Micromechanical modeling of the interaction of diffusion mechanisms and surface energy with nonlinear material deformation: Applications to powder densification and void growth.

摘要

Diffusive processes coupled to nonlinear material behavior assume importance in such important technological problems as consolidation of powders, diffusive cavitation at grain-boundary interfaces, and void growth and coalescence in solids. The first three chapters of this thesis are devoted to the study of powder densification using a small-strain finite-element scheme. In the first chapter, the coupled action of stress-driven diffusion and curvature-driven diffusion over the interparticle contact areas and the pore surfaces respectively, and elasticity and power-law creep processes in the bulk of the particles is studied. Numerical results indicate that the interaction of the deformation mechanisms is very important in determining the overall densification rates of the powder aggregate, and that models that focus on a single, dominant densification mechanism underestimate the densification rate. In the second chapter, the macroscopic strain rate of a particle aggregate is obtained from an analytically-constructed and numerically-obtained potential function in terms of the applied loads, the relative density of the compact, and material parameters. The predictions of this potential agree quantitatively with experimentally obtained densification data for copper wires. The interparticle diffusion process is modified in the third chapter to account for the situation when part of the externally delivered power is expended in driving the interface reaction (addition to or removal of atoms from the interparticle boundaries). Numerical computations reproduce experimentally observed decrease in overall densification rates with increasing interface reaction strength. In order to study densification to a larger range of relative density, the densification problem is recast in finite-strain form in the fourth chapter, and it is observed that the small-strain model underestimates the relative density increase for a given amount of time.; Void growth in nonlinearly creeping solids under plane-strain conditions is studied in the fifth chapter. Numerical results reveal a rich variety of solutions; in general, void shape is controlled by the strength of the diffusion process relative to the bulk creep process, whereas void size depends critically on the surface energy of the void in relation to the void size and applied load.