Evolution of cracks in the shear bands of granite residual soil

The evolution of shear bands and cracks plays an important role in landslides.However,there is no systematic method for classification of the cracks,which can be used to analyze the evolution of cracks in shear bands.In this study,X-ray computed tomography(CT)is used to observe the behavior of granite residual soil during a triaxial shear process.Based on the digital volume correlation(DVC)method,a crack classification method is established according to the connectivity characteristics of cracks before and after loading.Cracks are then divided into six classes:obsolete,brand-new,isolated,split,combined,and compound.With evolution of the shear bands,a large number of brand-new cracks accelerate the damages of materials at the mesoscale,resulting in a sharp decrease in strength.The volume of brandnew cracks increases rapidly with increasing axial strain,and their volume is greater than 50%when the strain reaches 12%,while the volume of compound cracks decreases from 54%to 21%.As cracks are the weakest areas in a material,brand-new cracks accelerate the development of shear bands.Finally,the coupling effect of shear bands and cracks destroys the soil strength.

Failure transition of shear-to-dilation band of rock salt under triaxial stresses

Great potential of underground gas/energy storage in salt caverns seems to be a promising solution to support renewable energy.In the underground storage method,the operating cycle unfortunately may reach up to daily or even hourly,which generates complicated pressures on the salt cavern.Furthermore,the mechanical behavior of rock salt may change and present distinct failure characteristics under different stress states,which affects the performance of salt cavern during the time period of full service.To reproduce a similar loading condition on the cavern surrounding rock mass,the cyclic triaxial loading/unloading tests are performed on the rock salt to explore the mechanical transition behavior and failure characteristics under different confinement.Experimental results show that the rock salt samples pre-sent a diffused shear failure band with significant bulges at certain locations in low confining pressure conditions(e.g.5 MPa,10 MPa and 15 MPa),which is closely related to crystal misorientation and grain boundary sliding.Under the elevated confinement(e.g.20 MPa,30 MPa and 40 MPa),the dilation band dominates the failure mechanism,where the large-size halite crystals are crushed to be smaller size and new pores are developing.The failure transition mechanism revealed in the paper provides additional insight into the mechanical performance of salt caverns influenced by complicated stress states.

Shear band evolution and acoustic emission characteristics of sandstone containing non-persistent flaws

Direct shear tests were conducted on sandstone specimens under different constant normal stresses to study the coalescence of cracks between non-persistent flaws and the shear sliding characteristics of the shear-formed fault.Digital image correlation and acoustic emission(AE)techniques were used to monitor the evolution of shear bands at the rock bridge area and microcracking behaviors.The experimental results revealed that the shear stresses corresponding to the peak and sub-peak in the stressdisplacement curve are significantly affected by the normal stress.Strain localization bands emerged at both the tip of joints and the rock bridge,and their extension and interaction near the peak stress caused a surge in the AE hit rate and a significant decrease in the AE b value.Short and curvilinear strain bands were detected at low normal stress,while high normal stress generally led to more microcracking events and longer coplanar cracks at the rock bridge area.Furthermore,an increase in normal stress resulted in a higher AE count rate and more energetic AE events during friction sliding along the shearformed fault.It was observed that the elastic energy released during the crack coalescence at the prepeak stage was much greater than that released during friction sliding at the post-peak stage.More than 75%of AE events were located in the low-frequency band(0e100 kHz),and this proportion continued to rise with increasing normal stress.Moreover,more AE events of low AF value and high RA value were observed in specimens subjected to high normal stress,indicating that greater normal stress led to more microcracks of shear nature.

Mesoscopic measurement of damage and shear bands of granite residual soil using Micro-CT and digital volume correlation

The mesomechanics of geotechnical materials are closely related to the macromechanical properties,especially the mesoscale evolution of shear bands,which is helpful for understanding the failure mechanism of geotechnical materials.However,there is lack of effective quantitative analysis method for the complex evolution mechanism of threedimensional shear bands.In this work,we used X-ray computed tomography(CT)to reconstruct volume images and used the digital volume correlation(DVC)method to calculate the three-dimensional strain fields of granite residual soil samples at different loading stages.The trend of the failure surface of the shear bands was obtained by the planar fitting method,and the connectivity index was constructed according to the projection characteristics of the shear bands on the failure trend surface.The results support the following findings:the connectivity index of the shear band increases rapidly and then slowly with increasing axial strain,which is characterized by a near'S'curve.As the stress reaches the peak value,the connectivity index of the shear bands almost exceeds 0.7.The contribution of the new shear band volume to the connectivity of the shear bands becomes increasingly small with increasing axial loading.Affected by quartz grains and stress at the initial stage,the dip angle gradually and finally approaches the included angle of the maximum shear stress from the discrete state with increasing axial loading.The tendency and dip angle of the resulting shear bands are dynamic,and the tendency slightly deflects with increasing loading.

