Manual for Calibrating Sound Speed and Poisson’s Ratio of (Split) Hopkinson Bar via Dispersion Correction Using Excel® and Matlab® Templates

Abstract

This manual presents a procedure to calibrate the one-dimensional sound speed (co) and Poisson’s ratio (ν) of a (split) Hopkinson bar using the open-source templates written in Excel® and Matlab® for dispersion correction. The Excel® template carries out the Fourier synthesis and one-time dispersion correction of a traveling elastic pulse under a given set of co and ν. The MATLAB® template performs the Fourier synthesis and iterative dispersion correction of a traveling elastic pulse for a range of co and ν sets. In the case of the iterative dispersion correction, a set of co and ν is assumed at each iteration step, and the sound speed vs. frequency (cdc vs. fdc) relationship necessary for dispersion correction is obtained under the assumed set by solving the Pochhammer–Chree equation. Subsequently, dispersion correction is carried out by using the cdc vs. fdc relationship. The co and ν values of the bar are determined in the iteration process when the dispersion-corrected pulse profiles are reasonably consistent with the measured ones at two travel distances (2103 and 4000 mm) in the bar. In the case of the experimental profile considered herein, the ν and co values were calibrated to six and four decimal places, respectively. The calibration algorithm is described with the tips for using the open-source templates, which are available online in a publicly accessible repository.