High strain rate compressive strength behavior of cemented paste backfill using split Hopkinson pressure bar

The stability of cemented paste backfill(CPB)is threatened by dynamic disturbance,but the conventional low strain rate laboratory pressure test has difficulty achieving this research purpose.Therefore,a split Hopkinson pressure bar(SHPB)was utilized to investigate the high strain rate compressive behavior of CPB with dynamic loads of 0.4,0.8,and 1.2 MPa.And the failure modes were determined by macro and micro analysis.CPB with different cement-to-tailings ratios,solid mass concentrations,and curing ages was prepared to conduct the SHPB test.The results showed that increasing the cement content,tailings content,and curing age can improve the dynamic compressive strength and elastic modulus.Under an impact load,a higher strain rate can lead to larger increasing times of the dynamic compressive strength when compared with static loading.And the dynamic compressive strength of CPB has an exponential correlation with the strain rate.The macroscopic failure modes indicated that CPB is more seriously damaged under dynamic loading.The local damage was enhanced,and fine cracks were formed in the interior of the CPB.This is because the CPB cannot dissipate the energy of the high strain rate stress wave in a short loading period.

Relationship between diameter of split Hopkinson pressure bar and minimum loading rate under rock failure

In order to investigate the relationship between bar diameter and loading rate of the split Hopkinson pressure bar(SHPB) setup under the failure of rock specimen and realize the medium strain rate loading of specimen,new SHPB setups with different elastic bar's diameters of 22,36,50 and 75 mm were constructed.The tests were carried out on these setups at different loading rates,and the specimens had the same diameter of elastic bars and same ratio of length to diameter.The test results show that the larger the elastic bar's diameter is,the less the loading rate is needed to cause specimen failure,they show good power relationship,and that under the same strain rate loading,specimens are broken more seriously with larger diameter SHPB setup than with smaller one.

Water‑immersion softening mechanism of coal rock mass based on split Hopkinson pressure bar experiment

The coal mining process is afected by various water sources such as groundwater and coal seam water injection.Understanding the dynamic mechanical parameters of water-immersed coal is helpful for coalmine safe production.The impact compression tests were performed on coal with diferent moisture contents by using theϕ50 mm Split Hopkinson Pressure Bar(SHPB)experimental system,and the dynamic characteristics and energy loss laws of water-immersed coal with diferent compositions and water contents were analyzed.Through analysis and discussion,it is found that:(1)When the moisture content of the coal sample is 0%,30%,60%,the stress,strain rate and energy frst increase and then decrease with time.(2)When the moisture content of the coal sample increases from 30%to 60%,the stress“plateau”of the coal sample becomes more obvious,resulting in an increase in the compressive stress stage and a decrease in the expansion stress stage.(3)The increase of moisture content of the coal sample will afect its impact deformation and failure mode.When the moisture content is 60%,the incident rod end and the transmission rod end of the coal sample will have obvious compression failure,and the middle part of the coal sample will also experience expansion and deformation.(4)The coal composition ratio suitable for the coal immersion softening impact experiment is optimized.

Calibration of split Hopkinson pressure bar system with special shape striker

In order to present basic guidance for system calibration of split Hopkinson pressure bar(SHPB) with the special shape striker,wave characteristics and dynamic responses of SHPB under striker impact were analyzed.Stress generated by the special shape striker tends to have a half-sine waveform and has little wave dispersion during its propagation.Impact velocities of the special shape striker and peak values of generated stress still have linear relation but with a different coefficient from that of cylindrical strikers.From stress histories on the surfaces of the input bar impacted by the special shape striker off-axially and obliquely,it is found that the misalignment impacts usually trigger wave distortion and amplitude decrease,which can be used to identify the poor system adjustment.Finally,the system calibration of SHPB with the special shape striker can be classified into four steps:system adjustment,wave distortion identification,measurement calibration and transmission calibration,where the measurement calibration factor and transmission calibration factor are elaborated and redefined.

