A Layerwise Higher-Order Approach for the Free-Edge Effect in Angle-Ply Laminates

The free edges of layered structures require special attention in design processes. Due to the discontinuous material properties, singular stress concentrations occur where the layer interfaces meet the free edge. These bi-material points have to be closely examined as possible starting points for delamination processes. In the present study, we propose an efficient approximate closed-form method to analyze the interlaminar shear stresses in symmetric angle-ply laminates under uniform axial extension and homogeneous thermal loading. The method bases on a higher-order layerwise displacement approach. The resulting displacement and stress distributions of a first-order and a third-order analysis are compared and validated against numerical reference data gained by a self-developed finite element formulation. Especially, the results of the third-order analysis show a good agreement to the reference data along the interface, even if the singular behavior of the stresses in the very close vicinity of the free-edge cannot be reproduced exactly. A comparison of the displacement and stress distributions in thickness direction shows the benefit of the third-order over the first-order approach. In addition, the influence of the ply angle on the results is reproduced by both approaches.