Split Hopkinson Pressure Bar Equipment Research Articles

Mechanical behavior and constitutive model of frozen soil subjected to cyclic impact loading

During the construction and service of projects in cold regions, frozen soil generally experiences strong dynamic loads, such as high-speed collisions and impact tunneling. Notably, during the mining of frozen soil in cold regions, the soil suffers from multiple impact loads owing to the drilling and blasting. To ensure project safety, the deformation and failure of frozen soil near the excavation face under load must be controlled using passive support technology. Thus, the cyclic dynamic response and constitutive model of frozen soil under a one-dimensional strain state must be studied for the safe implementation of projects in cold regions. Cyclic impact is the main driving force for defect development, which can induce multiple types of damage, such as sliding friction and instability propagation of microcracks, non-reversible plastic failure, ice phase transition, and weak interval of structure formation. Frequent impact loading is accompanied by the permeation and reflection of stress waves and the dissipation and propagation of energy, ultimately leading to a decline in the bearing performance of frozen soil, which exhibits dynamic fatigue characteristics. Based on the split Hopkinson pressure bar equipment, this study analyzed the strength deformation characteristics and toughness evolution law of frozen soil under cyclic impact loading and clarified the influence mechanism of damage, the coupling effect between defects, and the connection between wave impedance and the number of cycles. In the process of constructing the constitutive model, first, the slip friction of microcracks was considered based on the meso-mechanical theory. The macro-mesoscale transition and Drucker-Prager yield criteria were combined to construct a mesoscopic constitutive model of frozen soil under passive confining pressure. Subsequently, combined with the irreversible law of energy dissipation, the degradation behavior of frozen soil under cyclic impact loading was characterized by a specific energy absorption value. Furthermore, according to the boundary characteristics and loading conditions, the evolution mode and interaction mechanism of stress-induced defects at the mesoscale were analyzed, including crack propagation, plastic deformation, and progressive thermal damage. A coupling law of multistep damage was constructed based on the wing-shaped crack growth model, cavity collapse model, and relationship between temperature rise and phase transformation. Finally, a thermal–mechanical coupling cyclic mesoscopic model of frozen soil under a one-dimensional strain state was established. The rationality of the model was verified by predicting the strength and deformation behavior of frozen soil over a wide pressure range.

Experimental and theoretical study of dynamic mechanical behavior of concrete subjected to triaxial confining and impact loads

Confining stress is a key factor affecting the dynamic mechanical behaviour of concrete. To explore the mechanism of triaxial confining stress on the dynamic compressive properties of concrete, a series of static–dynamic combined compression experiments were performed using three–dimensional Split Hopkinson Pressure Bar equipment. The results show that there is an obvious strain rate effect of concrete under triaxial confining conditions, which is closely associated with the static triaxial confining stress and strain rate of impact loads. The confining stress significantly affects the dynamic response stress (strain) and dynamic stress (strain) along the loading direction. Moreover, the effects would decrease with an increase in the dynamic loading strain rate. Obvious fractures will occur on the concrete surface when the effective dissipated energy ratio exceeds 2.56 J/cm3, which proves that it is suitable to describe the fracture features of concrete under triaxial static–dynamic loads. In this study, a dynamic strength criterion of concrete was proposed for concrete under triaxial dynamic loads. The testing data and reference results matched well with suggested value of the proposed dynamic strength criterion. This can provide the theoretical guidance for concrete engineering construction.

Ballistic impact performance of composite laminates based on high‐density polyethylene/montmorillonite nanocomposite and Aramide fiber

AbstractNanostructured thermoplastic consisting of high‐density polyethylene (HDPE) modified with exfoliated montmorillonite (MMT) was successfully used as the matrix for the development of composite for ballistic applications. The effect of HDPE and HDPE/MMT as the matrix on the mechanical and ballistic properties of para‐aramid plain‐woven fabric‐based composites was compared with the commercial composite constituted by polyvinyl‐butyral–phenolic resin as the matrix. The dynamic compressive tests using split Hopkinson pressure bar equipment revealed a remarkable increase of maximum compression strength, outstanding dynamic compressive response, and superior tenacity for the composite containing HDPE/MMT as the matrix. Moreover, the ballistic limit of the HDPE/MMT‐based composite was the highest one. Mechanical failures indicated that this matrix was able to interact with a greater fiber volume and was responsible for improving the ballistic impact energy absorption. Thus, the use of MMT in thermoplastic matrix may be considered a promising ballistic solution due to the possibility of combining lightweight and ballistic resistance.

