Theoretical assessment of stress-strain curve estimates in Split Hopkinson Bar experiments

Abstract
The determination of the stresses and strains based on split Hopkinson pressure bar (SHPB) measurements is an important step in the identification of reliable experimental data on the mechanical behavior of materials at high strain rates. Modern SHPB systems provide accurate measurements of the forces and velocities at the boundaries of a dynamically loaded specimen, while approximations need to be made to obtain the stress-strain curve based on these measurements. Several formulas have been proposed in the past to estimate the stress-strain curve from dynamic experiments. Here, we make use of the theoretical solution for the waves in an elastic specimen to evaluate the accuracy of these estimates. It is found that it is important to avoid an artificial time shift in the processing of the experimental data. Moreover, it is concluded that the combination of the output force based stress estimate and the average strain provides the best of the commonly used stress-strain curve estimates in standard SHPB experiments.