Deformation, Phase Transformation and Recrystallization in the Shear Bands Induced by High-Strain Rate Loading in Titanium and Its Alloys

α-titanium and its alloys with a dual-phase structure （α＋β） were deformed dynamically under strain rate of about 10^4 s^-1. The formation and microstructural evolution of the localized shear bands were characterized by scanning electron microscopy （SEM） and transmission electron microscopy （TEM）. The results reveal that both the strain and strain rate should be considered simultaneously as the mechanical conditions for shear band formation, and twinning is an important mode of deformation. Both experimental and calculation show that the materials within the bands underwent a superhigh strain rate （9×10^5 S^-1） deformation, which is two magnitudes of that of average strain rate required for shear band formation; the dislocations in the bands can be constricted and developed into cell structures; the phase transformation from α to α2 within the bands was observed, and the transformation products （α2） had a certain crystallographic orientation relationship with their parent; the equiaxed grains with an average size of 10 μm in diameter observed within the bands are proposed to be the results of recrystallization.

Dynamic Mechanical Behavior and Adiabatic Shear Bands of Ultrafine Grained Pure Zirconium

Dynamic compression tests were carried out to investigate dynamic mechanical behavior and adiabatic shear bands in ultrafine grained(UFG)pure zirconium prepared by equal channel angular pressing(ECAP)and rotary swaying.The cylindrical specimens were deformed dynamically on the split Hopkinson pressure bar(SHPB)at different strain rates of 800 to 4000s^-1 at room temperature.The temperature distribution of the shear bands was estimated on the basis of temperature rise of uniform plastic deformation stage and thermal diffusion effect.The results show that the true stress-true strain curves of UFG pure zirconium are concave upward trend of strain in range of 0.02-0.16 due to the effects of strain hardening,strain rate hardening and thermal softening.The formation of the adiabatic shear bands is the main reason of UFG pure zirconium failure.A large number of micro-voids are observed in the adiabatic shear bands,and the macroscopic cracks develop from the micro-voids coalescence.The fracture surface of UFG pure zirconium exhibits quasi cleavage fracture with the characteristic features of shear dimples and river pattern.The highest temperature within the shear bands of UFG pure zirconium is about 592 K.

Adiabatic Shear Bands in 30CrNi_3MoV Structural Steel Induced during High Speed Cutting

The width and spacing of adiabatic shear bands (ASBs) in the serrated chips generated during high speed orthogonal cutting of 30CrNi3MoV structurai steel were measured by opticai microscopy (OM), the temperature rise in the shear band was estimated. The microstructures of the ASBs were also characterized by SEM and TEM. The results show that the width and spacing of ASBs decrease with the increase of the cutting speed. The further observations show that the microstructure between the matrix and the center of the ASB gradually changes, and that the martensitic phase transformation, carbide precipitation and recrystallization may occur in the ASB.

EXACT SOLUTION FOR ORTHOTROPIC MATERIALS WEAKENED BY DOUBLY PERIODIC CRACKS OF UNEQUAL SIZE UNDER ANTIPLANE SHEAR

Orthotropic materials weakened by a doubly periodic array of cracks under far-field antiplane shear are investigated, where the fundamental cell contains four cracks of unequal size. By applying the mapping technique, the elliptical function theory and the theory of analytical function boundary value problems, a closed form solution of the whole-field stress is obtained. The exact formulae for the stress intensity factor at the crack tip and the effective antiplane shear modulus of the cracked orthotropic material are derived. A comparison with the finite element method shows the efficiency and accuracy of the present method. Several illustrative examples are provided, and an interesting phenomenon is observed, that is, the stress intensity factor and the dimensionless effective modulus are independent of the material property for a doubly periodic cracked isotropic material, but depend strongly on the material property for the doubly periodic cracked orthotropic material. Such a phenomenon for antiplane problems is similar to that for in-plane problems. The present solution can provide benchmark results for other numerical and approximate methods.