Approach to minish scattering of results for split Hopkinson pressure bar test

Split Hopkinson pressure bar（SHPB） apparatus, usually used for testing behavior of material in median and high strain-rate, is now widely used in the study of rock dynamic constitutive relation, damage evolvement mechanism and energy consumption. However, the possible reasons of sampling disturbance, machining error and so on often lead to the scattering of test results, and bring ultimate difficulty for forming general test conclusion. Based on the stochastic finite element method, the uncertain parameters of specimen density ps, specimen radius Rs, specimen elastic modulus Es and specimen length Ls in the data processing of SHPB test were considered, and the correlation between the parameters and the test results was analyzed. The results show that the specimen radius Rs has direct correlation with the test result, improving the accuracy in preparing and measuring of specimen is an effective way to improve the accuracy of test and minish the scattering of results for SHPB test.

Testing of High-Strength Zr-Based Bulk Metallic Glass with the Split Hopkinson Pressure Bar

The split Hopkinson pressure bar （SHPB） was used to determine the dynamic compressive strength of the high-strength Zr38Ti17Cu10.5Co12Be22.5 bulk metallic glass at strain rate on the order of 102 s^-1. It is shown that at high strain rates beyond about 1 000 s^-1, uniform deformation within the metallic glass specimen could not be achieved and dispersion in the transmitted pulse can lead to discrepancies in measuring the dynamic failure strength of the present Zr-based bulk metallic glass. Based on these reasons, a copper insert was placed between the strike bar and the input bar to obtain reliable and consistent experimental data for testing of the Zr38Ti17Cu10.5Co12Be22.5 bulk metallic glass using the SHPB. Negative strain rate sensitivity was found in the present Zr-based bulk metallic glass.

DEVELOPMENT OF EXPERIMENTAL METHODS FOR IMPACT TESTING BY COMBINING HOPKINSON PRESSURE BAR WITH OTHER TECHNIQUES

The split Hopkinson pressure bar（SHPB） technique and the wave propagation inverse analysis（WPIA） technique are both extensively used to experimentally investigate the impact behavior of materials, although neither of them alone provides a fully satisfactory analysis. In the present paper, attention is given to new experimental techniques by incorporating a damagemodified constitutive model into the SHPB technique and combining the Hopkinson pressure bar（HPB） technique with WPIA. First, to distinguish the response due to dynamic constitutive behavior and the response due to dynamic damage evolution, the SHPB method incorporating a damage-modified constitutive model is developed, including an explicit damage-modified Zhu–Wang–Tang model and an implicit damage-modified constitutive model. Second, when the SHPB results become invalid, a method of combining new Lagrange inverse analyses with the HPB technique is developed, including cases of the HPB arranged in front of a long specimen and behind the specimen. As examples of these new methods, typical results are given for nonlinear viscoelastic polymers and concretes considering damage evolution, a super-elastic Ti–Ni alloy with phase transformation and an aluminum foam with shock waves propagating within it.

Dynamic rock tests using split Hopkinson （Kolsky） bar system - A review

Dynamic properties of rocks are important in a variety of rock mechanics and rock engineering problems. Due to the transient nature of the loading, dynamic tests of rock materials are very different from and much more challenging than their static counterparts. Dynamic tests are usually conducted using the split Hopkinson bar or Kolsl^j bar systems, which include both split Hopkinson pressure bar （SHPB） and split Hopkinson tension bar （SHTB） systems. Significant progress has been made on the quantification of various rock dynamic properties, owing to the advances in the experimental techniques of SHPB system. This review aims to fully describe and critically assess the detailed procedures and principles of tech- niques for dynamic rock tests using split Hopkinson bars. The history and principles of SHPB are outlined, followed by the key loading techniques that are useful for dynamic rock tests with SHPB （i.e. pulse shaping, momentum-trap and multi-axial loading techniques）. Various measurement techniques for rock tests in SHPB （i.e. X-ray micro computed tomography （CT）, laser gap gauge （LGG）, digital image corre- lation （DIC）, Moir~ method, caustics method, photoelastic coating method, dynamic infrared thermog- raphy） are then discussed. As the main objective of the review, various dynamic measurement techniques for rocks using SHPB are described, including dynamic rock strength measurements （i.e. dynamic compression, tension, bending and shear tests）, dynamic fracture measurements （i.e. dynamic imitation and propagation fracture toughness, dynamic fracture energy and fracture velocity）, and dy- namic techniques for studying the influences of temperature and pore water.

