Theory of dynamic mode-II delamination in end-loaded split tests

The dynamic mode-II energy release rate (ERR) of the end-loaded split (ELS) test with applied time-dependent displacement is derived for the first time with the effect of vibration included. Dynamic Euler-Bernoulli beams are used together with a deflection condition to simulate contact. To understand 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 ELS specimen. Certain vibration modes are dominant dependent on the spatial factor. In addition, for a given spatial factor, there may be a certain vibration mode, which makes approximately zero contribution to the ERR. The developed theory is verified against results from finite-element method (FEM) simulations and it is in excellent agreement. This work now allows the loading rate-dependent mode-II delamination toughness of materials to be determined by using ELS 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 against vibration-driven delamination.