On measuring the strength of metals at ultrahigh strain rates

Abstract

The strain rate sensitivity of materials is normally measured through a combination of quasistatic, Hopkinson bar, and pressure-shear experiments. Recent advances in uniaxial strain ramp loading provide a new means to reach strain rates significantly higher than achievable in pressure-shear experiments. One way to determine strength in ramp loading is by comparing the uniaxial stress-strain response to an appropriate pressure-density response obtained from an equation of state for the material. Using this approach, strengths for aluminum are obtained for strain rates of 105–108 s−1. Two issues arise in this calculation: heating due to plastic work and the effect of the superimposed hydrostatic stress on the strength. Heating due to plastic work is calculated and accounted for within the context of the equation of state for the material in a straightforward manner, but neglecting this heating can lead to significant errors in the calculated strength at higher compression levels. A simple scaling of strength with the pressure-dependent shear modulus is utilized to estimate the strength at zero pressure for ramp loading and pressure-shear experiments. When examined in this manner, the strain rate dependence of aluminum is found to be less than previously reported, with little increase in strength below strain rates of about 107s−1. The effects on ramp loading strength measurements of heating due to plastic work and of hydrostatic pressure are also examined for copper and tantalum using simple equation of state and strength models. The effect of plastic heating is similar for the three materials for a given strain level but quite different for a constant stress, with aluminum showing greater effects than the other materials. The effect of hydrostatic pressure in ramp loading experiments is similar for all three materials, but the effect is likely to be much greater in pressure-shear experiments for aluminum than the other materials.