Dynamic split tensile test of Flattened Brazilian Disc of rock with SHPB setup

Abstract

The Flattened Brazilian Disc (FBD) specimens were impacted diametrically by a pulse shaping split Hopkinson pressure bar to measure dynamic tensile strength of a brittle rock. With application of strain gauge technique, the stress waves traveling through the incident bar, the transmission bar as well as the FBD specimen were recorded and analyzed. The loading history was determined based on the one-dimensional stress wave theory. The dynamic equilibrium condition in the specimen was approximately satisfied, this claim was supported by the numerical simulation of dynamic stress evolution in the specimen, with the conclusion that a short time after impact the pattern of dynamic stress distribution in the specimen was symmetric and similar to that of the counterpart static loading. The validity of the test was further verified experimentally, as the waveforms acting on the two flat ends of the FBD specimen, respectively, were of nearly the same shape, and the rupture modes of the specimens were generally such that crack first initiated at the center of the disc and subsequently propagated along the loading diameter, whereas crush zones were implied to form lastly near the two flat ends of the broken specimen. The dynamic tensile strength of marble was measured at the critical point when the tensile strain wave recorded at the disc center got peak value of the strain derivative with respect to time.

Introduction

The tensile strength of rock material is typically an order of magnitude smaller than the compressive strength, tensile failure often occurs in rock masses. In addition, in many rock related engineering projects, e.g. blast and fragmentation in mining and military operation, rock breakage is often affected by loading rate. Hence research on various methods to measure dynamic tensile strength of rock materials is important for application in geotechnical engineering and development in rock mechanics. However, a direct tension test of rock is very difficult to perform, so that an indirect tension, such as the Brazilian test, also called the split tensile test, has been a popular choice. International Society for Rock Mechanics (ISRM) issued the suggested method for testing static rock tensile strength with the Brazilian disc specimen (ISRM, 1978). American Society for Testing and Material also adopted a similar method for testing concrete (ASTM C496/C496M-04). The main drawback of the Brazilian test is that it is not easy to maintain an ideal contact between the platens of a test machine and the circular boundary of a disc specimen, and the stress concentration caused by the point load on the disc may bring about premature breakage of the specimen at the contact point. As the crack is not first initiated from the center of the disc as expected, the underlying principle of the Brazilian test is violated. In order to avoid this unreasonable failure mode of the disc specimen, a pair of rounded anvils has been adopted by many researchers, among them the early practitioners are Awaji and Sato (Awaji and Sato, 1979). However, the match between the anvils and the periphery of a disc specimen is very complicated, it is difficult to determine an accurate contact width between the anvils and the disc (Awaji and Sato, 1979); and for discs of different diameters, differently sized anvils may be required to test them. Another solution to the problem was to machine two parallel flat ends on the disc circumference for appliance of a distributed load, then the regular complete disc was modified and became the Flattened Brazilian Disc (FBD) (Wang and Xing, 1999). We are just promoting the FBD specimen from the static test to the dynamic split tensile test (Wang et al., 2006). Being used in the dynamic test, the flat ends of the FBD specimen may be especially more convenient than the curved anvils or glued bearing strips proposed by ISRM and ASTM, as the anvils or strips may have a negative influence on the stress wave behavior in the dynamic Brazilian test.

The strain rate of rock fragmentation is usually in the range of 10¹–10⁴ s⁻¹, a split Hopkinson pressure bar (SHPB) setup is suitable for testing rock at such strain rates (Wang et al., 2006, Kolsky, 1949, Rodriguez et al., 1994, Buchar and Rolc, 2006, Gomez et al., 2001, Gomez et al., 2002, Grantham et al., 2004, Frew et al., 2001, Pan et al., 2005). “Proper experiments need to be carefully designed and constructed to acquire accurate and reliable material properties” (Pan et al., 2005). Specifically wave propagation should be considered when studying the dynamic mechanical properties of materials at such high strain rates. For a comprehensive evaluation of the dynamic split test, attention was focused on three key aspects for the tested specimen (Rodriguez et al., 1994): the assumption of elastic behavior; the evolution history of stress distribution; and the failure mode. Dynamic split tests were reported recently for various materials including rocks, ceramics and an explosive simulant (Wang et al., 2006, Rodriguez et al., 1994, Buchar and Rolc, 2006, Gomez et al., 2001, Gomez et al., 2002, Grantham et al., 2004). The test result for ceramics was shown to agree with result of the Taylor test in a comparison study (Buchar and Rolc, 2006). Especially worth mentioning is the photoelastic dynamic experiment using complete disc specimens performed by Gomez et al., 2001, Gomez et al., 2002, they validated the dynamic split test by stating that “the photoelastic experiments determined that the specimens were in equilibrium, and the dynamic stress field resembled the static field.” Another significant contribution to this topic is the high-rate experiment with an explosive simulant done by Grantham et al. (2004), they concluded that “The essential features of low-rate Brazilian tests are found to occur in the high-rate experiments, with the samples reaching equilibrium quickly and remaining in equilibrium throughout the experiment” (Grantham et al., 2004). In our study, differently sized FBD specimens of marble were diametrically impacted at the flat end by SHPB with varied impact speeds. In order to obtain an ideal loading wave, a thin aluminum circular plate was glued on the end surface of the incident bar as a pulse shaper for the incident wave, the pulse shaper was stricken by the projectile. A numerical simulation using finite element method was performed to show the evolution of dynamic stress distribution in various specimens. The results indicate that at a certain stage of time, i.e., after several reverberation of stress wave in the specimen, similar to that of the counterpart static test, a symmetric pattern of stress between left end and right end of the specimen is reached. Besides that, according to the stress waves recorded on the incident bar and the transmission bar respectively, the forces acting on the two flat ends of the FBD specimen are nearly equal, thus dynamic equilibrium is further shown experimentally. The splitting rupture mode of the FBD specimens is observed: center crack initiation and crack propagation along the loading diameter. The measured dynamic tensile strength of marble shows strain rate effect as compared with the counterpart static value.