An Analysis of the Hopkinson Split Bar Method of Rock Testing

Abstract

American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc. Abstract The Hopkinson split bar has been used for about 20 years to study properties of rock and rock failure under dynamic loading conditions. The mathematical analysis needed to construct stress-strain curves from the measured waves requires that the rock specimen be very short compared to the wave length of the impact generated wave. In practice, specimens of several different lengths are often used with the same length wave, always making the assumption that the specimen is "short" enough for the analysis to apply. This paper describes the results of a study on the effect of the ratio of specimen length to wave length on the stress-strain curves derived from strain wave measurements. A computer simulation of the Hopkinson split bar has been made in which a rock having known elastic properties (ER, rho R) and given length is assumed to be placed between two steel bars also of known properties (ES, rho R). An incident wave of given shape and wave length is assumed to travel toward the steel-rock interface. Using plane wave assumptions, it is possible to compute the shapes of the reflected possible to compute the shapes of the reflected and transmitted waves. These are then used as if they were experimental results to compute the stress-strain relationship for the rock. This is then compared with the specified value. It is found that the slope and shape of the calculated curve for a given incident wave length is very dependent upon the specimen length. Similarly, the method of superposition of the measured waves is very critical. It is suggested that apparent rate of loading effects observed by some authors in comparing "static" and "dynamic" (Hopkinson bar) stress-strain curves may be a result of the analysis rather than a true rock behavior. A Hopkinson split bar was constructed and used to test four rock types. When the measured strain waves were analyzed using the techniques suggested from the computer simulation, it was found that the resulting stress-strain curves agreed well with the static curves. Introduction A knowledge of the dynamic properties of rock is important, for the development of improved rock fragmentation methods (percussive drilling, rock blasting, etc.) as well as the improved design of structures constructed in or on rock subjected to dynamic loading. Although several methods have been used to obtain dynamic rock properties, the Hopkinson split bar is perhaps the simplest for high stress level studies. This device, shown diagrammatically in Fig. 1, consists basically of two cylindrical steel bars to which strain gauges have been bonded, the sample which is sandwiched between the bars, and the loading system. In many laboratories including that of the present authors, the loading system consists of a striker that is accelerated down a long tube under the action of compressed air and impacts the end of the first steel bar. Quite a range of loading rates can be produced by merely changing striker length and controlling the velocity at impact. As the impact-produced strain wave,, reaches the sample, part of the wave is reflected and back part of the wave is reflected and back into the first bar and part is transmitted into the second steel bar. From measurements of the incident, reflected and transmitted waves, and assuming plane wave theory to apply, one can construct stress-strain curves for the rock sample. A comparison of these "derived" dynamic curves with those obtained by static methods can then be made.