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.

Particle flow study on strength and meso-mechanism of Brazilian splitting test for jointed rock mass

A discrete element method （DEM） called particle flow code （PFC2D） was used to construct a model for Brazilian disc splitting test in the present study. Based on the experimental results of intact Brazilian disc of rock-like material, a set of micro-parameters in PFC2D that reflected the macro-mechanical behavior of rock-like materials were obtained. And then PFC2D was used to simulate Brazilian splitting test for jointed rock mass specimens and specimen containing a central straight notch. The effect of joint angle and notch angle on the tensile strength and failure mode of jointed rock specimens was detailed analyzed. In order to reveal the meso-mechanical mechanism of crack coalescence, displacement trend lines were applied to analyze the displacement evolution during the crack initiation and propagation. The investigated conclusions can be described as follows. （1） The tensile strength of jointed rock mass disc specimen is dependent to the joint angle. As the joint angle increases, the tensile strength of jointed rock specimen takes on a nonlinear variance. （2） The tensile strength of jointed rock mass disc specimen containing a central straight notch distributes as a function of both joint angle and notch angle. （3） Three major failure modes, i.e., pure tensile failure, shear failure and mixed tension and shear failure mode are observed in jointed rock mass disc specimens under Brazilian test. （4） The notch angle roles on crack initiation and and joint angle play important propagation characteristics of jointed rock mass disc specimen containing a central straight notch under Brazilian test.

Tensile strength of sea ice using splitting tests based on the digital image correlation method

The splitting test is a competitive alternative method to study the tensile strength of sea ice owing to its suitability for sampling.However,the approach was questioned to the neglect of local plastic deformation during the tests.In this study,splitting tests were performed on sea ice,with 32 samples subjected to the regular procedure and 8 samples subjected to the digital image correlation method.The salinity,density,and temperature were measured to determine the total porosity.With the advantage of the digital image correlation method,the full-field deformation of the ice samples could be determined.In the loading direction,the samples mainly deformed at the ice-platen contact area.In the direction vertical to the loading,deformation appears along the central line where the splitting crack occurs.Based on the distribution of the sample deformation,a modified solution was derived to calculate the tensile strength with the maximum load.Based on the modified solution,the tensile strength was further calculated together with the splitting test results.The results show that the tensile strength has a negative correlation with the total porosity,which agrees with previous studies based on uniaxial tension tests.

Wedge Splitting Test and Inverse Analysis on Fracture Behaviour of Fiber Reinforced and Regular High Performance Concretes

The fracture behaviour of three fiber reinforced and regular HPC （high performance concretes） is presented in this paper. Two mixes are based on optimization of HPC whereas the third mix was a commercial mix developed by CONTEC ApS （Denmark）. The wedge splitting test setup with 48 cubical specimens was used experimentally and the cracked non-linear hinge model based on the fictitious crack model was applied for the interpretation of the results. The stress-crack opening relationships were extracted by using inverse analysis algorithm for various multi-linear softening curves. This showed that the refinement of the softening curves reflects in improved accuracy of the WST （wedge splitting test） simulation in comparison with bi-linear softening curves with acceptable increase of computational time. Furthermore, the fracture mechanics parameters such as COD （crack opening displacement）, fracture energy and characteristic length were experimentally determined. Experiments were performed at 1, 3, 7 and 28 days. Fracture energy, Gf, was found to increase with age, while the characteristic length, Lch, was found to decrease.

Application of Wedge Splitting Test in Refractories

This paper mainly describes fracture mechanics and the application of the newly developed wedge splitting test in evaluating the thermal shock resistance of refractories. It is necessary to evaluate fracture properties owning to the heterogeneity of refractories.

Tensile strength and damage of open-cell ceramic foams under cylindrical splitting test

To widen the understanding of tensile failure of reticulated ceramic foams and expand the available mechanical method,a cylindrical splitting test is developed in the present study based on alumina open-cell foams of three different pore densities.The biaxial method is validated by characterization of mechanical parameters,and the in-situ fracture process is validated by a digital image correlation,followed by a formula correction for effective tensile strength with consideration of discrete crack paths.For experimental setup curved loading platens,compliant pad and intermediate quasi-static loading rate are proposed for guaranteeing tensile failure under a radial compressive load.Tensile strength,fracture energy,and brittleness increase with the foam pore density,and the fracture behavior is a balanced result of materials and foam structural support strength.An analytical model of splitting tensile strength with structural parameters is derived,which implies its dependence on cell size and critical stress intensity factor of strut materials.

Regulation of Pore Structure and Hightemperature Fracture Behavior of CACbonded Alumina-Spinel Castables Based on Hydration Design

The lamellar hydrates of CAC were designed with the introduction of nano CaCO_(3)or Mg-Al hydrotalcite(M-A-H),and the effects on the green strength,pore structures,and high-temperature fracture behavior of alumina-spinel castables were investigated.The results show that nano CaCO_(3)or M-A-H stimulates rapidly the hydration of CAC and the formation of lamellar C_(4)AcH_(11)or coexistence of C_(2)AH_(8)and C_(4)AcH_(11)at 25℃.The formation of lamellar hydrates can contribute to a more complicated pore structure,especially in the range of 400-2000 nm.Meanwhile,the incorporation of well-distributed CaO or MgO sources from nano CaCO_(3)or M-A-H also regulates the distribution of CA_(6)and spinel(pre-formed and in-situ).Consequently,the optimized microstructure and complicated pore structure can induce the deflection and bridging of cracks,thus facilitating the consumption of fracture energy and enhancing the resistance to thermal stress damage.

