Split Hopkinson Pressure Bar Tests Research Articles

Numerical and experimental studies on specimens with integrated pulse-shaper used for the instrumented Taylor impact test to measure stress-strain curves at high rates of strain

In the previous studies, an instrumented Taylor impact test was established to measure the stress-strain curve at an ultrahigh strain rate. To calculate the axial stress distribution in the specimen, a bi-linearity of the internal force distribution in both the elasticity- and plasticity-dominant regions was assumed. However, the unavoidably generated excessive local deformation (ELD) near the impact surface results in early unloading and a strong nonlinear distribution of the internal force in the region near the impact surface. Consequently, the measurable stress-strain curve was limited to 0.1 of the axial strain. On the other hand, the pulse-shaping technique, which is widely used in split Hopkinson pressure bar tests, can be employed to increase the strain until the stress-strain curve is measurable through Taylor impact tests because the short rise time is considered to be a possible reason of ELD generation. For the first time, this study introduced the pulse-shaping technique to the instrumented Taylor impact test to expand the measurability of the stress-strain curve to a higher strain range. To suppress the ELD, the dimensions of the pulse shaper are determined through finite element analyses after a discussion of the mechanism to suppress ELD. Then, the proposed method with a newly designed specimen is validated conducting the real Taylor impact test.

Study on Damage Characteristics and Failure Modes of Gypsum Rock under Dynamic Impact Load.

The objective of this work was to investigate the damage characteristics and failure modes of gypsum rock under dynamic impact loading. Split Hopkinson pressure bar (SHPB) tests were performed under different strain rates. The strain rate effects on the dynamic peak strength, dynamic elastic modulus, energy density, and crushing size of gypsum rock were analyzed. A numerical model of the SHPB was established using the finite element software, ANSYS 19.0, and its reliability was verified by comparing it to laboratory test results. The results showed that the dynamic peak strength and energy consumption density of gypsum rock increased exponentially with strain rate, and the crushing size decreased exponentially with the strain rate, both findings exhibited an obvious correlation. The dynamic elastic modulus was larger than the static elastic modulus, but did not show a significant correlation. Gypsum rock fracture can be divided into crack compaction, crack initiation, crack propagation, and breaking stages, and is dominated by splitting failure. With increasing strain rate, the interaction between cracks is noticeable, and the failure mode changes from splitting to crushing failure. These results provide theoretical support for improvements of the refinement process in gypsum mines.

Strain rate effect and dynamic constitutive model of 7A04-T6 high-strength aluminium alloy

In recent decades, various aluminium alloys have been developed and employed in construction engineering. They are light, corrosion-resisting and recyclable, making them attractive to engineers and researchers. Among these aluminium alloys, 7A04 high-strength aluminium alloy, which is an Al-Zn-Mg-Cu alloy, has now gained focus for its excellent strength-to-weight ratio, hardness, formability, etc. To date, the investigations into its dynamic mechanical properties are still limited. In this context, the mechanical behaviour of 7A04-T6 aluminium alloy at high strain rates was studied in this work. A split Hopkinson pressure bar test system was employed to conduct the dynamic experiments. 6061-T6 aluminium alloy was also included in the tests for reference. Then, comparisons were made between the tested 7A04-T6 and 6061-T6 aluminium alloys and among the studied 7A04-T6 aluminium alloy and steels with approximate yield strengths (Q420 and Q550 structural steels) and similar strength-density ratios (4340 M and Aermet 100 steels), to assess the strain rate sensitivity of 7A04-T6 aluminium alloy. Based on the Johnson-Cook model and the Cowper-Symonds model, which are widely used models that describe the dynamic constitutive behaviour of metallic materials, a modified dynamic constitutive model was developed for 7A04-T6 aluminium alloy, in which the influence of deformation-induced temperature rise on the dynamic mechanical properties is well considered.

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.

