Continuous vs discontinuous bridged-crack model for fiber-reinforced materials in flexure

Abstract

Two different nonlinear fracture mechanics models are proposed for analysis of the constitutive flexural behavior of brittle-matrix composites with localized or distributed continuous ductile reinforcements. The models analyze the potential crises for brittle crack propagation and reinforcement yielding or debonding and can be fitted into the general framework of the bridged-crack model. A rigid-plastic bridging law is assumed. Local discontinuous phenomena, as well as a ductile to brittle transition in the constitutive relationship, when a characteristic dimension of the body decreases, are predicted. A comparison between the continuous and discontinuous formulations shows that, in the limit case of a sufficiently high number of localized reinforcements, the theoretical models converge to the same global results.