Transmission Bar Research Articles

A digital-twin driven Split Hopkinson bar layout for the tensile characterization of thin, low impedance, sheet-like materials

The Split Hopkinson or Kolsky bar is one of the most popular devices when it comes to the mechanical characterization of material samples under high strain-rates. While testing of high impedance materials, such as metal alloys, is relatively straight forward, samples with low impedance pose certain challenges. The present work focuses on the detailed implementation of a high strain-rate tensile testing method for thin, low impedance, sheet-like materials by using the Split Hopkinson test principle. In order to find a suitable Split Hopkinson setup a digital twin was created using explicit finite element methods. With the help of the digital twin, the design of the transmission bar and the sample holders including the friction liners were explored. The numerical model indicated, that a hollow transmission bar with a moderate tapering (hollow bar 1.0) is suited for the characterization of low impedance materials over a wide strain-rate range. Furthermore, this setup has to be combined with an asymmetrical sample holder configuration (heavier on the incident side and lighter on the transmission side) and aluminum friction liners to return accurate results. This numerically derived setup was validated against experimental tests on paper, representative of low impedance, sheet-like materials.

Dynamic impact mechanical properties of red sandstone based on digital image correlation method

ABSTRACT In the process of underground blasting excavation, the safety and stability of rock mass are significantly influenced by dynamic load. To study the full-field strain and displacement behaviour of rock materials subjected to dynamic compressive force, the impact tests were done on red sandstone specimens using an electromagnetically driven Hopkinson pressure bar. At the same time, the data were collected by a high-speed camera, and non-contact measurements of the red sandstone were carried out with the digital image correlation method. The resulting images were screened and analysed, based on which the stress-strain curve, full-field strain cloud diagram and displacement cloud diagram were obtained. Results show that the dynamic peak stress increases with the increase of impact velocity. During the impact process, substantial internal uneven deformation occurs in the red sandstone close to the transmission bar’s end face. Under the impact load, the cracks initiate from the upper and lower sides near the transmission bar’s end face, followed by formation of cracks in the middle part. These cracks expand throughout the rock to form through-cracks, eventually resulting in complete failure. For rock materials, the evolution of their strain field during the failure process can reflect the initiation and propagation of their internal cracks. Therefore, the use of digital image correlation method proves effective for studying the deformation and failure mechanisms of rock. The conclusions obtained in this study provide a valuable reference for the macro-meso deformation and failure mechanisms of geotechnical materials.

Stress wave attenuation in chocolate

The stress wave attenuation in five types of chocolate (extra dark, dark, milk, white, and ruby) was studied. The main acoustics properties of these chocolates were described in terms of longitudinal and transversal wave velocities. The attenuation of the stress waves was studied using the experimental technique known as the Split Hopkinson Pressure Bar (SHPB). The SHPB set-up consists of a specimen and linear elastic incident and transmission bar. Experimental data have been evaluated both in the time as well as frequency domain. Attenuation of the stress wave was described namely using the frequency dependence of the transmission coefficient of the stress wave. This damping increases with the plastic strain of the tested chocolate specimens. From a technological point of view, the fat content of the chocolate has the highest influence on the reduction of the longitudinal wave propagation velocity. The lowest attenuation was observed for the dark chocolate.

On the development of a high strain-rate tensile testing method for thin low-impedance materials

This work deals with the high strain-rate characterization of paper under uniaxial tension using a Split Hopkinson test bench. An aluminum bar system featuring a highly sensitive hollow transmission bar was used. Paper tests were performed in a strain-rate range between approximately 60 s−1 and 210 s−1. The experimental tests showed that the breaking strength appears to decrease with increasing strain-rate. To verify these results, a digital twin of both the paper specimen and the entire test rig was created in an explicit Finite Element method environment. The numerical model was then used to perform a parameter study with different types of transmission bars. It was shown that the system is quite sensitive to additional masses caused by the specimen fixtures, as well as to drastic reductions in the cross section of the transmission bar. As a result, the transmitted measuring signal can be distorted and may need to be corrected using the digital twin.

