Micromechanics of crack bridging in sapphire/epoxy composites

Abstract

Fracture-mechanics analyses of matrix-cracking stress and fracture toughness of brittle-matrix composites require knowledge of the crack-closure tractions applied by the bridging fibers. The closure traction is expressed as a relationship between a distributed closure stress ( p) and the local crack-opening displacement ( u). The p/u relationship is typically derived from a micromechanics analysis of stress transfer from the matrix to the fiber in the vicinity of the matrix crack. This paper describes measurements of bridging stresses and crack openings in a model composite made of a brittle epoxy matrix and sapphire filaments coated with release agents to prevent interfacial bonding. Stresses in the crack-bridging sapphire filaments were determined by measuring the shift of the fluorescence lines of trace chromium impurity with a laser microprobe. The measured p/u data were compared with micromechanical models applicable to composites with unbonded, frictional interfaces and found to be consistent with models that predict a lower-bound bridging stress at the crack tip equal to the far-field fiber stress. The implications of this finding for the prediction of the matrix-cracking stress of brittle-matrix composites are discussed in the paper.