Bridged versus cohesive crack in the flexural behavior of brittle matrix composites

A nonlinear fracture mechanics model, which explains and reproduces the constitutive flexural behavior of a brittle-matrix composite, is proposed. It embraces in a unified dimensionless formulation two peculiar models, i.e., the cohesive-crack and the bridged-crack, which are used to analyze the composite failure process. Dimensionless parameters, which depend on the mechanical and geometrical properties, characterize the structure in flexure. It is shown that, based on the assumptions of the bridged-crack model, which simulates the composite as a multiphase material, the flexural response is controlled by two dimensionless parameters, whereas, based on the assumptions of the cohesive-crack model, which simulates the composite as a homogeneous material, the parameters reduce to one. The influence of the dimensionless parameters on the behavior is studied, along with the size-scale effects on the structural ductility. It is also shown how the matrix toughness affects the response. The two theoretical models are compared through the simulation of an experimental test on a fiber-reinforced beam, and it is shown that both the models can predict approximately the same overall behavior.