Three-Dimensional Solution for a Through-Thickness Crack in a Cross-Plied Laminate

A three-dimensional solution is given to the problem of a through-thickness edge crack in a thin 90/0/0/90 laminate under uniform tension normal to the crack direction. The solution is obtained from a three-dimensional finite-element analysis based on the hybrid stress model, and formulated through the Hellinger-Reissner variational, principle. The results indicate that the classical 1/√r stress singularity is maintained for the in-plane stresses which vary through the thickness and are discontinuous at the ply interface. The interlaminar shear and normal stresses also increase rapidly as the crack tip is approached; the interlaminar shear stresses are always maximum at the ply interface, while the interlaminar normal stress may be maximum at the interface or at the laminate center. The in-plane stresses follow a similar distribution and give an average through-thickness stress-intensity factor similar to two-dimensional predictions. The interlaminar stresses show a strong interaction of the crack tip singular and free-edge effects, as well as a strong influence of the degree of biaxiality of the in-plane stresses. The results suggest several aspects of subsequent subcritical crack extension.