A dynamic constitutive model for high-density rigid polyurethane foam subjected to impact loading

This study experimentally and numerically investigated the dynamic response of high-density rigid polyurethane foam (RPUF). Firstly, drop-weight tests were conducted under three impact velocities, 2.42 m/s, 3.43 m/s, and 4.85 m/s. Test results showed that the dent depth and absorbed energy rise as impact velocity increases. Then the constitutive model for high-density RPUF based on an ideal elastoplastic constitutive model is proposed based on the measured mechanical properties, including quasi-static uniaxial compression tests, quasi-static uniaxial tensile tests, triaxial confining pressure tests, and split-Hopkinson pressure bar tests. Finally, the numerical simulation of the drop-weight tests was conducted. It was shown that the proposed dynamic constitutive model can accurately describe the dynamic performance of a high-density RPUF subjected to impact loading.

Determination of Johnson-Cook constitutive model coefficients considering initial gap between contact faces in SHPB test

When a material is deformed at high speed, it is well known that the flow stress is highly dependent on the strain rate and temperature. So, many studies of the stress-strain relationship at high strain rate condition have been conducted using the Split Hopkinson Pressure Bar (SHPB) test. Studies about the effects of friction, eccentricity, declination, and joints were also conducted. However, no study has been conducted about the effects of gaps formed by surface roughness of the contact faces. In this study, effect of initial gap between specimen and bars was investigated by SHPB test. The process of compressing initial gaps formed by rough places on contact surfaces was described as the initial gap compression effect. The proposed effect on measured stress-strain relation was confirmed experimentally and numerically by adjusting the surface roughness. Considering the initial gap compression effect, an equivalent gap compensation method was proposed for efficient finite element analysis. A methodology for determining Johnson-Cook (JC) coefficients using the optimization-based inverse method and the proposed equivalent gap model was presented. Also, the friction coefficients were measured to increase the accuracy of the determined coefficient. As a result, it was shown that accurate JC coefficients could be determined using the proposed methodology; the determined JC coefficients were considered to be reliable for various strain rates. Also, stress-strain relations obtained with and without initial gap compensation were compared to show the necessity of gap compensation. Consequently, it was revealed that consideration of the initial gap compression effect is essential for accurately determining plastic constitutive model parameters.

Experimental investigation on dynamic compressive properties of SHCC after freeze-thaw cycles

In this paper, the split Hopkinson pressure bar (SHPB) test was used to investigate the variation of dynamic compressive properties of SHCC with various freeze-thaw (FT) cycles and strain rates. The full-field strain distribution and cracking characteristics of FT-damaged SHCC after the SHPB test were quantitatively and characterized by the high-speed digital image correlation (DIC) technique. The internal damage was analyzed using an X-ray CT imaging technique and SEM (Scanning electron microscope). Results show that dynamic compressive strength, energy absorption ability and dynamic increase factor (DIF) increase as the increase of strain rate, and these increase trends are weakened by the FT damage. The DIF model is established considering the number of FT cycles and strain rates. Variation of crack width in SHCC obtained through the high-speed DIC technique can be divided into three stages: linear increase stage, plateau stage and slow increase stage.

Dynamic Mechanical Strength Prediction of BFRC Based on Stacking Ensemble Learning and Genetic Algorithm Optimization

Split Hopkinson pressure bar (SHPB) tests are usually used to determine the dynamic mechanical strength of basalt-fiber-reinforced concrete (BFRC), but this test method is time-consuming and expensive. This paper makes predictions about the dynamic mechanical strength of BFRC by employing machine learning (ML) algorithms and feature sets drawn from experimental data from prior works. However, there is still the problem of improving the accuracy of the dynamic mechanical strength prediction by the BFRC, which remains a challenge. Using stacking ensemble learning and genetic algorithms (GA) to optimize parameters, this study proposes a prediction method that combines these two techniques for obtaining accurate predictions. This method is composed of three parts: (1) the training uses multiple base learners, and the algorithms employed by the learners include extreme gradient boosting (XGBoost), gradient boosting (GB), random forest (RF), and support vector regression (SVR); (2) multi-base learners are combined using a stacking strategy to obtain the final prediction; and (3) using GA, the parameters are optimized in the prediction model. An experiment was conducted to compare the proposed approach with popular techniques for machine learning. In the study, the stacking ensemble algorithm integrated the base learner prediction results to improve the model’s performance and the GA further improved prediction accuracy. As a result of the application of the method, the dynamic mechanical strength of BFRC can be predicted with high accuracy. A SHAP analysis was also conducted using the stacking model to determine how important the contributing properties are and the sensitivity of the stacking model. Based on the results of this study, it was found that in the SHPB test, the strain rate had the most significant influence on the DIF, followed by the specimen diameter and the compressive strength.

