Crack propogation in bimaterial multilayered periodically microcracking composite media

The macroscopically anisotropic homogenization of a multilayered medium implicitly assumes that the spatial wavelength of material inhomogeneity is smaller than the macroscopic quantity of interest and hence, is a reasonable approximation of the bulk behavior. However, close to the crack tip, gradients in field quantities are strongly influenced by the local heterogeneity, which the isotropic or anisotropic homogenization fails to capture. In the present work it is shown that, to the first order, the effect of moduli inhomogeneity, residual stresses and inelastic strains on crack tip stress intensity factor are superposable in a multilayered inhomogeneous medium with smooth interfaces. This method provides an efficient means to study thermoelastic crack problems in complex heterogeneous media, alleviating the numerical or analytical difficulties associated with the traditional methods. The results show that the material inhomogeneity plays a significant role in effecting the crack tip driving force. This method is used further in an R-curve analysis, [1], of a crack propagating through a similar medium with periodic microcracking in one of the two constituent materials.