Effect of Modulus Heterogeneity on the Equilibrium Shape and Stress Field ofαPrecipitate in Ti-6Al-4V

For media with inclusions(e.g.,precipitates,voids,reinforcements,and others),the difference in lattice parameter and the elastic modulus between the matrix and inclusions cause stress concentration at the interfaces.These stress fields depend on the inclusions’size,shape,and distribution and will respond instantly to the evolving microstructure.This study develops a phase-field model concerningmodulus heterogeneity.The effect of modulus heterogeneity on the growth process and equilibrium state of theαplate in Ti-6Al-4V during precipitation is evaluated.Theαprecipitate exhibits strong anisotropy in shape upon cooling due to the interplay of the elastic strain and interfacial energy.The calculated orientation of the habit plane using the homogeneous modulus ofαphase shows the smallest deviation fromthat of the habit plane observed in the experiment,compared to the case where the homogeneous modulus ofβphase is adopted.In addition,the equilibrium volume ofαphase within the systemusing homogeneousβmodulus exhibits the largest dependency on the applied stresses.The stress fields across theα/βinterface are further calculated under the assumption of modulus heterogeneity and compared to those using homogeneous modulus of eitherαorβphase.This study provides an essential theoretical basis for developing mechanics models concerning systems with heterogeneous structures.

Support design method for deep soft-rock tunnels in non-hydrostatic high in-situ stress field

Due to the long-term plate tectonic movements in southwestern China,the in-situ stress field in deep formations is complex.When passing through deep soft-rock mass under non-hydrostatic high in-situ stress field,tunnels will suffer serious asymmetric deformation.There is no available support design method for tunnels under such a situation in existing studies to clarify the support time and support stiffness.This study first analyzed the mechanical behavior of tunnels in non-hydrostatic in-situ stress field and derived the theoretical equations of the ground squeezing curve(GSC)and ground loosening curve(GLC).Then,based on the convergence confinement theory,the support design method of deep soft-rock tunnels under non-hydrostatic high in-situ stress field was established considering both squeezing and loosening pressures.In addition,this method can provide the clear support time and support stiffness of the second layer of initial support.The proposed design method was applied to the Wanhe tunnel of the China-Laos railway in China.Monitoring data indicated that the optimal support scheme had a good effect on controlling the tunnel deformation in non-hydrostatic high in-situ stress field.Field applications showed that the secondary lining could be constructed properly.

The 2023 Turkey earthquake doublet: Earthquake relocation, seismic tomography, and stress field inversion

On February 6,2023,two earthquakes with magnitudes of M_(W) 7.8 and M_(W) 7.5 struck southeastern Turkey,causing significant casualties and economic losses.These seismic events occurred along the East Anatolian Fault Zone,a convergent boundary between the Arabian Plate and the Anatolian Subplate.In this study,we analyze the M_(W) 7.8 and M_(W) 7.5 earthquakes by comparing their aftershock relocations,tomographic images,and stress field inversions.The earthquakes were localized in the upper crust and exhibited steep dip angles.Furthermore,the aftershocks occurred either close to the boundaries of low and high P-wave velocity anomaly zones or within the low P-wave velocity anomaly zones.The East Anatolia Fault,associated with the M_(W) 7.8 earthquake,and the SürgüFault,related to the M_(W) 7.5 earthquake,predominantly experienced shear stress.However,their western sections experienced a combination of strike-slip and tensile stresses in addition to shear stress.The ruptures of the M_(W) 7.8 and M_(W) 7.5 earthquakes appear to have bridged a seismic gap that had seen sparse seismicity over the past 200 years prior to the 2023 Turkey earthquake sequence.

Data-model coupling driven stress field measurements

This paper presents a method for measuring stress fields within the framework of coupled data models,aimed at determining stress fields in isotropic material structures exhibiting localized deterioration behavior without relying on constitutive equations in the deteriorated region.This approach contributes to advancing the field of intrinsic equation-free mechanics.The methodology combines measured strain fields with data-model coupling driven algorithms.The gradient and Canny operators are utilized to process the strain field data,enabling the determination of the deterioration region's location.Meanwhile,an adaptive model building method is proposed for constructing coupling driven models.To address the issue of unknown datasets during computation,a dataset updating strategy based on a differential evolutionary algorithm is introduced.The resulting optimal dataset is then used to generate stress field results.Validation against finite element method calculations demonstrates the accuracy of the proposed method in obtaining full-field stresses in specimens with local degradation behavior.