Crack healing phenomenon of TiZrNbV high-entropy alloy during dynamic load

The dynamic compressive behavior of TiZrNbV BCC-structured refractory high-entropy alloys (RHEAs) was studied in this work. A remarkable phenomenon of flow stress re-rising was observed from the dynamic compressive stress-strain curve obtained from split Hopkinson pressure bar test. Microstructure characterization including X-ray diffraction, scanning electron microscope, electron back scattering diffraction and macroscopical electric resistivity measurement jointly reveal that a "crack healing" phenomenon does exist in TiZrNbV RHEA during dynamic compression, and then leads to the recovery of flow stress. It is believed that explosive welding dynamic compression results in the "crack healing" phenomenon and then affect the dynamic mechanical behavior of TiZrNbV RHEA based on comparative experiment of alloys with different plasticity. The finding for the crack healing phenomenon is helpful to understand the essence about the dynamic compressive behavior of BCC-structured RHEAs.

Subroutine Embedding and Finite Element Simulation of the Improved Constitutive Equation for Ti6Al4V during High-Speed Machining.

The Johnson-Cook (J-C) constitutive model is not suitable for Ti-6Al-4V alloy in the high-speed cutting finite element simulation, as it has no response dynamic recrystallization softening effect under heavy impact and high temperature. In this paper, an improved constitutive model considering the recrystallization effect was established, and the parameters were fitted with the data of flow stress-strain of the Split Hopkinson Pressure Bar (SHPB) test. The relevant theories of cutting finite element simulation were studied, such as nonlinear constitutive elastic-plastic deformation, strain state, and material yield. A subroutine that included the Recht shear failure instability criterion and the improved model was coded in Fortran and embedded in the finite element simulation software AdvantEdge FEM, along with the return mapping stress integration algorithm. The simulated stress of the improved model dropped dramatically from 460 MPa to 220 MPa when the temperature rises from 950 °C to 1000 °C, and its decline reached 46.7%, while the J-C model only decreased by 10%. Comparative studies indicate that the stress change of the improved constitutive simulation is closer to the SHPB test results than the J-C constitutive, and the new one is more suitable when it expresses the high temperature and heavy impact in the high-speed milling.

Requirements of specimen dimension considering maximum coarse aggregate size for concrete split Hopkinson pressure bar tests

Dynamic increase factors (DIF) of concrete compressive strength have been proposed through experiments on specimens including small aggregates without considering the effect of the coarse aggregate size, which was due to the limitations in the size of specimens and test apparatus. Therefore, this study conducted an experimental investigation of the effect of the maximum coarse aggregate size (Gmax) on the DIF of normal-strength concrete. Split Hopkinson pressure bar (SHPB) tests were performed for mortar and concrete specimens with various sizes of Gmax, and the apparent and pure rate DIFs were obtained. Moreover, the pure rate DIF of each Gmax was verified through numerical analysis of the SHPB tests. The test and analysis results indicated that Gmax affected the dispersion of the apparent DIF and the values of the pure rate DIF. Based on these results, a guideline for the fabrication of specimens considering Gmax for concrete SHPB tests was suggested.