Numerical investigation of the failure mechanism of cubic concrete specimens in SHPB tests

Cylindrical specimens are commonly used in Split Hopkinson pressure bar (SHPB) tests to study the uniaxial dynamic properties of concrete-like materials. In recent years, true tri-axial SHPB equipment has also been developed or is under development to investigate the material dynamic properties under tri-axial impact loads. For such tests, cubic specimens are needed. It is well understood that static material strength obtained from cylinder and cube specimens are different. Conversion factors are obtained and adopted in some guidelines to convert the material strength obtained from the two types of specimens. Previous uniaxial impact tests have also demonstrated that the failure mode and the strain rate effect of cubic specimens are very different from that of cylindrical ones. However, the mechanical background of these findings is unclear. As an extension of the previous laboratory study, this study performs numerical SHPB tests of cubic and cylindrical concrete specimens subjected to uniaxial impact load with the validated numerical model. The stress states of cubic specimens in relation to its failure mode under different strain rates is analyzed and compared with cylindrical specimens. The detailed analyses of the numerical simulation results show that the lateral inertial confinement of the cylindrical specimen is higher than that of the cubic specimen under the same strain rates. For cubic specimen, the corners are more severely damaged because of the lower lateral confinement and the occurrence of the tensile radial stress which is not observed in cylindrical specimens. These results explain why the dynamic material strengths obtained from the two types of specimens are different and are strain rate dependent. Based on the simulation results, an empirical formula of conversion factor as a function of strain rate is proposed, which supplements the traditional conversion factor for quasi-static material strength. It can be used for transforming the dynamic compressive strength from cylinders to cubes obtained from impact tests at different strain rates.

A unified viscoplastic model and strain rate–temperature equivalence of frozen soil under impact loading

Based on the double-pulse shaping technology, a method for obtaining long rising edge loading pulse by using the structural response of a pulse shaper is proposed. The traditional split Hopkinson pressure bar (SHPB) was improved to be suitable for testing the dynamic mechanical properties of low wave impedance materials. The dynamic mechanical properties of frozen soil at different temperatures and strain rates were tested using the improved SHPB equipment. The increase in the strength of frozen soil was associated with a decrease in temperature and increase in strain rate. The strain rate–temperature equivalence of frozen soil is proposed by regression analysis of the experimental data. The relationship between the temperature and strain rate of frozen soil satisfied the Arrhenius equation and could be explained by the thermal activation mechanism. The thermal softening characteristics of frozen soil caused by the adiabatic heating under impact loading were analyzed, and described by the damage variable driven by the adiabatic heating. The damage dynamic constitutive model is proposed based on the unified viscoplastic theory. The comparison between the model and experimental results indicate the applicability of the model.

Dynamic Characteristics of Deep Dolomite Under One-Dimensional Static and Dynamic Loads

The failure characteristics of rock subjected to impact disturbance under one-dimensional static axial compression are helpful for studying the problems of pillar instability and rock burst in deep, high geostress surrounding rock under blasting disturbances. Improved split Hopkinson pressure bar equipment was used for one-dimensional dynamic–static combined impact tests of deep-seated dolomite specimens under axial compression levels of 0, 12, 24, and 36 MPa. The experimental results demonstrate that the dolomite specimens exhibit strong brittleness. The dynamic strength always maintains a strong positive correlation with the strain rate when the axial compression is fixed; when the strain rate is close, the dynamic elasticity modulus and peak strength of the specimens first increase and then decrease with the increase in axial compression, and the peak value appears at 24 MPa. The impact resistance of specimens can be enhanced when the axial compression is 12 or 24 MPa, but when it increases to 36 MPa, the damage inside the specimen begins to cause damage to the dynamic rock strength. Prior to the rock macroscopic failure, the axial static load changes the rock structure state, and it can store strain energy or cause irreversible damage.