Dynamic tensile strength of rock specimens with different defect lengths

Rock masses contain defects at various scales. The presence of these defects and imperfections must be considered in the design of rock structures particularly when dynamic loading due to earthquake or rock blasting is involved. The role of an existing defect or notch on the tensile strength of a synthetic rock under static and dynamic loads is examined in this study. Brazilian specimens with diameter = 50 mm and thickness = 10 mm were prepared from molded gypsum to represent the synthetic rock. Both intact and notched specimens were tested. The mode I loading was applied to the specimens; the notch was aligned with the applied diametric line load. The Split Hopkinson Pressure Bar (SHPB) equipment was utilized for the dynamic testing. Different notch lengths of 10 to 40 mm were considered. The Bonded Particle Model (BPM) was employed to identify the crack formation and evolution in the specimens for the numerical analysis. The numerical simulation was performed byemploying the CA3 finite element - bonded particle software. The whole SHPB device was modeled, including the incident and transmission bars, together with the rock specimen. The physical and numerical data suggest that specimens with notches demonstrate stronger responses to the stress rate compared to the intact specimens. In particular, the fracture toughness increases substantially as the loading rate is intensified. Furthermore, it is shown that while the physical and numerical static tensile strengths decrease as the notch length increases, the dynamic tensile strength remains unchanged with increasing the notch length when loading rates of high intensity are applied. The reason for this observation is scrutinized and it is shown that the crack tip opening velocity is responsible for this peculiar finding. The numerical model is able to capture this phenomenon due to the appropriate rate dependent micromechanical model used in this study. Finally, based on the published studies and the results of this work, an equation is derived which suggests a linear relationship between the rock tensile strength and the strain rate. This equation is valid for the physical and numerical specimens with different notch lengths.

Design, development, and calibration of split Hopkinson pressure bar system for Dynamic material characterization of concrete

Split Hopkinson pressure bar (SHPB) system is significantly used for dynamic material characterization in the range of strain rates 102–104 s-1; however, there is no standard design methodology or readily available technique for the development of this apparatus. The objective of this study is to present a detailed design, development and calibration of SHPB apparatus for dynamic material characterization of concrete in compression. The calibration of the loading and bar components has been presented with the help of experimental results and validated following an analytical approach for one-dimensional stress wave propagation. The experimental pulse duration, 124.5 microsecond, and elastic wave speed, 4820 m/s, was measured with 2% deviation from the analytical results. Under three different impact velocities, a minimum 1.09% and maximum 4.14% decrement was observed in the incident wave as compared to analytical formulation. The recorded strain signals were captured in the transmission bar with a decrement of 1, 3, and 3.3% in peak strain when compared to the incident bar, at 4.5, 4.9, and 5.7 m/s impact velocities. The incident and transmission bars had almost identical wave characteristics demonstrating that the bar system has been perfectly and precisely aligned, and almost complete wave transfer is seen to have occurred. Experiments performed on M35 concrete specimens using the developed SHPB setup have been presented and discussed. The results demonstrated that the developed SHPB setup is capable to provide accurate results for the dynamic material characterization of concrete at high strain rate loading.

Research on Wave Dissipation and Energy Absorption Characteristics of Different Boundary Materials Under Static–Dynamic Coupling Loading

