On the calculation of energy release rate and mode mixity in delaminated laminated beams

A method is presented for the analysis of laminated beams with general stacking sequences and arbitrarily located, through-the-width delaminations. First, the relative displacements and concentrated forces at the crack tip are determined based on classical lamination theory and Timoshenko beam kinematics. Next, new quantities, called crack-tip displacement rates, are defined as the relative displacements per unit increase in crack length. The previously computed quantities are then used to calculate the energy release rate and its mode I and II contributions via an adaptation of the virtual crack closure technique. Results for homogeneous and bimaterial delaminated beams are presented and compared to the predictions of other methods in the literature. Lastly, applications to some non-standard delamination test specimens are illustrated