Conventional Split Hopkinson Pressure Bar Research Articles

Dynamic increase factor of concrete compressive strength in confined split hopkinson pressure bar tests

This study presented a methodology to evaluate the pure strain-rate effect on concrete compressive strength and developed a pure rate dynamic increase factor (DIF) model through numerical and experimental investigations into confined split Hopkinson pressure bar (SHPB) tests. The numerical investigation proposed the methodology to determine the pure rate DIF through confined SHPB tests. Subsequently, the confined SHPB tests were conducted on concrete specimens, and a pure rate DIF model was developed based on this methodology. Additionally, conventional SHPB tests were performed to obtain an apparent DIF, which was then compared to the developed pure rate DIF. The results indicated that the apparent DIF exceeded the pure rate DIF, thus confirming its tendency to overestimate the strain-rate effect on concrete. Therefore, the proposed methodology using confined SHPB tests provides an alternative approach to overcome the limitations of the apparent DIF determined from conventional SHPB tests. Lastly, the developed pure rate DIF model was validated through numerical analyses on conventional SHPB tests and drop-weight impact tests of reinforced concrete beams. This validation demonstrated that the proposed pure rate DIF model effectively considers the strain-rate effect on concrete structures, thereby enabling assessment of the performance of concrete structures under extreme loading conditions.

Review of SHPB Dynamic Load Impact Test Characteristics and Energy Analysis Methods

Since the split-Hopkinson pressure bar (SHPB) test technology was proposed, it has played an important role in the study of dynamic mechanical properties of materials under the impact of dynamic load. It is a major test technology for the study of dynamic mechanical properties of materials. The expansion of the range of materials studied has also posed a challenge to the SHPB test technique, requiring some improvements to the conventional SHPB test apparatus and analysis methods to meet the test conditions and ensure the accuracy of its results. Based on a systematic review of the development of the SHPB test technique and the test principles, the main factors that influence the test’s ability to meet the two basic assumptions at this stage are analyzed, and the ways to handle them are summarized. The stress wave dispersion phenomenon caused by the transverse inertia effect of the pressure bar means that the test no longer satisfies the one-dimensional stress wave assumption, while the pulse-shaping technique effectively reduces the wave dispersion phenomenon and also has the effect of achieving constant strain rate loading and promoting the dynamic stress equilibrium of the specimen. Impedance matching between the pressure bar and specimen effectively solves the problem of the test’s difficulty because the transmitted signal is weak, and the assumption that the stress/strain is uniformly distributed along the length of the specimen is not satisfied when studying low-wave impedance material with the conventional SHPB test device. The appropriate pressure bar material can be selected according to the value of the wave impedance of the test material. According to the wave impedance values of different materials, the corresponding suggestions for the selection of pressure bar materials are given. Moreover, a new pressure bar material (modified gypsum) for materials with very-low-wave impedance is proposed. Finally, for some materials (foamed concrete, aluminum honeycomb, porous titanium, etc.) that cannot meet the two basic assumptions of the test, the Lagrangian analysis method can be combined with SHPB test technology application. Based on the analysis and calculation of the energy conservation equation, the dynamic constitutive relationship of the materials can be obtained without assuming the constitutive relationship of the experimental materials.

Experimental Investigation of the Dynamic Mechanical Properties of Polypropylene-Fiber-Reinforced Foamed Concrete at High Temperatures.

Polypropylene-fiber-reinforced foamed concrete (PPFRFC) is often used to reduce building structure weight and develop engineering material arresting systems (EMASs). This paper investigates the dynamic mechanical properties of PPFRFC with densities of 0.27 g/cm3, 0.38 g/cm3, and 0.46 g/cm3 at high temperatures and proposes a prediction model to characterize its behavior. To conduct the tests on the specimens over a wide range of strain rates (500~1300 s-1) and temperatures (25~600 °C), the conventional split-Hopkinson pressure bar (SHPB) apparatus was modified. The test results show that the temperature has a substantial effect on the strain rate sensitivity and density dependency of the PPFRFC. Additionally, the analysis of failure models demonstrates that with the melting of polypropylene fibers, the level of damage in PPFRFC under dynamic loading increases, resulting in the generation of a greater number of fragments.

