Indentation of porous solids

Abstract

The effect of porosity upon indentation resistance is explored for a sticking conical indenter. Two material models are used: the Gurson model which is appropriate for lower porosities, where there are well separated voids that are roughly spherical in shape, and the particle yield model of Fleck et al. (1992) J. Mech. Phys. Solids which is appropriate for a microstructure consisting of spherical particles joined by discrete necks. Finite strain finite element calculations and a cavity expansion model both show that the indentation pressure is 2–3 times the uniaxial yield strength of the porous solid, for initial porosities of up to 0.3. Compaction occurs in a plastic zone of roughly hemispherical shape surrounding the indenter. Full density is achieved along the flanks of the indenter for initial porosities of less than 0.1, but not for higher porosities. Both the finite element and cavity expansion models suggest that the average indentation pressure increases as the cone is made sharper (smaller included angle at the apex of the cone), as the yield strain of the material decreases and as the level of initial porosity decreases. For comparison purposes, finite element results are presented for fully dense solids. The predictions of the finite element analysis for a porous solid are also compared with the experimental results for indentation of a sintered steel. Very good agreement is found for both the indentation load and for the deformation field.