Dynamic compressive properties of lightweight rubberized concrete

This study experimentally examines the dynamic characteristics of concrete made of waste car tyres as both fine and coarse aggregates (rubberized concrete), resulting in light-weight concrete with the densities of 2350 kg/m3, 2091 kg/m3, and 1833 kg/m3 for 0%, 15%, and 30% rubber content, respectively. The dynamic compressive characteristic of the rubberized concrete was quantified by using a Split Hopkinson Pressure Bar equipment up to the strain rate of 182 s−1. The experimental results have consistently shown excellent impact resistance of rubberized concrete as compared to that of normal concrete, including the progressive failure, crack propagation and normalized energy absorption. Under the same impact, rubberized concrete was still almost intact while normal concrete was fragmented into pieces. Rubberized concrete significantly slowed down the crack propagation and exhibited progressive failure as compared to normal concrete. The compressive strength and axial strain at maximum dynamic stress of rubberized concrete are sensitive to the strain rate and the sensitivity increases with the rubber content. Young’s modulus of rubberized concrete showed inconsistent strain rate sensitivity. Meanwhile, rubberized concrete was more sensitive to the strain rate than normal concrete. In addition, new equations to estimate the DIFs of rubberized concrete with different rubber contents were proposed, in which the lateral inertia confinement effect was removed.

A constitutive model of the compressive mechanical properties of ultra high molecular weight polyethylene (UHMWPE) at different temperatures and different strain rates

The impact resistance of UHMWPE is related to temperature and strain rate. In order to determine the compressive mechanical properties of UHMWPE, quasi-static and dynamic compression tests were conducted on UHMWPE using an MTS universal testing machine and split Hopkinson pressure bar equipment, respectively. Stress–strain curves for UHMWPE over the temperature range of −40 °C∼100 °C and strain rate range of 0.001∼3300 s−1 was generated. By comparing the stress–strain curves of UHMWPE with molecular weights (MWs) of 3, 6 and 9 million in a quasi-static state, it was found that UHMWPE with a MW of 6 million had better compressive mechanical properties than other UHMWPE samples. Using the stress–strain curves for UHMWPE with a MW of 6 million at different strain rates and temperatures, the yield strength of UHMWPE increased with an increasing strain rate and decreased with increasing temperature were obtained. Based on the quasi-static and dynamic experimental results for UHMWPE with a MW of 6 million, a constitutive model of plasticity at different temperatures and strain rates was established. This model agreed well with the experimental results. This study provides both theoretical and empirical reference for the study of the mechanical properties of UHMWPE materials.

Rock Dynamic Crack Propagation under Different Loading Rates Using Improved Single Cleavage Semi-Circle Specimen

The objective of this paper is to investigate the complete process of dynamic crack propagation in brittle materials under different loading rates. By using Improved Single Cleavage Semi-Circle (ISCSC) specimens and Split Hopkinson Pressure Bar equipment, experiments were conducted, with the fracture phenomenon and crack propagation of tight sandstone investigated. Meanwhile, the process of crack propagation behaviour was simulated. Moreover, with the experimental–numerical method, the crack propagation dynamic stress intensity factor (DSIF) was also calculated. Then, the crack propagation toughness of tight sandstone under different loading rates was investigated and illustrated elaborately. Investigation results demonstrate that ISCSC specimens can achieve the crack arrest position unchanged, and the numerical simulation could effectively deduce the actual crack propagation, as their results were well matched. During crack propagation, the crack propagation DSIF in the whole process increases with the rising loading rate, and so does the crack propagation velocity. Several significant dynamic material parameters of tight sandstone are also given, for engineering reference.

