Split Hopkinson Pressure Bar Experiments Research Articles

Compression behaviour of self-compacting concrete under high strain rate loadings at different ages

Self-compacting concrete (SCC) is widely used in reinforced concrete (RC) buildings due to its ability to consolidate by weight and its lack of requirement for external vibration. RC buildings can be subjected to high strain rate loadings during the early days of construction or in their service life. Thus, it is critical to understand the behaviour of concrete under high strain rate loadings at different ages. Previous research shows that minimal studies have focused on the early-age behaviour of concrete under a high strain rate. This study tries to fill this knowledge gap. It focuses on the behaviour of M40 grade SCC under three levels of strain rate loading at the age of one, three, seven, 14 and 28 days. The Split-Hopkinson Pressure Bar (SHPB) setup is used to test the SCC specimens with a diameter of 100 mm and thickness of 50 mm under high strain rates. Forty-five specimens were tested at strain rates ranging from 30 s−1 to 110 s−1 at the age of one to 28 days. The compressive strength, peak strain and elastic modulus results from the SHPB experiment are compared with the quasi-static test results of SCC specimens. The dynamic increase factor (DIF) of the SCC specimens from the SHPB experiment is compared with the CEB – fib code model. The results indicate that the DIF reduces as the concrete's strength and age increase.

FCA-based efficient prediction of effective properties for 3D braided composites considering the effect of strain rate

The existing fast concurrency algorithms are difficult to predict the dynamic mechanical performance of three-dimensional (3D) braided composites from different scales. A modified Finite Element Method Cluster Analysis (FCA) method is employed to address this challenge. The modified FCA method is consisted of an offline and an online stage. In the offline stage, the high-fidelity Representative Unit Cell (RUC) is compressed to form a cluster-based RUC via the k-means method. Additionally, the cluster interaction matrix is calculated. In the online stage, the cluster interaction matrix is updated according to the strain rate levels for predicting the stress–strain curves for the RUC. Based upon the comparison with the data obtained from the Split Hopkinson Pressure Bar (SHPB) experiments, it is found that the modified FCA method can accurately predict the stress–strain curves under different strain rates for RUCs. Additionally, the modified FCA method provides a great improvement on computing efficiency when predicting the dynamic behavior of 3D braided composites.

Modeling of strain hardening behaviors of 6061 aluminum alloy considering strain rate and temperature effects

This paper focuses on the plastic strain hardening behaviors of 6061 aluminum alloy (AA6061), considering its dependence on strain rate and temperature. Quasi-static tensile tests were conducted over a wide temperature range (20 °C-300 °C), and the digital image correlation technique was used to capture the deformation process of specimens. Additionally, the uniaxial compressive mechanical response of AA6061 was tested utilizing quasi-static compression and split Hopkinson pressure bar experiments over a wide range of strain rates (0.001 s−1–6000 s−1). Experimental results showed that the flow stress decreased and increased nonlinearly with temperature and strain rate, respectively. A modified Johnson–Cook (MJC) model was developed by incorporating a temperature-dependent strain softening term, along with corrections to the temperature and strain rate product terms, to reproduce the nonlinear dependence. Furthermore, the MJC model was proven to be able to accurately reproduce the deformation of the specimens tested in Taylor impact experiments (strain rates up to 105 s−1), suggesting its effectiveness for interpolating and extrapolating stress-strain relationships. This model provides applicable modeling for materials with nonlinear rate sensitivity and temperature sensitivity, and it is expected to be applied in engineering problems involving ultra-high strain rates.

Triply periodic minimal surface structures: Energy absorption performance under impact loading and their graded design

This study focuses on dynamic mechanical properties of gyroid TPMS structure and their functionally graded design. Numerical impact model is constructed by finite element method, and its effectiveness is validated through Split Hopkinson Pressure Bar experiment. The influence of impact velocity and density on mechanical response is systematically investigated. Moreover, we computationally analyze the dynamic response of gyroid structures with different gradient thickness, which exhibit increase energy absorption performance (up to 15.56%) compared to uniform structure. The dynamic responses of TPMS structures are theoretically predicted using rigid-perfectly plastic-locking and D-rigid-plastic hardening models, highlighting their potential for predicting dynamic mechanical response.