Impact of well placement and flow rate on production efficiency and stress field in the fractured geothermal reservoirs

Geothermal energy has gained wide attention as a renewable alternative for mitigating greenhouse gas emissions.The advancements in enhanced geothermal system technology have enabled the exploitation of previously inaccessible geothermal resources.However,the extraction of geothermal energy from deep reservoirs poses many challenges due to high‐temperature and high‐geostress conditions.These factors can significantly impact the surrounding rock and its fracture formation.A comprehensive understanding of the thermal–hydraulic–mechanical(THM)coupling effect is crucial to the safe and efficient exploitation of geothermal resources.This study presented a THM coupling numerical model for the geothermal reservoir of the Yangbajing geothermal system.This proposed model investigated the geothermal exploitation performance and the stress distribution within the reservoir under various combinations of geothermal wells and mass flow rates.The geothermal system performance was evaluated by the criteria of outlet temperature and geothermal productivity.The results indicate that the longer distance between wells can increase the outlet temperature of production wells and improve extraction efficiency in the short term.In contrast,the shorter distance between wells can reduce the heat exchange area and thus mitigate the impact on the reservoir stress.A larger mass flow rate is conducive to the production capacity enhancement of the geothermal system and,in turn causes a wider range of stress disturbance.These findings provide valuable insights into the optimization of geothermal energy extraction while considering reservoir safety and long‐term sustainability.This study deepens the understanding of the THM coupling effects in geothermal systems and provides an efficient and environmentally friendly strategy for a geothermal energy system.

3-D finite element modeling for evolution of stress field and interaction among strong earthquakes in Sichuan-Yunnan region

Based on the latest achievement about activities of geological structure, a 3-D finite-element model containing four layers of upper crust, lower crust (two layers) and upper mantle is established in the paper. By repeated tests and revisions, the boundary conditions of the model are determined. And then the background stress field, the stress field caused by fault creep and the stress field triggered by strong earthquake in Sichuan-Yunnan region, as well as their dynamic variations are calculated. The results indicate that the latter earthquake often occurs in the area with positive Coulomb rupture stress change associated with the former one, the former earthquake has a triggering effect on the latter one to a certain extent, and strong earthquake often occur in groups under the background of high stress, which is of great significance for distinguishing seismic anomalies, as well as for improving the level of earthquake prediction.

Recent tectonic stress field and major earthquakes of the Bohai Sea basin

渤海位于北华北新生代裂陷盆地的东部，是一个晚第四纪形成的内陆海盆．渤海盆地活动断裂发育，地震活动强烈，交会于渤海中部的NE向营口潍坊断裂带北段、庙西北一黄河口一临邑断裂带及NW向北京一蓬莱断裂带是主要的活动构造带，将海区分成4个次级新构造区，成为现代应力场作用的构造基础．综合研究38个震源机制解和75个井区应力场等资料，以及构造应力场二维数值模拟计算结果表明，渤海及其邻区现代构造应力场的压应力方向为NE60°～90°，张应力为SN—NW30°；以水平和近水平应力作用为主；不同构造区主应力方向存在一定的差异．现今渤海地区地壳发育以NNE-NE和NW-WNW走向的共轭剪切破裂为特征，是控制地震活动的主要构造．

Contemporary tectonic stress field in China

The contemporary tectonic stress field in China is obtained on the basis of Chinese stress field database and Harvard CMT catalogue. Result of the inverted tectonic stresses shows that the maximum principal stress axis strikes nearly north-south direction in the west part of Tibet plateau, ENE direction in North China. In Central China, its strikes show a ra- diated pattern, i.e., NNE in north part and NNW in south part. The detailed stress field parameters of nearly whole China are given and can be used in geodynamic stress field simulation and earthquake prediction.

Active Faulting Pattern,Present-day Tectonic Stress Field and Block Kinematics in the East Tibetan Plateau

This paper examines major active faults and the present-day tectonic stress field in the East Tibetan Plateau by integrating available data from published literature and proposes a block kinematics model of the region. It shows that the East Tibetan Plateau is dominated by strike-slip and reverse faulting stress regimes and that the maximum horizontal stress is roughly consistent with the contemporary velocity field, except for the west Qinling range where it parallels the striking of the major strike-slip faults. Active tectonics in the East Tibetan Plateau is characterized by three faulting systems. The left-slip Kunlun-Qinling faulting system combines the east Kunlun fault zone, sinistral oblique reverse faults along the Minshan range and two major NEE-striking faults cutting the west Qinling range, which accommodates eastward motion, at 10--14 mm/a, of the Chuan-Qing block. The left-slip Xianshuihe faulting system accommodated clockwise rotation of the Chuan-Dian block. The Longmenshan thrust faulting system forms the eastern margin of the East Tibetan Plateau and has been propagated to the SW of the Sichuan basin. Crustal shortening across the Longmenshan range seems low （2-4 mm/a） and absorbed only a small part of the eastward motion of the Chuan-Qing block. Most of this eastward motion has been transmitted to South China, which is moving SEE-ward at 7-9 mm/a. It is suggested from geophysical data interpretation that the crust and lithosphere of the East Tibetan Plateau is considerably thickened and theologically layered. The upper crust seems to be decoupled from the lower crust through a decollement zone at a depth of 15-20 kin, which involved the Longmenshan fault belt and propagated eastward to the SW of the Sichuan basin. The Wenchuan earthquake was just formed at the bifurcated point of this decollement system. A rheological boundary should exist beneath the Longmenshan fault belt where the lower crust of the East Tibetan Plateau and the lithospheric mantle of the Yangze block are juxtaposed.

