A nonoverlap model for the dispersion of spherical particles

The dispersion of randomly positioned spherical particles can be characterized in terms of probability functions for the center to center spacings to its neighbors. This model is used with a correction procedure for describing the dispersion of nonoverlapping spherical particles. Modification of the random model to account for the bias introduced by excluding overlap is carried out by setting the neighbor probability functions equal to zero for radial distances which cause overlap, and then renormalizing the functions. Comparison of the probability distributions and their moments for the nonoverlap model with Monte Carlo simulation data show that it provides a valid approximation for the dispersion of spherical particles with volume fractions as high as 30 pct. The effects of volume fraction and size distribution of the particles upon the nonoverlap probability functions and their moments are described. Radial density functions are also calculated for both the random and the nonoverlap models. Formerly with Division of Minerals Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA.     

A nonoverlap model for the dispersion of spherical particles

The dispersion of randomly positioned spherical particles can be characterized in terms of probability functions for the center to center spacings to its neighbors. This model is used with a correction procedure for describing the dispersion of nonoverlapping spherical particles. Modification of the random model to account for the bias introduced by excluding overlap is carried out by setting the neighbor probability functions equal to zero for radial distances which cause overlap, and then renormalizing the functions. Comparison of the probability distributions and their moments for the nonoverlap model with Monte Carlo simulation data show that it provides a valid approximation for the dispersion of spherical particles with volume fractions as high as 30 pct. The effects of volume fraction and size distribution of the particles upon the nonoverlap probability functions and their moments are described. Radial density functions are also calculated for both the random and the nonoverlap models.     

A theoretical model for the elevated temperature deformation of dispersion hardened metals

A theoretical model is presented to describe the elevated temperature (above 1/2T_m @#@) deforma-tion of dispersion hardened metals such as TD-nickel and SAP alloys. The model is based on two proposals: 1) Both dislocation glide and climb are influenced by matrix stresses at small, incoherent, second phase dispersed particles produced by surface tension effects at the particle-matrix interface. 2) Two concurrent processes may contribute to the elevated temperature deformation of polycrystalline dispersion hardened metals, dislocation motion and diffusion controlled grain boundary sliding. The model may explain the origins of high apparent activation enthalpies and large stress sensitivities which have been observed in dispersion hardened metals. It may also provide guidelines for optimization of elevated temperature strength.