Crack in a Bimaterial Functionally Graded Multilayered Media

The macroscopically anisotropic homogenization of a multilayered media 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. The present work addresses the issues related to the influence of material inhomogeneity on local crack tip driving force. 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. Detailed analytical model is developed for quantifying the effect of moduli inhomogeneity for the case of bimaterial multilayered media with functional interfaces, i.e., compositionally graded finite thickness 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.