Energy transfer rules and damage characteristics analysis of layered mortar specimen under low-velocity impact

The energy transfer rule and failure pattern of layered mortar specimen are helpful to analyze the seismic performance of layered structure. Split Hopkinson pressure bar equipment was used for one-dimensional impact tests of specimens with double fissures under low-velocity. Experimental results show that when the impact speed is lower than 5.26m/s, the energy consumption of the layered mortar specimens with a parallel fracture spacing of 18mm increases with the increase of the impact velocity. When the speed is increased from 5.26m/s to 6.04m/s, the energy consumption increases first and then decreases, and the impact velocity corresponding to the maximum value is determined by the physical and mechanical properties of the layered fracture of the specimen and the impact strength of the material. Within the low speed range of 3.38m/s~5.26m/s, damage variable presented an increase weak power function relationship with the increasing impact speed, meeting d = –10014.08e−v/032 + 0.83, and the damage value of the specimen was about 0.72. The results of this study provide a reference for the analysis of the dynamic characteristics of laminated cement mortar material in construction engineering.

Impact of high-temperature-water cooling damage on the mechanical properties of concrete

Abstract A series of impact tests were conducted on split Hopkinson pressure bar equipment to study the influence of high-temperature-cooling damage on the mechanical properties of concrete. The experimental investigation showed the influence on the peak stress, peak strain, and fracture mode. The results indicate that the strain rate is directly related to the loading rate and heating temperature. The test results of natural cooling and water immersion cooling treatment were compared, which showed that the strength of water-cooled specimens is higher than that of naturally cooled specimens before the heating temperature reaches 400 °C and becomes much lower when the heating temperature is higher than 400 °C. Based on the experimental study, a dynamic non-linear elastic constitutive equation was established using a particle swarm optimization algorithm and an inversion analysis method. These results could provide theoretical references for the design of the ultimate strength of concrete materials for practical applications, such as fire and explosion prevention.

Effect of maximum coarse aggregate size on dynamic compressive strength of high-strength concrete

Dynamic increase factor (DIF) is a measure of the rate effect in the analysis and design of structures subjected to impact or impulsive loads. A variety of DIFs have been suggested based on the results of split Hopkinson pressure bar (SHPB) tests, which is the test technique most commonly used to obtain dynamic material properties. However, due to the lack of a standard test method and some limitations in the SHPB equipment, most SHPB tests have been conducted for mortar or concrete specimens containing small size coarse aggregate that is very different from the actual concrete used in construction. The DIFs that are provided in most structural design codes are based on these test results. Therefore, it is necessary to investigate the effect of coarse aggregate size on the dynamic concrete compressive strength. In this study, a series of SHPB tests were conducted for mortar and concrete specimens with various maximum aggregate sizes. The test results indicated that the larger maximum coarse aggregate sizes induce larger heterogeneity of specimens. On the other hand, the pure rate DIFs did not exhibit a dependency on the maximum coarse aggregate size. Based on these results, guidance as to the maximum coarse aggregate size of concrete specimens for SHPB tests is provided.

Sensitivity and uncertainty analysis of interfacial effect in SHPB tests for concrete-like materials

The Split Hopkinson Pressure Bar (SHPB) equipment has been widely used to measure the dynamic properties of concrete-like materials at high strain rate between 10s-1 and 103s-1. As we know, a crucial factor that influences the accuracy of SHPB tests is the interfacial effect between specimen and bars. In our work, interfacial effect was investigated and summarized into three types of parameters, i.e., interfacial friction coefficient, specimen diameter and specimen non-parallelism. A series of concrete-like (cement mortar) specimens with two different strengths were tested at three different strain rates on SHPB equipment, and the uncertainty of the interfacial effect was transformed into intervals of these three types of parameters. A numerical model was established in ABAQUS and verified to study the interfacial effect, then the sensitivity analysis of three types of parameters was undertaken to figure out a sensitivity ranking using the full factorial design method. The sensitivity analysis provides an effective measure to promote the experimental accuracy and it is meaningful for understanding the interfacial effect in SHPB tests. Moreover, uncertainty analysis was conducted to give an interval of dynamic response of SHPB tests based on a non-probabilistic interval analysis method. The uncertainty analysis can provide an effective estimation of SHPB experimental results considering the uncertainty of interfacial effect.