不同含水率红陶土的SHPB动力学性能实验

为研究动态加载下红陶土的动态力学特性,利用分离式霍普金森压杆系统,开展了含水率分别为5%、7%、9%、11%、13%和15%,冲击速度分别为6、8、10 m/s,分析了不同含水率和应变率条件下红陶土的动力学特性。结果表明:随着冲击速度的增大,红陶土应变率效应显著;在冲击荷载作用下,红陶土的动态应力-应变关系曲线随加载应变率提高呈现2种曲线类型,分别为脆-塑性破坏和脆性破坏,随着应变率的增加,红陶土破坏过程由塑-脆性破坏逐转变为脆性破坏;红陶土的抗压强度、动态弹性模量均随应变率的增大而增加,并随着含水率的增大先减小后增大。

Effect of dry-wet cycles on dynamic properties and microstructures of sandstone:Experiments and modelling

Underground pumped storage power plant(UPSP)is an innovative concept for space recycling of abandoned mines.Its realization requires better understanding of the dynamic performance and durability of reservoir rock.This paper conducted ultrasonic detection,split Hopkinson pressure bar(SHPB)impact,mercury intrusion porosimetry(MIP),and backscatter electron observation(BSE)tests to investigate the dynamical behaviour and microstructure of sandstone with cyclical dry-wet damage.A coupling FEM-DEM model was constructed for reappearing mesoscopic structure damage.The results show that dry-wet cycles decrease the dynamic compressive strength(DCS)with a maximum reduction of 39.40%,the elastic limit strength is reduced from 41.75 to 25.62 MPa.The sieved fragments obtain the highest crack growth rate during the 23rd dry-wet cycle with a predictable life of 25 cycles for each rock particle.The pore fractal features of the macropores and micro-meso pores show great differences between the early and late cycles,which verifies the computational statistics analysis of particle deterioration.The numerical results show that the failure patterns are governed by the strain in pre-peak stage and the shear cracks are dominant.The dry-wet cycles reduce the energy transfer efficiency and lead to the discretization of force chain and crack fields.

Al/Hf ratio-dependent mechanisms of microstructure and mechanical property of nearly fully dense Al—Hf reactive material

This study proposed three types of Al—Hf reactive materials with particle size ratios(a),which were almost completely dense(porosity of<5.40%)owing to their preparation using hot-pressing technology.Microstructure characteristics and phase composition were analyzed,and the influence of particle size ratios on dynamic mechanical behavior and damage mechanism were investigated.The prepared sample with a=0.1 exhibited continuous wrapping of the Hf phase by the Al phase.Hf—Hf contact(continuous Hf phase)within the sample gradually increased with increasing a,and a small amount of fine Hf appeared for the sample with a=1.The reactive materials exhibited clear strain-rate sensitivity,with flow stressσ0.05and failure strainεfincreasing approximately linearly with increasing strain rate.ε.It is found that the plastic deformation of the material increased with increasing strain rate.As a increased from 0.1 to 1,the flow stress gradually increased.Impact failure of the material was dominated by ductile fracture with a large Al phase plastic deformation band for lower a,while brittle fracture with crushed Hf particles occurred at higher a.Finally,a constitutive model based on BP neural network was proposed to describe the stress-strain relationships of the materials,with an average relative error of 2.22%.