Investigation on mechanical properties of Ti-6Al-4 V multilayer micro-lattice biomaterials under dynamic compression loading

Novel skull repair Ti-6Al-4 V multilayer micro-lattice biomaterials (MMBs) proposed recently have promising application in clinical practice. Herein, the dynamic compression performances of MMBs are concerned and investigated by Split Hopkinson Pressure Bar (SHPB) system and finite element (FE) methods. Typical shear band, strut yielding and damage deformation modes of MMBs are characterized by FE and SHPB experiment. Through density gradient regulation, deformation mode of MMBs is transformed from shear band to localized collapse pattern. It is interesting that MMBs with different unit cell sizes exhibit different strain rate sensitivities. For strain rate-insensitive MMBs (BCC(3), BCC(5) and BCCZ(3)), the influence of relative density on strength shows a linear increasing trend under both low and high strain rates. For strain rate-sensitive ones (BCC(7), BCCZ(5) and BCCZ(7)), the influence of relative density on strength under low strain rate is stronger than that under high strain rate. The strength range of MMBs matches skull/bone materials well under same loading strain rate. This work not only reveals dynamic mechanical properties of MMBs but also has enlightenment for investigating dynamic properties of porous metamaterials.

Viscoelastic-damage constitutive model and mechanical characterisations of Aluminium/polytetrafluoroethylene under impact loading

As a typical structural energy-containing material, aluminium/polytetrafluoroethylene (Al/PTFE) exhibits excellent mechanical properties under conventional conditions and releases large amounts of energy through chemical reactions under impact loading. In this research, a viscoelastic-damage constitutive model suitable for polymer-based reactive materials was developed, which consisted of an elastic element, two Maxwell elements, and a SCRAM damage element. The effect of damage on the stress–strain relationship was obtained by analysing the crack evolution process and deformation field. A modified Split Hopkinson pressure bar experiment investigated the mechanical characteristics of aluminium/polytetrafluoroethylene under uniaxial/multiaxial impact loading. The results indicated that the viscoelastic-damage constitutive model could describe the effects of the initial crack size and initial crack density on the mechanical properties of aluminium/polytetrafluoroethylene. With the decrease in initial crack length and density, the damage to the aluminium/polytetrafluoroethylene under impact loading was limited, which caused the dynamic mechanical properties to increase. When the pre-stress increases from 0 MPa to 10 MPa, the dynamic ultimate compressive stress of aluminium/polytetrafluoroethylene increases from 77.2 MPa to 89.8 MPa at 2910 s−1 strain rate. A comparison of the experimental and calculated strain–stress curves shows that the established constitutive model is feasible to predicting the mechanical behaviour of aluminium/polytetrafluoroethylene.

FE modeling and simulation of the turning process considering the cutting induced hardening of workpiece materials

The accuracy of the cutting simulation model greatly depends on the constitutive models, thermophysical models, and friction models. However, accurate modeling of physical and mechanical relationships is not enough. The physical and mechanical behavior of the machined surface from the last cut should be modelled in the FE model. In this study, the cutting simulation model of S316L stainless steel was established. The above model consists of two subsequent simulated cuts. The first simulated cut was used to obtain the machined surface with the residual stress, and the second simulated cut was subsequent with the first cut to obtain the actual simulated results. The constitutive model was obtained by the split Hopkinson pressure bar (SHPB) and high-temperature hardness experiments. The specific heat capacity and thermal conductivity models were developed by laser thermal conductivity experiments with various temperatures. The friction model between the workpiece and the tool was established by orthogonal cutting experiments. The simulated cutting forces of the first and second cut were extracted and compared with the experimental results to verify the accuracy of the simulation models. The results showed that the average error of cutting forces for the first cut is 28.33 %, but that for the second cut is 8.02 %, which verifies the accuracy of the two-subsequent cutting simulation model. Additionally, the significant differences in the simulated cutting forces between the first and second cutting depict that the residual stress cannot be ignored for the accuracy verification of cutting simulation models.

