Crack-tip micro mechanical fields in layered elastic composites: crack parallel to the interfaces

Periodically layered bimaterial composites containing cracks parallel to the interfaces at the mid-plane of a layer are considered. The analytical solutions of the plane elastostatic problems under mode-l, mode-If and mixed-mode loading conditions are presented and equations for the crack-tip micro mechanical fields are developed using principles of asymptotic homogenization and the method of complex elastic potentials. An elastic stress singularity of the order r-1~ʹ2 is shown to exist. The dominating stress intensity factors are found to match with the corresponding values for the equivalent homogeneous orthotropic system. For all cases considered, the stress intensity factors dominating the micro stress field are also defined directly in terms of the stress functions. Comparisons of the analytical results with numerical solutions obtained via refined finite element analyses are presented. Numerical analyses have revealed that the stress field in the immediate vicinity of the crack-tip corresponds to the universal isotropic field dominated by the tip stress intensity factor which depends on the homogenized material properties and those of the layer containing the crack. The effects of micro structural heterogeneity and global anisotropy become predominant beyond the small isotropic region wherein the micro mechanical field is very nicely described by the analytical model. Crack location effects studies are also presented. Implications of the above near-tip fields on delamination fracture in layered systems are discussed. © 1997 Elsevier Science Ltd.