Effect of dynamic loading orientation on fracture properties of surrounding rocks in twin tunnels

For expedited transportation,vehicular tunnels are often designed as two adjacent tunnels,which frequently experience dynamic stress waves from various orientations during blasting excavation.To analyze the impact of dynamic loading orientation on the stability of the twin-tunnel,a split Hopkinson pressure bar(SHPB)apparatus was used to conduct a dynamic test on the twin-tunnel specimens.The two tunnels were rotated around the specimen’s center to consider the effect of dynamic loading orientation.LS-DYNA software was used for numerical simulation to reveal the failure properties and stress wave propagation law of the twin-tunnel specimens.The findings indicate that,for a twin-tunnel exposed to a dynamic load from different orientations,the crack initiation position appears most often at the tunnel corner,tunnel spandrel,and tunnel floor.As the impact direction is created by a certain angle(30°,45°,60°,120°,135°,and 150°),the fractures are produced in the middle of the line between the left tunnel corner and the right tunnel spandrel.As the impact loading angle(a)is 90°,the tunnel sustains minimal damage,and only tensile fractures form in the surrounding rocks.The orientation of the impact load could change the stress distribution in the twin-tunnel,and major fractures are more likely to form in areas where the tensile stress is concentrated.

Deformation characteristics and damage ontologies of soft and hard composite rock masses under impact loading

As one of the most common occurring geological landforms in deep rock formations, the dynamic mechanical properties of layered composite rock bodies under impact loading have been widely studied by scholars. To study the dynamic properties of soft and hard composite rocks with different thickness ratios, this paper utilizes cement, quartz sand and gypsum powder to construct soft and hard composite rock specimens and utilizes a combination of indoor tests, numerical calculations, and theoretical analyses to investigate the mechanical properties of soft and hard composite rock bodies. The test results reveal that:(1) When the proportion of hard rock increases from 20% to 50%, the strength of the combined rock body increases by 69.14 MPa and 87 MPa when the hard rock face and soft rock face are loaded, respectively;however, when the proportion of hard rock is the same, the compressive strength of the hard rock face impact is 9%-17% greater than that of the soft rock face impact;(2) When a specimen of soft and hard combined rock body is subjected to impact loading, the damage mode involves mixed tension and shear damage, and the cracks generally first appear at the ends of the specimen, then develop on the laminar surface from the impact surface, and finally end in the overall damage of the soft rock part. The development rate and the total number of cracks in the same specimen when the hard rock face is impacted are significantly greater than those when the soft rock face is impacted;(3) By introducing Weibull’s statistical strength theory to establish the damage variables of soft-hard combined rock bodies, combined with the DP strength criterion, the damage model and the Kelvin body are concatenated to obtain a statistical damage constitutive model, which can better fit the full stress-strain curve of soft-hard combined rock body specimens under a single impact load.

Damage constitutive model of lunar soil simulant geopolymer under impact loading

Lunar base construction is a crucial component of the lunar exploration program,and considering the dynamic characteristics of lunar soil is important for moon construction.Therefore,investigating the dynamic properties of lunar soil by establishing a constitutive relationship is critical for providing a theoretical basis for its damage evolution.In this paper,a split Hopkinson pressure bar(SHPB)device was used to perform three sets of impact tests under different pressures on a lunar soil simulant geopolymer(LSSG)with sodium silicate(Na_(2)SiO_(3))contents of 1%,3%,5%and 7%.The dynamic stressestrain curves,failure modes,and energy variation rules of LSSG under different pressures were obtained.The equation was modified based on the ZWT viscoelastic constitutive model and was combined with the damage variable.The damage element obeys the Weibull distribution and the constitutive equation that can describe the mechanical properties of LSSG under dynamic loading was obtained.The results demonstrate that the dynamic compressive strength of LSSG has a marked strain-rate strengthening effect.Na_(2)SiO_(3) has both strengthening and deterioration effects on the dynamic compressive strength of LSSG.As Na_(2)SiO_(3) grows,the dynamic compressive strength of LSSG first increases and then decreases.At a fixed air pressure,5%Na_(2)SiO_(3) had the largest dynamic compressive strength,the largest incident energy,the smallest absorbed energy,and the lightest damage.The ZWT equation was modified according to the stress response properties of LSSG and the range of the SHPB strain rate to obtain the constitutive equation of the LSSG,and the model’s correctness was confirmed.