The primary influence of shear band evolution on the slope bearing capacity

Slope bearing capacity is one of the most important characteristics in slope engineering and is strongly influenced by weak planes,loading conditions,and slope geometry.By presenting the evolution of slip surfaces,this paper explored how the slope bearing capacity is affected by widely observed influencing factors.The initiation and propagation of slip surfaces are presented in laboratory model tests of slope using the transparent soil technique.Shear band evolution under various weak planes,loading conditions,and slope geometries were experimentally presented,and slope bearing capacities were analyzed with the process of shear band evolution.This paper verified that slip surface morphologies have a strong relation with the slope bearing capacity.The same slip surface morphology can have different evolutionary processes.In this case,it is the shear band evolution that determines the slope bearing capacity,not the morphology of the slip surface.The influencing factors such as pre-existing weak planes,loading conditions,and slope geometry strongly affect the slope bearing capacity as these factors govern the process of shear band evolution inside the slope.

Antiplane shear crack in a prestressed elastic medium based on the couple stress theory

A prestressed elastic medium containing a mode-Ⅲcrack is studied by means of the couple stress theory(CST).Based on the CST under initial stresses,a governing differential equation along with a mixed boundary value problem is established.The singularities of the couple stress and force stress near the crack tips are analyzed through the asymptotic crack-tip fields resulting from the characteristic expansion method.To determine their intensity,a hypersingular integral equation is derived and numerically solved with the help of the Chebyshev polynomial.The obtained results show a strong size-dependence of the out-of-plane displacement on the crack and the couple stress intensity factor(CSIF)and the force stress intensity factor(FSIF)around the crack tips.The symmetric part of the shear stress has no singularity,and the skew-symmetric part related to the couple stress exhibits an r^(-3/2)singularity,in which r is the distance from the crack tip.The initial stresses also affect the crack tearing displacement and the CSIF and FSIF.

Shear Bond Strength of Different Types of Cement Used for Bonding Band and Loop Space Maintainer

Purpose: The present study aimed to evaluate the effects of thermal aging on the shear bond strength of three different types of cement used to retain band and loop space maintainers cemented on extracted human permanent molar teeth. Methods: A total of 66 newly extracted permanent molars were used in this study. Eighteen teeth were used as a control and did not undergo thermal aging (six per group). All sample teeth were randomly divided into three groups: KetacCem, RelyX Luting Plus, and RelyX Unicem 2. After bonding procedures, all experimental groups undergo thermal aging. The shear bond strength of all samples was conducted using the Ultratester machine. Findings were statistically analyzed using the ANOVA and Turkey’s post hoc tests. Results: Among the examined groups, Ketac Cem presented with the highest recorded shear bond (11.4 MPa), while RelyX Luting Plus showed the lowest (3.2 MPa). The control groups recorded the highest shear bond strength compared to all examined groups;Ketac Cem showed the highest shear bond strength (12.8 Mpa), and RelyX Luting Plus had the least recorded reading (5.4 Mpa). Conclusion: Within the limitation of the present study, there was a statistically significant difference between the examined groups;Ketac Cem showed a higher shear bond cement than RelyX luting Plus and RelyX Unicem.

Occurrence of Dynamic Shear Bands in AISI 4340 Steel under Impact Loads

In this study, occurrence of adiabatic shear bands in AISI 4340 steel under high velocity impact loads is investigated using finite element analysis and experimental tests. The cylindrical steel specimen subjected to impact load was divided into different sections separated by nodes using finite element method in ABAQUS environment with boundary conditions specified. The material properties were assumed to be lower at the section where the adiabatic shear bands are expected to initialize. The finite element model was used to determine the maximum flow stress, the strain hardening, the thermal softening, and the critical strain for the formation of adiabatic shear bands. Experimental results show that deformed bands were formed at low strain rates and there was a minimum strain rate required for formation of transformed band in the alloy. The experimental results also show that cracks were initiated and propagated along transformed bands leading to fragmentation under the impact loading. The susceptibility of the adiabatic shear bands to cracking was markedly influenced by strain-rates. The simulation results obtained were compared with experimental results obtained for the AISI 4340 steel under high strain-rate loading in compression using split impact Hopkinson bars. A good agreement between the experimental and simulation results was obtained.

