Necessary and sufficient fracture criteria for a composite with a brittle matrix. Part 1. Weak reinforcement

Fracture of a composite medium with a brittle matrix is studied. The brittle or plastic material of the reinforcing elements is highly deformable. For normal-rupture macrocracks, necessary criteria of brittle strength and sufficient criteria of quasibrittle strength are proposed. Simple analytical dependences of the macrocrack length on the loading parameter, structural, rigidity, and strength parameters of the medium, and damage parameters of the material of the components are obtained. The critical loads for these criteria may differ substantially even if the reinforcement coefficient is small and the material of reinforcing elements is highly deformable. If the necessary criterion is satisfied, crack extension occurs and microcracks are formed in the bonds of the structure located ahead of the macrocrack tip. The number of damaged bonds depends on the macrocrack opening and characteristics of postcritical deformation of the damaged bonds.