Study on Impact Dynamic Behavior and Failure Characteristics of Coal based on True Triaxial Split–Hopkinson Pressure Bar Experiments

Study on Impact Dynamic Behavior and Failure Characteristics of Coal based on True Triaxial Split–Hopkinson Pressure Bar Experiments

Frequency Characteristics of High Strain Rate Compressions of Cf-MWCNTs/SiC Composites

The incorporation of ductile reinforcements into ceramics helps restrain crack deflection, which can enhance ceramics’ toughness and overcome the matrix’s brittleness. In this paper, we produced a ceramic composite reinforced by carbon fibers coated by multi-wall carbon nanotubes (shortened by Cf-MWCNT/SiC composites) for enhanced impact resistance at a high strain rate that commonly occurs in composite materials used in astronautics, marine, and other engineering fields. The fabrication process involves growing multi-wall carbon nanotubes (MWCNTs) on a carbon fiber woven fabric (Cf) to create the fibril/fabric hybrid reinforcement. It is then impregnated by polymer solution (precursor of the ceramics), forming composites after the pyrolysis process, known as the liquid polymer infiltration and pyrolysis (PIP) technique. To assess the impact resistance of the Cf-MWCNT/SiC under high-strain rate compressions, the split Hopkinson pressure bar (SHPB) technique is employed. Since the failure behavior of the Cf-MWCNT/SiC composites in the absence of the ductile phase is not well understood, the study employs the Hilbert–Huang transform (HHT) to analyze the stress–time curves obtained from the SHPB experiments. By applying the HHT, we obtained the frequency–time spectrum and the marginal Hilbert spectrum of the stress signals. These analyses reveal the frequency characteristics of the Cf-MWCNT/SiC composite and provide insights into the relationship between transformed signal frequency and fracture behavior. By understanding the dynamic fracture behavior and frequency response of the Cf-MWCNT/SiC, it becomes possible to enhance its impact resistance and tailor its performance for specific protective requirements. Therefore, the findings of this study can guide the future design and optimization of Cf-MWCNT/SiC structures for various protective applications, such as body armor, civil structures, and protections for vehicles and aircraft.

Mechanical properties of periodic rectangular tube sandwich structure subjected to out-of-plane impact compression loading

Owing to its unique deformation form, negative Poisson’s ratio sandwich structure has attracted significantly widespread interest, especially in the impact protection field. However, inferior mechanical properties severely limit their practical applications. To enhance its mechanical properties, a new type of periodic sandwich structure of rectangular tube was designed and fabricated, and the structure presents negative Poisson’s ratio characteristic under out-of-plane impact compression load. To evaluate its mechanical properties, the deformation form and equivalent yield strength of the periodic rectangular tube sandwich structure were obtained through the split Hopkinson pressure bar (SHPB) experiment. A numerical model of the different wall thicknesses of periodic rectangular tube sandwich structure (PRTSS) was established, and the accuracy of the model was verified by comparing it with the deformation form and equivalent yield strength obtained from experimental results. The results show that with the increase of rectangular tube wall thickness in PRTSS, the equivalent yield strength increases, and the equivalent yield platform strain decreases. Moreover, through the simulation results under four different strain rates, it is obtained that the equivalent yield stress of PRTSS increases with the increase of strain rate, and the straining length of the equivalent yield platform decreases with the increase of strain rate. The effect of wall thickness and strain rate on PRTSS was analyzed, which provided certain guiding significance for the application of the structure in the field of impact protection.

SHPB experiments and FDM-DEM coupled simulations on calcareous sand under uniaxial to triaxial deformation

The impact behavior of sand is paramount to geotechnical and protective engineering. Although the one-dimensional impact responses of sand are extensively studied, the behavior of shear under impact loading remains poorly understood as the shear stresses in uniaxially compressed sand cannot attain the failure state. This paper reports the macroscopic responses of crushable calcareous sand under uniaxial to triaxial deformation by split Hopkinson pressure bar (SHPB) experiments. In addition, the mesoscopic mechanism is analyzed by coupled finite difference method (FDM) and discrete element method (DEM) numerical simulations. With an increasing lateral confined stiffness, the p-q curves exhibit a clockwise rotation, signifying a deviation of the stress path from the critical state line (CSL) during the transition from triaxial to uniaxial deformation, meanwhile the Mohr circle experiences a shift from intersecting to tangential contact with the failure line, indicating that shear failure occurs under triaxial deformation. The stress-strain relationships for both compression and shear exhibit four distinct regimes, the initial elastic stage mainly overcomes intergranular friction through particle rotation; the yield stage mainly compresses the skeleton by contribution of displacement; the hardening stage experiences critical particle breakage and then promotes particle displacement and rotation; and the unloading stage with strain softening caused by the asynchrony between impact loading and deformation. Both compressed and shear yield stress increases with an increasing confined stiffness, but the shear friction angle decreases. This indicates that the governing factor in triaxial compression under impact loading is the stress state rather than kinetic friction. Particle breakage in triaxial compression state tends to approach the splitting mode, while in uniaxial squeezing state it tends to approach the Mixed mode.

