Damage analysis of laminated composite beams under bending loads using the layer-wise theory

摘要

A finite element model based on the layer-wise theory and the von K?rm?n typenonlinear strains is used to analyze damage in laminated composite beams. In theformulation, the Heaviside step function is employed to express the discontinuousinterlaminar displacement field at the delaminated interfaces. Two types of the mostcommon damage modes in composite laminates are investigated for cross-ply laminatedbeams using a numerical approach.First, a multi-scale analysis approach to determine the influence of transversecracks on a laminate is proposed. In the meso-scale model, the finite element modelbased on the classical laminate theory provides the material stiffness reduction in termsof the crack density by computing homogenized material properties of the cracked ply.The multiplication of transverse cracks is predicted in a macro-scale beam model underbending loads. In particular, a damage analysis based on nonlinear strain fields incontrast to the linear case is carried out for a moderately large deformation. Secondly, the effect of delamination in a cross-ply laminated beam underbending loads is studied for various boundary conditions with various cross-ply laminatelay-ups. The crack growth of delamination is predicted through investigating the strainenergy release rate.Finally, the interactions of a transverse crack and delamination are considered forbeams of different configurations. The relationships between the two different damagemodes are described through the density of intralaminar cracks and the length of theinterlaminar crack.It is found that geometric nonlinearity plays an important role in progression ofinterlaminar cracks whereas growth of intralaminar cracks is not significantly influenced.This study also shows that the mixture of fracture mode I and II should be considered foranalysis of delamination under bending loads and the fracture mode leadingdelamination changes as the damage develops. The growth of delamination originatedfrom the tip of the transverse crack is found to strongly depend on the thickness of 90-degree layers as well as the transverse crack density. Further, the effect of interfacialcrack growth on the transverse cracking can be quatitatively determined by thedelamination length, the thickness of 90-degree layers and the transverse crack density.