Computation of Energy Release Rate and Mode Separation in Delaminated Composite Plates by Using Plate and Interface Variables

Abstract

A model for analyzing mixed-mode delamination problems in laminated composite plates under general loading conditions is studied. The first-order shear deformable laminated plate theory and the interface methodology, which in turn is based on fracture mechanics, are adopted. The laminate is modeled as an assembly of laminated plate and interface layers in the thickness direction. When the limit case of interface stiffness coefficients approaching infinity is considered, a perfect adhesion between plate models is simulated. On the other hand, delamination between sublaminates is taken into account by assuming zero values for interface stiffnesses. Lagrange and penalty methods are adopted to simulate connections between plate elements. By using a variational approach and the virtual crack closure concept, expressions for total energy release rate and its mode components along the delamination front are obtained, in terms of both interface variables and plate stress resultant discontinuities. These formulas shed light on the effect of transverse shear in interface fracture analysis and establish the improvement and the accuracy of the proposed formulation compared to other plate-based delamination models existing in the literature. The method is implemented in a two-dimensional finite element analysis, which makes use of shear deformable plate elements and interface elements. To illustrate the present method, some typical delamination problems involving mode I, mode II, and mode III are examined and the numerical energy release rate distributions are compared to highly accurate three-dimensional (3D) finite element solutions. These results show that the procedure is accurate when a reasonable number of plate models are included in the analysis and more computationally efficient than 3D finite element models, for which determining fracture energies may lead to a remarkable increase in model complexity.