Deformation Localization-A Review on the Maximum-Effective-Moment(MEM) Criterion

The essential difference in the formation of conjugate shear zones in brittle and ductile deformation is that the intersection angle between brittle conjugate faults in the contractional quadrants is acute （usually ～60°） whereas the angle between conjugate ductile shear zones is obtuse （usually 110°）. The Mohr-Coulomb failure criterion, an experimentally validated empirical relationship, is commonly applied for interpreting the stress directions based on the orientation of the brittle shear fractures. However, the Mohr-Coulomb failure criterion fails to explain the formation of the low-angle normal fault, high-angle reverse fault, and the conjugate strike-slip fault with an obtuse angle in the ~1 direction. Although it is ten years since the Maximum-Effective-Moment （MEM） criterion was first proposed, and increasingly solid evidence in support of it has been obtained from both observed examples in nature and laboratory experiments, it is not yet a commonly accepted model to use to interpret these anti- Mohr-Coulomb features that are widely observed in the natural world. The deformational behavior of rock depends on its intrinsic mechanical properties and external factors such as applied stresses, strain rates, and temperature conditions related to crustal depths. The occurrence of conjugate shear features with obtuse angles of -110~ in the contractional direction on different scales and at different crustal levels are consistent with the prediction of the MEM criterion, therefore -110° is a reliable indicator for deformation localization that occurred at medium-low strain rates at any crustal levels. Since the strain-rate is variable through time in nature, brittle, ductile, and plastic features may appear within the same rock.

Deformation Localization and Shear Fracture of a Rapidly Solidified Al-Fe-V-Si Alloy at Elevated Temperature

The tensile and fatigue behavior of a dispersoid strengthened, powder metallurgy Al-Fe-V-Si alloy at ambient and elevated temperatures was investigated. The results show that the strength and ductility of the alloy decrease significantly with increasing temperature and decreasing strain rate. Micro-structural examinations reveal that this change in mechanical behavior with increasing temperature is related to the mode of deformation of the alloy. Further observations show that localized shear deformation is responsible for the losses in both strength and ductility of the alloy at elevated temperature.

DEFORMATION LOCALIZATION AND SHEAR BAND FRACTURE IN STRONG ANISOTROPY SHEET TENSION

The tensile deformation localization and the shear band fracture behaviors of sheet metals with strong anisotropy are numerically simulated by using Updating Lagrange finite element method, Quasi-how plastic constitutive theory([1]) and B-L planar anisotropy yield criterion([2]). Simulated results are compared with experimental ones. Very good consistence is obtained between numerical and experimental results. The relationship between the anisotropy coefficient R and the shear band angle theta is found.

Research on the mechanism of rockburst induced by mined coal-rock linkage of sharply inclined coal seams

In recent years,the mining depth of steeply inclined coal seams in the Urumqi mining area has gradually increased.Local deformation of mining coal-rock results in frequent rockbursts.This has become a critical issue that affects the safe mining of deep,steeply inclined coal seams.In this work,we adopt a perspective centered on localized deformation in coal-rock mining and systematically combine theoretical analyses and extensive data mining of voluminous microseismic data.We describe a mechanical model for the urgently inclined mining of both the sandwiched rock pillar and the roof,explaining the mechanical response behavior of key disaster-prone zones within the deep working face,affected by the dynamics of deep mining.By exploring the spatial correlation inherent in extensive microseismic data,we delineate the“time-space”response relationship that governs the dynamic failure of coal-rock during the progression of the sharply inclined working face.The results disclose that(1)the distinctive coal-rock occurrence structure characterized by a“sandwiched rock pillar-B6 roof”constitutes the origin of rockburst in the southern mining area of the Wudong Coal Mine,with both elements presenting different degrees of deformation localization with increasing mining depth.(2)As mining depth increases,the bending deformation and energy accumulation within the rock pillar and roof show nonlinear acceleration.The localized deformation of deep,steeply inclined coal-rock engenders the spatial superposition of squeezing and prying effects in both the strike and dip directions,increasing the energy distribution disparity and stress asymmetry of the“sandwiched rock pillar-B3+6 coal seam-B6 roof”configuration.This makes worse the propensity for frequent dynamic disasters in the working face.(3)The developed high-energy distortion zone“inner-outer”control technology effectively reduces high stress concentration and energy distortion in the surrounding rock.After implementation,the average apparent resistivity in the rock pillar and B6 roof substantially increased by 430%and 300%,respectively,thus guaranteeing the safe and efficient development of steeply inclined coal seams.

