A discrete damage zone model for mixed-mode delamination of composites under high-cycle fatigue

Abstract

A discrete damage zone model is developed to describe the mode-mix ratio and temperature dependent delamination of laminated composite materials under high cycle fatigue loading within the framework of the finite element method. In this approach, discrete nonlinear spring elements are placed at the finite element nodes of the laminate interface, and a combination of static and fatigue damage growth laws is used to define its constitutive behavior. The model is implemented in the commercial software Abaqus using the user element subroutine. The static damage model parameters are estimated from fracture mechanics principles, whereas the fatigue damage model parameters are calibrated by fitting the numerical results to published experimental data. A quadratic relation is proposed to describe the non-monotonic variation of fatigue damage model parameters with mode-mix ratio. Next, an Arrhenius relation is proposed for the temperature dependence of fatigue damage, in addition to the incorporation of the temperature dependence of critical fracture energy. The model is convergent upon mesh refinement; however, for accurate prediction the mesh size used for model calibration should be sufficiently small. The model predicted fatigue crack growth rates are in agreement with those obtained from a quadratic relation for the Paris law parameters for variable mode mix conditions, thus verifying the approach. While the model captures the temperature effects on delamination for mode I and 50 % mode II, our prediction deviates from experiments for pure mode II, since the corresponding damage mechanism entirely changes with temperature.