Stress concentrations around voids in three dimensions: The roots of failure

We present stress concentration factors at the edges of 3D voids in uniaxial compression. Variations in these stress concentration factors due to Poisson's ratio of the host material, void shape, and void-void proximity are explicitly quantified. Voids loaded by a vertical compressive stress are hypothesised to fail in one or two ways: (1) tension crack development due to tensile stress concentrations at the void poles; or (2) compressive stress concentrations at the void sides causing the void wall to fail in shear. The stress concentration factors in this study are found using the numerical displacement discontinuity method. Equations are provided to assess the proximity of a void to the two hypothesised modes of failure. For 3D voids thinned in an axis that lies parallel to the compressive stress these have increasingly high stress concentrations at their sides. Changes in stress concentrations due to the Poisson's ratio of the matrix are minor, apart from for the intermediate stress at the void sides. Void shape, void separation, and void alignment are critical factors in the concentration of stresses. This suggests a significant departure from strength predictions for porous material that are based solely on scalar values of porosity.