High-Rate Stress Upturn of Brittle Materials

Abstract

High-rate stress upturn of ductile materials at rates between 10³-10⁴/s has been known since the 1980s, and previously we’ve shown how to model this behavior based on our overstress approach to dynamic viscoplasticity. It turns out that brittle materials undergo high-rate stress upturn as well, but at a lower rate of 1-10/s. Most available data on high-rate stress upturn of brittle materials are for concrete (from obvious reasons), and they are usually represented by the quantity DIF as function of strain rate, where DIF=Dynamic Increase Factor. Here we model high-rate stress upturn of brittle materials using our overstress response model. Our overstress model for brittle materials includes: 1) damage onset curves for both compression and tension; 2) damage accumulation rate relation as function of the damage onset overstress; 3) damage onset reduction relation as function of the damage level, all the way down to the fully damaged state; 4) rate of plastic flow of the fully damaged material, which is what we usually use for a granular material; and 5) a finite upper limit for the damage accumulation rate. This last item stems from the finite rate of fracturing of brittle materials and from the finite speed of crack growth, and it turns out that this is the feature that leads to the high-rate stress upturn response. To demonstrate how the model works we compute several examples in cylindrical symmetry, with different ratios of radial to axial velocities.