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.

Improvements to the ɛ-α porous compaction model for simulating impacts into high-porosity solar system objects

“…A popular approach in cases where pores are too small to be modeled explicitly is the p-model [3,4]. In this model, compaction is quantified by distension ( = s / ; the ratio of solid density to bulk density), which is equivalent to 1/(1-porosity).…”

Phenomenological Modeling of Deformation of Porous and Cellular Materials Taking Into Account the Increase in Stiffness Because of the Collapse of Pores

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A Mesomechanical Modelling of Porous Aluminum under Dynamic Loading : Comparison Experiment-Calculation

“…For low level of stresses (< 10 GPa), models of porous materials like P-a model [2] where P is the mean stress and a the distention expressing the porosity, or hollow sphere model [3] only take into account the influence of the mean stress on void collapse. To take into account the influence of the shearing stresses, theoretical formulations [4] [5] of the yield law F(r, P, 4, Y) = 0 for a ductile porous material are proposed where z is the second invariant of the stress deviator tensor, P the mean stress, 4 the porosity and Y the current flow stress of the matrix.…”