Rate-Dependent Scaling of Dynamic Tensile Strength of Quasibrittle Structures

This paper investigates the effect of strain rate on the scaling behavior of dynamic tensile strength of quasibrittle structures. The theoretical framework is anchored by a rate-dependent finite weakest link model. The model involves a rate-dependent length scale, which captures the transition from localized damage to diffused damage with an increasing strain rate. As a result, the model predicts a rate- A nd size-dependent probability distribution function of the nominal tensile strength. The transitional behavior of the strength distribution directly leads to the rate and size effects on the mean and standard deviation of the tensile strength. The model is verified by a series of stochastic discrete element simulations of dynamic fracture of aluminum nitride specimens. The simulations involve a set of geometrically similar specimens of various sizes subjected to a number of different strain rates. Both random microstructure geometry and fracture properties are considered in these simulations. The simulated damage pattern indicates that an increase in the strain rate results in a more diffusive cracking pattern, which supports the theoretical formulation. The simulated rate and size effects on the mean and standard deviation of the nominal tensile strength agree well with the predictions by the rate-dependent finite weakest link model.