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Author Fraizier, E. ♦ Delattre, S. ♦ Mougeot, M. ♦ Faure, Ph. ♦ Roy, G. ♦ Poggi, F.
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Copyright Year ©2012
Abstract A thermodynamically consistent Equation Of State (EOS) was developed to predict and analyse the behaviour of multiphase metals under shock wave loading. Assuming the Mie-Gruneisen hypothesis together with the Birch (for example) formulation, the EOS gives the relation between pressure P, temperature T and atomic volume V. Experimental data (P,V,T) for each phase are provided mainly by X-ray diffraction measurements with diamond anvil cells. In this work, mathematical tools are designed to optimize the determination of the EOS parameters and evaluate uncertainty. The general EOS form is y = fϑ(x) where y = P, x = (V,T) and ϑ is the parameter vector to calibrate. Using experimental data (xi,yi), the least square (non-linear) regression provides an optimal value ϑ∗ for the fit parameters. The measurement errors on y and x give biased estimation of ϑ∗ with the standard method. Assuming centered and known variance laws for the errors, a statistical procedure is proposed to estimate ϑ∗ and determine confidence intervals. Thanks to a Bayesian approach it is possible to introduce physical interval knowledge of the parameters in this procedure. Moreover, various EOS fϑ∗ formulations are evaluated with a chi-squared type statistical test. The present method is applied on experimental data for multi phase tin (β and γ phases and liquid state) in order to provide an optimized multi-phase model. Furthermore, the method is used to design further experimental campaign and to evaluate the gain of new experimental data with the corresponding estimated errors.
Learning Resource Type Article
Publisher Date 2012-01-01
Journal EPJ Web of Conferences
Issue Number 26