About the dynamic strength enhancement of concrete-like materials in a split Hopkinson pressure bar test

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Abstract

Split Hopkinson pressure bar (SHPB) technique has been used widely to measure the dynamic strength enhancement of concrete-like materials at high strain-rate between 101 and 103 s−1. Although SHPB technique has been verified for metallic materials, the validity and accuracy of SHPB results for non-metallic materials have not been thoroughly studied. The present paper examines the application of SHPB to determine the dynamic strength of concrete-like materials whose compressive strength is hydrostatic-stress-dependent. It shows that the apparent dynamic strength enhancement beyond the strain-rate of 102 s−1 is strongly influenced by the hydrostatic stress effect due to the lateral inertia confinement in a SHPB test. This apparent dynamic strength enhancement has been wrongly interpreted as strain-rate effect and has been adopted in both dynamic structural design and concrete-like material models for analytical and numerical simulations, which may lead to over-prediction on the dynamic strength of concrete-like materials. The SHPB test is simulated in the present paper using FE method and Drucker–Prager model to investigate how the hydrostatic stress affects the SHPB test results of concrete-like materials. A rate-insensitive material model is used in order to examine this pseudo-strain-rate sensitive phenomenon. A collection of SHPB test results of concrete-like materials are compared with simulation results, which confirms quantitatively that the apparent dynamic strength enhancement of concrete-like materials in a SHPB test is caused by the lateral inertia confinement instead of the strain-rate sensitivity of the tested material.

Introduction

The strain-rate effect on the strength of various concrete-like materials, e.g., concrete, mortar and geo-materials, has become an important factor in both the material model and the design of structures that may experience high strain-rate in a range of applications when impact or blast loading is involved. It is generally accepted that there is an apparent increase of the dynamic strength when the concrete-like material is subjected to high strain-rate. The dynamic increase factor (DIF), defined by the ratio of the dynamic strength to the quasi-static strength in uniaxial compression, has been widely accepted as an important parameter to measure the strain-rate effect on the strength of concrete-like materials.

The dynamic strength enhancement of concrete has attracted great interest in structural design and analysis due to the broad applications of concrete in impact and blast loading environment. European CEB recommended DIF formulas for concrete in both tension and compression (Comite Euro-International du Beton, 1993), which take bilinear relations between DIF and log(ε̇) with a change in slope at strain-rate of 30 s−1. A great number of tests have been conducted to find the dependence of DIF on strain-rate by using various test methods, e.g., drop-hammer techniques, servo-hydraulic loading rigs, split Hopkinson pressure bar (SHPB) and explosive devices. A critical review on the compressive behaviour of concrete at high strain-rates was conducted by Bischoff and Perry (1991), where various experimental techniques and test results were summarized. Williams (1994) gave a comprehensive review about the strain-rate effects on the compressive strength of concrete, where DIF measured by various researchers was plotted against the strain-rate from quasi-static to 102 s−1 for concrete of quasi-static strength between 16.5 and 103 MPa.

Although it has been shown that DIF increases 50% in average when strain-rate varies from 10−5 to 101 s−1, as shown in Fig. 1, it has great uncertainty about the test results and their interpretations (Bischoff and Perry, 1991). These uncertainties may come from following sources, (1) different testing techniques; (2) specimen size effect; (3) material differences, e.g., concrete quality, aggregate grade, curing and moisture condition, age, etc., and (4) dynamic and boundary effects. It is interesting to know whether the test results at high strain-rates purely reflect the strain-rate-dependence of material itself, or the dynamic effects due to the test set-up and the method of measurement have great influence on the strain-rate-sensitivity of concrete-like materials.

Comparative studies on the dynamic strength of concrete should be based on consistent experimental results, preferably from a systematic and consistent test program, in order to reduce experimental uncertainties to minimum. In recent years, SHPB technique, which was developed originally to test the dynamic stress–strain relation of metallic specimens, has been widely applied to study the dynamic compressive strength of concrete at high strain-rate from 101 to 103 s−1. The SHPB-based experimental results suggested that the strain-rate influence on DIF becomes significant when the strain-rate is beyond a critical value between 101 and 102 s−1 (Malvern and Ross, 1985; Tedesco and Ross, 1998; Grote et al., 2001), which will be studied in the present paper.

The objective of the present study is to verify the validity of SHPB technique for testing concrete-like materials. It shows that the strain-rate-dependence of DIF obtained from SHPB tests is mainly caused by the existence of lateral inertia confinement in a SHPB test, and thus, the DIF obtained using the conventional SHPB technique should be modified to eliminate the lateral inertia confinement effect.

Section snippets

SHPB technique and its limitations

A SHPB system consists of incident and transmitter pressure bars with a short specimen sandwiched between them. Three waves are involved in a SHPB test, i.e., an incident compressive pulse generated by the impact of a striker, a reflected tensile pulse due to the low impedance of the specimen and a transmitted compressive wave. Stress wave reflects at interfaces between specimen and pressure bars to homogenize the stress distribution in the specimen (Davies and Hunter, 1963). According to

Methodology

Two important issues should be addressed in the numerical verification of a SHPB test. First of all, it is necessary to prove that the obtained SHPB test results represent the material property of the tested specimen rather than the structural response of the specimen in a SHPB system. Secondly, the apparent strain-rate effect on the stress measured in a SHPB test should be due to material strain-rate sensitivity rather than other causes.

A “reconstitution method” will be used in the present

Numerical results and discussion

Instead of modeling the collision between an impact bar and the incident pressure bar, a stress pulse of trapezium shape is inputted into the incident pressure bar. The rising time of the pulse varies from 0 to 180 μs, the pulse duration varies from 30 to 240 μs and the stress intensity varies from 45 to 1000 MPa. Different combinations of the pulse parameters are used to obtain desired strain rates at the measured ultimate stress of the SHPB test. The actual shape of the input pulse will be

Conclusions

Numerical simulations show that the lateral inertia force of the specimen increases the lateral confinement in a SHPB test, which causes an apparent increase of the DIF for concrete and concrete-like materials whose stress–strain relation can be represented by a hydrostatic-stress-dependent constitutive law, e.g., Drucker–Prager model. This effect becomes significant when the nominal strain-rate is around 102 s−1, which coincides with the experimentally obtained transition point from a weak

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