An elastoplastic damage constitutive model for capturing dynamic enhancement effect of rock and concrete through equivalent stress history

The strength enhancement effect of rock and concrete under dynamic loading is one of the significant response characteristics differing from quasi-static loading. Typically, current dynamic constitutive models describe this phenomenon by adopting strain/stress rate dependent functions. In this study, a novel elastoplastic damage constitutive model that captures the dynamic strength increase through the equivalent stress history is developed by coupling the incubation characteristic time (ICT) criterion and the unified strength theory (UST). Specifically, the ICT criterion substitutes the stress history for the strain/stress rate to predict dynamic yield strength of rock and concrete. And the equivalent stress expressed by the UST provide an appropriate selection of the stress history in the ICT criterion under complex stress states. Furthermore, based on the non-associated plastic flow rule and the plastic-damage evolution law, combined with the equation of state, the proposed constitutive model is established and implemented numerically. The dynamic stress-strain curves of granite were reconstructed by a series of numerical tests on a single element, which verified the accuracy of the proposed constitutive model and the reliability of the numerical algorithm by comparing the experimental data. The proposed model was applied to the numerical simulation of dynamic compression-shear tests on inclined sandstone specimens loading by the split Hopkinson pressure bar (SHPB) and fragmentation experiments of single borehole granite specimens under blast loading, respectively. And the experimental dynamic crack patterns on the specimen surface captured by high-speed cameras match the simulated damage distribution well. In addition, several common concrete constitutive models and the proposed model were employed to simulate the dynamic response of reinforced concrete beams under near-field blast loading. The damage patterns and the mid-span residual displacement calculated numerically by the proposed model are more consistent with the experiments than other concrete models. As a conclusion, the proposed model, coupled the ICT criterion and the UST, provides a new perspective and paradigm for characterizing the responses of rock and concrete subjected to intense dynamic loads.

Material Point Simulation Method for Concrete Medium Fracture and Fragmentation under Blast Loading

The nature of the fracture and fragmentation processes in concrete medium under blast loading is the transformation of the medium from continuum to discontinuity. Coupled with the significant rate correlation of concrete medium, its mechanical behavior presents a high degree of complexity. When tackling this problem, the finite element method (FEM) frequently encounters problems such as grid distortion and even negative volume, whereas the material point method (MPM) can efficiently avoid these problems. Furthermore, the original Holmquist-Johnson-Cook (HJC) model does not take the segmented characteristics of the calculation function for the dynamic increasing factor into consideration. As a result, in this article, first, the calculation function for the dynamic increasing factor in the HJC model was modified by the Split-Hopkinson Pressure Bar (SHPB) experiment, and an improved HJC model was proposed; second, an MPM simulation program was developed, and the improved HJC concrete model was embedded into the simulation program; and finally, the simulation program was verified by numerical examples, and the results show that the developed simulation program can better simulate the fracture and fragmentation process of the concrete medium under blast loading, especially the pulverization characteristics of the medium in the near zone of the load.

Experimental investigation on effect of loading rate on fracture behavior of coal-seam roof rock

The fracture behavior of coal-seam roof rock in coal mining is a key and controlling factor for the mode optimization of the artificial roof caving. However, the fracture mechanism of roof rock under loading is not clear. In the work, the split Hopkinson pressure bar (SHPB) experiment was carried out using semicircular bending samples from the sandstone of coal-seam roof rock in the Junger mining area of Inner Mongolia at the loading rate of 0.35–3.78 GPa·m0.5·s−1, and the dynamic fracture behavior and energy dissipation mechanism of samples under different loading rates were investigated. The result shows that the dynamic stress–strain process of the hard roof rock includes four stages: linear instantaneous compaction, linear elastic compression, failure, and fracture extension, in which the failure forms changes from brittle fracture to ductile fracture with the increase of loading rate. The mode I fracture toughness increases linearly under confining pressure. In addition, the propagation orientation of induced fractures is parallel to the loading direction, and the gravel in the samples can inhibit fracture extension, resulting in changing the fracture extension path. Further, the energy absorption efficiency of the samples during the fracture process decreases with the increase in the loading rate.

