Progressive matrix crack modeling in off-axis plies

Composite laminates are engineered to exhibit tendencies toward gradual (or progressive) failure as opposed to the less desirable catastrophic failure. Localized failures begin to occur early in the loading history of a laminate, but due to the laminate's ability to redistribute its load internally, the laminate as a whole remains unfailed and continues to perform its load-carrying function. In trying to model laminate failure it is important to recognize the progressive nature of the failure process in order to obtain a correct strength prediction. Localized failures can generally be categorized into various modes: transverse matrix cracking (through the thickness cracks running parallel to the fiber direction), periodic matrix cracks (cracks running perpendicular to the fiber direction and bridged by the fibers), fiber failure (cracking or splitting), and delamination. The onset of transverse matrix cracking has been found to be a key occurrence in the laminate failure process, and as a result much research has been devoted to its modeling. Continuum damage models as well as many shear-lag approaches have been proposed for analyzing cross-ply laminates. In this paper, we extend the shear-lag analysis for modeling transverse matrix cracking to a general symmetric multilayer system. The elasticity problem for the region of the laminate between two parallel matrix cracks having a general off-axis orientation is set up from equilibrium considerations in terms of the average (through the thickness) stresses and solved using the generalized shear-lag relation and the appropriate boundary conditions. This model is then included in a computer program designed for probabilistic laminate analysis, and the results are compared to those determined using the ply drop-off technique.