According to the scientific research needs of deep multi-field coupling true triaxial compression testing machines, it is necessary to find a suitable boundary material to be placed between the rock and the transmission bar to achieve the effects of wave elimination and energy absorption. This enables the conditions of the test requirements to be met under the interaction of true triaxial and strong disturbance. Therefore, the improved split Hopkinson pressure bar (SHPB) device was used to carry out a series of experiments on the wave elimination and energy absorption characteristics of different boundary materials, and to study the energy evolution characteristics and stress wave propagation laws of different materials under static–dynamic coupling loading. The results show that under single impact loading, owing to the difference in wave impedance between the material and the rock rod, the porous material will not only reflect the tensile wave that has a greater impact on the rock rod, but also its weakening effect on the reflection stress is weaker than that of the wave-absorbing metal plate. In terms of overall energy conversion, the energy absorption rate of the porous material PM-1 is superior, and the conversion rate of the reflection and transmission energies is also greatly reduced. Under the impact of cyclic loading, the reflection stress of the wave-absorbing metal plate increased slightly with an increase in the number of impacts. However, with the increase of impact times, the reflection peak stress of porous material PM-1 decreases at first and then increases, and the reflected wave changes from tensile wave to compression wave, which is not as good as that of wave dissipation metal plate in terms of repeatability and fatigue resistance.

A modified split-Hopkinson pressure bar setup enabling stereo digital image correlation measurements for flexural testing

A novel experimental setup for dynamic material characterisation that combines a ring-on-ring test configuration for equibiaxial flexural testing with a modification of the well-known split-Hopkinson pressure bar (SHPB) is presented. The design is generic, but in the present paper intended for and validated by experiments on flat circular glass samples at high strain rates. The novel modification allows an unobstructed view of a significant part of the sample’s tensile surface that is made possible by replacing the conventional transmission bar with a tube through which the incident bar passes. This modification enables the application of high-speed cameras for assessing the fracture together with stereo digital image correlation (stereo-DIC) for non-contact out-of-plane displacement measurements and, at the same time, reduces the total length of the setup compared to the original design. An FE-model of the bar/tube system was generated to characterise the setup better. From that, information on strain gauge locations was extracted. Two similar experiments on glass show that the required dynamic force equilibrium could be established and that the application of high-speed cameras work as intended. Lastly, promising results were achieved from the pilot stereo-DIC measurements, indicating pure bending deflections of the sample in line with theory.

Design of Split-Hopkinson Pressure Bar Specimen Fixture to Accommodate Punch and Double-Notch Shear Testing

This study focused on the design of a specimen fixture which can be installed on the end of a conventional transmission bar so that shear testing (punch and double-notch) can be conducted with any conventional split-Hopkinson apparatus. The research was conducted by using the finite element method in Abaqus/CAE with 6061-T651 Aluminum as the specimen material. The research successfully determined the effect of the fixture’s geometry and dimensions on the split-Hopkinson shear bar testing results. The optimum double-notch fixture provides great accuracy, having only a shear stress value difference of 1.49% with the original setup, while attaining force equilibrium after only 70 μs. The punch fixture, however, could only reach force equilibrium after 100 μs, thus providing too few observable data. Future work on the punch fixture is needed.

Evaluating effectiveness of public health intervention strategies for mitigating COVID-19 pandemic.

Coronavirus disease 2019 (COVID‐19) pandemic is an unprecedented global public health challenge. In the United States (US), state governments have implemented various non‐pharmaceutical interventions (NPIs), such as physical distance closure (lockdown), stay‐at‐home order, mandatory facial mask in public in response to the rapid spread of COVID‐19. To evaluate the effectiveness of these NPIs, we propose a nested case‐control design with propensity score weighting under the quasi‐experiment framework to estimate the average intervention effect on disease transmission across states. We further develop a method to test for factors that moderate intervention effect to assist precision public health intervention. Our method takes account of the underlying dynamics of disease transmission and balance state‐level pre‐intervention characteristics. We prove that our estimator provides causal intervention effect under assumptions. We apply this method to analyze US COVID‐19 incidence cases to estimate the effects of six interventions. We show that lockdown has the largest effect on reducing transmission and reopening bars significantly increase transmission. States with a higher percentage of non‐White population are at greater risk of increased Rt associated with reopening bars.

Young's Modulus Calculus Using Split Hopkinson Bar Tests on Long and Thin Material Samples.

