Analytical approach to the strain rate effect on the dynamic tensile strength of brittle materials

An explicit mathematical expression for the dynamic load-carrying capacity of brittle materials under dynamic tensile loads is derived based on a kind of structural-temporal failure criterion [1] and the one-dimensional longitudinal plane wave propagation model. It is shown that the dependence of the dynamic load-carrying capacity on the strain rate can be determined only by the static material parameters such as tensile strength, density, incubation time, critical failure length and constitutive constants, which verifies that the well known strain rate effect on material strength can be considered as an structural rather than material behavior, as pointed out by Cotsovos and Pavlović [2] recently. Moreover, it is found that, under constant strain rate, the dynamic load-carrying capacity depends also on the amplitudes of imposed boundary loads, which explains, to a significant extent, the scatter that characterizes the available experimental data. Furthermore, the derived expression can also be used as a foundation of theoretical analyses on other problems involving the strain rate effect such as dynamic size effect, dynamic failure of quasi-brittle materials and composites.