Prediction of compressive strength and kink bands in composites using a work potential

Abstract

A recently developed method of characterizing nonlinear, inelastic behavior of composites is described and then used to provide constitutive equations for use in the compressive strength problem of unidirectional fiber composites. This constitutive theory, which is based on a work potential, appears to be valid for the strain state and levels of strain needed to predict kink band angles and compressive strength. A one-dimensional deformation model of fiber waviness growth is then described and used to make a case that a band of wavy fibers initiates a kink band when local matrix cracking occurs and the axial stress equals or exceeds the predicted critical stress for local buckling. This requirement of matrix cracking serves to define the kink band angle. For multiaxial stresses this angle and the compressive strength depend on all components of the overall or average stresses; the multiaxial state of stress may arise from external loading or from ply-to-ply interactions in a multi-directional laminate. Equations are developed for predicting the behavior for general in-plane loading and arbitrarily large geometric nonlinearities when the failure mechanism is microbuckling. A geometrically approximate, analytical solution is also developed. Results for several cases are given in order to illustrate the predicted behavior and to show that the predictions are consistent with experimental observations.