Split Hopkinson Pressure Bar Loading Research Articles

Experimental and numerical simulation study of fiber-reinforced high strength concrete at high strain rates

With the widespread use of fiber-reinforced high strength concrete (FRHSC) in military and civil fields, it is necessary to have an accurate understanding of the mechanical properties and failure modes of FRHSC under impact. The dynamic compression experiments were performed on FRHSC using the large-size split Hopkinson pressure bar (SHPB) apparatus. The experimental results were analyzed to determine the reasonable strain rate range of FRHSC under large-size SHPB loading conditions. The strain rate effect, critical strain, and failure mode of FRHSC under dynamic impact were studied. The strain rate and strength parameters in the Holmquist-Johnson-Cook (HJC) model were determined based on the experimental results, and the numerical simulation of SHPB was completed by LS-DYNA. The results revealed that the reasonable strain rate of FRHSC under large-size SHPB loading did not exceed 100 s−1. The material presented an obvious strain rate effect, and the critical strain was almost unchanged with the increased strain rate. Steel fiber improves the toughness of FRHSC. Under quasi-static loading, the tensile-compression ratio of the material was 0.13, and there was no apparent damage under impact. The rationality of the strain rate and strength parameters in the HJC model was verified by comparing the stress wave curve of the pressure bar, the stress-strain curve, and the failure mode of the specimen obtained by experiment and simulation.

Experimental Investigation on Multiscale Fracturing in Thermally Treated Sandstone under SHPB Impact Loading

To study the effect of temperature on the dynamic mechanical behaviors and fracture characteristics of thermally treated sandstone, compressive dynamic loading experiments were performed on a series of samples using a split Hopkinson pressure bar (SHPB). In the tests, the dynamic uniaxial compressive strength of the thermally treated sandstone was inversely proportional to the temperature treatment in the range of 200°C–1000°C, while the dynamic elastic modulus first increased and then gradually decreased after different temperature treatments. The results show that two classical mechanical types (i.e., Class I and Class II) are observed from the dynamic stress-strain responses of SHPB tests for thermally treated sandstone. By means of scanning electron microscopy (SEM), the microdifference of postloading microfracture characteristics in Class I and Class II behavior was identified. In Class I behavior, intercrystalline cracks (IE) are the chief form of cracks on the fracture surface of a specimen fractured by SHPB loading even though there some intracrystalline cracks may also be present. In contrast, Class II behavior results from the chief cracking type being intracrystalline cracks.

An asymmetric semi-circular bend method for investigating fracture behavior of brittle rocks under dynamic mixed mode I/II loading.

Understanding the fracture behavior of brittle rocks under dynamic mixed mode I/II loading is imperative and beneficial for the stability analysis of rock engineering structures. However, available research studies on the dynamic mixed mode fracture of brittle rocks are rather rare, and existing testing methods own some complexity in the specimen preparation or experimental operation. In this study, a novel and efficient experimental method is developed for investigating the fracture behavior of brittle rocks under mixed mode I/II impact loading. For the first time, the asymmetric semi-circular bend (ASCB) specimen is introduced into a split Hopkinson pressure bar loading system to obtain dynamic mixed mode fracture toughness of granite. By virtue of digital image correlation techniques combined with high-speed photography, the progressive fracture processes of specimens with different mode mixity are also visualized. Results show that the dynamic force equilibrium and the crack tip initiation are satisfied for all the tests, validating the feasibility and reliability of this method. The fracture path of the ASCB specimen under dynamic mixed mode I/II loading deviates from the original loading direction and finally generates a curved crack, which is quite different from the straight fracture path under pure mode I loading. In addition, experimental results indicate the significant loading rate dependence of the dynamic fracture toughness, and the dynamic effective fracture toughness under mode I loading is greater than that under mode II loading at a given loading rate. Our proposed method is convenient and reliable to investigate dynamic mixed mode I/II fracture of brittle rocks.

Crack propagation and dynamic properties of coal under SHPB impact loading: Experimental investigation and numerical simulation

To investigate the crack propagation and dynamic mechanical properties of coal under high strain rate loading, 24 sets of Brazilian disk (BD) coal specimens with vertical and horizontal beddings were made, and tests were conducted by a split Hopkinson pressure bar (SHPB) system. Under different impact velocities, a high-frame and high-resolution camera was employed to capture the fracture process, and two high-dynamic strain gauges were used to record the stress pulse signals simultaneously. Using one-dimensional stress wave theory, the dynamic mechanical properties of coal with different bedding directions under different impact velocities were analyzed and discussed. Experimental results indicate that bedding directions not only have a major influence on dynamic mechanical properties such as dynamic tensile strength, strain rate and strain energy but also have a great influence on the crack propagation path. Then, based on the image processing technique and fractal method, cracks conforming to the fractal have been proven, and the results further illustrate that the fractal dimension of cracks on the coal surface increased in the fracture process under SHPB loading. Finally, a numerical model based on bond-based Peridynamic theory was proposed to simulate crack propagation and dynamic mechanical properties of coal under the SHPB test, and the displacement-strain-stress fields were also calculated, which further reveal the fracture mechanism and dynamic behavior of coal under different impact loading conditions.