Experimental and numerical studies on pulse shaping techniques used in split Hopkinson pressure bar for testing concrete material

Split Hopkinson pressure bar (SHPB) is commonly used to characterise materials under high strain rates. However, conventional SHPB tests on brittle materials have encountered several experimental challenges for high strain rate loading. In relatively brittle materials like concrete, the deformation of the specimen is very small when subjected to impact loading; hence, it is very difficult to obtain the prerequisites of valid SHPB tests such as dynamic equilibrium and constant strain rate in the specimen. To overcome these issues, the current study presents the importance of the pulse shaper approach in SHPB application for the dynamic characterisation of concrete material. Selection of the appropriate dimension of pulse shaper assists in facilitating dynamic stress equilibrium and constant strain rate in the specimen. In the present study, copper pulse shapers are used for the evaluation of concrete under high strain rate loading using an SHPB set-up. Parameters such as the effect of dimensions (diameter and thickness) of pulse shapers on loading pulses, dynamic equilibrium, constant strain rate and material responses are studied. Experimental results reveal the prediction of suitable pulse shapers for 50–200/s strain rates. In addition, numerical simulation is also performed and results are validated with the experimental data.

Influence of stress state on dynamic breakage of quartz glass spheres subjected to lower velocity impacting

The breakage process of glass spheres under impact loading is very complex due to the transition of two failure mechanisms, i.e. tensile failure and shear failure, with the increase of loading rate. In order to investigate the influences of stress state adjustment on sphere breakage, three kinds of transmission bars, i.e. steel bar, aluminum bar, PMMA bar, and double-sphere specimens are employed by the modified conventional Split Hopkinson Pressure Bar (SHPB) device. These experiments are conducted under lower impact velocity, which evaluated by the critical state of single sphere failure. Larger critical strain and lower critical strain rate for sphere breakage are obtained when replacing the steel transmission bar with the PMMA bar. The failure properties of inner geometric structures by adjusting failure sequences of the double-sphere specimens. Based on the evolution of particle size distributions and local deformation distribution by the Digital Image Correlation (DIC) method, two-stage failure model is obtained. The first stage of sphere breakage results from the diffusion of local Hertz cracks at the contact areas, which mainly caused by local shear failures, and the second stage results mainly from the penetrated oblique cracks along impact direction, which mainly caused by transversal tensile failures. Adjustment of stress and strain fields by these two schemes reveals these intrinsic influences on sphere breakage, and failure law, involving the effects of local strain, local strain gradients, and local strain rates, is preliminarily discussed. Further theoretical analyses are conducted to investigate the movement of the diffusion fronts. It is of significant reference for understanding the dynamic failure mechanism of brittle granular matter.

Mechanical response of two different molecular weight polycarbonates at varying rates and temperatures

Polymers are widely used for lightweight design in industrial applications, such as helmets and car bumpers, where the most common causes of failure or damage are dynamic impact events. It is well known that the mechanical response of most polymers is highly dependent on the loading rate and temperature, and that it is not sufficient to use properties measured under static loads in the analysis of dynamic events. However, the time-temperature equivalence phenomenon offers the chance to predict high-rate performance using low-rate data. In this study, information about the constitutive behaviour of two different molecular weight polycarbonates, is obtained in low-rate experiments and then compared with the high-rate response. A master curve of storage modulus constructed from Dynamic Mechanical Analysis data is employed to understand the viscoelastic response under small-strain loading at various frequencies and temperatures. For the large-strain constitutive response, experiments at strain rates from 0.001 s-1 to 3000 s-1 are performed using a conventional crosshead device, hydraulic device, and split-Hopkinson pressure bar. Moreover, experiments at strain rates of 0.01 s-1 and temperatures from -60 to 120 °C are also performed, and the results are compared. This approach can distinguish ’constitutive’ rate dependence from the effects of specimen self-heating due to adiabatic heating under high-rate deformation. Meanwhile, the molecular weight effects on the mechanical response at varying rates and temperatures are also noted.