Shear bands of as-cast and semi-solid Ti_(48)Zr_(27)Cu_(6)Nb_(5)Be_(14)bulk metallic glass matrix composites

The as-cast Ti_(48)Zr_(27)Cu_(6)Nb_(5)Be_(14)bulk metallic glass matrix composites(BMGMCs)were fabricated using a copper mold suction casting method.Then,the semi-solid BMGMC samples were obtained following an isothermal treatment(heating at 900°C for 10 min,then cooling with water).The microstructure and compression property were investigated by scanning electronic microscopy(SEM)and universal mechanical tester.As a result of the isothermal treatment,the crystal shapes change from fine,granular,and dendritic to spherical or vermicular,and the average crystal size of the as-cast and semi-solid samples is 2.2μm and 18.1μm,respectively.The plasticity increases from 5.31%in the as-cast to 10.23%in the semi-solid samples,with an increase of 92.66%.The shear bands from different areas of the side surfaces of as-cast and semisolid compression fracture samples were observed.The characteristic changes of multiplicity,bend,branch and intersection of shear bands in different areas indicate that the deformation of as-cast and semi-solid samples is non-uniform during compression.It is found that poor plasticity of the as-cast samples or good plasticity of the semi-solid samples are reflected by characteristics of the shear bands.The semi-solid isothermal treatment improves the plasticity by forming large crystals which can block the expansion of shear bands and promote the multiplicity of shear bands.

Mechanical behaviors of backfill-rock composites: Physical shear test and back-analysis

The shear behavior of backfill-rock composites is crucial for mine safety and the management of surface subsidence.For exposing the shear failure mechanism of backfill-rock composites,we conducted shear tests on backfill-rock composites under three constant normal loads,compared with the unfilled rock.To investigate the macro-and meso-failure characteristics of the samples in the shear tests,the cracking behavior of samples was recorded by a high-speed camera and acoustic emission monitoring.In parallel with the experimental test,the numerical models of backfill-rock composites and unfilled rock were established using the discrete element method to analyze the continuous-discontinuous shearing process.Based on the damage mechanics and statistics,a novel shear constitutive model was proposed to describe mechanical behavior.The results show that backfill-rock composites had a special bimodal phenomenon of shearing load-deformation curve,i.e.the first shearing peak corresponded to rock break and the second shearing peak induced by the broken of aeolian sand-cement/fly ash paste backfill.Moreover,the shearing characteristic curves of the backfill-rock composites could be roughly divided into four stages,i.e.the shear failure of the specimens experienced:stage I:stress concentration;stage II:crack propagation;stage III:crack coalescence;stage IV:shearing friction.The numerical simulation shows that the existence of aeolian sand-cement/fly ash paste backfill inevitably altered the coalescence type and failure mode of the specimens and had a strengthening effect on the shear strength of backfillrock composites.Based on damage mechanics and statistics,a shear constitutive model was proposed to describe the shear fracture characteristics of specimens,especially the bimodal phenomenon.Finally,the micro-and meso-mechanisms of shear failure were discussed by combining the micro-test and numerical results.The research can advance the better understanding of the shear behavior of backfill-rock composites and contribute to the safety of mining engineering.

An improved strain-softening constitutive model of granite considering the effect of crack deformation

This paper presents an improved strain-softening constitutive model considering the effect of crack deformation based on the triaxial cyclic loading and unloading test results.The improved model assumes that total strain is a combination of plastic,elastic,and crack strains.The constitutive relationship between the crack strain and the stress was further derived.The evolutions of mechanical parameters,i.e.strength parameters,dilation angle,unloading elastic modulus,and deformation parameters of crack,with the plastic strain and confining pressure were studied.With the increase in plastic strain,the cohesion,friction angle,dilation angle,and crack Poisson's ratio initially increase and subsequently decrease,and the unloading elastic modulus and the crack elastic modulus nonlinearly decrease.The increasing confining pressure enhances the strength and unloading elastic modulus,and decreases the dilation angle and Poisson's ratio of the crack.The theoretical triaxial compressive stress-strain curves were compared with the experimental results,and they present a good agreement with each other.The improved constitutive model can well reflect the nonlinear mechanical behavior of granite.