Deformation mechanism of fine grained Mg-7Gd-5Y-l.2Nd-0.5Zr alloy under high temperature and high strain rates

Fine grained Mg-7Gd-5Y-1.2Nd-0.5Zr alloy was investigated by dynamic compression tests using a Split Hopkinson Pressure Bar under the strain rates in the range 1000-2000 s^(-1) and the temperature range 293-573 K along the normal direction.The microstructure was measured by optical microscopy,electron back-scattering diffraction,transmission electron microscopy and X-ray diffractometry.The results showed that Mg-7Gd-5Y-1.2Nd-0.5Zr alloy had the positive strain rate strengthening effect and thermal softening effect at high temperature.The solid solution of Gd and Y atoms in Mg-7Gd-5Y-1.2Nd-0.5Zr alloy reduced the asymmetry of α-Mg crystals and changed the critical shear stress of various deformation mechanisms.The main deformation mechanisms were prismatic slip and pyramidal(a)slip,{102}tension twinning,and dynamic recrystallization caused by local deformation such as particle-stimulated nucleation.c 2020 Published by Elsevier B.V.on behalf of Chongqing University.

On the physical model of earthquake precursor fields and the mechanism of precursors＇timespace distribution（Ⅲ）──anomalies of seismicity and crustal deformation and their mechanisms when a strong earthquake is in prep

By studying the seismicity pattern before 37 earthquakes with M≥6. 0 in North China and the pattern of crustal deformation in the Capital Area from 1954 to 1992, some abnormal characteristics of these patterns before strong earthquakes have been extracted. A comparison has been made between the anomalies of these two kinds of Patterns. From the results we can know the following. ① Before a strong earthquake, the seismicity will strengthen and the crustal deformation rate will increase. ② Several years before a strong earthquake, there will be seismic gaps and deformation gaps around the epicenter of the quake. ③ The dynamic parameters of patterns all show a decrease in information dimension. This means that the crustal deformation has become more and more localized with time and it gives an important indication showing that a strong earthquake is in preparation. At the end of the paper, the physical mechanisms of the abnormal patterns of seismicity and crustal deformationhave been explained in a unified way in terms of the earthquake-generating model of a inhomogeneous strongbody in inhmogeneous media.

Corrosion-Facilitating Local Plastic Deformation for α-Ti in Methanol

The effect of corrosion process on facilitating local plastic deformation for α-Ti in methanol has been investigated with the micro-multiplicative moire interferometer technique. The size of plastic zone and the plastic strain ahead of loaded notch have been measured. The results show that the anodic dissolution, or corrosion process itself can enhance the plastic zone and the plastic strain ahead of a loaded notch during stress corrosion of α-Ti in methanol solution

TEM OBSERVATION OF LOCAL DEFORMATION BAND AT CRACK TIP

The thin foil specimen of a ferrite-austenite duplex stainless steel was tensiled under transmis- sion electron microscope(TEM).It was found that both in ferrite and austenite the local deformation band at crack tip was formed near to the crack propagating direction.Its forma- tion was related with the crack tip Schmid factor,dislocation shielding,latent hardening and hardening coefficient.When the crack tip emitted dislocations to a slip system by the action of pure mode Ⅱ stress resolute,and the decreasing rate of hardening coefficient was suitable,lo- cal deformation band was easy to form.

THE APPLICATION OF NONLINEAR GAUGE MATHOD TO THE ANALYSIS OF LOCAL FINITE DEFORMATION IN THE NECKING OF CYLINDRICAL BAR

Localized deformation and instability is the focal point of research in mechanics. The most typical problem is the plastic analysis of cylindrical bar neckingand shear band under uniaxial tension. Traditional elasto-plastic mechanics of infinitesimal deformation can not solve this problem successfully. In this paper, on the basis of S(strain) -R(rotation) decomposition theorem, the authors obtain the localstrain distribution and progressive state of axial symmetric finite deformation of cylindrical bar under uniaxial tension adopting nonlinear gauge approximate method and computer modelling technique.

Research of pattern dynamics parameters of crustal deformation field in seismogenic process

There are fractal character and fractal dimensions with time in crustal deformation field of seismogeny process.The occurrence of strong earthquake is after the process of the dimension lowering, entrolpy decreasing and ordering,the fractal dimension, entropy value and order degree are all resumed normal datum after the occurrence of strong earthquake, it reflects the evolution of crustal deformation field is the process from the homogeneous deformation - heterogeneous deformation - disturbance - homogeneous deformation. We regarded the fractal dimension, information entropy and order degree as pattern dynamics parameters of crustal deformation field to use, and the deformation localize process is quantitatively described by the parameters.

