Stress redistribution due to cracking in periodically layered composites

Abstract

The stress redistribution caused by a brittle fracture of one or several layers in a bi-material periodically layered composite is considered. It is assumed that one of the composite constituents possess low crack resistance and is subject to cracking. In the case of a uniaxial tension parallel to the layering direction and in the presence of weak interfaces, the fracture pattern may be quite complicated including branching cracks. In particular, it can have the form of H-crack which is the case addressed in the present investigation. A direct numerical analysis of this problem by standard methods may be more time consuming due to the necessity to account for a relatively large number of degrees of freedom. This is required due to the fine composite microstructure and steep stress field gradients in the vicinity of the crack. Therefore a novel approach is employed which is based on the combined use of the high fidelity generalized method of cells model, the representative cell method and the higher-order theory. The crack existence is modeled by introducing fictitious unknown eigenstresses which are computed by an iterative procedure. This modeling is verified by a comparison with known analytical solution for a crack in a homogeneous plane. In addition, a verification by comparison with a known numerical solution for the special case of a transverse crack embedded in a periodically layered material is given.The influence of the volume fraction and elastic moduli ratio of the constituents as well as the H-crack aspect ratio on the stress field variation is examined, and the shielding effect of the interface cracks is quantified. The limiting situation of long interfacial cracks corresponding to the case of an incomplete layer is considered. The effect of a thermal loading on the cracked layered composite is demonstrated.