Reversal in Failure Scaling Transition of Fibrous Composites

Abstract

A nonlinear fracture mechanics model is proposed for analysis of the flexural behavior of brittle-matrix composites with uniformly distributed secondary phases. In accordance with the Barenblatt-Dugdale model the bridging or cohesive zone of the material is replaced by a fictitious crack along which a closing traction distribution is applied. The dimensionless formulation brings out the parameters synthetically controlling the structural behavior and the size-scale effects. Different scaling transitions are predicted in the flexural behavior of the composite depending on different modeling of the toughening mechanisms. When a homogenized toughening mechanism for the whole composite is considered along with closing tractions as a linearly decreasing function of the crack opening displacement, a ductile to brittle transition is found as the beam depth increases. On the other hand, when the matrix toughness and the toughening mechanism of the reinforcements are separately modeled, and the closing tractions have a constant value until a critical crack opening displacement, a double brittle-ductile-brittle transition is found. Experimental tests on fiber-reinforced mortar beams in bending are successfully simulated.