Variation analysis ofprecision mechanical assembly consideringform errors and local deformation

A method to analyze the effect of form errors and local deformation on the assembly accu- racy and its stability in a non-rigid assembly system is proposed. The contact finite element method was used to obtain local deformation of mating surfaces, which was superposed onto form errors to obtain real mating surface data of assemblies. Then mating variation was obtained by establishing vir- tual contact planes. Finally, an experiment of the assembly of two cylindrical components was car- ried out to verify the validity of the proposed method. By comparing the calculation accuracies of 3D assembly with and without taking into account local deformation, the results showed that the effects of local deformation of mating surfaces on calculation accuracy of mating variation was not neglect- able compared with form errors.

A FINITE ELEMENT ANALYSIS OF THE LARGE PLASTIC DEFORMATION BEHAVIOR OF AMORPHOUS GLASSY CIRCULAR POLYMERIC BARS

The BPA eight-chain molecular network model is introduced into the finite element formulation of elastic-plastic large deformation. And then, the tensile deformation localization development of the amorphous glassy circular polymeric bars (such as polycarbonates) is numerically simulated. The simulated results are compared with experimental ones, and very good consistence between numerical simulation and experiment is obtained, which shows the efficiency of the finite element analysis. Finally, the influences of the microstructure parameter S-ss on tensile neck-propagation and triaxial stress effect are studied.

ANALYSIS OF THE LOCALIZATION OF DAMAGE AND THE COMPLETE STRESS-STRAIN RELATION FOR MESOSCOPIC HETEROGENEOUS BRITTLE ROCK SUBJECTED TO COMPRESSIVE LOADS

A micromechanics-based model is established. The model takes the interaction among sliding cracks into account, and it is able to quantify the effect of various parameters on the localization condition of damage and deformation for brittle rock subjected to compressive loads. The closed-form explicit expression for the complete stress-strain relation of rock containing microcracks subjected to compressive loads was obtained. It is showed that the complete stress-strain relation includes linear elasticity,nonlinear hardening,rapid stress drop and strain softening.The behavior of rapid stress drop and strain softening is due to localization of deformation and damage. Theoretical predictions have shown to be consistent with the experimental results.

ANALYSIS OF THE LOCALIZATION OF DAMAGE AND THE COMPLETE (STRESS-STRAIN) RELATION FOR MESOSCOPIC HETEROGENEOUS ROCK UNDER UNIAXIAL TENSILE LOADING

The mechanical behavior of rock under uniaxial tensile loading is different from that of rock under compressive loads. A micromechanics-based model was proposed for mesoscopic heterogeneous brittle rock undergoing irreversible changes of their microscopic structures due to microcrack growth. The complete stress-strain relation including linear elasticity, nonlinear hardening,rapid stress drop and strain softening was obtained. The influence of all microcracks with different sizes and orientations were introduced into the constitutive relation by using the probability density function describing the distribution of orientations and the probability density function describing the distribution of sizes. The influence of Weibull distribution describing the distribution of orientations and Rayleigh function describing the distribution of sizes on the constitutive relation were researched. Theoretical predictions have shown to be consistent with the experimental results.

Adiabatic shear sensitivity of ductile metal based on gradient-dependent JOHNSON-COOK model

Based on the expression proposed by WANG for the local plastic shear deformation distribution in the adiabatic shear band（ASB） using gradient-dependent plasticity,the effects of 10 parameters on the adiabatic shear sensitivity were studied.The experimental data for a flow line in the ASB obtained by LIAO and DUFFY were fitted by use of the curve-fitting least squares method and the proposed expression.The critical plastic shear strains corresponding to the onset of the ASB for Ti-6Al-4V were assessed at different assigned ASB widths.It is found that the proposed expression describes well the non-linear deformation characteristics of the flow line in the ASB.Some parameters in the JOHNSON-COOK model are back-calculated using different critical plastic shear strains.The adiabatic shear sensitivity decreases as initial static yield stress,work to heat conversion factor and strain-rate parameter decrease,which is opposite to the effects of density,heat capacity,ambient temperature and strain-hardening exponent.The present model can predict the ASB width evolution process.The predicted ASB width decreases with straining until a stable value is reached.The famous model proposed by DODD and BAI only can predict a final stable value.

Crashworthiness design of density-graded cellular metals

Crashworthiness of cellular metals with a linear density gradient was analyzed by using cell-based finite element models and shock models. Mechanisms of energy absorption and deformation of graded cellular metals were explored by shock wave propagation analysis. Results show that a positive density gradient is a good choice for protecting the impacting object because it can meet the crashworthiness requirements of high energy absorption, stable impact resistance and low peak stress.

