Theory of dynamic mode-II delamination in end-notched flexure tests

The dynamic mode-II energy release rate of the end-notched flexure (ENF) test with applied time-dependent displacement is derived for the first time with the effect of vibration included. A dynamic Euler-Bernoulli beam theory is employed together with a deflection condition to simulate contact. To investigate the dynamic effect and the relative dynamic contribution from each vibration mode, a dynamic factor and a spatial factor are defined. It is found that the contribution of the ith vibration mode is dependent on the spatial factor (which is a function of the delamination length and the total length of the ENF specimen) and that certain vibration modes are dominant (depending on the delamination-length ratio). In addition, for a given spatial factor, there may be a certain vibration mode with a zero contribution to the ERR. The developed theory is verified against results from finite-element-method simulation for two cases of ENF tests and they are in excellent agreement. This work now allows the loading ratedependent mode-II delamination toughness of layered materials to be determined using ENF tests. In addition, it provides understanding of the structural dynamic response in the presence of mode-II delamination and can guide the design of structures to mitigate the vibration-driven delamination.