High Strain-Rate and Shock Response of Carbon SupercompositeTM

This study focuses on assessing the dynamic behaviors of carbon SupercompositeTM laminates when subjected to high strain-rates and air blast loads, using a shock tube for testing. The investigation aims to understand the response of these advanced materials under extreme conditions, which is crucial for applications in aerospace, military, and other high-performance industries. SupercompositeTM (CZE) prepreg, made up of a 3K plain weave carbon fabric with milled carbon fibers as interlaminar reinforcements impregnated with epoxy, is used to create SupercompositeTM (CZE) laminates. A woven carbon composite (CBE) laminate was also created using 3K plain weave Carbon/Epoxy (CBE) prepreg. Both types of laminates were designed and fabricated using the autoclave process. The dynamic behaviors of CZE and CBE laminate under transverse compression loads were evaluated using a modified Split Hopkinson Pressure Bar (SHPB). The study found that the 3D reinforcement with milled carbon fibers significantly affected the dynamic behavior of the CZE laminate. Stereo imaging videos, captured using two SHIMADZU high-speed video cameras in shock tube experiments, recorded the time history of back surface deflection. The plate specimens exhibited low deflections without any visible damage. The experimentally observed center point deflections of the CZE plates decayed sooner than those of the CBE laminates, indicating an improvement in damping due to the presence of 3D reinforced milled carbon fibers. This research shows that optimized utilization of milled carbon fibers as 3D reinforcement can withstand high stress in the thickness direction and higher energy absorption when subjected to impact and high strain-rate loading.

Dynamic behaviors of water-saturated and frozen sandstone subjected to freeze-thaw cycles

In high-altitude cold areas,freeze-thaw(F-T)cycles induced by day-night and seasonal temperature changes cause numerous rock mass slope engineering disasters.To investigate the dynamic properties of rock in the natural environment of a high-altitude cold area,standard specimens were drilled from the slope of the Jiama copper mine in Tibet,and dynamic compression tests were performed on watersaturated and frozen sandstone with different numbers of F-T cycles(0,10,20,30,and 40)by the split Hopkinson pressure bar(SHPB)system with a cryogenic control system.The influence of water-saturated and frozen conditions on the dynamic performance of sandstone was investigated.The following conclusions are drawn:(1)With increasing strain rate,the attenuation factor(la)of water-saturated sandstone and the intensifying factor(li)of frozen sandstone linearly increase.As the number of F-T cycles increases,the dependence factor(ld)of water-saturated sandstone linearly decreases,whereas the ld of frozen sandstone linearly increases.(2)The prediction equation of the dynamic compressive strength of water-saturated and frozen sandstone is obtained,which can be used to predict the dynamic compressive strength of sandstone after various F-T cycles based on the strain rate.(3)The mesoscopic mechanism of water-saturated and frozen sandstone’s dynamic compressive strength evolution is investigated.The water softening effect causes the dynamic compressive strength of water-saturated sandstone to decrease,whereas the strengthening effect of pore ice causes it to increase.(4)The decrease in the relative dynamic compressive strength of water-saturated sandstone and the increase in the relative dynamic compressive strength of frozen sandstone can be attributed to the increased porosity.

Damage evolution and strength attenuation characteristics of carbonaceous slate under low velocity dynamic impact

Rock is subjected to impact loading during tunnel and subsurface engineering.For understanding the damage evolution of rock under dynamic impact, mechanical research was performed on the carboniferous slate surrounding the Muzhailing tunnel under different influencing factors based on the Split Hopkinson Pressure Bar(SHPB)experimental system. The results show that:(1)carbonaceous slate exhibits a continuous failure process, which develops more rapidly in the presence of joints;simultaneously, a negative correlation was found between the joint density and the dynamic strength of rock;(2) under different impact velocities and wavelengths, the method of using incident energy to represent the dynamic damage threshold of carbonaceous slate under high in situ stress was proposed based on the kinetic energy theorem, and the damage threshold of carbonaceous slate was calculated to be 53 J;(3) impact times is the most critical core variable and negatively correlated with peak strength and positively correlated with strain rate, maximum strain, and cumulative damage. The carbonaceous slate is subjected to repeated load impacts, which is followed by accumulation of damage, continuous strength attenuation, and internal dominant fracture expansion. In particular,when the samples break, there is only one main rupture surface, which is the most significant difference from the single impact rupture form.

