Abstract
This study is a numerical exercise to theoretically analyze toughening in brittle materials consisting of ductile reinforcements, on the basis of crack bridging by ductile particles. The effects of the particle constitute behavior, the shape of the stress-displacement law, the matrix fracture toughness and the overall elastic modulus of the composite on toughness have been illustrated by simple fracture mechanics calculations of self-consistent crack opening displacement profiles and crack bridging stress distributions. An approach to calculate the crack surface displacements, crack bridging stresses and stress intensity factors in any specimen geometry, using weight functions, is presented. Different types of idealized particle stress-displacement responses were used in the calculations. The opening characteristics of a bridge crack and the evolution of toughness for these types have been examined. The conditions for maximum bridging and toughness as well as the conditions at which a fully bridged crack transforms to a partially bridged one have been identified. The role of individual parameters used in constructing the stress-displacement law on composite toughness has been assessed. The toughness has been found to manifest from a complex interaction of the matrix fracture toughness, the composite modulus and the flow behavior of the ductile particle.
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