On the Logarithmic Singularity of Free-Edge Stress in Laminated Composites Under Uniform Extension

Abstract

The stress singularities at the free edge of an interface between adjacent layers in a laminated composite are studied. Each layer of the composite is assumed to be of the same orthotropic material with one of the principal axes being the fiber direction. The angle θ, however, which is the fiber orientation, varies from layer to layer. The composite is subjected to uniform extension in the plane of the layers. At the interface between adjacent layers having fiber angles (0/90), (θ/θ′ ), and a family of special combinations of (θ/θ′ ) shown in the paper, the singularity of the type k*rδ (δ<0), seems to be the only possibility. For an interface with other combinations of fiber orientations in the the adjacent layers, it is shown that an additional singularity of the form k(ln r) exists. Since the constant k* depends on the stacking sequence of the layers and the complete boundary conditions, and may vanish in some cases, the existence of a k*rδ singularity at a free edge is not certain until a complete problem is solved. In contrast, the constant k, which is called the logarithmic stress-intensity factor, is independent of the stacking sequence of the layers and the complete boundary conditions. Its value is determined once the fiber orientations on both sides of the interface are known. Therefore, at the interface between adjacent layers for which k≠0, the free-edge stress is inherently singular. Moreover, the singularity is logarithmic.