Energy absorption characteristics and theoretical analysis of frozen clay with pre-existing cracks under uniaxial compressive impact load

Two important engineering design parameters, namely, dynamic energy dissipation and fragment size distribution, are closely associated with the crushing efficiency of the frozen soil in the cold regions. The crack distribution inside the frozen soil exerted a notable effect on its mechanical properties and energy dissipation characteristics under dynamic loads. In this study, a conventional split Hopkinson pressure bar with 50 mm diameter was used to conduct uniaxial impact compressive test in the frozen soil under different pre-existing crack conditions. The effects of pre-existing cracks on the energy dissipation and fractal dimension of the frozen soil were investigated based on the relationship among the energy absorbency rate, fractal dimension, and dynamic peak strength. The experimental results showed that energy absorbency rate and fractal dimension decreased as the growth of the number of pre-existing cracks, while both the energy absorbency rate and fractal dimension of frozen soil specimen with pre-existing cracks at the end surface remained less than those at the side surface. The effect of crack length on the energy absorbency rate and fractal dimension was larger than compared to the number and obliquity of cracks. In addition, the energy–time curves under different test conditions were also compared. Finally, the adaptability of the constitutive model was verified by comparing the theoretical and experimental curves based on the energy dissipation results.

Energy Dissipation and Particle Size Distribution of Granite under Different Incident Energies in SHPB Compression Tests

To investigate energy dissipation and particle size distribution of rock under dynamic loads, a series of dynamic compression tests of granite specimens were conducted using a conventional split-Hopkinson pressure bar (SHPB) device with a high-speed camera. The experimental results show that the dissipated energy increases linearly with an increasing incident energy, following two different inclined paths connected by a critical incident energy, and the linear energy dissipation law in the dynamic compression test has been confirmed. This critical incident energy was found to be 0.29–0.33 MJ/m3. As the incident energy was smaller than the critical incident energy, the rock specimens remained unruptured after the impact. When the incident energy was greater than the critical incident energy, the rock specimens were ruptured or fragmented after the impact. In addition, the experimental results indicate that the dissipated energy and energy consumption ratio of a rock specimen, either unruptured or fragmented, increase with an increasing strain rate. Furthermore, it was found that fragment sizes at each mesh decrease with an increasing incident energy; that is, fragmentation becomes finer as incident energy increases.

Dynamic impact testing of cellular solids and lattice structures: Application of two-sided direct impact Hopkinson bar

Direct impact testing with a Hopkinson bar is, nowadays, a very popular experimental technique for investigating the behavior of cellular materials, e.g., lattice metamaterials, at high strain-rates as it overcomes several limitations of the conventional Split Hopkinson Pressure Bar (SHPB). However, standard direct impact Hopkinson bars (DIHB) have only single-sided instrumentation complicating the analysis. In this paper, a DIHB apparatus instrumented with conventional strain-gauges on both bars (a so called Open Hopkinson Pressure Bar - OHPB) is used for dynamic impact experiments of cellular materials. Digital image correlation (DIC) is used as a tool for investigating the displacements and velocities at the faces of the bars. A straight-forward wave separation technique combining the data from the strain-gauges with the DIC is adopted to increase the experiment time window multiple times. The experimental method is successfully tested at impact velocities in a range of 5−30m·s−1 with both linear elastic and visco-elastic bars of a medium diameter. It is shown that, under certain circumstances, a simple linear elastic model is sufficient for the evaluation of the measurements with the visco-elastic bars, while no additional attenuation and phase-shift corrections are necessary. The applicability of the experimental method is demonstrated on various experiments with conventional metal foams, hybrid foams, and additively manufactured auxetic lattices subjected to dynamic compression.

