A re-examination of the analysis of toughening in brittle-matrix composites

The effect of interfacial friction on the use of the J-integral for calculating the toughness of a brittle-fibre reinforced composite has been examined. A simple micro-mechanical model that includes friction as the only dissipative mechanism yields a lower bound on the toughness. When the same constitutive equations are used with a J-integral formulation, an upper bound is obtained which incorporates other energy losses associated with the mechanics of fibre failure. Finally, a method is provided by which the J-integral can be correctly combined with statistical models of fibre failure to incorporate the effects of fibre pull-out on the toughness of a composite.