Development of an LEFM dynamic crack criterion for correlated size and rate effects in concrete beams

The strength of concrete under severe dynamic loading depends on the specimen size and the loading rate. Although the size effect, under quasi-static loading, has been explained by the size-dependent strain energy rate, the main causes of the size and rate effects for dynamic loading cases have not been clarified. In this study, a linear elastic fracture mechanics (LEFM) dynamic crack criterion for a notched three-point bend specimen is developed to explain the size and rate effects, and the possible correlation of these effects. This was achieved by using energy balance, force equilibrium, and Griffithʹs crack model. From the proposed LEFM dynamic crack criterion, it was shown that (1) the kinetic energy rate seems to be the main cause of the rate effect, (2) the size and rate effects are not independent phenomena.