Analysis of the Influence of Silty Sands Moisture Content and Impact Velocity in SHPB Testing on Their Compactability and Change in Granulometric Composition

This paper presents the results of a test cycle of two types of silty sand (siSa) with different contents of fine fractions. Fine fractions are understood as soil grains with a grain diameter of less than 63 µm (as the sum of silt and clay fractions). The soils tested had a content of fine fractions of fSi+Cl,1 = 15.14% and fSi+Cl,2 = 20.48%, respectively, before the study. Changes in the content of these fractions after the experiments were analyzed. These experiments consisted of dynamic bar projectile impact loading, and a split Hopkinson pressure bar (SHPB) test stand was used in the study. Changes in the granulometric composition of the silty sands studied were carried out in a laser particle size analyzer, allowing measurement of fractional content in the grain size range from 0.01 µm to 3500 µm. As a result, a summary of changes in soil grain size curves in the range of fine fractions was compiled. Repeated trends were observed in the changes in the granulometric composition of the soil samples as a function of the moisture content of the soil sample (w1 = 0%, w2 = 5%, w3 = 10%, and w4 = 15%) and the impact velocity of the loading bar projectile for SHPB pneumatic launcher pressures (p1 = 1.2 bar → v1 = 12.76 m/s, p2 = 1.8 bar → v2 = 17.69 m/s and p3 = 2.4 bar → v3 = 21.32 m/s). The influence of the initial moisture content of the investigated soil on the value of the optimum moisture content obtained during its dynamic compaction was discussed. The trend in the behavior of the change in the granulometric composition of the tested samples was determined, taking the value of the initial moisture content of the soil in relation to the optimum moisture content of the reference sample as a reference. The largest percentage change in granulometric composition through an increase in the value of the silt and clay fraction relative to the reference sample fSi+Cl for both types of silty sand tested occurs for the same moisture content variant w2 = 5%–for soil fSi+Cl,1 = 15.14% there is an increase in the fine fraction of 11.08% and for soil fSi+Cl,2 = 20.48% there is an increase in the fine fraction of 15.17%. In general, it can be seen that more silty soil is more strongly susceptible to the phenomenon of grain crushing for moisture content w1 = 0% and w2 = 5% less than its optimum moisture content wopt,1 = 8.70%. In contrast, less silty soil is more susceptible to the phenomenon of grain crushing for moisture contents w3 = 10% and w4 = 15% greater than its optimum moisture content wopt,2 = 9.20%. The presented dynamic physical phenomenon of soil behavior is crucial during explosive and impact impacts on structures made of soil, e.g., as ground protection layers.

Dynamic mechanical properties of nanoparticle-enhanced aluminum alloys fabricated by arc-directed energy deposition

The nanoparticle-enhanced aluminum alloys fabricated by arc-directed energy deposition (Arc-DED) have gained much attention due to their improved microstructure and enhanced mechanical properties, and are expected to be applied in aerospace, defense, and marine fields. The dynamic properties of nanoparticle-enhanced aluminum alloys are required in the aforementioned fields. In this work, the dynamic behaviors of AA7075 and TiC/AA7075 samples fabricated by Arc-DED in as-built and heat-treated states are investigated by Split-Hopkinson pressure bars tests with the strain rates of 2000–5000 s−1 at room temperature. The results show that adding TiC nanoparticles improve the dynamic properties of aluminum alloys, especially their performance after heat treatment. The improved performance can be attributed to the refined grain and the generated strengthening phase. The metallographic structure shows that the adiabatic shear band (ASB) is first generated with an increase in the strain rate. Then, cracks appear along ASB, leading to the final shear failure. A modified Johnson-Cook constitutive model is proposed based on the strain softening and strain rate softening effects. The results obtained by the proposed model agree with the experimental results. This work is the first to study the dynamic behavior of aluminum alloys fabricated by Arc-DED, which has potential value for applicating aluminum alloys in various industries.