Reformability evaluation of blasting-enhanced permeability in in situ leaching mining of low-permeability sandstone-type uranium deposits

It is essential to evaluate the blasting-enhanced permeability (BEP) feasibility of a low-permeability sandstone-type uranium deposit. In this work, the mineral composition, reservoir physical properties and rock mechanical properties of samples from sandstone-type uranium deposits were first measured. Then, the reformability evaluation method was established by the analytic hierarchy process-entropy weight method (AHP-EWM) and the fuzzy mathematics method. Finally, evaluation results were verified by the split Hopkinson Pressure Bar (SHPB) experiment and permeability test. Results show that medium sandstone, argillaceous sandstone and siltstone exhibit excellent reformability, followed by coarse sandstone and fine sandstone, while the reformability of sandy mudstone is poor and is not able to accept BEP reservoir stimulation. The permeability improvement and the distribution of damage fractures before and after the SHPB experiment confirm the correctness of evaluation results. This research provides a reformability evaluation method for the BEP of the low-permeability sandstone-type uranium deposit, which contributes to the selection of the appropriate regional and stratigraphic horizon of the BEP and the enhanced ISL of the low-permeability sandstone-type uranium deposit.

Critical assessment and demonstration of high-emissivity coatings for improved infrared signal quality for Taylor–Quinney coefficient experimentation

Over the infrared (IR) spectrum metals have relatively low emissivity. Considering that modern studies focused on determining the Taylor–Quinney coefficient rely on IR-based measurements to quantify temperature rise, there is a need to improve measurement certainty. This is of particular concern during the earliest stages of deformation when small temperature rises result in a low IR-signal to noise ratio. Herein an economical approach to improving signal quality is presented based on the deposition of a thin high emissivity coating on the material substrate (i.e., specimen) of interest. Coating material and coating thickness selection are founded on both heat transfer and electromagnetic performance. A maximum allowable thickness of 1μm was determined for the coating to ensure the recorded temperature of the coating closely matches the temperature of the deforming substrate (i.e., specimen) during the sub-millisecond duration of a split-Hopkinson (or Kolsky) pressure bar experiment. Using the transfer matrix method, the spectral emissivity of coatings made from commonly available metallic deposition sources with increasing thicknesses was calculated. Theoretical predictions identified a 250 nm thick Ti coating as a promising candidate for increasing surface emissivity without the coating acting as a thermal barrier. Confirmation of the coating layer’s ability to substantially improve IR signal amplitudes was examined experimentally for two low emissivity materials, specifically OFHC copper (Cu) and Magnesium (Mg) alloy AZ31B. IR detector calibration experiments showed a four to six times improvement in signal amplitude compared to native Cu and Mg surfaces. Additionally, the calibration curves of coated specimens converge exhibiting the same behavior allowing for a unified calibration curve to be used regardless of substrate material. Split-Hopkinson pressure bar experiments supported by IR thermography were conducted on coated specimens and Taylor–Quinney coefficients are reported. Taylor–Quinney coefficients obtained, are compared to literature values when appropriate, and show positive agreement to previously reported values. Real-time high-speed imaging and post-mortem analysis showed robust adhesion between the substrate to the thin Ti layer up to 16% strain.

Aging and temperature effects on the dynamic characteristics of asphalt mortar under impact loading

Asphalt pavement structures are subjected to impact loading during the milling process. This study aims to investigate the dynamic behavior of asphalt mortar under high strain rates ranging from 281.7 to 830.3 s−1 through the Split Hopkinson Pressure Bar (SHPB) experiments. The effects of temperature and long-term oven aging on the dynamic properties of asphalt mortar under impact loading were statistically analyzed. The results indicated that the dynamic strength and the impact toughness are both enhanced with the increase in the strain rate and temperature. Laboratory oven aging of asphalt mortar at 85 °C for 72 h indicates a significant increase in the carbonyl and sulfoxide indices, a decrease in compressive strength, and rising in elastic modulus. The failure patterns show a strong correlation with the strain rates. An increase in the temperature produces a better gradation of the fragments at higher strain rates regardless of the aging state.

