Measurements of Particle Velocity Within a Kolsky Bar with Applications to Wave Separation
Several methods of measuring particle velocity at points along a Kolsky bar are investigated. Direct particle velocity measurements are of interest because they can be used in conjunction with strain gages to permit wave separation; this can be used to ex
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Measurements of Particle Velocity Within a Kolsky Bar with Applications to Wave Separation Daniel T. Casem and Michael B. Zellner
Abstract Several methods of measuring particle velocity at points along a Kolsky bar are investigated. Direct particle velocity measurements are of interest because they can be used in conjunction with strain gages to permit wave separation; this can be used to extend the lower strain-rate range accessible with the Kolsky bar technique. Two methods are evaluated with a PMMA Kolsky bar. They include (1) strain-gradient based measurements of acceleration, which is then integrated to obtain particle velocity, and (2) laser extensometer measurements of displacement, which is then differentiated to obtain velocity. Each of these methods has its limitations, and it is suggested that they can be used together to provide a velocity diagnostic useful for practical testing. Finally, preliminary experiments are presented with a Photon Doppler Velocimeter to measure particle velocity with a steel pressure bar.
8.1
Introduction
Over the past few decades, the Kolsky bar, or Split Hopkinson Pressure Bar, has become the standard method for characterizing the mechanical response of materials at high strain-rates, i.e., in the range of 103/s–104/s [1–3]. The most common arrangement is shown in Fig. 8.1. The specimen is placed between two elastic bars, called the incident bar and the transmitter bar, as shown in the figure. A projectile impacts the incident bar and a compressive stress wave, the incident pulse, propagates into the bar. When this wave arrives at the specimen the specimen begins to deform. A reflected wave then propagates back into the incident bar while a third wave, called the transmitted pulse, propagates into the transmitter bar. These three waves are measured using strain gages at the mid-point of each bar, i.e., the incident bar strain gage, SG1, is used to measure the strain due to the incident and reflected pulses and the transmitter bar strain gage, SG2, is used to measure the transmitted pulse. Provided the bars remain elastic, the wave propagation is known and the forces applied to the specimen and its resulting deformation can be determined using an appropriate wave theory (i.e., forces F1, F2, and interface velocities v1, v2, in the figure). In the simplest case, the wave propagation can be described by basic linear elastic one-dimensional bar wave propagation (uniaxial stress). In this case, the waves propagate through the bars without change in form at a fixed bar wave speed given by c0 ¼ (E/r)1/2, where E is the elastic modulus of the bar material and r is it’s density. This description is adequate provided the wavelengths of the relevant stress waves are large in comparison to the diameter of the bar, i.e., relatively low frequencies. When high frequencies are significant, dispersion effects may become noticeable and more sophisticated theories [4–6] may be required. Furthermore, some researchers use polymeric bars to increase sensitivity and these materials may be visco
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