The fracture toughness of a particulate-reinforced brittle matrix

An analytical modeling approach capable of evaluation of principal micromechanical processes taking place in brittle matrix composites reinforced by ductile particles is presented. The model addresses the effects associated with discrete particle distribution and particle-matrix interface properties. As is well known, the reinforcing mechanism is based on formation of a system of restrictive forces imposed on the crack surfaces by the plastic particles behind the propagating crack front. The particles form a bridging zone and, thus, constrain the crack opening. This is the principal aspect of the toughening mechanism in these systems. The analytical approach is based on these physical features; it enforces the natural stress state surrounding the particles and the constant volume plastic flow of the particles, and does not rely on an approximation of the stress-crack opening displacement relationship of the representative cell. The analysis allows one to trace the crack propagation through this system. This detailed analysis explains certain aspects of the particulate reinforcement mechanism not discussed in the literature previously. The resistance curves are presented for several composite systems.