Effective interlaminar shear moduli in composites containing transverse ply cracks

The effective interlaminar shear modulus for [ θ / 90 m ° ] S and [ ± θ / 90 m ° ] S laminates containing transverse cracks through the middle 90 m ° layers are determined analytically. The cracks are assumed to be evenly spaced and to extend across the entire laminate width. The θ ply and 90 m ° ply cluster are treated as a single homogeneous plate, while the ± θ plies are treated as a single laminated plate. The two plates are connected through continuity of displacements and tractions at the interface. In addition to determining the effective shear modulus, a singularity analysis is presented in conjunction with a [0°/90°] S bi-directional laminate. The singularity is then utilized in conjunction with the laminate model to look at the interlaminar shear stress near the crack tip along the 0°/90° interface. Numerical results are compared to both a finite element analysis and to a previously developed self-consistent model.