Ballistic tests on hot-rolled Ti-6Al-4V plates:Experiments and numerical approaches

Superior ballistic performance and the lightweight character of Ti alloys are considered as main reasons for their use in armour applications against a broad spectrum of ballistic threats,e.g.bullet,fragment or blast impact.Because dynamic loading caused by typical penetrators is characterized by high strain rates,only specific test methods allow a closer investigation of the respective material behaviour.In the present study,quasi-static and dynamic compression tests as well as ballistic tests were conducted on a twophase a+βalloy Ti-6Al-4V(in m%)manufactured by hot-rolling.Post-deformation heat treatments,influencing microstructure and mechanical properties were applied in order to compare three different microstructural configurations:as-rolled,mill-annealed and bimodal.While,on the one hand,ballistic tests were employed for the determination of the ballistic limit velocity v_(50),compression tests,on the other hand,delivered essential input parameters for the application of the Johnson-Cook constitutive model in a finite element simulation of the impact event.The comparison of experimental results to simulation results was supplemented by means of microstructural characterization of tested samples with the focus set on the prevalently observed deformation and damage mechanisms,as for example adiabatic shearing.

Strain-Rate Dependency of a Unidirectional Filament Wound Composite under Compression

This article presents the results of experimental studies concerning the dynamic deformation and failure of a unidirectional carbon fiber reinforced plastic(T700/LY113)under compression.The test samples were manufactured through the filament winding of flat plates.To establish the strain rate dependencies of the strength and elastic modulus of the material,dynamic tests were carried out using a drop tower,the Split Hopkinson Pressure Bar method,and standard static tests.The samples were loaded both along and perpendicular to the direction of the reinforcing fiber.The applicability of the obtained samples for static and dynamic tests was confirmed through finite elementmodeling and the high-speed imaging of the deformation and failure of samples during testing.As a result of the conducted experimental studies,static and dynamic stress-strain curves,time dependencies of deformation and the stress and strain rates of the samples during compression were obtained.Based on these results,the strain rate dependencies of the strength and elasticity modulus in the strain rate range of 0.001-6001/s are constructed.It is shown that the strain rate significantly affects the strength and deformation characteristics of the unidirectional carbon fiber composites under compression.An increase in the strain rate by 5 orders of magnitude increased the strength and elastic modulus along the fiber direction by 42%and 50%,respectively.Perpendicular loading resulted in a strength and elastic modulus increase by 58%and 50%,respectively.The average strength along the fibers at the largest studied strain rate was about 1000MPa.The obtained results can be used to design structural elements made of polymer composite materials operating under dynamic shock loads,as well as to build models of mechanical behavior and failure criteria of such materials,taking into account the strain rate effects.

Static and dynamic tensile failure characteristics of rock based on splitting test of circular ring

Static and dynamic splitting tests were conducted on ring marble specimens with different internal diameters to study the tensile strength and failure modes with the change of the ratio of internal radius to external radius （ρ） under different loading rates. The results show that the dynamic tensile strength of disc rock specimen is approximately five times its static tensile strength. The failure modes of ring specimens are related to the dimension of the internal hole and loading rate. Under static loading tests, when the ratio of internal radius to external radius of the rock ring is small enough （ρ〈0.3）, specimens mostly split along the diametral loading line. With the increase of the ratio, the secondary cracks are formed in the direction perpendicular to the loading line. Under dynamic loading tests, specimens usually break up into four pieces. When the ratio ρreaches 0.5, the secondary cracks are formed near the input bar. The tensile strength calculated by Hobbs’ formula is greater than the Brazilian splitting strength. The peak load and the radius ratio show a negative exponential relationship under static test. Using ring specimen to determine tensile strength of rock material is more like a test indicator rather than the material properties.