Young’s modulus is a key parameter of materials. The method of its calculation in the current paper is concerned with the mismatch of the mechanical impedance at the bar/specimen interface for a compression SHPB (split Hopkinson pressure bar) test. By using long and thin specimens, the signal recorded in the transmission bar presents itself as a multistep signal. The ratio between the heights of two successive steps represents the experimental data that are considered in the formula of the elastic modulus this article is devoted to. The oscillatory nature of the real signals on the horizontal or quasi-horizontal segments prevents a precise determination of the two successive step heights ratio. A fine tuning of this value is made based on the characteristic time necessary for the signal to rise from one level to the next one. The FEM (Finite Element Method) simulations are also used in calculation of the Poisson coefficient of the tested complex concentrated alloy.

Machine learning method to predict dynamic compressive response of concrete-like material at high strain rates

Machine learning (ML) methods with good applicability to complex and highly nonlinear sequences have been attracting much attention in recent years for predictions of complicated mechanical properties of various materials. As one of the widely known ML methods, back-propagation (BP) neural networks with and without optimization by genetic algorithm (GA) are also established for comparisons of time cost and prediction error. With the aim to further increase the prediction accuracy and efficiency, this paper proposes a long short-term memory (LSTM) networks model to predict the dynamic compressive performance of concrete-like materials at high strain rates. Dynamic explicit analysis is performed in the finite element (FE) software ABAQUS to simulate various waveforms in the split Hopkinson pressure bar (SHPB) experiments by applying different stress waves in the incident bar. The FE simulation accuracy is validated against SHPB experimental results from the viewpoint of dynamic increase factor. In order to cover more extensive loading scenarios, 60 sets of FE simulations are conducted in this paper to generate three kinds of waveforms in the incident and transmission bars of SHPB experiments. By training the proposed three networks, the nonlinear mapping relations can be reasonably established between incident, reflect, and transmission waves. Statistical measures are used to quantify the network prediction accuracy, confirming that the predicted stress-strain curves of concrete-like materials at high strain rates by the proposed networks agree sufficiently with those by FE simulations. It is found that compared with BP network, the GA-BP network can effectively stabilize the network structure, indicating that the GA optimization improves the prediction accuracy of the SHPB dynamic responses by performing the crossover and mutation operations of weights and thresholds in the original BP network. By eliminating the long-time dependencies, the proposed LSTM network achieves better results than the BP and GA-BP networks, since smaller mean square error (MSE) and higher correlation coefficient are achieved. More importantly, the proposed LSTM algorithm, after the training process with a limited number of FE simulations, could replace the time-consuming and laborious FE pre- and post-processing and modelling.

Deformation evolution and diffusion characteristics of polymethyl methacrylate under impact loading

Dynamic compression experiments on cubic polymethyl methacrylate (PMMA) specimens and two kinds of trapezoid PMMA specimens are carried by changing the transmission bars into steel bar and aluminum bar on the experimental device of split Hopkinson pressure bar (SHPB). The compression processes of PMMA specimens are recorded by high-speed photography, and the breakage processes of PMMA specimens are analyzed based on the force displacement curves and high-speed images. The evolutions of deformation and diffusion resistances of PMMA specimens under impact loading are discussed. The results show that the failure of the sample is caused mainly by the partial failure front at the contact end, and then the failure front propagates to the inside of the sample, leading the sample to break. The failure front of cubic sample is generated preferentially at the transmission end under low speed impact and at the incident end under the higher speed impact. After changing the shape of the specimen and the material of the transmission bar, the relaxation phenomenon is prominent, and the failure front occurs only at the incident end. The compressive deformation of the trapezoid sample before breakage is non-uniform, and the stress and strain in the sample gradually decrease with the increase of the cross section, and show a linear diffusion distribution. The strain distribution and shear activation diffusion equation are used to obtain the generalized diffusion resistance distribution of the failure front. The generalized diffusion resistance increases first in front of the failure front and decreases after the failure front, and the amplitude of the generalized diffusion resistance is related to the release of local strain energy.

