An improved and complete closed-form solution for the mixed mode bending test for delamination in composite laminates

Most existing closed-form solutions for the Mixed-Mode Bending (MMB) test, used to investigate the delamination behaviour in laminated composites, are limited to cases where the delamination length a is less than the half-span L of the specimen. More critically, since these solutions are typically derived using beam theory, the predicted mode I and mode II energy release rates become increasingly inaccurate as the delamination approaches the specimen's mid-span. The few available solutions for delamination length a > L are either erroneous or significantly inaccurate. In this study, a complete closed-form solution is developed using a sub-laminated beam model based on first order shear deformation beam theory. The accuracy of the solution is validated through comparison with results obtained from the virtual crack closure technique and cohesive zone model simulations, using 2D finite element analysis. The proposed formulation enables accurate evaluation of energy release rates for a complete delamination length range ( a < L and a ≥ L ). The solution is also applicable to thick specimens with cross-ply layups. Potentially, this work may help pave the way for permitting delamination propagation beyond the mid-span in the MMB test—an approach that is currently not recommended by the ASTM standard.