Experimental and numerical investigation of crack propagation and dynamic properties of rock in SHPB indirect tension test

To explore the dynamic mechanical properties and crack propagation law of rock under high strain rate impact loading, an experimental investigation with 12 sets of Brazilian disk (BD) rock specimens under Split Hopkinson Pressure Bar (SHPB) loading was undertaken. Unlike the previous researches that study the dynamic mechanical properties and crack propagation law individually, the relationship of them has also been investigated and discussed. More specifically, a dynamic resistance strain gauge and a high-frame camera were employed to simultaneously record stress wave data and rock destruction process videos under different impact velocities. Based on image processing technique, a new calculation method of crack propagation velocity was proposed and then the stress-strain characteristics and crack propagation features were analyzed. The experimental results indicate that: (1) Crack propagation rate of the crack along X-Y direction both rises with the impact velocity increase; (2) the strain of rock along the loading axis is much larger than the vertical direction; (3) there is a certain quantitative relationship between the stress-strain state and the crack area of the rock specimen after it has been damaged. Finally, a numerical model based on Peridynamic theory was developed to simulate crack propagation and dynamic constitutive relationship of rock materials with BD configuration in indirect tension test under SHPB loading, and further reveal the fracture behavior and mechanism of rock materials under high strain rate loading.

Experimental Study of Fracture Characterizations of Rocks under Dynamic Tension Test with Image Processing

To investigate the fracture characterizations of rocks under high strain rate tensile failure, a series of dynamic Brazilian tests was conducted using Split Hopkinson pressure bar (SHPB), and a high‐speed digital camera at a frame rate of 50,000 frames per second (FPS) with a resolution of 272 × 512 pixels was adopted to capture the real‐time images and visualize the failure processes. Using the extracted cracks and image processing technique, the relationship between loading condition (impact velocity), crack propagation process (crack velocity, crack fractal characteristic, and crack morphological features), and dynamic mechanical properties (absorbed energy and strain‐stress parameters) was explored and analyzed. The experimental results indicate that (1) impact velocity plays a critical role in both crack propagation process and dynamic mechanical properties, (2) the crack fractal dimension is positively correlated with crack propagation velocity and has a linear relationship with the proposed morphological feature of crack, (3) mean strain rate and max strain of rocks under SHPB loading both decrease with the increase of crack propagation velocity, and (4) the energy absorbed by the rocks increases with increasing impact velocity and has a strong negative correlation with a proposed novel crack descriptor. Experimental studies pertaining to the measurement of crack propagation path and velocity, in particular, some crack feature extraction approaches, present a promising way to reveal the fracture process and failure mechanisms of rock‐like materials.

Deformation to fracture evolution of a flexible polymer under split Hopkinson pressure bar loading

The deformation-to-fracture evolution of a flexible polymer material under high-strain-rate compressive loading conducted by a split Hopkinson pressure bar (SHPB) setup was investigated. Representative tests were carried out at different strain rate levels, followed by the characterization of dynamic damage after each test. Craze and crack patterns on the end surface of the specimen were carefully analyzed. The failure patterns appear along the radial and circumferential directions. The sequence of their formation with increasing strain/stress level was revealed. The mechanisms resulting in the craze and crack patterns were analyzed. The heterogeneous stress distribution in the specimen and the resultant damage morphologies were demonstrated. This research not only shows the deformation-to-fracture evolution of a flexible polymer material under SHPB loading, but also provides a better clarification of the localized stress distribution in the tested material via SHPB technique.

