Rate-dependent bridging law and its application to dynamic crack growth in brittle-matrix composite materials

Finite element analysis (FEA) is carried out for Mode I dynamic crack propagation in fibre reinforced brittle matrix composites under the conditions of small-scale bridging and high loading rate. The fracture process involves two distinct mechanisms: fibre bridging and matrix cracking. A rate-dependent bridging law based on micromechanical analysis is used to simulate the degradation of crack-bridging, and a softening cohesive law characterises matrix separation. An embedded reinforcement and cohesive zone model represents the fracture process zone (FPZ) of bridged-cracks. Outside the FPZ, the bulk material is transversely isotropic and orthotropic elastic. Numerical results show an accelerated regime in the crack-resistance curves, in contrast to the abrupt rise for brittle materials. There is a competition between the rate-weakening effect on bridging stress and the inertia effect influencing the energy flux to the crack-tip. The fracture resistance depends on both loading rates and rate-sensitivity factors of the bridging law. Fibres break randomly at higher loading rates and rate sensitivity factors, while successive fibre breaks occur at lower rates and rate sensitivities. Thus, the crack-bridging zone has a zigzag opening profile and the non-singular fibre stresses experience oscillations with time at higher rate-sensitivity factors and loading rates.