Mechanical and fractal characteristics of sandstone with Pre-existing fissures of different lengths under varying impact loads in SHPB tests

The Split Hopkinson Pressure Bar (SHPB) with a 100 mm diameter was used to investigate the impact of pre-existing fissure length on the mechanical properties of sandstone under different launch pressure (P = 0.3 MPa, P = 0.45 MPa, and P = 0.6 MPa). Subsequently, CT scanning was conducted on sandstone samples with pre-existing fissure after failure to examine the relationship between pre-existing fissure length (Lc) and fractal characteristics under different launch pressures. Our findings indicate that, compared to intact sandstone, the proportion of plastic deformation in the stress–strain curve of sandstone with pre-existing fissure increases. As Lc increases, the initial plastic deformation stress and secant modulus decrease. After CT scanning, sandstone failure was classified into three conditions for different Lc: (1) Axial-splitting-tensile failure is caused by the development of natural defects, and in this case, the degree of development of pre-existing fissure is low, (2) Radial-splitting -tensile-failure is caused by the development of pre-existing fissure, in which the degree of development of pre-existing fissure is high and dominates the macroscopic failure of sandstone, while the degree of development of natural defects is low, and; (3) Combined-splitting-tensile failure: The failure of sandstone includes both axial-splitting-tensile failure and radial –splitting-tensile failure. At this time, both the degree of development of natural defects and pre-existing fissure are high, which jointly dominate the macroscopic failure of sandstone. With increasing launch pressure (P) and Lc, the failure mode of sandstone transitions from axial splitting-tensile failure to radial splitting-tensile failure, and eventually to combined splitting-tensile failure. However, local compression-shear failure occurs with increased launch pressure. Moreover, Lc significantly affects the fractal characteristics of sandstone. Under 0.3 MPa launch pressure, the fractal dimension (DH) on different height (H) slices initially increases and then decreases with increased Lc. Under 0.45 MPa launch pressure, the DH on different H slices exhibits two changes with increasing Lc. For H = 70 mm and H = 100 mm, the variation of DH is decreasing-increasing–decreasing-increasing, while for H = 0 mm and H = 30 mm, the variation of DH is increasing–decreasing-increasing. Under 0.6 MPa launch pressure, the DH on different H slices increases first and decreases secondly with the increase of Lc, but Lc is different when DH reaches its maximum.

Effect of water saturation on dynamic behavior of sandstone after wetting-drying cycles

Fully understanding the influence of water on the rock materials' mechanical properties is of great significance to the safety design and evaluation in rock engineering. In this study, sandstone was pretreated with different wetting-drying cycles (0-15), and its pore characteristics were characterized by low-field nuclear magnetic resonance (LF-NMR) and scanning electron microscope (SEM) methods. Then, the split Hopkinson pressure bar (SHPB) tests with the same impact velocity were carried out in its dry and saturated states, respectively. The effects of water saturation on the dynamic behavior of sandstone under different porosity conditions and their mechanisms were emphasized. The results show that with the increase of cycle numbers, the porosity of sandstone increases, the dynamic strength and the total energy dissipation decreases. Moreover, the proportion of post-peak energy dissipation rises, and the degree of fragmentation intensifies. With the increase of porosity, the effect of water saturation on dynamic strength changes from enhancement to weakening. This may be related to the competition between the the Stefan effect and the contribution of pore water pressure. Finally, a dynamic damage constitutive model considering the coupling effect of the wetting-drying cycles and dynamic loads was established, and its effectiveness was verified.

DYNAMIC COMPRESSIVE PROPERTIES OF ALUMINIUM-MATRIX COMPOSITES REINFORCED WITH SiC PARTICLES

The aluminium-matrix composites (AMCs) consisted of (5, 10 and 15) x/% SiC particles (SiCp) in an aluminium alloy 7055 matrix. Specimens were taken from hot-press sintering. High-strain-rate tests were performed using the split-Hopkinson pressure bar (SHPB) method. The microstructures were observed with a scanning electron microscope (SEM) to understand the damage mechanisms of the SiCp/7055 Al composites at high strain rate. The SHPB test results show that the SiCp-reinforced composites are more sensitive to strain rate than the unreinforced material. The strain-rate sensitivity of the flow stress of these composites increases substantially with the increase of the strain rate. The flow stress of SiCp/7055Al composites with 10 x/% and 15 x/% SiCp at 3000 s–1 first increases and then decreases with the increase of the plastic strains, which was caused by the heat generated during adiabatic compression. Microstructure-characterization results show that SiCp cracking and SiCp/7055Al interface debonding are the main damage mechanisms of the composites. The SiCp volume fraction and strain rate affect the damage of composites during the dynamic compressive deformation of the SiCp /7055Al composites.

