An analytical study on the energy release rate of end-loaded split specimens under high-speed loading

In this work an analytical solution for the calculation of the Energy Release Rate (ERR) under high-speed mode II loading conditions for an End-Loaded Split specimen, at crack initiation, is obtained. The analytical formulation is based on the Timoshenko beam theory and on a simple contact condition for the unbonded region of the specimen. The contribution of the shear effects added to the analytical model through the Timoshenko beam theory and the existence or not of pure mode II loading during a high-speed loading are studied. The proposed model is validated against numerical results obtained from finite element analysis. Also, a comparison against a previous analytical model based on the Euler theory is performed. Finally, a methodology is proposed in order to estimate a lower boundary limit for the crack initiation time after which the loading conditions can be assumed as pure mode II for testing using the standard End-Loaded Split configuration. The results show the dependency of the dynamic ERR on the vibrational characteristics of the specimen and also that accounting for the shear effects in the analytical model produces results closer to the numerical ones. It is also proven that in order to load in pure mode II an ELS specimen under high-speed loading the displacement must be applied on both adherents. This is to avoid the complex contact conditions and the asymmetry of the boundary conditions that result in a mode I component for the ERR.