Uncertainty Estimation and Hierarchical Bayesian Analysis of Mechanical Dynamic Tests

A methodology is presented to quantify uncertainties resulting from the analysis of dynamic tests performed on classic split Hopkinson pressure bar system in order to improve material parameter estimation within the framework of Bayesian inference. Since the experimental setup is imperfectly known, the proposed methodology consists in modeling experimental parameters as random variables. Then, cumulative effects of all experimental uncertainties are estimated by a statistical analysis based on one-dimensional wave interpretation. For each test, results consist in stress and strain-rate given as normal random variables. In addition, an experimental campaign is performed on the aluminum alloy AA7075-O, in order to identify material variability and repeatability of tests. Additional tests in the quasi-static regime are performed at two different temperatures to characterize temperature dependence of behavior. Material parameters of a simple Steinberg-Cochran-Guinan model are then estimated by (i) standard Bayesian inference exploiting data in the quasi-static regime, and (ii) a hierarchical Bayesian model exploiting data in the dynamic regime. The fitted model agrees well with the measurements and model uncertainties are easily quantified. Results are presented in the form of posterior probability density functions. The systematic quantification of uncertainties in dynamic tests opens interesting perspectives to analyze the response of structures and materials to impact.