Effect of sludge ceramsite particle grade on static and dynamic mechanical properties of alkali-activated slag lightweight concrete at early age

Sewage sludge (SS) produced in water supply and drainage plants is a kind of solid waste with pollution and high water content. SS mixed with fly ash and other materials to make sludge ceramide (SC) can be used as light environmental protection building materials. Alkali-activated lightweight concrete (ASLC) is prepared by mixing SC with alkali-activated slag mortar with low carbon emission, which has lightweight and early strength characteristics. Using the split Hopkinson pressure bar test system, the dynamic and static uniaxial compressive tests of ASLC at an early age were carried out. The influence of aggregate particle gradation on the mechanical properties of ASLC was comprehensively evaluated from static compressive strength and dynamic peak stress. Experiments show that small-size SC has better mechanical properties and lower air content. SEM test shows that the paste has closely meshed with SC, which proves that SC has good compatibility with alkali-activated slag material. The air content of ASLC was quantified by mesopore characterization. The results show that the increase in SC size will increase the air content of the specimen and weaken the compressive performance of ASLC.

Direct calculation of Johnson-Cook constitutive material parameters for oblique cutting operations

Characteristics and behaviors of materials during manufacturing processes highly depend on their mechanical properties and microstructures. However, these characteristics and behaviors can be greatly influenced by other factors such as strain, strain rate, and temperature during the process. The Johnson-Cook (J-C) constitutive material model has been extensively used to describe the material behavior under such circumstances. The J-C parameters are usually determined using the Split Hopkinson Pressure Bar (SHPB) test which is time consuming and costly. Other methods that have been introduced to numerically determine the J-C parameters are inverse methods that minimize the difference between the experimentally measured and theoretically calculated data. These numerical methods still require a combination of experimentally measured cutting forces and chip thickness. These two items are easy to obtain for simple machining processes like turning in which chip thickness and thus cutting force have almost steady state constant values. Nevertheless, majority of these numerical methods are not applicable to more complex machining processes, e.g., milling, in which tool-workpiece engagement is complex and the chip thickness and consequently cutting forces are varying during the process. To address this limitation, this paper presents a model to identify the J-C strain rate hardening and temperature softening parameters for complex oblique machining processes. The proposed model searches for an optimum set of J-C parameters by matching the calculated cutting forces using Oxley model with those obtained from experimental measurements. In addition, simulation and experiments were performed to compare the results and to validate the proposed model. The results proved the validity of the proposed model in estimating the J-C parameters directly from milling tests as an oblique cutting operation.

Damage Evolution and Constitutive Model of Marble under Dynamic Loading

Through the application of SHPB (split Hopkinson pressure bar) test, the failure mode and dynamic stress-strain curves of marble samples were obtained. The dynamic constitutive model of marble was established with the fracture mechanical parameters (brittleness index), and the calculated curves were compared with the experimental curves. The evolution characteristic of damage variable D was analyzed. The results show that there are three main stages of marble deformation under dynamic impact load, which are linear elastic deformation stage, crack growth stage, and macroscopic failure stage. The sample shows obvious brittleness in the macroscopic failure stage. It is found that with the increase of strain rate, the degree of damage is getting worse. The stress-strain curves obtained based on the constitutive model are in good agreement with the experimental curves. The damage variable D can theoretically explain the evolution law of macroscopic failure of the sample. To some extent, there is a mechanism inside the rock to regulate the damage development of the rock, and the final failure degree of rock sample depends on △ σ BC and ε b .

Incident Strain Pulse Sensitivity in Split Hopkinson Pressure Bar Testing Setup for Variable Conditions: A Numerical and Statistical Approach

Incident Strain Pulse Sensitivity in Split Hopkinson Pressure Bar Testing Setup for Variable Conditions: A Numerical and Statistical Approach