Toughening of Ceramics through Crack Bridging by Ductile Particles

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Abstract
The fracture problem for a brittle matrix reinforced by ductile particles is considered. In the usual manner it is assumed that the crack surface bridging forces provided by the unbroken particles improve the fracture toughness of the matrix. Depending on the relative strength of the interfacial bonding between the matrix and the particles, two particle force models are introduced, namely, a force that is independent of the crack opening displacement (δ) and a force that is a highly non‐linear function of δ. The problem is studied for a penny‐shaped or plane strain crack in an infinite medium and for a surface crack in a semi‐infinite medium under plane strain conditions. The toughness improvement in the matrix is shown to depend on a dimensionless bimaterial constant representing the inherent toughness of the matrix and the yield behavior of the particles. The effective toughness of the composite medium is calculated as a function of the crack size and the bimaterial constant.

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