Dynamic Increase Factor of High Strength Concrete with Silica Fume at High Strain Rate Loading

The dynamic mechanical properties (stress-strain diagram, ultimate stress, ultimate strain and strain rate) and of high strength concrete (HSC) with 5% and 10% silica fume (SF) addition at high strain rate of 10 s-1 to 102 s-1 (3.8 MPa, 4.1 MPa and 4.8 MPa) are determined using Split Hopkinson Pressure Bar equipment. The compressive strength of the HSC at design strength of 80 and 90 MPa is also determined. Results show that the compressive strength of the 5%SF and 10%SF HSC are 83 MPa and 92 MPa, respectively. The dynamic stress-strain diagrams show that the higher the pressure load, the higher the values of ultimate dynamic stress, σu and the ultimate strain rate, ἐu for both percentages of SF addition concrete. The ultimate dynamic stress, σu are between 200 – 250 Mpa and the ultimate strain rate, ἐu is in the range of 95 s-1 and 160 s-1. The ultimate dynamic strain, εu between 0.005-0.008 mm/mm. The dynamic increase factors (DIF) of the HSC are more than 2 compare to normal strength concrete.

Determination of dynamic elastic modulus of polymeric materials using vertical split Hopkinson pressure bar

This paper is focused on the determination of dynamic elastic modulus of polymer materials under high strain rate loading using the split Hopkinson pressure bar (SHPB) technique. Experiments conducted on the epoxy specimen by the traditional SHPB and the proposed vertical SHPB equipment demonstrates that the vertical SHPB can give more accurate measurements. The related factors, namely, the effect of stress inequilibrium in specimen, indentation in bars due to specimen and the tilt between specimen and bars, are extensively studied. It is concluded through theoretical analysis and numerical calculations that the influence of stress inequilibrium becomes negligible after two characteristic times. The numerical study on the indentation effect shows that the bar to specimen specific elastic modulus ratio and specific diameter ratio are critical to the level of influence on indentation. However, polymers with low elastic modulus values can still be accurately measured regardless of the indentation displayed. The numerical investigation on tilt effect indicates that the imperfect contact condition severely affects the accuracy of measured elastic modulus. This issue can be rectified by the newly proposed vertical SHPB. It can improve the contact conditions between bars and specimen significantly and offer acceptable accurate measurements for the dynamic elastic modulus of polymeric materials.

Dynamic compression property of a low-carbon quenching and partitioning steel

The dynamic compression properties of a low carbon quenched and partitioned (Q&P) steel were investigated over the strain rate range of 500–2500s−1 using split-Hopkinson pressure bar equipment. Traditional quenched and tempered (Q&T) steel with an identified composition was used for comparison. For both types of steel, the flow stress and yield strength gradually increased as the strain rate was increased from 500 to 2000s−1, indicating that strain-rate hardening dominates the deformation behavior. At a higher strain rate (2500s−1), the flow stress and yield strength begin to decrease, indicating that the thermal softening of the martensite matrix caused by adiabatic heating begins to exceed the effect of the strain-rate hardening. Based on the Johnson–Cook equation, which describes the deformation behavior as well as the parameters calculated by this equation, the Q&P specimens exhibited less pronounced strain-rate dependencies than the Q&T specimens. In addition, the impact shearing tests demonstrated that adiabatic shear failure is less likely to occur in Q&P specimens than in Q&T specimens. Analysis revealed that a considerable amount of retained austenite in the Q&P specimen was responsible for these differences, and in turn, its stability was affected by the strain rate. At a relatively low strain rate, stress/strain induced martensitic transformations easily occur. With higher strain rates, martensitic transformations are suppressed because adiabatic heating decreases the driving force of martensitic transformations.