Complete splitting process of steel fiber reinforced concrete at intermediate strain rate

The complete splitting process of steel fiber reinforced concrete （SFRC） at intermediate strain rate was studied by experiment. The basic information of a self-developed SFRC dynamic test system matching with lnstron 1342 materials testing machine was given, and the experiment principle and the loading mode of cubic split specimen were introduced. During the experiment, 30 cubes of 150 mm×150 mm×150 mm and 36 cubes of 100 mm×100 mm×100 mm, designed and prepared according to C20 class SFRC with different volume fractions of steel fiber （0, 1%, 2%, 3%, 4%） were tested and analyzed. At the same time, the size effect of SFRC at intermediate strain rate was investigated. The experimental study indicates that SFRC size effect is not influenced by the loading speed or strain rate. When the steel fiber content increases from 0 to 4%, the splitting strength of SFRC increases from 100% to 261%, i.e. increasing by 161% compared with that of the common concrete. The loading rate increases from 1.33 kN/s to 80.00 kN/s, and the splitting tensile strength increases by 43.55%.

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%.

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.

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.

The Application of Dynamic Shock Mechanics Test in Engineering Blasting

With the continuous advancement of China’s infrastructure construction to the west,according to the geographic situation in the southwest region,such as mountainous areas and complex terrain,the road construction process is inevitably accompanied by earth and rock blasting.To improve the quality and safety of the project,this paper addresses the problems of land and rock blasting faced in the construction of mountain road projects,taking the research of rock dynamic mechanics test as the starting point,and using a combination of theoretical analysis and experimental research methods.The specific research content includes the following parts:dynamic impact compression test(SHPB),dynamic splitting tensile test,and stress-strain curve analysis of the test results,which provides the theoretical basis and numerical parameters for the numerical simulation of future engineering blasting.

Properties of Phenolic Resins——CarboresP Binders for Magnesite Carbon Refractories

An environmental friendly carbonaceous material- carboresP （one of the Carbores series materials） was investigated for the production of MgO-C refractories in laboratory scale and field tests. The MgO-C specimens were produced with different CarboresP contents. The bulk density （180℃ × 48h）, CCS, apparent porosity （1000℃ ×3h ） and hot modulus of rupture （1400℃ ×0. 5h ） were tested and contrasted. The appropriate amount of carboresP was 1.0%. The amount of metallic additions can be partially substituted （reduced to 1.5% ）. The microstructure of resin-carboresP binder is anisotropic structure with high oxidation resistance and good thermal-shock stability. The Stress/strain curve indicates that the characteristic length, （LCH） of MgO-C brick with resin/CarboresP bonding has been improved, which means the MgO-C bricks have good mechanical flexibility and stresses absorbability. Field tests were done in slag line of a 40t LF-VD refining steel ladle using Resin/CarboresP bonded ＂ MT-14A MgO-C bricks. The result shows that the MgO-C bricks by ＂soft bonding＂ have good physical properties and excellent workability during production of the bricks . In contrast with traditional MgO-C brick used for secondary refining furnaces, the spalling tendency of the bricks could be reduced significantly. The average lining life of the resin/ CarboresP bricks has increased by 18. 4% comparing with the pure resin-bonded types.

Fractographic and Fracture Mechanical Investigations of Refractories under Different Loading Conditions

Crack initiation and propagation have been investigated under tensile and shear loading in ceramically and carbon bonded refractories.A wedge splitting test procedure and a modified shear test have been applied.Test results have been used for material characterization especially with respect to brittleness.Furthermore a microscopic fractographic test procedure was developed and applied on fractured test specimens.In order to explain brittleness dependence on structure properties correlation of fractographic and fracture mechanical results has been evaluated.Frequently brittleness reduction is achieved by a lower amount of transgranular crack propagation associated with a strength decrease while maintaining specific fracture energy unchanged.Deviations from pure linear fracture mechanics increase with decreasing brittleness and contribute to specific fracture energy.Shear specimens may show two generations of cracks,a first one initiated by tensile loads （stable propagation） and a second one by shear loads （unstable propagation）.

