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.

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.

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.

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.

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.

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.

EXPERIMENTAL AND NUMERICAL STUDIES ON DYNAMIC COMPRESSIVE BEHAVIOR OF REACTIVE POWDER CONCRETES

Split Hopkinson pressure bar （SHPB） technique is used to determine the dynamic strength of reactive powder concretes （RPCs） with different steel-fiber contents. Two types of pulse shapers with different thicknesses are considered to reduce the high-frequency-oscillation effect and achieve a nearly constant strain rate over a certain deformation range. It is known that the compressive strength of concrete-like materials is hydrostatic-stress-dependent, and the apparent dynamic strength enhancement comes from both the effects of the hydrostatic stress and strain rate. In order to differentiate them, numerical method is used to calculate the contribution of the hydrostatic stress, and then the genuine strain-rate effect on dynamic compressive strength of RPCs is determined. In addition, the effect of steel-fibers on dynamic strength and failure mode of RPCs is discussed.

Dynamic behavior of frozen soil under uniaxial strain and stress conditions

The split Hopkinson pressure bar （SHPB） method is used to investigate the dynamic behavior of the artificial frozen soil under the nearly uniaxial strain and uniaxial stress conditions. The tests are conducted at the temperatures of -3 ℃, -8 ℃, -13℃, -17℃, -23℃, and -28℃ and with the strain rates from 900 s^-1 to 1500 s^-1. The nearly uniaxial stress-strain curves exhibit an elastic-plastic behavior, whereas the uniaxial stress-strain curves show a brittle behavior. The compressive strength of the frozen soil exhibits the positive strain rate and negative temperature sensitivity, and the final strain of the frozen soil shows the positive strain under the nearly uniaxial strain is greater rate sensitivity. The strength of the frozen soil than that under the uniaxial stress. After the negative confinement tests, the specimens are compressed, and the visible cracks are not observed. However, the specimens are catastrophically damaged after the uniaxial SHPB tests. A phenomenological model with the thermal sensitivity is established to describe the dynamic behavior of the confined frozen soil.

Dolomite fracture modeling using the Johnson-Holmquist concrete material model:Parameter determination and validation

In this paper,the Johnson-Holmquist concrete(JHC)constitutive model is adopted for modeling and simulating the fracture of dolomite.A detailed step-by-step procedure for determining all required parameters,based on a series of experiments under quasi-static and dynamic regimes,is proposed.Strain rate coefficients,failure surfaces,equations of state and damage/failure constants are acquired based on the experimental data and finite element analyses.The JHC model with the obtained parameters for dolomite is subsequently validated using quasi-static uniaxial and triaxial compression tests as well as dynamic split Hopkinson pressure bar(SHPB)tests.The influence of mesh size is also analyzed.It shows that the simulated fracture behavior and waveform data are in good agreement with the experimental data for all tests under both quasi-static and dynamic loading conditions.Future studies will implement the validated JHC model in small-and large-scale blasting simulations.

Dynamic mechanical behaviors of Fangshan marble

Dynamic strength parameters are extensively used in mining engineering and rock mechanics.However,there are no widely accepted dynamic failure models for rocks.In this study,the dynamic punching shear strength,uniaxial compressive strength(UCS) and tensile strength of fine-grained Fangshan marble(FM)are first measured by using a split Hopkinson pressure bar(SHPB) system.The pulse-shaping technique is then implemented to maintain the dynamic force balance in SHPB tests.Experimental results show that the dynamic punching shear strength,UCS and tensile strength increase with the loading rate.A recently developed dynamic Mohr-Coulomb theory is then used to interpret the testing data.In this model,the angle of internal friction φ is assumed to be independent of loading rate and is obtained using the static strength values.According to the dynamic Mohr-Coulomb theory,the dynamic UCS and the dynamic tensile strength are predicted from the dynamic punching shear strength.Furthermore,based on this dynamic theory,the dynamic UCS is predicted from the dynamic tensile strength.The consistency between the predicted and measured dynamic strengths demonstrates that the dynamic Mohr-Coulomb theory is applicable to FM.

Dynamic compressive property and failure behavior of extruded Mg-Gd-Y alloy under high temperatures and high strain rates

For the purpose of investigating the dynamic deformational behavior and failure mechanisms of magnesium under high strain rates,the Split Hopkinson Pressure Bar(SHPB)was used for investigating dynamic mechanical properties of extruded Mg-Gd-Y Magnesium alloy at ambient temperature(300 K),200℃(473 K)and 300℃(573 K)temperature.The samples after compression were analyzed by scanning electron microscope(SEM)and metallographic microscope.Dynamic mechanical properties,crack performance and plastic deformation mechanism of extruded Mg-Gd-Y Magnesium alloy along the extrusion direction(ED)were discussed.The results show that,extruded Mg-Gd-Y Magnesium alloy has the largest dynamic compressive strength which is 535 MPa at ambient temperature(300 K)and strain rate of 2826 s^(−1).When temperature increases,dynamic compressive strength decreases,while ductility increases.The dynamic compression fracture mechanism of extruded Mg-Gd-Y Magnesium alloy is multi-crack propagation and intergranular quasi-cleavage fracture at both ambient temperature and high temperature.The dynamic compressive deformation mechanism of extruded Mg-Gd-Y Magnesium alloy is a combination of twinning,slipping and dynamic recrystallization at both ambient temperature and high temperature.

Dynamic failure of dry and fully saturated limestone samples based on incubation time concept

This paper outlines the results of experimental study of the dynamic rock failure based on the comparison of dry and saturated limestone samples obtained during the dynamic compression and split tests. The tests were performed using the Kolsky method and its modifications for dynamic splitting. The mechanical data(e.g. strength, time and energy characteristics) of this material at high strain rates are obtained. It is shown that these characteristics are sensitive to the strain rate. A unified interpretation of these rate effects, based on the structuraletemporal approach, is hereby presented. It is demonstrated that the temporal dependence of the dynamic compressive and split tensile strengths of dry and saturated limestone samples can be predicted by the incubation time criterion. Previously discovered possibilities to optimize(minimize) the energy input for the failure process is discussed in connection with industrial rock failure processes. It is shown that the optimal energy input value associated with critical load, which is required to initialize failure in the rock media, strongly depends on the incubation time and the impact duration. The optimal load shapes, which minimize the momentum for a single failure impact, are demonstrated. Through this investigation, a possible approach to reduce the specific energy required for rock cutting by means of high-frequency vibrations is also discussed.