Influence of confining pressure and impact loading on mechanical properties of amphibolite and sericite-quartz schist

In order to investigate the dynamic mechanical properties of amphibolite and sericite-quartz schist under confining pressure, two rocks are subjected to impact loadings with different strain rates and confining pressures by using split Hopkinson pressure bar equipment with a confining pressure device. Based on the experimental results, the stress-strain curves are analyzed and the effects of confining pressure and strain rates on the dynamic compressive strength, peak strain and failure mode are summarized. The results show that: (1) The characteristics of two rocks in the ascent stage of the stress-strain curve are basically the same, but in the descent stage, the rocks gradually show plastic deformation characteristics as the confining pressure increases. (2) The dynamic compressive strength and peak strain of two rocks increase as the strain rate increases and the confining pressure effects are obvious. (3) Due to the effect of confining pressure, the normal stress on the damage surface of the rock increases correspondingly, the bearing capacity of the crack friction exceeds the material cohesion and the slippage of the fractured rock is controlled, which all lead to the compression and shear failure mode of rock. The theoretical analysis and experimental methods to study the dynamic failure mode and other related characteristics of rock are useful in developing standards for engineering practice.

Dynamic Testing at High Strain Rates of AZ31 Magnesium Alloys on SHPB Equipment

The mechanical behaviour of as-cast AZ31 Mg alloy has been investigated at strain rates up to 2.0×103s-1. Dynamic tests were carried out at room temperature using a Split Hopkinson Pressure Bar (SHPB) apparatus. Microstructural characteristic were analysed by Image MAT A1 optical microscopy. The results demonstrated that AZ31 Mg alloy exhibited obvious yield phenomena and strain hardening behaviour at high strain rates. The basically same curvature of stress-strain curves exhibited an similar strain hardening rate. The dynamic yield strength changes little and the peak stress increases with the strain rates. An examination by optical microscopy after high strain rate deformation reveals the occurrence of twinning and twin area percentage increases with the strain rate increasing.

Mechanical behavior of fiber-reinforced high-strength concrete subjected to high strain-rate compressive loading

This paper presents an experimental study on effect of high strain rate on compressive behavior of plain and fiber-reinforced high-strength concrete (FRHSC) with strength between 80 and 90MPa. A Split Hopkinson pressure bar equipment was used to determine the concrete behavior at strain rates from 40 to 300s−1. Fracture patterns of the specimens, concrete matrix, and fibers at high strain rates were discussed. Compressive strength, elastic modulus, critical strain, and toughness of the concrete were increased with strain rate. Ratios of these properties at high strain rates to their counterparts at static loading were discussed and compared with those recommended by CEB-FIP code. The CEB-FIP equation can be used but underestimates the dynamic increase factors (DIFs) for compressive strength (DIF-fc) for the plain HSC, and it overestimates the DIF-fc for the FRHSC. The CEB-FIP equation generally underestimates the DIF for critical strain (DIF-εc1), but overestimates the DIF for elastic modulus (DIF-E) for the high-strength concretes.

Effect of high strain rate loading on compressive behaviour of fibre-reinforced high-strength concrete

This paper presents a laboratory experimental study on the effect of high strain rate loading on compressive behaviour of plain and fibre-reinforced high-strength concrete with similar strength of 80–90 MPa. Steel fibres, polyethylene fibres and a combination of these were used in the fibre-reinforced high-strength concrete. Split-Hopkinson pressure bar equipment and a hydraulic test machine were used to determine the concrete behaviour at strain rates from about 10 to 300/s and from about 10−4 to 10−1/s, respectively. Dynamic increase factor and fracture patterns of the specimens, concrete matrix and fibres are discussed. The CEB–FIP equation is found to be applicable to the high-strength concrete, but overestimated the dynamic increase factor of fibre-reinforced high-strength concrete at strain rates beyond a transition strain rate of 30/s. A modified dynamic increase factor equation is proposed for plain high-strength concrete and fibre-reinforced high-strength concrete.