Stress Singularity due to Kink Band Weakening a Unidirectional Composite under Compression

Abstract

A Williams type of eigenfunction expansion approach is used to compute the local stress singularity representing a measure of the degree of inherent flaw sensitivity of unidirectional fiber reinforced composites subjected to compression. Previous experimental studies have qualitatively linked the formation of kink bands to the presence of fabrication defects, such as fiber misalignment. These local singular stress regions serve as the primary trigger mechanism for kink band propagation in 0°-plies. The present analysis also explains the previous test results relating to propagation of failure from a notch in a unidirectional composite under compression. Furthermore, the present investigation is the first to quantify, in the context of LEFM (linear elastic fracture mechanics), the sensitivity of these composites to inherent local flaws, such as fiber misalignments, and also shows the inadequacy of the conventional elastic micro-buckling type of analysis to fully explain the experimental results. Although because of the assumed isotropy of the fiber and matrix materials, the present study is primarily suited to glass fiber reinforced composites, the conclusions drawn here are general enough to apply to carbon fiber reinforced composites as well. Numerical results presented include the effects of fiber included wedge angle, and the ratios of fiber-matrix shear moduli and Poisson's ratios on the strengths of the mode I and mode II singularities. Of special practical interest is the present LEFM type of analysis applied to quantitatively investigate the inherent flaw sensitivity of two E-glass/epoxy composites experimentally investigated earlier. Compression fracture type of failure of these composites can be fully explained and quantified by the present two-dimensional LEFM-based method, which is beyond the scope of one-dimensional micro-buckling approach.