Crack Propagating in a Bimaterial Functionally Graded Multilayered Composite Media

Abstract The macroscopically anisotropic homogenization of a multilayered composite 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 [1]. However, close to the crack tip, gradients in field quantities are strongly influenced by the local heterogeneity, which the anisotropic homogenization fails to capture. Thus, given the insights from a homogenized continuum study, the next level of refinement is to study the effect of inhomogeneity on crack driving force. Asymptotic studies of cracks perpendicular and parallel to a bimaterial interface and in a layer between two materials have been very widely researched over the past two decades. Recently the advent of the use of functionally gradient materials (FGM) in composites, nano-composites and other multi-material structural systems has spurred interest in the fracture mechanics of such inhomogeneous materials. The problems considered in the literature typically assume a functional form for the material property variation, usually in one direction only, and calculate the driving force at the crack tip for a crack at some orientation to the direction of variation. The interest in FGM’s is due to their superior performance as interfacial layers in general and in particular in high temperature applications. Discontinuities in material properties between joined material constituents act as stress concentrators, especially due to thermal expansion mismatches under thermal processing or service loads. The use of a FGM as an interfacial layer smooths the discontinuity and reduces the stress concentrations. In this paper an analytic solution for the effect of periodic inhomogeneity on crack driving force is studied. Via Williams eigenfunction expansion approach it is seen that, for continuously differentiable moduli inhomogeneity the nature of the stress singularity at the crack tip is the same as in a homogeneous media, though the eigenvalue (Stress Intensity Factor) does depend on the inhomogeneity [1]. In order to study the effect of layered inhomogeneity on the Stress Intensity Factor(s), the Bueckner-Rice weight function approach for homogeneous media [2–3] is incorporated here to study the layered media problem. In this chapter the moduli perturbation approach, [4], is further extended to the case of multilayered media, especially in a functionally gradient material sense. 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. The results provide insight into the influence of residual stress and periodic moduli inhomogeneity on effective crack driving force for cracks propagating through multilayered bimaterial media. Further, this method in general allows one to study thermoelastic crack problems in complex heterogeneous media, alleviating difficulties associated with some of the traditional methods.