Advanced Measures to Characterize Mechanical Properties of Refractories

The thermomechanical modelling method is becoming an important tool nowadays for the refractory researchers, suppliers and end-users. On one hand, applications focus on the post-mortem thermomechanical analysis to interpret the occurred fitiluw phenomena of refractories in service. On the other hand, a priori investigation is very helpful for the design of refractory lining con- cepts before putting them into effect; as a result it will minimize the probability of refractory lining premature .failure and save costs for the refractory suppliers as well as for the end-users. For both investigation routines, suitable material constitutive models and testing approa- ches are of relevance. Existing material constitutive mod- els often used for refractories are the fictitious crack model acting for tensile failure, the Mohr - Coulomb or Drucker- Prager model describing shear failure, and the Norton - Bailey model representing creep. To charac- terize tbe tensile and shear fitilure of refractories at room temperatare and elevated temperatures, a wedge splitting test and a modified shear test can be applied, respectively. The creep behavior and corresponding creep parameters of refractories can be determined with an appropriate creep testing device at elevated loads. The proper appli- cation of material constitutive models and testing approa-ches allows for improving the thermo-mechanical modelling and the optimizatian of the lining design.

Acoustic emissions evaluation of the dynamic splitting tensile properties of steel fiber reinforced concrete under freeze-thaw cycling

This study empirically investigated the influence of freeze-thaw cycling on the dynamic splitting tensile properties of steel fiber reinforced concrete(SFRC).Brazilian disc splitting tests were conducted using four loading rates(0.002,0.02,0.2,and 2 mm/s)on specimens with four steel fiber contents(0%,0.6%,1.2%,and 1.8%)subjected to 0 and 50 freeze-thaw cycles.The dynamic splitting tensile damage characteristics were evaluated using acoustic emission(AE)parameter analysis and Fourier transform spectral analysis.The results quantified using the freeze-thaw damage factor defined in this paper indicate that the degree of damage to SFRC caused by freeze-thaw cycling was aggravated with increasing loading rate but mitigated by increasing fiber content.The percentage of low-frequency AE signals produced by the SFRC specimens during loading decreased with increasing loading rate,whereas that of high-frequency AE signals increased.Freeze-thaw action had little effect on the crack types observed during the early and middle stages of the loading process;however,the primary crack type observed during the later stage of loading changed from shear to tensile after the SFRC specimens were subjected to freeze-thaw cycling.Notably,the results of this study indicate that the freeze-thaw damage to SFRC reduces AE signal activity at low frequencies.

Dynamic tensile properties and microstructural evolution of extruded EW75 magnesium alloy at high strain rates

The dynamic tensile properties and microstructural evolution of an extruded EW75 magnesium alloy deformed at ambient temperature and different high strain rates(from 1000 to 3000 s^(-1))along extrusion direction(ED)were investigated by Split Hopkinson Tension Bar(SHTB).The corresponding deformation mechanisms,texture evolution and microstructure changes were analyzed by optical microscope(OM),electron backscatter diffraction(EBSD)and transmission electron microscope(TEM).The results show that the extruded EW75 magnesium alloy along ED exhibits a conventional positive strain rate sensitivity that the dynamic flow stresses increase with in creasing strain rate.Texture measurements show that after dynamic tension,the initial weak texture of extruded EW75 magnesium alloy tansforms to a relatively strong<10-10>//ED texture with increasing strain rates.The microstructural analysis demonstrates that dislocation motion are main deformatin mode to accommodate dynamic tensile deformation at high strain rates.In addition,the interactions of dislocation-dislocation and dislocation-second phase lead to the in crease of flow stress and strain hardening with increasing strain rate.

Failure of rock under dynamic compressive loading

Split Hopkinson Pressure Bar(SHPB) test was simulated to investigate the distribution of the first principal stress and damage zone of specimen subjected to dynamic compressive load. Numerical models of plate-type specimen containing cracks with inclined angles of 0°,45° and 90° were also established to investigate the crack propagation and damage evolution under dynamic loading. The results show that the simulation results are in accordance with the failure patterns of specimens in experimental test. The interactions between stress wave and crack with different inclined angles are different; damage usually appears around the crack tips firstly; and then more damage zones develop away from the foregoing damage zone after a period of energy accumulation; eventually,the damage zones run through the specimen in the direction of applied loading and split the specimen into pieces.

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.

Critical crack tip opening displacement of different strength concrete

Critical crack tip opening displacement (CTODc) of concrete using experimental and analytical evaluation with seven different compressive strengths ranging from 30 up to 150 MPa was studied based on two types of fracture tests:three-point bending (TPB) and wedge splitting (WS).In the tests,the values of CTODc were experimentally recorded using a novel technique,in which fiber Bragg grating (FBG) sensors were used,and two traditional techniques,in which strain gauges and clip gauges were deployed.The values of CTODc of tested concrete were also predicted using two existing analytical formulae proposed by JENQ & SHAH and XU,respectively.It is found that the values of CTODc obtained by both experimental measurements and analytical formulae exhibit a negligible variation as the compressive strength of concrete increases,and the test geometry adopted has little impact on the value of CTODc.Regarding the experimental measurement of CTODc,the clip gauge method generally leads to a larger value of CTODc and shows a more significant scatter as compared with the other two methods,while the strain gauge method leads to a slightly lower CTODc as compared with the FBG sensor method.The analytical formula proposed by JENQ and SHAH is found to generally lead to an overestimation,while the analytical formula proposed by XU shows a good accuracy.