Uncertainty quantification and global sensitivity analysis of longitudinal wave propagation in circular bars. Application to SHPB device

The experimental characterisation of materials at intermediate strain rates often implies the use of split Hopkinson pressure bars. Shifting the measured pulses in the bars requires to take dispersion into account. However, the dispersion correction, in the case of linear elastic bars, relies on physical parameters which are measured with a given accuracy (bar velocity c0, bar radius r0, Poisson’s ratio ν and propagation distance x). The object of the present article is to evaluate the influence of the uncertainty on these parameters and quantify the uncertainty on the resulting propagated pulse. A common dispersion correction method is based on a nonlinear curve fitting approach of the real dispersion curve. The accuracy of this approximate method is first assessed and we show that it can lead to non negligible errors on the computation of the propagated pulse in the context of SHPB (typically a few percent). The numerical solving of the dispersion equation is therefore preferred. We then use Latin hypercube sampling to perform an uncertainty quantification (UQ) on the propagated pulse. The next step is a Sobol’ sensitivity analysis (SA) to identify the most influential parameters on the error on the propagated pulse. For an identical relative uncertainty on the parameters of 0.1%, the maximum uncertainty on the propagated pulse is 3% of the pulse amplitude. Therefore, even with carefully measured parameters, the UQ on the dispersion correction procedure for SHPB tests cannot be neglected. The SA gives the order of decreasing importance of the parameters: c0, r0; x and ν. This can be helpful if one wants to reduce the uncertainty as it indicates on which parameter(s) the measurement accuracy must be improved in priority.