A general theory for laminated plates with delaminations

Abstract

An approximate analytical model for the behavior of a laminated composite plate in the presence of delaminations and other local effects is presented. The model is based on a generalized displacement formulation implemented at the layer level. The governing equations for a layer are obtained using the principle of virtual work. These governing equations for a layer are used in conjunction with the explicit satisfaction of both the interfacial traction continuity and the interfacial displacement jump conditions between layers to develop the governing equations for a laminated composite plate, including delaminations. The fundamental 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. delamination) as well as for the layer behavior can be incorporated in a consistent fashion into the theory. The interfacial displacement jumps are expressed in an internally consistent fashion in terms of the fundamental unknown interfacial tractions. The current theory imposes no restrictions on the size, location, distribution, or direction of growth of the delaminations. Therefore, the theory can predict the initiation and growth of delaminations at any location as well as interactive effects between delaminations at different locations within the laminate.Pagano'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 exact solution. This extension was used to validate the approximate plate theory. The correlation between the approximate approach and the exact solution is seen to be excellent. The approximate plate theory is seen to give very accurate predictions for the interfacial tractions in a direct and consistent fashion, i.e. without the need to use integration of the pointwise equilibrium equations. This allows the interfacial displacement jumps in the presence of delaminations to be modeled accurately. It is seen that these displacement jumps have a significant effect on both the macroscopic and microscopic behavior of a laminated plate.