Prediction of shear bands in sand based on granular flow model and two-phase equilibrium

In contrast to the traditional interpretation of shear bands in sand as a bifurcation problem in continuum mechanics,shear bands in sand are considered as high-strain phase(plastic phase) of sand and the materials outside the bands are still in low-strain phase(elastic phase),namely,the two phases of sand can coexist under certain condition.As a one-dimensional example,the results show that,for materials with strain-softening behavior,the two-phase solution is a stable branch of solutions,but the method to find two-phase solutions is very different from the one for bifurcation analysis.The theory of multi-phase equilibrium and the slow plastic flow model are applied to predict the formation and patterns of shear bands in sand specimens,discontinuity of deformation gradient and stress across interfaces between shear bands and other regions is considered,the continuity of displacements and traction across interfaces is imposed,and the Maxwell relation is satisfied.The governing equations are deduced.The critical stress for the formation of a shear band,both the stresses and strains inside the band and outside the band,and the inclination angle of the band can all be predicted.The predicted results are consistent with experimental measurements.

Monitoring shear deformation of sliding zone via fiber Bragg grating and particle image velocimetry

Monitoring shear deformation of sliding zones is of great significance for understanding the landslide evolution mechanism,in which fiber optic strain sensing has shown great potential.However,the cor-relation between strain measurements of quasi-distributed fiber Bragg grating(FBG)sensing arrays and shear displacements of surrounding soil remains elusive.In this study,a direct shear model test was conducted to simulate the shear deformation of sliding zones,in which the soil internal deformation was captured using FBG strain sensors and the soil surface deformation was measured by particle image velocimetry(PIV).The test results show that there were two main slip surfaces and two secondary ones,developing a spindle-shaped shear band in the soil.The formation of the shear band was successfully captured by FBG sensors.A sinusoidal model was proposed to describe the fiber optic cable deformation behavior.On this basis,the shear displacements and shear band widths were calculated by using strain measurements.This work provides important insight into the deduction of soil shear deformation using soil-embedded FBG strain sensors.

Development of the Shear Bandsin Saturated Soil

This paper describes the development of shear bands in saturated soil under simple shear using a matching technique at the moving boundary of a shear band, and it is shown that the development of shear bands is affected by the coupling strain rate and pore pressure of material.Some numerical solutions have been presented.

HYPERSINGULAR INTEGRAL EQUATIONS FOR PERIODIC ARRAYS OF PLANAR CRACKS IN A PERIODICALLY-LAYERED ANISOTROPIC ELASTIC SPACE UNDER ANTIPLANE SHEAR STRESS

Hypersingular integral equations are derived for the problem of determining the antiplane shear stress around periodic arrays of planar cracks in a periodically-layered anisotropic elastic space. The unknown functions are directly related to the jump in the displacements across opposite crack faces. Once the integral equations are solved, crack parameters of interest, such as the clack tip stress intensity factors, may be readily computed.For some specific examples of the problem, the integral equations are solved numerically by using a collocation technique, in order to compute the relevant stress intensity factors.

Microstructural Characterization of the Shear Bands in Fe-Cr-Ni Single Crystal by EBSD

An investigation has been made into the microstructural characterization of the shear bands generated under high-strain rate （≈10^4 s^-1） deformation in Fe-15%Cr-15%Ni single crystal by EBSD-SEM （electron backscatter diffraction-scanning electron microscopy）, TEM （transmission electron in microscopy） and HREM （high- resolution electron microscopy）. The results reveal that the propagation of the shear band exhibits an asymmetrical behavior arising from inhomogenous distribution in plasticity in the bands because of different resistance to the collapse in different crystallographic directions; The γ-ε-α′phase transformations may take place inside and outside the bands, and these martensitic phases currently nucleate at intersections either between the twins and deformation bands or between the twins and ε-sheet. Investigation by EBSD shows that recrystallization can occur in the bands with a grain size of an average of 0.2μm in diameter. These nano-grains are proposed to attribute to the results of either dynamic or static recrystallization, which can be described by the rotational recrystallization mechanism. Calculation and analysis indicate that the strain rate inside the shear band can reach 2.50×10^6 s^-1, which is higher, by two or three orders of magnitude, than that exerted dynamically on the specimen tested.