Very High Strain Rate Range

International audienceThe classical Split Hopkinson Pressure Bar (SHPB) system is considered to be able to perform tests at strain rates ranging from 102 to 104s−1. However, some modifications can be carried out to extend the reachable strain rate within the specimen. The mean strain rate defined within the specimen:$$\dot{\varepsilon}_s =\frac{V_\text{out}-V_\text{in}}{l_s}$$where $V_\text{out}$ and $V_\text{in}$ stand for the velocity of output and input cross-sections of the specimen respectively, shows that the achievable strain rate varies inversely proportionally to the length of the specimen $l_s$, while the achievable stress is confined by the elastic limit of the bars, especially by the incident bar sustaining the entire impacting energy. From this viewpoint, extending the strain rate in the test can be either achieved by scaling down the size of the specimen and consequently that of the entire device, or by dispensing with the limit on the stress of the incident bar by removing it. Two modified Hopkinson devices are widely adopted to test the material at the strain rates beyond 104s−1, referred to as the miniaturized Hopkinson bar and Direct-Impact (DI) devices

Numerical investigation of the dynamic compressive behaviour of rock materials at high strain rate

The dynamic compressive strength of rock materials increases with the strain rate. They are usually obtained by conducting laboratory tests such as split Hopkinson pressure bar (SHPB) test or drop-weight test. It is commonly agreed now that the dynamic increase factor (DIF) obtained from impact test is affected by lateral inertia confinement, friction confinement between the specimen and impact materials and the specimen sizes and geometries. Therefore, those derived directly from testing data do not necessarily reflect the true dynamic material properties. The influences of these parameters, however, are not straightforward to be quantified in laboratory tests. Therefore, the empirical DIF relations of rock materials obtained directly from impact tests consist of contributions from lateral inertia and end friction confinements, which need be eliminated to reflect the true dynamic material properties. Moreover, different rocks, such as granite, limestone and tuff have different material parameters, e.g., equation of state (EOS) and strength, which may also affect the DIF of materials but are not explicitly studied in the open literature. In the present study, numerical models of granite, limestone and tuff materials with different EOS and strength under impact loads are developed to simulate SHPB tests and to study the influences of EOS and strength, lateral inertia confinement and end friction confinement effects on their respective DIFs in the strain rate range between 1 and 1,000 s-1. The commercial software AUTODYN with user-provided subroutines is used to perform the numerical simulations of SHPB tests. Numerical simulation results indicate that the lateral inertia confinement, friction confinement and specimen aspect (L/D) ratio significantly influence DIF obtained from impact tests and the inertia confinement effect is different for different rocks. Based on the numerical results, quantifications on the relative contributions from the lateral inertia confinement and the material strain rate effect on DIF of granite, limestone and tuff material compressive strength are made. The effects of friction coefficient, L/D ratio and rock type on DIF are discussed. Empirical relations of DIF with strain rate for the three rock materials representing the true material strain rate effect are also proposed