A traction law for inclined fiber tows bridging mixed-mode cracks

Prior detailed microscopic observations have revealed the essential mechanisms of damage in through-thickness reinforcing tows when a delamination crack passes. An earlier model demonstrated that these mechanisms could be represented with appealing simplicity in the special case of pure mode II cracking when the tows are initially normal to the fracture plane. Here, generalized micromechanical models are presented that show how a bridging tow should behave if it is initially inclined to the fracture plane and subject to mixed-mode loading. From these models, the effective bridging law for a bridged crack model of the delamination can be derived. Once again, approximations guided by experiments enable simple relationships between the bridging tractions and the crack displacements to be derived, which can be evaluated by elementary numerical steps. The solution space of the most generally posed problem is complex and rich, but simple and even closed-form analytical expressions for the traction law are available for certain cases.