International Journal of Rock Mechanics and Mining Sciences
Technical NoteStress uniformity of split Hopkinson pressure bar under half-sine wave loads
Introduction
To make feasible the application of split Hopkinson pressure bar (SHPB) in dynamic tests for brittle materials, loading techniques with non-rectangular waves have been developed in recent years [1], [2]. Among such techniques, the special shape striker method, dedicated to generating half-sine waves with tapered ends from short cylinders, has been proved to have several advantages [1], [3], [4], [5], [6]: (a) capability of avoiding the premature failure of brittle specimens; (b) better stress equilibrium in specimens; (c) less oscillation in signals and the resultant stress–strain curves and (d) easier to keep the specimen deforming at a constant strain rate, which is vital for tests of rate-dependant materials.
However, the existing SHPB systems with special shape strikers still inherit the conventional design principles or simply replace the conventional cylindrical striker with a special shape striker. In fact, when the special shape striker is used in SHPB system, it will not only alter the loading wave, but also change the loading conditions at the front of the input bar, e.g., change from uniformly coaxial impact to partial-contact local impact or even off-axial impact. In these cases, the cross sectional stress non-uniformity in the input bar becomes serious near the loading end and gradually decreases with the distances far away. Then a too-short input bar cannot ensure to transfer even load to the specimen, while a too-long input bar will lead to material waste, high manufacturing requirements and high installation cost. It is worthwhile to investigate the wave propagation characteristics and stress uniformity along bar under local impacts and off-axial impacts, so as to offer guidance for SHPB test with special shape strikers.
As to the impact on elastic bars, scattered information can be found in some researches mainly devoted to the research of DSVP (dynamic Saint-Venant’s principle) [7], [8], [9], [10], [11], [12], [13]. Comparing the stress wave-fronts generated in a cylindrical bar, Jones and Norwood [10] founded that the stress distribution along the bar stays the same while the distance is twenty times the bar diameter despite of different loading conditions. Bell [11] observed the stress in a cylindrical rod under transient loading with different distributions of contact areas and concluded that the stress distribution at distances larger than 0.5 the diameter of the bar is the same. Tyas and Watson [12] gave a comprehensive analysis for the transient response of a bar under concentrated and arbitrary distributed loads in detailed frequency domain, and showed that five times the radius of the bar let the spatial distribution of stress on the bar immaterial to the applied stress with low to moderately high frequencies. Meng and Li [13] investigated the mismatch between the specimen/bar cross sections with FE code and indicated 1.5 bar diameter is insensitive to the mismatch. These results give useful references to SHPB design and tests, but are rather inconclusive.
In what follows, wave propagation and stress distribution of an elastic thick bar are numerically analyzed when different half-sine wave loads are applied at the front end of the bar with different spatial distributions. The aim of this work is to investigate the stress evolution and cross sectional stress uniformity along the thick bar, so as to give practicable guidance for proper choice of striker profile and bar dimension for SHPB system with special shape strikers.
Section snippets
Purpose to use special shape strikers in SHPB system
Classical SHPB, originally developed to determine the dynamic plastic properties of metal materials, has a cylindrical striker with the same diameter as the input/output bar [14], [15]. With merits of easy operation, good repeatability and accurate results, SHPB has become a more and more popular experimental technique to test materials out of metals. Recently, it has been imported into dynamic tests of rock materials to obtain design parameters for drilling, blasting, underground protection
Stress non-uniformity analyses
For dynamic problems, the full-scale monitoring and capturing of valid signals are usually very challenging at laboratory, and 3D effects make the theoretical analysis complicated or even impossible. Numerical methods, on the other hand, can give reliable time and spatial information in tractable manners when the analysis models are elaborately established. In this study, the well-known FE code LS-DYNA is used to conduct the simulation.
Suggestions and conclusions
SHPB with special shape strikers tends to be a good alternative to conduct dynamic tests for rock materials. However, there is still little knowledge about this technique. Especially, the special shape strikers bring up many new problems that are different from that of conventional SHPB system. In this technical note, half-sine wave is chosen to represent the special waveform produced by special shape strikers. Then wave propagation and stress uniformity have been numerically investigated for a
Acknowledgments
Financial support from the National Natural Science Foundation of China (50904079, 50934006) and National Basic Research Program of China (2010CB732004) are greatly acknowledged.
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