Flow Stress of beryllium: Attempt for a Bayesian Crossed-data Analysis from Hopkinson Bars to Rayleigh-Taylor Instabilities

Abstract

In this paper, we demonstrate by a Bayesian approach the incapacity of the Preston-Tonks-Wallace (PTW) strength model to represent, with the same set of parameters, the flow stress of beryllium in both moder-ate and highly dynamic experiments, and suggest hypotheses explaining that limitation. Usual plasticity models such as Johnson-Cook (JC) and PTW are mostly adjusted onto quasi-static and dynamic uni-axial compression data acquired thanks to compression machines and split Hopkinson pressure bars. Nonetheless, they may be used beyond the range of mechanical loading in which they have been fitted. This is the case of the simulations of solid Rayleigh-Taylor instabilities (RTI) driven by high explosives. A recent work of Henry de Frahan et al. noticed the inability of various plasticity models to stand for the growth of beryllium RTI. Amongst them, the PTW model has been particularly examined through four different sets of parameters, each of them largely un-derestimates the growth of the experimental instability. Thus, this work is an attempt, regarding the plastic flow modeling of beryllium, to conciliate uni-axial compression tests (CT) and RTI by means of a crossed Bayesian analysis.