Ply-Cracking Damage Theory for Cross-Ply Laminate and Its Application to Finite Element Method

Abstract

This paper deals with a theory of ply-cracking damage on 90° and 0° plies in cross-ply laminate and its application to finite element method. An energy approach is extended to predict the initiation and evolution of ply-crcaking damage on 90° and 0° plies and the corresponding nonlinear stress-strain behavior of the cross-ply laminate under multiaxial in-plane loading. In this appraoch, the stress and strain condition for the progressive damage are determined by equating the decrease in potential energy to the released energy, where the former and latter are estimated from the stiffness reduction due to ply-cracking damage and from the mixed-mode critical energy release rate for cracking of unidirectional ply, respectively. This approach provides us with the constitutive relation of cross-ply laminates including the progressive ply-cracking damage. This theory is applied to the finite element method in order to analyze the ply-cracking damage and stress/strain distributions of the structures made of cross-ply laminates. As an example, finite element analysis is carried out on the seven kinds of CFRP cross-ply laminates with a circular hole. The numerical results show that the transverse cracking damage in 90° plies is widely spread out on the ligament of the plate, and the splitting damage in 0° plies extends in the longitudinal direction from the edge of the hole. The details of the damage evolution around a circular hole in CFRP cross-ply laminate depend on the stacking lay-up.