Boundary layers in wedges of a laminated composite strip under generalized plane deformation

Abstract

Based upon Lekhnitskii``s formulation and the Stroh formalism, the structure of the asymptotic solution has been examined for the boundary layer on the wedge type cross section of a laminated composite strip. The composite strip is assumed under the so-called generalized plane deformation, which includes tension, bending and/or torsion by the terminal tractions as well as the generalized plane strain problem. The solution structures are obtained, with the aid of numerical calculation, for various kinds of wedge geometry including the free edge and the delamination cracks with the crack faces opened or closed. The nature of the asymptotic solution is discussed, including the mode mixity of singular stress field ahead of the wedge tip; it is found that for a free edge problem the mode mixity of the singular asymptotic traction vector on the interfacial plane near the free edge remains invariant under varying types of remote loadings once a pair of adjacent materials (or ply orientations) is given, and that accordingly one single scaling parameter governs the near field response. Numerical example is carried out to illustrate a solution procedure for the case of delamination cracks originating from transverse cracking under generalized plane strain deformation, wherein there are no particular solution involved. The procedure of finding complete numerical solutions for the elastic boundary layer field in wedges of a laminated composite strip under the generic loadings of generalized plane deformation is discussed together with numerical examples for free edge problems and delamination crack problems. The solution procedure, which yields the solution in terms of loading parameters, is applicable to an arbitrary wedge angle and ply orientation, and any type of loadings within the range of generalized plane deformation. For the free edge problem, the so called free edge stress intensity and the mode vector are defined and the free edge stress intensity is found to be...