EFFECT OF CARBON MIGRATION ON CREEP PROPERTIES OF Cr5Mo DISSIMILAR WELDED JOINTS WITH Ni-BASED AND AUSTENITIC WELD METAL

In this paper, the effect of carbon migration on creep properties of Cr5Mo dissimilar welded joints with Ni-based (Inconel 182) and Cr23Nil3 (A302) austenitic weld metal was investigated. Carbon migration near the weld metal/ferritic steel interface of Cr5Mo dissimilar welded joints was analyzed by aging method. Local creep deformations of the dissimilar welded joints were measured by a long-term local creep deformation measuring technique. The creep rupture testing was performed for Cr5Mo dissimilar welded joints with Inconel 182 and A302 weld metal. The research results show that the maximum creep strain rate occurs in the decarburized zone located on heat affect zone (HAZ) of Cr5Mo ferritic steel. The creep rupture life of Cr5Mo dissimilar welded joints with A 302 weld metal decreases due to carbon migration and is about 50% of that welded with Inconel 182 weld metal.

A new approach to numerical simulation of source development of earthquake

By considering the heterogeneity of geomechanical materials, the source development of earthquake under compression boundary conditions is studied with a newly developed numerical method, Rock Failure Process Analysis code (RFPA2D). The process of fault forming and associated micro seismicities in a rectangle area with a inclusion but without any clear structural features of original fault is modeled. The modeling demonstrates the whole process of source development of earthquake from deformation, micro failure to collapse and the behavior of temporal spatial distribution of micro seismicities. The stress, strain and the temporal spatial distribution of micro seismicities vividly depict the phenomena of localization, temporal transitions, dilatation or rise, elastic rebound and conjugate (X type) deformation zone.

Using the Maximum Effective Moment Criterion to Interpret Quartz -Fabric Patterns

The Maximum Effective Moment(MEM)criterion predicts that the initial orientation of ductile shear zones and shear bands is^55°relative to the maximum principal stress axis(σ1)and that the kinematic vorticity number(Wk)is^0.94.These preferred orientations should be reflected in the pattern of quartz<c>-fabrics in shear zones and shear bands.Common quartz<c>-fabrics in plane strain can be divided into low-temperature(L)and high-temperature(H)fabrics,with each group showing three patterns.A steady flow with a constant value of Wk≈0.94 gives rise to L-1 and H-1 patterns,which are commonly characterized by a single<c>axis girdle normal to the shear zone and a single<c>-point maximum parallel to the shear zone.Once the conjugate set develops,L-1 and H-1 have opening angles of^70°and^110°,respectively.L-2 and H-2 are asymmetric patterns associated with variable deformation partitioning and vorticity values of0<Wk<0.94.In contrast,L-3 and H-3 are symmetric patterns associated with 100%deformation partitioning and Wk=0.The opening angle in quartz<c>-fabrics is implicitly linked to the temperature during deformation.The opening angle is^70°at low temperature and^110°at high temperature.However,a linear correction between the opening angle and the temperature cannot be established.During deformation partitioning,synthetic shear bands form earlier than antithetic bands and are more easily developed.This may result in opening angles of<70°for low-temperature fabrics and of>110°for high-temperature fabrics.The following criteria can be used to recognize reworked shear zones that have experienced multiple orogenic phases and changes in the stress state:1)the initial Wk is larger or smaller than^0.94;2)the change in Wk is abrupt,rather than progressive;3)inconsistent shear senses are inferred for the different phases of deformation;and4)a negative value of Wk is found in reworked shear zones.

MECHANISM AND CATASTROPHE THEORY ANALYSIS OF CIRCULAR TUNNEL ROCKBURST

Mechanism of circular tunnel rockburst is that, when the carrying capacity of the centralized zone of plastic deformation in limiting state reduces, the comparatively intact part in rock mass unloads by way of elasticity; rockburst occurs immediately when the elastic energy released by the comparatively intact part exceeds the energy dissipated by plastic deformation. The equivalent strain was taken as a state variable to establish a catastrophe model of tunnel rockburst, and the computation expression of the earthquake energy released by tunnel rockburst was given. The analysis shows that, the conditions of rockburst occurrence are relative to rock＇s ratio of elastic modulus to descendent modulus and crack growth degree of rocks; to rock mass with specific rockburst tendency, there exists a corresponding critical depth of softened zone, and rockburst occurs when the depth of softened zone reaches.