Response of high-strength concrete to dynamic compressive loading

An experimental investigation into the dynamic compressive response of high-strength concrete with three different strengths – 60MPa, 80MPa and 110MPa, denoted by C60, C80 and C110, respectively – was undertaken. Concrete specimens were subjected to quasi-static and dynamic compression, using a Denison Universal Testing Machine and a Split Hopkinson Pressure Bar (SHPB) device, and the effects of strain rate on their mechanical properties (e.g. stress-strain relationship, compressive strength) examined. Significant rate dependence was observed for all three concretes – i.e. the compressive strength increases with strain rate and the dynamic strength is much higher than the static value; C60 and C80 exhibited similar rate sensitivity, while C110 displayed a relatively noticeably lower rate dependence. The rate sensitivity was quantified via a Dynamic Increase Factor (DIF, the ratio between the dynamic and static strength), and this was compared with predictions by the CEB-FIP 2010 equation, commonly utilised to estimate rate sensitivity for normal strength concrete. The comparison indicates that the model is not suitable for high-strength concrete, as it predicts a sharper rise in rate-sensitivity, and the mismatch increases with concrete strength, becoming notably significant for C110. Interpretation of rate dependence of concrete materials based on SHPB test results, as to whether it is an intrinsic material property, or generated primarily by radial inertia, was examined by finite element modelling of SHPB tests. Concrete material properties were taken to correspond to a concrete damaged plasticity model, and the quasi-static stress-strain response, coupled with the Dynamic Increase Factor determined from dynamic tests, was utilised. The simulation results correlated closely with experiments, in terms of strain gauge signal histories in the SHPB loading bars, indicating that for the strain rate range investigated (30–110 s−1), radial inertia is not significant, and the rate dependence observed is attributable to material response.

Dislocation density and mechanical threshold stress in OFHC copper subjected to SHPB loading and plate impact

The dislocation density and mechanical threshold stress (MTS) of oxygen-free high-thermal-conductivity (OFHC) copper loaded at strain rates in the range of 102 to 106s−1 were measured. Moderate-strain-rate (102 to 104s−1) experiments were performed using a Split Hopkinson Pressure Bar (SHPB). A steel collar was placed around each specimen to control the maximum loading strain. High-strain-rate (105 to 106s−1) experiments were carried out using a 57-mm-bore single-stage gas gun. The radial release effect was eliminated using the momentum trapping technique. The loaded samples were recovered, and the dislocation characteristics and dislocation density were determined by X-ray diffraction profile analysis. The fraction of the screw dislocation was found to decrease with increasing loading strain and strain rate. The dislocation density was found to lie between 1.8×1014 and 2.2×1015m−2. Quasi-static reload compression tests were performed on the recovered samples at room temperature. The mechanical threshold stress (or the flow stress at 0K) was obtained by fitting the reload stress–strain data to the MTS model. The results of analysis of the equivalent strain, mechanical threshold stress, and dislocation density measurements suggest that the relation between the mechanical threshold stress and the dislocation density can be described well by the Taylor relationship.

Dynamic crystal rotation resolved by high-speed synchrotron X-ray Laue diffraction.

Dynamic compression experiments are performed on single-crystal Si under split Hopkinson pressure bar loading, together with simultaneous high-speed (250-350 ns resolution) synchrotron X-ray Laue diffraction and phase-contrast imaging. A methodology is presented which determines crystal rotation parameters, i.e. instantaneous rotation axes and angles, from two unindexed Laue diffraction spots. Two-dimensional translation is obtained from dynamic imaging by a single camera. High-speed motion of crystals, including translation and rotation, can be tracked in real time via simultaneous imaging and diffraction.

A theory for plastic-bonded materials with a bimodal size distribution of filler particles

Plastic-bonded materials are composites consisting of grains of filler material embedded in a polymeric matrix. A micromechanics model is proposed for investigating the mechanical behaviour of plastic-bonded materials having two disparate grain sizes. A hybrid theory is proposed to handle some aspects of the bimodal grain size distribution. Our model uses the first-order method of cells with an eight-cell representative volume element where one of the eight cells contains a large grain and the seven remaining cells contain a mixture of small grains embedded in the polymeric binder material. A Mori–Tanaka-based analysis is used to describe the small grain-binder mechanical response. The small grains in this analysis are assumed to be spherical and uniformly distributed in the binder. In this work, we use the explosive PBX 9501, in its unreacted state, as our test system. The explosive grain particle size distribution of PBX 9501 consists of two broad peaks centred at approximately 1 and 200 µm. The constitutive behaviour of the large explosive grains are assumed to be elastic-plastic and damage by way of micro-crack brittle fracture. Only linear elasticity of the small grains is considered. The rate and temperature dependence of the mechanical response of the polymer binder is accounted for by a generalized Maxwell viscoelasticity model. The theoretical uniaxial stress–strain response for PBX 9501 is reported for quasi-static and split Hopkinson pressure bar loading rates and compared to experimental measurements.