A Conical Striker Bar to Obtain Constant True Strain Rate for Kolsky Bar Experiments
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BRIEF TECHNICAL NOTE
A Conical Striker Bar to Obtain Constant True Strain Rate for Kolsky Bar Experiments M. J. Forrestal1 · T. L. Warren2 Received: 30 April 2020 / Accepted: 29 August 2020 © Society for Experimental Mechanics, Inc 2020
Abstract Many split Hopkinson pressure bar (SHPB) or Kolsky bar techniques use pulse shaping methods to obtain constant engineering strain rate for the specimen response. However, constitutive models for numerical simulations use the axial rate of deformation which is the true axial strain rate. In this study, we present an equation for the incident bar strain produced by a truncated conical striker bar. These incident bar strains are shaped so that we can obtain constant true strain rate for the specimen. Keywords Conical striker bar · True strain rate · Kolsky bar · Pulse shaping
Introduction Constitutive models obtained from large strain compression data are typically fit to curves at nearly constant engineering strain rates [1]. For Kolsky bar experiments, constant engineering strain rates can be obtained with pulse shaping techniques that produce the desired wave shapes in the incident bar. The most common method for pulse shaping is to place copper [2] or copper-steel [3] discs on the impact surface of the incident bar. After impact by the striker bar, the pulse shaper plastically deforms and spreads the pulse in the incident bar so that the specimen reaches dynamic force equilibrium and constant engineering strain rate. However, as discussed in [4], constitutive models used for numerical simulations use the axial rate of deformation which is the true axial strain rate. Casem [5] presents a variable impedance, inverse approach [6] for the striker bar design. This method is used to design the striker bar cross-section to shape the incident strain pulse and obtain constant true strain rate for the specimen response. This wave shaping technique uses a thin copper disc or a small amount of grease on the incident bar and striker bar with a variable cross section. The striker bar consists of a series * T. L. Warren [email protected] 1
Present Address: Fort Worth, TX, USA
Present Address: Albuquerque, NM, USA
2
of cylindrical sections that decrease in diameter away from the impact end. Wave motion in the segmented striker bar is calculated with a detailed numerical analysis. Casem [5] demonstrates his procedure with experiments conducted on nylon specimens for a true strain rate of about 2500 1/s and axial strains that reach 0.60. We observe that the striker bar with a series of cylindrical sections used in [5] could be closely approximated with a smooth, conical striker bar that simplifies the machining. More important, the conical striker bar wave motion could be analyzed with classical mathematical methods to obtain closed-form equations. For this study, we derive closedform equations with the Laplace transform method for the stress and strain in the incident bar impacted by a conical striker bar. We compare our incident strain–time predictions with the predictions gi
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