Study on deformation evolution and diffusion characteristics of PMMA under impact loading

Dynamic compression experiments were carried out on cubic PMMA specimens and two kinds of trapezoid PMMA specimens by changing the transmission bars to steel and aluminum bar with the Loading device of split Hopkinson pressure bar (SHPB). The compression process of PMMA specimens was recorded by high-speed photography, and the breakage process of PMMA specimens was analyzed based on the force displacement curves and high-speed images. The evolution of deformation and diffusion resistance of PMMA specimens under impact loading was discussed. The results show that the failure of the sample is mainly caused by the partial failure front at the contact end, and then the failure front propagates to the inside of the sample and leads to the breakage of the sample. The failure front of cubic samples is preferentially generated at the transmission end under low speed impact and generated at the incident end under the higher speed impact. After changing the shape of the specimen and material of the transmission bar, the relaxation phenomenon is obvious, and the failure front only occurs at the incident end. The compressive deformation of the trapezoid sample before breakage is non-uniform, and the stress and strain in the sample gradually decrease with the increase of the cross section, and show a linear diffusion distribution. The strain distribution and shear activation diffusion equation were used to obtain the generalized diffusion resistance distribution of the failure front. The generalized diffusion resistance increases first in front of the failure front and decreases after the failure front and the amplitude of the generalized diffusion resistance is related to the release of local strain energy.

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.

Dynamic three-point flexural performance of unsaturated polyester polymer concrete at different curing ages

In this study, the dynamic flexural performance of unsaturated polyester polymer concrete (UPPC) is investigated. We categorised specimens at different ages, then investigate how its flexural dynamic increase factors (DIF) relate to different ages, as well as compressive and tensile DIF. A split Hopkinson pressure bar (SHPB) is used for dynamic flexural tests under a high strain rate. The ends of the incident and transmission bars are equipped with special devices to perform a three-point flexural test. Test results indicate that the quasi-static flexural strength of the UPPC is the same as the compressive and tensile strengths, and it has a higher strength in the early stage of curing; in addition, UPPC has the same strain rate effect in the dynamic test that decreases as the curing age increases. The reason is that the unsaturated polyester resin does not react with cement thoroughly at the low curing age, and there is a weak zone. When the loading rate increases, the crack has no time to pass through the weak zone and directly penetrate the coarse aggregate. Further, the mid-span displacement of the UPPC had a strain rate effect. By comparing the fitting curves of aforementioned tests (i.e. flexural, tensile and compression test), it is clear that the flexural one shows the steepest gradient, roughly equals to the sum of compressive and tensile gradient, which means more sensitive to strain rates.

Modeling of sand particle crushing in split Hopkinson pressure bar tests using the discrete element method

The discrete element method (DEM) has been extensively used to study the micro-mechanical behavior of sand subjected to quasi-static strain rates. In most of these studies, the sand specimens were prepared with an upscaled particle size distribution (PSD) to reduce the computational cost. However, the effectiveness of this upscaling approach in replicating the dynamic sand response is not well understood, especially at high stresses where significant particle breakage occurs. In this paper, several split Hopkinson pressure bar (SHPB) tests reported in literature are modeled in DEM using two methodologies: 1) applying the reported strain rates directly to the DEM specimen without accounting for wave propagation in the incident and transmission bars; and 2) modeling the complete SHPB test setup including the incident and transmission bars. The results show that with well-calibrated parameters for contact behavior and particle crushing, specimens with upscaled PSD provide similar dynamic stress-strain response and PSD evolution as those reported in literature. This study shows the importance of particle breakage in the stress-strain response under high stresses as the specimens without particle breakage provide a much stiffer response compared to the specimens with particle breakage. The developed DEM model may be a useful tool to model the complete SHPB test setup as the incident, reflected and transmitted stress waves can be accurately replicated.

High-energy micrometre-scale pixel direct conversion X-ray detector.