A dynamic tensile method for M-shaped specimen loaded by Hopkinson pressure bar

The M-shaped specimen can be used in dynamic tensile testing only by using the conventional split Hopkinson pressure bar, which do not need the connection between specimen and bars. But the feasibility of this method has not been further verified widely. In this paper, the dynamic tensile testing of M-shaped specimen were analyzed and improved by the finite element and experimental method. The results show that: (1) the improved closed M-shaped specimen was proposed, which can enhance the total stiffness of the specimen, effectively reduce the distortion deformation of the specimen and the influence of additional bending moment in the tensile gage section, and easily realize dynamic tensile through Hopkinson pressure bar; (2) the influence of the elastic deformation of the M-specimen on the tensile displacement could be corrected by the stiffness coefficient of specimen, the plastic strain of the tensile section of the specimen can be analyzed accurately; (3) under higher loading rate, it is suggested to adopt loading through the pulse shaper of Hopkinson bar, which can significantly improve the wave oscillation and stress balance at both ends of the specimen, obtain an accurate dynamic stress-strain curve, and realize the dynamic tensile test up to 5 900 s−1 or even higher strain rate. The study provides an important reference for the design and application of tensile test of M-shaped specimen.

A New S-Shape Specimen for Studying the Dynamic Shear Behavior of Metals

A new S-shaped specimen geometry is developed in this study to investigate the shear behavior of materials under dynamic shear condition. Traditionally, hat-shaped geometry is used to study the dynamic shear of materials by a conventional split Hopkinson pressure bar apparatus. However, in this geometry, the force equilibrium on the two sides of the sample is difficult to fulfill, and the stress field in the shear region is not homogeneous. Hence, the calculated shear stress–strain curve from this geometry is not precise. To overcome this problem, the new S-shaped specimen is designed to achieve accurate shear stress–strain curve. This geometry can be used in a wide range of strain rates and does not require additional machining process for microstructure observation. The new S-shaped specimen is successfully coupled with digital image correlation method because of the flat surface. Digital image correlation results indicate that the fracture patterns of the new S-shaped specimen occur with maximum shear strains in the shear region in the middle of the sample. This result is also validated by finite element model simulation. The new S-shaped specimen geometry can be used to study the dynamic shear behavior of various metals.

Dynamic triaxial compression tests on sandstone at high strain rates and low confining pressures with split Hopkinson pressure bar

The effects of high strain rates and low confining pressures on the dynamic mechanical properties of sandstone were investigated experimentally with a modified triaxial split Hopkinson pressure bar (SHPB) system. For comparison, dynamic uniaxial compression tests of the sandstone were also conducted by using a conventional SHPB system. The confining pressures used in the dynamic triaxial compression tests are 5, 7.5, 10, 12.5 and 15 MPa, and the strain rate of these tests varied from approximately 40 s−1 to 160 s−1. The results show that the dynamic uniaxial and triaxial compressive strengths of the sandstone will linearly increase with the logarithm of the stain rate. Under approximately the same strain rate, the dynamic triaxial compressive strength will linearly increase with the confining pressure. Although the peak strain has no dependence on the confining pressure, it will generally increase with the strain rate. The secant modulus is independent of the strain rate and confining pressure. Three trend diagrams, which reflect the influences of strain rate or confining pressure on the dynamic mechanical properties of sandstone in the uniaxial and triaxial compression tests, are given, and the correlation between the failure modes of the sandstone specimens and the characteristics of the stress-strain curves is also analyzed.

Hybrid Split Hopkinson Pressure Bar to Identify Impulse-dependent Wave Characteristics of Viscoelastic Phononic Crystals

