Strain energy release rate under dynamic loading considering shear and crack tip root rotation effects

Abstract

A closed form solution for the calculation of the strain energy release rate (SERR), at the initiation of a crack, for a double cantilever beam (DCB) test, under dynamic loading conditions, is presented. The dynamics of a Timoshenko beam are used in the analytical formulation. The equations of motion are obtained using a variational approach and the adhesively bonded region is modelled via a Lagrangian multiplier method. The SERR is calculated based on the contour integral method and is a function of the vibrational mode and the beam's eigenfrequencies. The analytical formulation is applied on two representative joint cases. One consists of isotropic and the other of composite sub-laminates. Finite element analysis was used to validate the analytical formulation. The results demonstrate the advantages of the use of the Timoshenko beam theory and the consideration of crack tip root rotations in dynamic fracture mechanics and emphasize that the localized vibration cannot be neglected in the SERR calculation.