The objective of this work was to fabricate and characterize a new X-ray imaging detector with micrometre-scale pixel dimensions (7.8 µm) and high detection efficiency for hard X-ray energies above 20 keV. A key technology component consists of a monolithic hybrid detector built by direct deposition of an amorphous selenium film on a custom designed CMOS readout integrated circuit. Characterization was carried out at the synchrotron beamline 1-BM-B atthe Advanced Photon Source of Argonne National Laboratory. The direct conversion detector demonstrated micrometre-scale spatial resolution with a 63 keV modulation transfer function of 10% at Nyquist frequency. In addition, spatial resolving power down to 8 µm was determined by imaging a transmission bar target at 21 keV. X-ray signal linearity, responsivity and lag were also characterized in the same energy range. Finally, phase contrast edge enhancement was observed in a phase object placed in the beam path. This amorphous selenium/CMOS detector technology can address gaps in commercially available X-ray detectors which limit their usefulness for existing synchrotron applications at energies greater than 50 keV; for example, phase contrast tomography and high-resolution imaging of nanoscale lattice distortions in bulk crystalline materials using Bragg coherent diffraction imaging. The technology will also facilitate the creation of novel synchrotron imaging applications for X-ray energies at or above 20 keV.

Experimental investigation of scatter in fracture toughness data of SA516Gr.70 steel in the ductile-to-brittle transition regime for high rate of loading using split Hopkinson pressure bar test setup

Ferritic grade steels exhibit ductile to brittle transition in the sub-zero temperature regime and the fracture toughness data show scatter and temperature dependence. The fracture toughness variation also depends upon rate of loading in addition to neutron irradiation, specimen geometry and loading configuration. The material SA516Gr.70 steel is widely used in nuclear industry as material of transportation cask, vessels and piping etc. The study of the effect of rate of loading on the fracture toughness transition curve in the ductile-to-brittle transition regime of this material is important for designers and safety analysts. In this work, the split Hopkinson pressure bar test technique has been used to carry out fracture tests on sub-sized single-edged notched bend specimens in the temperature range of −100 to −60 deg. C by loading the specimens at a very high loading rate of 700 m/min. This loading rate is at least 6 orders of magnitude higher than the rates (i.e., fraction of mm/min) employed for quasi-static fracture tests. The strain pulses, during high rate of loading, have been captured through strain gages located in the incident and transmission bars of the test setup. The load–displacement data for the specimens have been evaluated from the strain signal and these have been used to evaluate fracture toughness for onset of cleavage fracture in terms of KJc. The scatter and temperature dependence of the data have also been modelled through Weibull’s statistical distribution and master curve bounds according to ASTM E1921. From the results of fracture experiments, it was observed that the fracture transition temperature T0 increased significantly for the high rate of loading when compared to quasi-static data of similar materials in literature. This observation has been explained in terms of micro-mechanism of the cleavage fracture in the process zone ahead of crack-tip which changes due to rate of loading. This study indicates that the rate of loading is an important parameter in the design and integrity analysis of ferritic grade steel components in addition to other parameters such as specimen geometry and loading conditions.

Numerical investigation on the effect of specimen gripping arrangement on dynamic shear characterization using Torsion Split Hopkinson Bar

Torsion Split Hopkinson Bar (TSHB) is widely used in the dynamic shear characterization of material under pure shear loading. In TSHB, tubular specimens with either circular or hexagonal flanges are used. The specimens with circular flanges are generally bonded using adhesive to the incident and transmission bars. The specimens with hexagonal flanges are gripped into the hexagonal holders that are fixed onto incident and transmission bars. In the current study, numerical simulations are carried out to see the effect of gripping arrangements on the dynamic shear characterization quality. Numerical experiments with three gripping configurations are studied—the first gripping configuration with a direct bond (numerically-tie) between specimen and bars. The second configuration with the specimen gripped by hexagonal holders fixed to bars. The third configuration with specimen directly gripped into the incident and transmission bars having hexagonal slots.