On the effects of friction, roughness and toughness on interfacial sliding in brittle composites

This computational analysis investigates the interaction between friction, roughness and toughness at interfaces with regard to sliding lengths which proceed from the tip of an impinging matrix fracture. Sliding lengths at interfaces are important to the fracture behavior of brittle fibrous composites. The computer model uses a two dimensional surface integral formulation to model a crack perpendicular to a nominally planar interface. The tractions at the interface satisfy a Coulomb relationship and are found through an iterative process involving the stress induced by the matrix crack, the stress induced by the developing slip and an initial normal compressive stress (presumed to result from setting and/or thermal coefficient mismatch). The interfacial roughness is simulated using surface integral elements arranged in a periodic, triangular array. The toughness of the interface is represented via a specialization of the surface integral formulation to embed the near-tip, elastic asymptotic solution. The results indicate that there are significant interaction effects between friction and the other parameters, i.e. the friction dictates the sensitivity of the sliding lengths to changes in interfacial toughness and roughness. Also, to achieve `long' sliding lengths, which may be desirable in reducing the stress concentration in the medium across the interface, the magnitude of the interfacial critical energy release rate must be significantly less than the magnitude required to ensure crack deflection.