A critical study of the Hopkinson pressure bar

Abstract The first part of this paper (§§ 1 to 9) contains a description of an electrical method for measuring the relation between pressure and time in experiments on high pressures of short duration. As in the method devised by Hopkinson, the pressure is applied normally to one end of a cylindrical steel bar, producing a stress pulse which gives rise to radial and longitudinal displacements in the bar. The radial displacement, or the longitudinal displacement at the end of the bar remote from the applied pressure, is used to produce a change in the capacity of a suitable condenser unit which is charged to a high potential and connected through a feed circuit and an amplifier to a double-beam cathode-ray oscillograph. The change in capacity of the condenser unit gives rise to a vertical deflexion of one of the beams of the oscillograph, the other beam being used for time-marking. At the appropriate instant, the two beams are traversed rapidly in a horizontal direction across the screen by a sweep circuit triggered by a switch on the pressure bar. By photographing the traces on the screen, an oscillogram , giving the variation with time of the displacement in the bar, is obtained, and from this record the variation of the applied pressure with time can be deduced. The second part of the paper (§§ 10 to 12) begins with a theoretical discussion of the propagation of extensional stress waves and pulses in a bar, using the exact equations due to Pochhammer and to Chree (§ 11), and also a less accurate wave equation due apparently to Love (§ 12). These investigations show that, owing to dispersion, a stress pulse is modified in its passage down the bar, the shorter waves lagging behind the longer ones. The theory provides a satisfactory explanation of certain features of the experimental results which are incompatible with elementary theory. It is found, for example, by the theory of group velocities, that a pulse whose initial duration is very short, becomes extended as it travels along the bar, its duration at distance x cm . from the origin being about 3.3x /isec. In the early stages of the disturbance, extending for the first 1.4x /tsec., only one dominant group exists; the later portion, extending over 1.9x sec., is com posed o f two dominant groups which give the characteristic pattern of two superposed oscillations. These conclusions are confirmed by experiment. The theory is used to discuss the errors in the experiments caused by the pressure bar itself, and it is shown that bars about 2 ft. long and 1 in. and 0.5 in. diameter can be used to measure pressures which last for about 20 and 10 /isec. respectively with an accuracy of about 2 to 3 % . T his was confirmed by experiments with bullet impacts and detonation waves in gaseous mixtures, in which the measured values of the pressure could be checked by calculation.