New insights into the development of brittle shear fractures from a 3-D numerical model of microcrack interaction

Existing models of brittle shear failure are unable to account for three-dimensional deformation involving the development of polymodal sets of fractures. Motivated by field observations of contemporaneous arrays of quadrimodal faults and deformation bands, we use an idealised micromechanical model to explain how brittle shear fractures can form oblique to all three remote principal stresses. We model tensile microcracks as finite ellipsoidal voids, subjected to small opening strains, in a linear isotropic elastic matrix. The geometry of the tensile stress lobes around the ends of an isolated microcrack promotes the en echelon interaction of neighbouring cracks with respect to the prescribed crack orientation. Coalescence of these interacting crack arrays into a through-going composite fracture surface leads to a brittle shear failure plane oriented obliquely to all three coordinate axes and all three remote principal stresses. Experimental evidence supports the idea that composite shear fractures can propagate in-plane through the coalescence of many constituent tensile microcracks. Our new model, based on the 3-D geometry of the elastic stress field around a mode I crack, can explain the oblique orientations of polymodal faults formed in a triaxially compressive stress field.