A GENERAL-THEORY FOR LAMINATED PLATES WITH DELAMINATIONS

An approximate analytical model for the behavior of a laminated compos ite plate in the presence of delaminations and other local effects is presented. The model is based on a generalized displacement formulatio n implemented at the layer level. The governing equations for a layer are obtained using the principle of virtual work. These governing equa tions for a layer are used in conjunction with the explicit satisfacti on of both the interfacial traction continuity and the interfacial dis placement jump conditions between layers to develop the governing equa tions for a laminated composite plate, including delaminations. The fu ndamental unknowns in the theory are the dis placements in the layers and the interfacial tractions. The theory is sufficiently general that any constitutive model for the interfacial fracture (i.e. delaminatio n) as well as for the layer behavior can be incorporated in a consiste nt fashion into the theory. The interfacial displacement jumps are exp ressed in an internally consistent fashion in terms of the fundamental unknown interfacial tractions. The current theory imposes no restrict ions on the size, location, distribution, or direction of growth of th e delaminations. Therefore, the theory can predict the initiation and growth of delaminations al any location as well as interactive effects between delaminations at different locations within the laminate. Pag ano's exact solution for the cylindrical bending of a laminated plate has been modified to include the effects of delamination. An interface model, which expressed the displacement jump as a linear function of the surface tractions, was implemented into this modification of the e xact solution. This extension was used to validate the approximate pla te theory. The correlation between the approximate approach and the ex act solution is seen to be excellent. The approximate plate theory is seen to give very accurate predictions for the interfacial tractions i n a direct and consistent fashion, i.e. without the need to use integr ation of the pointwise equilibrium equations. This allows the interfac ial displacement jumps in the presence of delaminations to be modeled accurately. It is seen that these displacement jumps have a significan t effect on both the macroscopic and microscopic behavior of a laminat ed plate. (C) 1997 Published by Elsevier Science Ltd.