An approximate three-dimensional theory of layered plates containing through thickness cracks

Abstract

The objective of this investigation is the development of an approximate three-dimensional theory of laminated plates for application to laminates containing through-the-thickness cracks. This is accomplished by assuming an approximate form for the stress field as a product of a function of the out-of-plane variables. The variational principle of minimum complementary potential energy is employed to obtain a system of partial differential equations and associated boundary conditions which govern the in-plane variation of the stress field. This approximate theory is then applied to the problem of a laminar composite plate containing a through-the-thickness crack subjected to in-plane loading normal to the crack face. The resulting mixed boundary value problem is solved by integral transform methods. The stress field in the vicinity of the crack edge is obtained in closed form demonstrating qualitative features characteristic of the exact three-dimensional asymptotic solution. The through-the-thickness variation of this stress field is chosen so as to enforce plane strain conditions within each layer of the composite plate. The results indicate the influence of the geometric parameters and material properties of the composite system on the amplitude and transverse variation of the stress field in the vicinity of the leading crack edge.