Static and Dynamic Pore-Collapse Relations for Ductile Porous Materials

Abstract

Static and dynamic pore‐collapse relations for ductile porous materials are obtained by analysis of the collapse of a hollow sphere of incompressible elastic‐plastic material, with appropriate pore radius and over‐all porosity. There are three phases of the pore‐collapse process: an initial phase, a transitional elastic‐plastic phase, and a plastic phase. The change in porosity during the first two phases is quite small. In the plastic phase, the static pore‐collapse relation is an exponential law that depends only on the yield strength of the material; the dynamic relation is a nonlinear second‐order ordinary differential equation that involves the yield strength and a material constant (with the physical dimension of time) that depends on the yield strength, the density, the initial porosity, and the pore radius. Comparison of the theoretical predictions with finite‐difference computer‐code calculations for pore collapse of a hollow sphere of compressible material indicates that the effect of elastic compressibility on pore collapse is quite small, so that the pore‐collapse relations obtained from the incompressible model should have a wide range of validity. Also, the specific internal energy at the pore boundary has a logarithmic singularity as the pore closes.