Analytical solution for plane stress/strain deformation of laminates with matrix cracks

An analytical, closed form solution for [0m/90n/±θr]s[0m/90n/±θr]s laminated composites with transverse matrix cracks is presented. The deformation is shown to consist of a homogeneous deformation plus a perturbation near the crack. A methodology is proposed to separate the perturbation from the homogeneous deformation to eliminate ill-conditioning of the eigenvalue/eigenvector problem. While the homogeneous deformation provides a macroscopic measure of damage in terms of reduced stiffness of the laminate, the perturbation solution provides the intralaminar shear near the crack, which is used to calculate the extent of shear lag and the maximum intralaminar shear stress. The equations of elasticity are reduced to one-dimension in a two-step approach, first assuming plane strain (stress) along one of the in-plane dimensions and then introducing approximations through the thickness of the laminate. The intact portion of the laminate is modeled without using a single equivalent laminate. Furthermore, plies are subdivided into multiple sub-plies to increase the accuracy of the representation of intralaminar/interlaminar shear, which is shown to have relevance on the predicted value of maximum interlaminar shear stress and is crucial for the prediction of matrix-crack induced delamination.