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.

A method for extracting the preseismic gravity anomalies over the Tibetan Plateau based on the maximum shear strain using GRACE data

The occurrence of earthquakes is closely related to the crustal geotectonic movement and the migration of mass,which consequently cause changes in gravity.The Gravity Recovery And Climate Experiment(GRACE)satellite data can be used to detect gravity changes associated with large earthquakes.However,previous GRACE satellite-based seismic gravity-change studies have focused more on coseismic gravity changes than on preseismic gravity changes.Moreover,the noise of the north–south stripe in GRACE data is difficult to eliminate,thereby resulting in the loss of some gravity information related to tectonic activities.To explore the preseismic gravity anomalies in a more refined way,we first propose a method of characterizing gravity variation based on the maximum shear strain of gravity,inspired by the concept of crustal strain.The offset index method is then adopted to describe the gravity anomalies,and the spatial and temporal characteristics of gravity anomalies before earthquakes are analyzed at the scales of the fault zone and plate,respectively.In this work,experiments are carried out on the Tibetan Plateau and its surrounding areas,and the following findings are obtained:First,from the observation scale of the fault zone,we detect the occurrence of large-area gravity anomalies near the epicenter,oftentimes about half a year before an earthquake,and these anomalies were distributed along the fault zone.Second,from the observation scale of the plate,we find that when an earthquake occurred on the Tibetan Plateau,a large number of gravity anomalies also occurred at the boundary of the Tibetan Plateau and the Indian Plate.Moreover,the aforementioned experiments confirm that the proposed method can successfully capture the preseismic gravity anomalies of large earthquakes with a magnitude of less than 8,which suggests a new idea for the application of gravity satellite data to earthquake research.

Revealing the role of local shear strain partition of transformable particles in a TRIP-reinforced bulk metallic glass composite via digital image correlation

The coupling effects of the metastable austenitic phase and the amorphous matrix in a transformation-induced plasticity(TRIP)-reinforced bulk metallic glass(BMG)composite under compressive loading were investigated by employing the digital image correlation(DIC)technique.The evolution of local strain field in the crystalline phase and the amorphous matrix was directly monitored,and the contribution from the phase transformation of the metastable austenitic phase was revealed.Local shear strain was found to be effectively consumed by the displacive phase transformation of the metastable austenitic phase,which relaxed the local strain/stress concentration at the interface and thus greatly enhanced the plasticity of the TRIP-reinforced BMG composites.Our current study sheds light on in-depth understanding of the underlying deformation mechanism and the interplay between the amorphous matrix and the metastable crystalline phase during deformation,which is helpful for design of advanced BMG composites with further improved properties.

Horizontal movement and strain characteristics in Tianshan and its adjacent region with GPS deformation data

Based on the multiple-term horizontal velocity solutions of 230 GPS monitoring sites in Tianshan and its adjacent region, the GPS site velocity fields and crustal horizontal strain fields in the area have been obtained. The results show that the crustal shortening rate of Tianshan, with the longitude （77°±1°）E as the boundary, gradually decreased towards two sides, from the south to the north, indicating that the pushing force of plate becomes weaker along with the fold deformation decreasing of the Tianshan. The direction of principal compressive strain of Tianshan and its adjacent area, nearly NNW, is basically perpendicular to the Tianshan cordillera trend, suggesting the distribution and variation of maximum principal compressive stress in Tianshan and its adjacent region resulted from collision and extrusion of Indian Plate. This paper indicates that the maximum shear strain field mainly con- centrates on two areas, one is Isyk lake of North Tianshan, Kyrgyzstan, and the other is the juncture of Jiashi （South Tianshan） and Pamir arc faults. In the above areas, it can be shown from the epicentral distribution that the strong earthquakes mostly occurs at the high shearing strain accumulation filed or its edge.

The coefficient of variation representing the non-uniformity of the strain field and its implication to detect earthquake precursor

Before the major earthquake or rock damage occurs,it is often accompanied by a sudden change in the degree of non-uniformity of the strain field.In order to find a stronger non-uniformity signal before the rock failure,the coefficient of variation(Cv)is examined and reformed in this study.We test the Cv calculation way of the"normal-abnormal"model proposed in the previous studies.Based on the analysis of the physical process of rock failure and its relationship to the shear strain field,we construct a new way to calculate the Cv value.The variation of shear strain field on rock sample with the increase of stress is obtained by the digital speckle correlation method(DSCM).The new Cv value calculation way is used to study the non-uniformity of the spatial distribution for the shear strain field.The results show that this Cv calculation way can get more obvious abnormal signals.When the number of observation points are limited,the specific distribution of points can increase the signal strength,which may provide reference for the research on precursor detection of earthquakes.

