FRACTURE-MECHANICS OF ORTHOTROPIC LAMINATED PLATES .1. THE THROUGH CRACK PROBLEM

In this paper a laminated plate which consists of an arbitrary number of dissimilar orthotropic layers under membrane and bending loads is c onsidered. The plate is assumed to have a through crack. The problem i s formulated by using Mindlin's first order shear deformation theory a nd a higher order theory due to Reddy. The sample solutions obtained f rom these two theories, from the classical theory, and from Reissner's stress-based first order theory show that the stress intensity factor s given by the classical theory are highly inaccurate and the three tr ansverse shear deformation theories give roughly the same results. Bec ause of the nonhomogeneous nature of the medium under consideration, t he simpler of the two displacement-based shear deformation theories wa s adopted to carry out the solution of the crack problem in the lamina ted plates. The main objective of the study is to investigate the infl uence of the material orthotropy, various stiffness ratios, and relati ve dimensions concerning the crack size and laminae thicknesses on the stress intensity factors. Only the mode I crack problem is considered . It is shown that if the laminate has a material symmetry with respec t to the midplane of the plate, then the membrane and bending solution s of the problem are fully uncoupled. Also, in laminates which consist of bonded dissimilar isotropic layers having the same Poisson's ratio , the membrane component of the crack problem can again be separated a nd can be treated as a generalized plane stress problem. Otherwise the problem is coupled. Examples are given for both symmetric and nonsymm etric laminates.