There has recently been a rising interest in the nonlinear wave transmission behavior of phononic crystals. However, experimental studies focusing on the nonlinear wave transmission behavior of phononic crystals have been predominantly performed on 1-D granular crystals using customized impact apparatus. In this study, we explore split Hopkinson pressure bar (SHPB) apparatus as a tool to study the nonlinear wave characteristics of a 1-D continuum viscoelastic phononic crystal. In order to resolve experimental challenges relating to signal-to-noise ratios and input impulse magnitudes, we propose a hybrid SHPB system composed of an aluminum input bar and a nylon output bar. For a considered viscoelastic phononic crystal, the application of the hybrid SHPB apparatus enabled us to observe some low transmission frequency zones, which were not identified from the linearly perturbed settings such as the analytical solution and the electrodynamic shaker tests. We further conducted a series of additional FE simulations to ensure the appearance of impulse-dependent low transmission frequency zones of the considered viscoelastic phononic crystal specimen. The additional sets of simulations evidently illustrate the impulse-dependent evolution of wave transmission coefficients, and demonstrate that the impulse-dependent wave transmission behavior can be experimentally investigated by adopting the hybrid SHPB apparatus. Thus, this study shows that the conventional SHPB apparatus can be employed effectively to study the emerging research field of nonlinear wave characteristics of phononic crystals.

Microstructural Characterization and High Strain Rate Plastic Flow Behavior of SMAW Armox500T Steel Joints from Spherical Indentation Experiments

Static indentation and uniaxial compression tests have been conducted on Armox500T steel and its weldments to predict the constraint factor (CF), i.e., ratio of Meyer’s hardness to uniaxial flow stress. Series of dynamic indentation experiments were carried out at impact velocities ranging from 5 to 300 m/s to estimate dynamic hardness as a function of average strain. Subsequently, dynamic indentation (DI) test data and CF determined under static indentation conditions have been used to study the high strain rate plastic flow behavior of Armox500T weldments in comparison with the base metal. It was observed that flow stress for Armox500T and its weldments under dynamic loading conditions (104 s−1) are significantly higher than flow stress measured under static loading conditions (10−3 s−1). The plastic flow behavior computed from DI is in good agreement with the data evaluated through conventional split Hopkinson pressure bar technique. Further, the study of the microstructure of base metal and weldments by optical microscopy and SEM revealed a considerable variation in the microstructure.

A New Multiaxial Specimen for Determining the Dynamic Properties of Adhesive Joints

Adhesive joints are increasingly employed for bonding critical parts of industrial structures. Therefore, adhesive joints become a key element in design, and their mechanical characterization is of the utmost importance. Significant advancement has been realized for their characterization under quasi-static loadings; however characterization techniques are rather limited for dynamic loadings. Indeed, due to the complex paths of waves through structures, existing dynamic characterization techniques will not characterize only the adhesive joint, but instead will characterize the complete assembly containing the joint and the adherents. Moreover, multiaxiality control of the loading on the adhesive joint is difficult to achieve. This paper proposes an innovative experimental technique for the characterization of adhesive joints under dynamic multiaxial loadings. The experimental method relies on three main components: i) a conventional split Hopkinson pressure bar (SHPB) apparatus, ii) a novel specimen, denoted as DODECA, which enables testing of three distinct multiaxial loadings using the same method and iii) local strain and stress measurements performed by digital image correlation (DIC). The paper describes all steps of the experimental procedure, including the underlying preparation of the specimen and the measuring methods. The stress and strain in the adhesive joint are estimated directly from the experimental data both during loading and at the failure point. Finally, the dynamic material behavior of the adhesive joint is identified from the data.

High Strain-Rate Compressive Properties of Carbon/Epoxy Laminated Composites – Effects of loading direction and temperature

The high strain-rate compressive characteristics of a cross-ply carbon/epoxy laminated composite in the three principal material directions or fibre (1-), in-plane transverse (2-) and throughthickness (3-) directions are investigated on the conventional split Hopkinson pressure bar (SHPB) over a range of temperatures between 20 and 80 °C. A nearly 10 mm thick cross-ply carbon/epoxy composite laminate fabricated using vacuum assisted resin transfer molding (VaRTM) was tested. Cylindrical specimens with a slenderness ratio (= length/diameter) of 0.5 are used in high strain-rate tests, and those with the slenderness ratios of 1.0 and 1.5 are used in low and intermediate strain-rate tests. The uniaxial compressive stress-strain curves up to failure at quasi-static and intermediate strain rates are measured on an Instron testing machine at elevated temperatures. A pair of steel rings is attached to both ends of the cylindrical specimens to prevent premature end crushing in the 1-and 2-direction tests on the Instron testing machine. It is shown that the ultimate compressive strength (or failure stress) exhibits positive strainrate effects and negative temperature ones over a strain-rate range of 10–3 to 103/s and a temperature range of 20 to 80 °C in the three principal material directions.