Elastic strain response in the modified phase-field-crystal model

To understand and develop new nanostructure materials with specific mechanical properties, a good knowledge of the elastic strain response is mandatory. Here we investigate the linear elasticity response in the modified phase-field-crystal（MPFC） model. The results show that two different propagation modes control the elastic interaction length and time, which determine whether the density waves can propagate or not. By quantitatively calculating the strain field, we find that the strain distribution is indeed extremely uniform in case of elasticity. Further, we present a detailed theoretical analysis for the orientation dependence and temperature dependence of shear modulus. The simulation results show that the shear modulus reveals strong anisotropy and the one-mode analysis provides a good guideline for determining elastic shear constants until the system temperature falls below a certain value.

SOLITARY WAVES IN FINITE DEFORMATION ELASTIC CIRCULAR ROD

A new nonlinear wave equation of a finite deformation elastic circular rod simultaneously introducing transverse inertia and shearing strain was derived by means of Hamilton principle. The nonlinear equation includes two nonlinear terms caused by finite deformation and double geometric dispersion effects caused by transverse inertia and transverse shearing strain. Nonlinear wave equation and corresponding truncated nonlinear wave equation were solved by the hyperbolic secant function finite expansion method. The solitary wave solutions of these nonlinear equations were obtained. The necessary condition of these solutions existence was given also.

Considerations of rock dilation on modeling failure and deformation of hard rocks-a case study of the mine-by test tunnel in Canada

For the compressive stress-induced failure of tunnels at depth, rock fracturing process is often closely associated with the generation of surface parallel fractures in the initial stage, and shear failure is likely to occur in the final process during the formation of shear bands, breakouts or V-shaped notches close to the excavation boundaries. However, the perfectly elastoplastic, strain-softening and elasto-brittle-plastic models cannot reasonably describe the brittle failure of hard rock tunnels under high in-situ stress conditions. These approaches often underestimate the depth of failure and overestimate the lateral extent of failure near the excavation. Based on a practical case of the mine-by test tunnel at an underground research laboratory (URL) in Canada, the influence of rock mass dilation on the depth and extent of failure and deformation is investigated using a calibrated cohesion weakening and frictional strengthening (CWFS) model. It can be found that, when modeling brittle failure of rock masses, the calibrated CWFS model with a constant dilation angle can capture the depth and extent of stress-induced brittle failure in hard rocks at a low confinement if the stress path is correctly represented, as demonstrated by the failure shape observed in the tunnel. However, using a constant dilation angle cannot simulate the nonlinear deformation behavior near the excavation boundary accurately because the dependence of rock mass dilation on confinement and plastic shear strain is not considered. It is illustrated from the numerical simulations that the proposed plastic shear strain and confinement-dependent dilation angle model in combination with the calibrated CWFS model implemented in FLAC can reasonably reveal both rock mass failure and displacement distribution in vicinity of the excavation simultaneously. The simulation results are in good agreement with the field observations and displacement measurement data.

Plastic deformation behavior of Fe_(40)Ni_(40)P_(14)B_6 bulk metallic glass investigated by nanoindentation

Fe40Ni40P14B6 bulk metallic glass rods have been prepared by water quenching the fluxed alloy. The deformation behavior was investigated by nanoindentation tests and compressing tests. The average hardness and elastic modulus of the as-prepared Fe40Ni40P14B6 BMG (bulk metallic glass) measured by nanoindentation tests are 8.347 and 176.61 GPa respectively. The displace- ment-load curve shows “pop-in” characteristics which correspond to the loading rate bursts. Many shear bands around the indent were observed. The as-prepared Fe-based BMG exhibits a compressive plastic strain of 5.21%, which is much larger than that of other Fe-based glassy alloys and most of other BMGs.

Comparative study of bulk metallic glass composites with high-volume-fractioned dendritic and spherical b. c. c. phase precipitates

A dendritic β-phase reinforced bulk metallic glass(BMG) composite named as D2 was prepared by rapid quenching of a homogenous Zr60Ti14.67Nb5.33Cu5.56Ni4.44Be10 melt, and characterized by means of X-ray diffraction(XRD), scanning electron microscopy(SEM) observation and room-temperature compression test. The microstructure and mechanical properties were compared with those of the spherical β-phase reinforced composite named as composite S2. It was found that the composite D2 contains β-phase dendrites up to 56% in volume-fraction, and exhibits a ductile compressive behavior with plastic strain of 12.7%. As the high-volumefractioned β-phase dendrites transferred to coarse spherical particles of about 20 μm in diameter in the composite S2, a much improved plastic strain up to 20.4% can be achieved. Micrographs of the fractured samples reveal different interaction modes of the propagating shear bands with the dendritic and spherical β phase inclusions, resulting in different shear strains in the composite samples. The matrix of composite S2 undergoes a significantly larger shear strain than that of the composite D2 before ultimate failure, which is thought to be mainly responsible for the greatly increased global plastic strain of the S2 relative to D2.

