Experimental issues and interpretation of the necking phenomena in the dynamic characterization via Hopkinson bar

The usual procedures for processing experimental data from Hopkinson bars (HB) are based on modeling hypotheses which, in some cases, may lead to considerable approximations. The effects of the specimen geometry and of the necking are analysed, both experimentally and by FE analyses, for assessing how much the conventional values of strain rate, strain and stress, based on strain gauges readings along the HB, are affected by approximations in different testing conditions. Also, from the way the necking affects the load/area ratio, useful considerations arise about the hardening response of metal alloys under high strain rates. The sensitivity of stress-strain curves to the time-translations of strain waves along the bars is assessed by comparing the above curves to others where the strain, the strain rate and the current cross section come from speed camera image analyses. This clearly shows that the effective strain rate in the most strained areas of the specimens is many times higher than the nominal value, and also allows to explore how much the engineering curve is poorly representative of the material response, due to strain localization in the post-necking phase. The necking-affected length compared to the total gauge length is also found to significantly influence the strain response of the specimens, in a way that can easily mislead the experimenters in the derivation of the material ductility. An empirical relationship, already found to be valid in the post-necking quasi-static regime for transforming the true stress (load / current area) into an estimation of the cross section-averaged equivalent stress, is also found to apply at high strain rates if only the appropriate considerations are done on the way the equivalent stress is considered.