Effect of pulsed current on plastic deformation of Inconel 718 under high strain rate and high temperature conditions

Based on the electroplastic effect induced by pulsed current, the dislocation states induced by pulsed current during material deformation were studied by introducing pulsed current into the Split Hopkinson Pressure Bar (SHPB) experiments with Inconel 718 as the research object, and the dislocation kinetic mechanism under the electroplastic effect was analyzed. Simulations and experiments’ results show that pulse current can promote the unpinning movement of dislocations and effectively improve the state of dislocation pileup. At the same time, it is found that the current can produce a similar skin effect on the excited magnetic field, so that the magnetic field is mainly concentrated on the surface of the material. The magnetic field are concentrated on the symmetry axis, and gradually decreases from the surface to the central axis. Finally, the dislocation slip theory is combined with the local energy-state theory which describes that the electronic wind force can reduce the dislocation energy barrier and the magnetic field change the dislocation magnetic core, and the relationship between the plastic deformation rate and the current density under the combined action of the electronic wind force and the magnetoplastic effect is deduced. At the same time, the obtained relationship is brought into the constitutive equation to obtain the constitutive equation under the pulse current. Through experimental verification and error analysis, it shows that in the range of current density 0∼0.2A/mm−2, the calculated stress-strain curve is consistent with the stress-strain curve obtained in the experiment.

Plastic deformation behavior of a Cu–10Ta alloy under strong impact loading

In this work, a Cu–10Ta alloy with a copper to tantalum mass ratio of 9:1 is prepared using powder metallurgy technology. Physical properties of the alloy, including density, microstructure, melting point, and constant-volume specific heat, are tested. Via the split Hopkinson pressure bar (SHPB) and flyer-plate impact experiments, the relationship between equivalent stress and equivalent plastic strain of the material is studied at temperatures of 298–823 K and under strain rates of 1 × 10−3–5.2 × 103 s−1, and the Hugoniot relationship at impact pressures of 1.46–17.25 GPa and impact velocities of 108–942 m/s is obtained. Evolution of the Cu–10Ta microstructure that occurs during high-strain-rate impact is analyzed. Results indicate that the Cu–10Ta alloy possesses good thermal stability, and at ambient temperatures of up to 50% its melting point, stress softening of less than 15% of the initial strength is observed. A modified J-C constitutive model is employed to accurately predict the variation of yield strength with strain rate. Under strong impact, the copper phase is identified as the primary source of plastic deformation in the Cu–10Ta alloy, while significant deformation of the high-strength tantalum particles is less pronounced. Furthermore, the longitudinal wave speed D is found to correlate linearly with the particle velocity u upon strong impact. Analysis reveals that the sound speed and spallation strength of the alloy increase with increasing impact pressure.

Adiabatic shear localization induced by dynamic recrystallization in an FCC high entropy alloy

Due to their strong strain hardening, face-centered cubic (FCC) high/medium entropy alloys (H/MEAs) have remarkable resistance to shear localization even under forced dynamic shear. In this work we investigated the dynamic mechanical behavior of an FCC Al0.1CoCrFeNi HEA via a series of split Hopkinson pressure bar (SHPB) experiments at 77 K and room temperature. This HEA exhibited very strong strain hardening capacity, remarkable strain rate sensitivity and moderate temperature dependence. Such a combination of mechanical properties should be strongly unfavorable for adiabatic shear bands (ASBs). However, its dynamic compressive failure at 77 K was found to be caused by crack propagation within the primary ASBs along the directions of maximum shear stress. Detailed examination of the specimens using electron backscatter diffraction (EBSD) and transmission electron microscopy (TEM) revealed convincing microstructural evidences for massive dynamic recrystallization (DRX) prior to ASB. We suggested that the expansion and coalescence of these DRX softened regions served as the root cause for the occurrence of ASBs and the final catastrophic fracture of specimens. The severe local shear flow, substantial adiabatic temperature rise and extremely fast quenching within the ASB resulted in ultrafine grains therein. Our results and analyses provided a plausible understanding of the formation mechanisms of ASBs in the FCC HEA under impact loading.