Pore Water Pressure Buildup Under Cyclic Rotation of Principal Stress and Stability Evaluation of Seabed Deposit

The cyclic rotation of principal stress direction with a constant amplitude is the characteristics of cyclic stress in seabed deposit induced by travelling waves. Presented in the paper are the results obtained from tests simulating the cyclic stress characteristics, with emphasis laid on the buildup of pore water pressure in soil samples. Regression analysis of test data shows that the pore water pressure can be expressed as the function of the number of cycles of cyclic loading, or as the function of generalized shear strain. Using the results thus obtained, the possibility of failure of seabed deposit under cyclic loading induced by travelling waves can be evaluated. The comparison with the results of conventional cyclic torsional shear tests shows that neglect of the effect of the cyclic rotation of the principal stress direction will result in considerable over-estimation of the stability of seabed deposit.

Characteristics of regional crustal deformation before 2016 Menyuan Ms6.4 earthquake

On January 21, 2016, a strong earthquake with a magnitude of Ms6.4 happened at Menyuan, Qinghai Province of China. In almost the same place, there was another strong earthquake happened in 1986, with similar magnitude and focal mechanism. In this paper, we analyze the characteristics of regional crustal deformation before the 2016 Menyuan Ms6.4 earth- quake by using the data from 10 continuous Global Positioning System （GPS） stations and 74 campaign-mode GPS stations within 200 km of this event： （a） Based on the velocity field from over ten years GPS observations, a regional strain rate field is calculated. The results indicate that the crustal strain rate and seismic moment accumulation rate of the Qilian- Haiyuan active fault, which is the seismogenic tectonics of the event, are significantly higher than the surrounding regions. In a 20 km~ 20 km area around the seismogenic region, the maximum and minimum principal strain rates are 21.5 nanostrain/a （NW-SE extension） and -46.6 nanostrain/a （NE-SW compression）, respectively, and the seismic moment accumulation rates is 17.4 Nm/a. The direction of principal compression is consistent with the focal mechanism of this event. （b） Based on the position time series of the continuous GPS stations for a time-span of about 6 years before the event, we calculate the strain time series. The results show that the dilatation of the seismogenic region is continuously reduced with a ＂non-linear＂ trend since 2010, which means the seismogenic region has been in a state of compression. However, about 2-3 months before the event, both the dilatation and maximum shear strain show significant inverse trends. These abnormal changes of crustal deformation may reflect the non-linear adjustment of the stress-strain accumulation of the seismogenic region, when the accumulation is approaching the critical value of rupture.

Grain Refi ning of Flange Plate for Welded H Section Steel Made under Asynchronous Rolling Condition

Asynchronous rolling technology was adopted for the accumulated ten passes cold rolling, flange plate steel, and for welded H section steel, respectively. The metallographic microstructure analysis, tensile test and annealing test were carried out for cold rolled pieces; thus the ratio of length to width of grain, tensile strength, relationship between the grain size and asynchronous rolling process parameters after annealing can be obtained. The experimental results show that the relationship between the asynchronous rolling and the shearing deformation of rolled pieces can make a reasonable interpretation of the mechanism that asynchronous rolling may improve the strain accumulated energy of rolled pieces and the strength of flange plate steel. This paper provides a theoretical basis for the application of asynchronous rolling in improving the strength of flange plate steel.

Study on Rheological Characteristics of a Grease Used in High Speed Bearing

On a self-made super-high shear strain rate rheometer, the rheological characteristics and apparent viscosity curves of a high-speed bearing grease were obtained under different working conditions. A new grease rheological model suited to a shear strain rate range of 0—3.5×10~6s^(-1) was presented. The results showed that the shear stress increased linearly at first and then increased nonlinearly with the increase in shear strain rate up to 1.5×10~6s^(-1), and finally the shear stress decreased slightly with the successive increase in shear strain rate. The shear stress increased with a decreasing rolling speed and an increasing contact pressure. The apparent viscosity decreased rapidly with the increase of shear strain rate at beginning and could approach the viscosity of the base oil if the shear strain rate surpassed 1.5×10~6s^(-1). The fits between the test data and the predicted values by the new model were fairly good.

QUASI-PRINCIPAL AXIS METHOD IN FINITE DEFORMATION

A quasi-quasi-principal axis frame means a unit orthogonal frame in which the shear strains are small. As an extension of Hill's principal axis method we establish the approximate representations for various strains. the.finite rotation tensor, spins, strain rates. conjugate stresses and their rates with respect to quasi-principal axes. The quasiprincipal axis method may function as a new basis of numerically analyzing finite deformation problems.

