Bridge-toughening analysis of the penny crack in a fiber reinforced composite with interfacial effect

A fracture mechanics analysis of bridge effect on a fiber reinforced composite containing a penny crack is presented. The integral equation governing bridge-toughening as well as crack opening displacement (COD) for the composite with interfacial layer is derived from the Castingliano's theorem and interface shear-lag model. A numerical result of the COD equation is obtained using iteration solution of the Fredholm integral equation of the second kind. In order to investigate the effect of various parameters on the toughening, an approximate analytical solution of the equation is presented and its error analysis is performed, which demonstrated the approximation solution to be appropriate. A parametric study of the influence of the length, interfacial shear modulus, thickness of the interphase, fiber radius, fiber volume fraction and properties of materials on composite toughening is therefore carried out.