Modeling of cracking induced damage in particulate and fiber-reinforced composites

Micromechanics analysis of damage in heterogeneous media and composites cannot ignore the interactions among cracks as well as the interactions between cracks and inclusions or voids. Several previous investigations came to this conclusion upon finding that states of (diffuse) distributed cracking (damage) cannot be obtained mathematically merely be analyzing crack systems in a homogeneous medium although stable states with distributed damage have been experimentally observed in heterogeneous materials such as concrete. This paper presents a method for analyzing interactions between a crack and many inclusions which may be arbitrarily distributed. The problem is solved by superposition; it is decomposed into several standard problems of elasticity for which well known solutions are available, and is finally reduced to a system of algebraic linear equations. The calculated estimates of the stress intensity factors are checked by comparison with exact solutions. The errors appear to be less than ten percent provided the crack or the inclusions are not very close to each other. As a simplified approach, crack propagation in a composite can be treated as propagation of a crack in an equivalent homogeneous material for which the fracture toughness increases or decreases as a function of the crack length. These variations of apparent fracture toughness are analogous to R-curves in nonlinear fracture mechanics. They depend on the volume fraction of the inclusions, their spatial distribution, and the difference in elastic properties of the inclusions and the matrix. Large variations of the apparent fracture toughness are found depending on the location of the crack and its direction of propagation with respect to the inclusions.