Evaluation of the Stress Equilibrium Condition in Axially Constrained Triaxial SHPB Tests

Over the years many improvements and modifications have been made to the split Hopkinson pressure bar (SHPB). For example, the triaxial SHPB has been developed and used to study various materials. The dynamic stress equilibrium condition for conventional SHPB tests has been well studied in the literature. However, the stress equilibrium in the axially constraint triaxial SHPB tests requires careful examination because the wave propagation is affected by the axial pre-load stress. In this study, we analyzed the stress equilibrium condition in such cases using stress wave analysis and numerical simulations. Based on the study, we offer methods and suggestions for performing valid stress equilibrium assessment in axially constrained triaxial SHPB tests.

Design and Development of an Integrated Compressive - Tensile Polymeric Split Hopkinson Pressure Bar Setup

Current finite element models of the human body lack accurate material properties of the soft tissues required to predict the pedestrian and occupant injuries during high speed automotive impacts. An accurate characterization of tensile and compressive properties of soft tissues in human body under high speed impact at high strain rates and their constitutive modeling is one of the significant interests. The conventional Split Hopkinson Pressure Bar (SHPB) is modified in order to test soft tissues under dynamic compressive and tensile loading using single integrated polymeric SHPB setup. An integrated polymeric compressive – tensile SHPB setup is designed to convert a compressive SHPB into a tensile SHPB by changing the specimen holding and striker bar loading attachment. Some preliminary numerical simulations of polymeric SHPB under dynamic compressive loading were done using Lagrangian method in LS-DYANA/Explicit to study the non-linear transient behavior of foam as soft material. The shape of stress – strain curves obtained is non linear and concave up and validated with already published results.

An Experimental Technique For The Characterization Of Adhesive Joints Under Dynamic Multiaxial Loadings

This paper deals with experimental testing of adhesive joints, whose characterization under static loadings drove a large number of studies and techniques. However, few studies deal with dynamic loadings and most of them are limited to the characterization of the shear strength of the bonded assembly. Indeed, dynamic tests often rely on single or double-lap joint specimens that do not enable to investigate multiaxial loadings. This paper is dedicated to the development of an innovative experimental technique for the characterization of adhesive joints under dynamic multiaxial loadings. The experimental apparatus consists in a conventional Split Hopkinson Pressure Bar (SHPB), a newly designed specimen named DODECA and local measurements performed by Digital Image Correlation (DIC). The specimen conception and sizing are detailed with numerical computations as well as preparation procedures. One of the advantages of the proposed specimen is the possibility of testing three distinct multiaxial loadings with the same methodology. This new technique enables to measure strains in adhesive joints accurately with a dynamic loading.

A Method of Restraining the Geometric Dispersion Effect on Split-Hopkinson Pressure Bar by the Modified Striker Bar

In order to restrain the geometric dispersion effect of the stress-wave propagation on conventional split-Hopkinson pressure bar (SHPB), the modified striker bar in Hopkinson bar-loaded test system is selected. Both the experiments and the simulation using ANSYS/LS-DYNA finite element method (FEM) were performed to investigate the modified effect. After verifying the effectiveness of the used program, six modified geometries of the striker bar were simulated. The optimization results in the simulation were further compared with that of the experiment. It was found that the geometric dispersion effect of the incident pulse under the same loading condition can be restrained effectively by modifying the striker bar. Moreover, the experimental incident pulse has a good agreement with that of the numerical simulation curves. By investigating various cases, several typical incident pulses can be obtained through different modified striker bars, and these modified approaches are simple and easy to be achieved.