Notch-sensitivity and shear bands in brittle matrix composites

Matrix cracking, fiber breaking and interface sliding cause nonlinear deformation in fiber-reinforced brittle matrix composites. When a notched sample is loaded in tension, the nonlinear deformation usually localizes around the notch, spreads the stress in the ligament more evenly, and thereby leads to a higher fracture load. We simulate the interplay of two deformation mechanisms: a tensile band ahead of, and shear bands perpendicular to, a notch. The shear deformation evens out the stress distribution in the tensile band, and the strength of the tensile band sets the extent of the shear deformation. Each band is simulated by a traction-deformation law. The work of fracture is computed from a small-scale inelastic problem, and the fracture loads of notched samples from a large-scale inelastic problem. Several important conclusions emerge from the simulation. First, weak shear bands can substantially increase the work of fracture. Second, the fracture loads of notched samples are well correlated with the unnotched strength, work of fracture and notch size, by a formula independent of the shear band description. The results of the simulation are used to explain the available experimental data, and to suggest an evaluation procedure for notch-sensitivity.