Compressive failure model for fiber composites by kink band initiation from obliquely aligned, shear-dislocated fiber breaks

Abstract

Predicting compressive failure of a unidirectional fibrous composite is a longstanding and challenging problem that we study from a new perspective. Motivated by previous modelling of tensile failure as well as experimental observations on compressive failures in single carbon fibers, we develop a new micromechanical model for the compressive failure process in unidirectional, planar composites. As the compressive load is increased, random fiber failures are assumed to occur due to statistically distributed flaws, analogous to what occurs in tension. These breaks are often shear-mode failures with slanted surfaces that induce shear dislocations, especially when they occur in small groups aligned obliquely. Our model includes interactions of dislocated and neighboring intact fibers through a system of fourth-order, differential equations governing transverse deformation, and also allows for local matrix plastic yielding and debonding from the fiber near and within the dislocation arrays. Using the Discrete Fourier Transform method, we find a ‘building-block’ analytical solution form, which naturally embodies local length scales of fiber microbuckling and instability. Based on the influence function, superposition approach, a computationally efficient scheme is developed to model the evolution of fiber and matrix stresses. Under increasing compressive strain the simulations show that matrix yielding and debonding crucially lead to large increases in bending strains in fibers next to small groups of obliquely aligned, dislocated breaks. From the paired locations of maximum fiber bending in flanking fibers, the triggering of an unstable kink band becomes realistic. The geometric features of the kink band, such as the fragment lengths and orientation angles, will depend on the fiber and matrix mechanical and geometric properties. In carbon fiber–polymer matrix systems our model predicts a much lower compressive failure stress than obtained from Rosen’s classic microbuckling model, yielding values much closer to those observed experimentally.