Influence of Asymmetric Monotonic Hot Rolling on Microstructures and Mechanical Property of Microalloyed Steel

For refining grain and obtaining excellent properties, the experiments of asymmetric and symmetric monotonic hot rolling were carried out to investigate the role of shear strain on the microstructures and mechanical properties of V-microalloyed steel. The study demonstrates that the gradient ferrite distribution and dispersive pearlite through the sheet thickness are observed in asymmetric rolled specimen, and the homogeneous microstructure with ferrite and large pearlite is found in symmetric rolled specimen. The average grain size in asymmetric rolled specimen is smaller than the one in symmetric rolled specimen. The styles of precipitate morphology in asymmetric rolled specimen are random precipitate and obvious interphase precipitate, while the ones in symmetric rolled specimen are random precipitate and unobvious interphase precipitate. The additional shear strain results in the microstructure difference between asymmetric rolled specimen and symmetric rolled specimen. The impact energy of asymmetric rolled specimen, 58 J, is more than the one of symmetric rolled specimen, 48 J. Both deflection-energy curve and fracture morphology show that the fracture style of asymmetric rolled specimen is ductile, and the ones of symmetric rolled specimen are brittle and ductile.

GEOMETRICALLY NONLINEAR ANALYSIS OF MINDLIN PLATE USING THE INCOMPATIBLE BENDING ELEMENTS WITHIN TERNAL SH

An approach of the incompatible elements with additional internal shear strain is,in the presem paper,suggested and applied to geometrically nonlinear analysis of Mi-ndlin plate bending problem.It provides a quite covenient way to avoid the whear loc-king troubles.An energy consistency condition for this kind of C°elements is offered.The nonlinear element formulations and some numerical results are presented.

Thermoelectric transport in holographic quantum matter under shear strain

We study thermoelectric transport under shear strain in two spatial dimensional quantum matter using the holographic duality.General analytic formulae for the DC thermoelectric conductivities subjected to finite shear strain are obtained in terms of black hole horizon data.Off-diagonal terms in the conductivity matrix also appear at zero magnetic field,resembling an emergent electronic nematicity,which cannot nevertheless be identified with the presence of an anomalous Hall effect.For an explicit model study,we numerically construct a family of strained black holes and obtain the corresponding nonlinear stress-strain curves.We then compute all electric,thermoelectric,and thermal conductivities and discuss the effects of strain.While the shear elastic deformation does not affect the temperature dependence of thermoelectric and thermal conductivities quantitatively,it can strongly change the behavior of the electric conductivity.For both shear hardening and softening cases,we find a clear metal-insulator transition driven by the shear deformation.Moreover,the violation of the previously conjectured thermal conductivity bound is observed for large shear deformation.

Effect of dual and new generation wide-base tire assembly on inverted pavements

The conventional flexible pavements have been constructed such that the stiffness of the layer reduces with depth.The crust thickness becomes significantly high for heavy traffic corridors resulting in the consumption of large quantities of construction materials and also increasing environmental pollution.Inverted pavements with the aggregate interlayer(AIL)or stress absorbing membrane interlayer(SAMI)are considered to be one of the alternatives for thick conventional flexible pavements for heavy traffic corridors.The AIL or SAMI is placed between a stiff cement-treated base and asphalt concrete layer to function as crack relief layers.This change in the composition alters the behaviour of inverted pavements compared to the conventional flexible pavements.On the other hand,wide-base tires are being increasingly preferred by trucking industries due to increased fuel economy and cargo capacity.However,the effect of wide-base tires on the performance of inverted pavements is yet to be investigated.In this study,the 3D finite element(FE)models of inverted pavements considering different crack relief layers were developed,and load from dual-wheel and wide-base tires were applied.The stress-strain evolution in the various layers of inverted pavements was investigated and discussed in this study.The results indicated the higher stress and strains due to wide base tires compared to the dual-wheel assembly.Further,pavement with SAMI was found to result in lower stress and strains in the asphalt concrete layer compared to AIL pavements.

New Formulas of Shear Strain during Equal-channel Angular Pressing Process with Consideration of Influences of Velocity and Motion Trajectory

The influences of die parameters on shear strain were investigated by using two-dimensional finite element simulation.New formulas of shear strain were proposed.According to the results of formulas,the shear strain showed a linear dependence on the difference between internal and external fillet radius and the slope was determined by the intersection angle.The simulation results indicated that the velocities of the points from different zones were different in the specimen and the motion trajectories of different points did not follow geometrical laws.The influences of the average velocity and the motion trajectory on shear strain were incorporated in the formula to calculate the shear strain produced during equalchannel angular pressing process.The reliability of simulation results has been partially validated by experiments.