Static and Dynamic Pore-Collapse Relations for Ductile Porous Materials

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.