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.

Combined effects of temperature and axial pressure on dynamic mechanical properties of granite

In order to get the dynamic mechanical properties of deep rock mass suffered both high temperature and high pressure,impact loading experiments on granite subjected to temperature and axial pressure were carried out. Furthermore, the internalstructure characteristics of granite under different temperatures were observed by scanning electron microscopy (SEM). The results show that the longitudinal wave velocity assumes a downward trend which shows a rapid drop before falling slowly as the temperature increases. The uniaxial compressive strength of the specimen decreases significantly at temperatures of 25?100 °C compared to that at temperatures of 100?300 °C. The peak strain rises rapidly before the dividing point of 100 °C, but increases slowly after the dividing point. The internal structure of the rock changes substantially as the temperature increases, such as the extension and transfixion of primary and newborn cracks. In addition, the thermal damage under axial pressure is greater than that described by the longitudinal wave velocity and the phenomenon shows obviously when the temperature increases.

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.

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.

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。

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.

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.

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.

Evaluation of dynamic performance and ballistic behavior of Ti-5Al-5Mo-5V-3Cr-1Zr alloy

Terminal ballistic tests using 7.62 mm armor-piercing incendiary （API） projectiles were performed to evaluate the resistance to penetration of Ti-5Al-5Mo-5V-3Cr-IZr （Ti-55531） alloy. The dynamic properties were determined by a split Hopkinson pressure bar （SHPB） test system. Ti-55531 plates were subjected to two kinds of heat treatments, leading to the formation of high-strength and high-toughness plates. The results of SHPB test exhibit that the maximum impact absorbed energy of the high-strength plate at a strain rate of 2200 s^-1 is 270 MJ/m^3; however, the maximum value for the high-toughness plate at a strain rate of 4900 s^-1 is 710 MJ/m^3. The ballistic limit velocities for the high-strength and high-toughness plates with dimensions of 300 mm×300 mm×8 mm are 330 and 390 m/s, respectively. Excellent dynamic properties of Ti-55531 alloy correspond to good resistance to penetration. The microstructure evolution related to various impact velocities are observed to investigate the failure mechanism.

Experimental and numerical study of failure behavior and mechanism of coal under dynamic compressive loads

A comprehensive understanding of the failure behavior and mechanism of coal is a prerequisite for dealing with dynamic problems in mining space.In this study,the failure behavior and mechanism of coal under uniaxial dynamic compressive loads were experimentally and numerically investigated.The experiments were conducted using a split Hopkinson pressure bar(SHPB)system.The results indicated that the typical failure of coal is lateral and axial at lower loading rates and totally smashed at higher loading rates.The further fractography analysis of lateral and axial fracture fragments indicated that the coal failure under dynamic compressive load is caused by tensile brittle fracture.In addition,the typical failure modes of coal under dynamic load were numerically reproduced.The numerical results indicated that the axial fracture is caused directly by the incident compressive stress wave and the lateral fracture is caused by the tensile stress wave reflected from the interface between coal specimen and transmitted bar.Potential application was further conducted to interpret dynamic problems in underground coal mine and it manifested that the lateral and axial fractures of coal constitute the parallel cracks in the coal mass under roof fall and blasting in mining space.

Dynamic mechanical properties and instability behavior of layered backfill under intermediate strain rates

To obtain dynamic mechanical properties and failure rule of layered backfill under strain rates from10to80s-1,impactloading test on layered backfill specimens(LBS)was conducted by using split Hopkinson pressure bar system.The results indicatethat positive correlation can be found between dynamic compressive strength and strain rate,as well as between strength increasefactor and strain rate.Dynamic compressive strength of LBS gets higher as the arithmetic average cement-sand ratio increases.Compared with static compressive strength,dynamic compressive strength of LBS is enhanced by11%to163%.In addition,theenergy dissipating rate of LBS lies between that of corresponding single specimens,and it decreases as the average cement contentincreases.Deformation of LBS shows obvious discontinuity,deformation degree of lower strength part of LBS is generally higherthan that of higher strength part.A revised brittle fracture criterion based on the Stenerding-Lehnigk criterion is applied to analyzingthe fracture status of LBS,and the average relevant errors of the3groups between the test results and calculation results are4.80%,3.89%and4.66%,respectively.

Effects of thermal treatment on physical and mechanical characteristics of coal rock

To study the physical and mechanical properties of coal rock after treatment at different temperatures under impact loading, dynamic compression experiments were conducted by using a split Hopkinson pressure bar(SHPB). The stress–strain curves of specimens under impact loading were obtained, and then four indexes affected by temperature were analyzed in the experiment: the longitudinal wave velocity, elastic modulus, peak stress and peak strain. Among these indexes, the elastic modulus was utilized to express the specimens' damage characteristics. The results show that the stress–strain curves under impact loading lack the stage of micro-fissure closure and the slope of the elastic deformation stage is higher than that under static loading. Due to the dynamic loading effect, the peak stress increases while peak strain decreases. The dynamic mechanical properties of coal rock show obvious temperature effects. The longitudinal wave velocity, elastic modulus and peak stress all decrease to different extents with increasing temperature, while the peak strain increases continuously. During the whole heating process, the thermal damage value continues to increase linearly, which indicates that the internal structure of coal rock is gradually damaged by high temperature.

Damage constitutive model of different age concretes under impact load

In order to investigate the mechanical properties and stress-strain curves of concrete at different ages under impact load,the impact compression tests of concrete at age of 1, 3, 7, 14 and 28 d were conducted with a large diameter split Hopkinson pressure bar, respectively. Based on statistical damage theory and Weibull distribution, combining the analysis of the change laws of stressstrain curves and viscosity coefficient of concrete with age, a damage constitutive model that can reflect the variation in dynamic mechanical properties with age was proposed. The stress-strain curves calculated from the proposed model are in good agreement with those from experimental data directly.

Mechanical properties and failure behavior of rock with different flaw inclinations under coupled static and dynamic loads

The deep fissured rock mass is affected by coupled effects of initial ground stress and external dynamic disturbance.In order to study the effect of internal flaw on pre-stressed rock mechanical responses and failure behavior under impact loading,intact granite specimens and specimens with different flaw inclinations are tested by a modified split Hopkinson pressure bar(SHPB)and digital image correlation(DIC)method.The results show that peak strain and dynamic strength of intact specimens and specimens with different flaw angles(α)decrease with the increase of axial static pressure.The 90°flaw has weak reduction effect on peak strain,dynamic strength and combined strength,while 45°and 0°flaws have remarkable reduction effect.Specimens with 90°flaw are suffered combined shear and tensile failure under middle and low axial static pre-stresses,and suffered shear failure under high axial static pre-stresses.Specimens with 45°and 0°flaws are suffered oblique shear failure caused by pre-existing flaw under different axial static pre-stresses.Besides,based on digital image correlation method,it is found that micro-cracks before formation of macro fractures(include shear and tensile fractures)belong to tensile cracks.Tensile and shear strain localizations at pre-existing flaw tip for specimen with 45°and 0°flaws are produced much earlier than that at other positions.