Growth behavior of internal delaminations in composite beam/plates under compression: effect of the end conditions

The effect of the end conditions, i.e. clamped-clamped vs. simply-supported ends on the initial postbuckling and growth behavior of delaminations in plates in studied. The study does not impose any restrictive assumptions regarding the delamination thickness and plate length. First, a closed form solution for the mode mixity, energy release rate and deformation quantities is derived for the case of a clamped-clamped delaminated plate, which complements the already existing solution for a delaminated simply-supported plate. A perturbation procedure is followed, which is based on an asymptotic expansion of the load and deformation quantities in terms of the distortion parameter of the delaminated layer, the latter being considered a compressive elastica. The additional complication in the clamped-clamped case arises because now the amplitude at the clamped end needs to be expanded in terms of the distortion parameter of the delaminated part, in addition to the amplitude at the common section and the distortion parameter of the base plate. The effects of the end conditions on the growth behavior are found to depend on the relative location of the delamination through the thickness. For the same plate length and thickness and the same delamination length and applied strain, delaminations located closer to the surface exhibit nearly the same energy release rate and mode mixity either in a clamped-clamped or a simply supported configuration. However, in delaminations located further away from the surface, for the same applied strain, the energy release rate is larger and there is also a higher mode II component in the simply-supported case. Moreover, the mid-point transverse displacement of the delaminated layer as well as that of the substrate part, is larger in the simply supported case. The same major trend that has been observed in the simply supported case, i.e. the increased growth resistance of the delaminations located near the surface relative to the ones located further inside the plate, is also observed in the clamped-clamped case.