "Inhibition Ratio", which compares the results collected for finite disks and spheres with the values expected for 2D and 3D point processes. INTRODUCTION Spatial heterogeneity in the distribution of secondary phases at the microscale can strongly influence the macroscopic properties of multiphase materials. In CSR particle distributions, some particle clustering is inevitable [1]. Particle distributions in real materials often deviate from CSR as a result of processes occurring during material synthesis, exhibiting more severe clustering, which will exacerbate any deleterious effects associated with particle clustering [2,3]. The importance of microscale spatial heterogeneity in the failure process has motivated the development of models that incorporate heterogeneous particle distributions. Representative volume element (RVE) models have been formulated in which particles are added to microscale volumes via Random Sequential Addition (RSA) [4,5]. To capture the multiscale nature of the failure process, in particular the mesoscale effects of spatial heterogeneity on the evolution of final failure, a cellular automata (CA) approach has been developed [6,7]. To date, RVE and CA models of heterogeneous materials have been randomly or arbitrarily generated, with no attempt made to directly simulate the spatial statistics of real (non CSR) material in finite element investigations. Particle distributions deviating from CSR may be reconstructed using an "energy minimization" technique based on statistical correlations [8,9]. An initially randomly generated microstructure evolves towards exhibiting the desired correlation function via a Metropolis algorithm, with the probability of particle move acceptance being based on an "energy" representing the difference between the current and target correlation functions. Application of this approach requires the selection of a correlation that successfully captures the extent and severity of particle clustering. A correlation based on comparing the mean center-to-center distance to the Nth-nearest neighbor particle in an actual microstructure () with the value expected for a CSR p
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