Crustal stress field in Yunnan: implication for crust-mantle coupling

We applied the g CAP algorithm to determine 239 focal mechanism solutions 3：0≤MW≤ 6：0） with records of dense Chin Array stations deployed in Yunnan,and then inverted 686 focal mechanisms（including 447 previous results） for the regional crustal stress field with a damped linear inversion. The results indicate dominantly strike-slip environment in Yunnan as both the maximum（r1） and minimum（r3） principal stress axes are sub-horizontal. We further calculated the horizontal stress orientations（i.e., maximum and minimum horizontal compressive stress axes： S H and S h, respectively） accordingly and found an abrupt change near ＊26°N. To the north, S H aligns NW-SE to nearly E-W while S h aligns nearly N-S. In contrast, to the south, both S H and S h rotate laterally and show dominantly fan-shaped patterns. The minimum horizontal stress（i.e., maximum strain axis） S h rotates from NW-SE to the west of Tengchong volcano gradually to nearly E-W in west Yunnan, and further toNE-SW in the South China block in the east. The crustal strain field is consistent with the upper mantle strain field indicated by shear-wave splitting observations in Yunnan but not in other regions. Therefore, the crust and upper mantle in Yunnan are coupled and suffering vertically coherent pure-shear deformation in the lithosphere.

The Structure of Ore-controlling Strain and Stress Fields in the Shangzhuang Gold Deposit in Shandong Province,China

The Shangzhuang altered-rock type gold ore deposit is located in the middle segment of and controlled by the Wang＇ershan fault zone in the northwestern part of the Jiaodong gold province, China. The deformation evolution, the structure of strain and stress fields and its ore-controlling effect in the Shangzhuang deposit are discussed in this paper. It is revealed that the deformation evolution has mainly undergone four phases： the early ductile deformation, the second NE-striking horizontal simple shear, the third NE-striking compression-shear and the final NW-striking compression. The mineralization happened during the third stage in which the maximum principal stress gradually transited from NE to NW. The 3-D numerical simulations of the stress field show that, on the condition that the maximum principal stress is NE-striking, the fracture development in the fault zone is favored, while when the maximum principal stress is NW-striking, the fault zone is relatively extensional and it is suitable for the influx and emplacement of ore-forming fluids. The compression-shear strain field during the mineralization is characterized by the λ-type structure, the positive flower structure, etc. Orebodies are mostly equidistantly located in the dilatational spaces, which are distributed in the integral compressional circumstances. And the dilatational spaces are developed where the fault attitude changes or shear joint systems develop. In the overall compression-shear stress field, the strain field bears self-similarity at multiple scales, including the orebody, ore deposit and orefield. The selfsimilarity of the structure comprises the subequidistant distribution of fractures at the same scale and the similar shape of the fractures at various scales. Yet, due to the special geological structure, the orebodies are mostly located in the hanging wall in the Shangzhuang deposit, which is different from most deposits in the Jiaodong gold province. Analyses of the ore-controlling stress and strain fields in the deposit provide an important basis for deposit seeking.

Source mechanism of small-moderate earthquakes and tectonic stress field in Yunnan Province

In the paper, source mechanisms of 33 small-moderate earthquakes occurred in Yunnan are determined by modeling of regional waveforms from Yunnan digital seismic network. The result shows that most earthquakes occurred within or near the Chuandian rhombic block have strike-slip mechanism. The orientations of maximum compressive stresses obtained from source mechanism are changed from NNW-SSN to NS in the areas from north to south of the block, and tensile stresses are mainly in ENE-WSW or NE-SE. In the eastern Tibetan Plateau, the orientations of maximum compressive stress radiate toward outside from the plateau, and the tensile stress orientations mostly parallel to arc structures. Near 28N the orientations of both maximum compressive stress and tensile stress changed greatly, and the boundary seems to correspond to the southwestern extended line of Longmenshan fault. Outside of the Chuandian rhombic block, the orientations of P and T axes are some different from those within the block. The comparison shows that the source mechanism of small-moderate events presented in the paper is consistence with that of moderate-strong earthquakes determined by Harvard University, which means the source mechanism of small-moderate events can be used to study the tectonic stress field in this region.

Simulation of Paleotectonic Stress Fields and Distribution Prediction of Tectonic Fractures at the Hudi Coal Mine, Qinshui Basin

Study on tectonic fractures based on the inversion of tectonic stress fields is an effective method. In this study, a geological model was set up based on geological data from the Hudi Coal Mine, Qinshui Basin, a mechanical model was established under the condition of rock mechanics and geostress, and the finite element method was used to simulate the paleotectonic stress field. Based on the Griffith and Mohr-Coulomb criterion, the distribution of tectonic fractures in the Shanxi Formation during the Indosinian, Yanshanian, and Himalayan period can be predicted with the index of comprehensive rupture rate. The results show that the acting force of the Pacific Plate and the India Plate to the North China Plate formed the direction of principal stress is N-S, NW - SE, and NE - SW, respectively, in different periods in the study area. Changes in the direction and strength of the acting force led to the regional gradients of tectonic stress magnitude, which resulted in an asymmetrical distribution state of the stress conditions in different periods. It is suggested that the low-stress areas are mainly located in the fault zones and extend along the direction of the fault zones. Furthermore, the high-stress areas are located in the junction of fold belts and the binding site of multiple folds. The development of tectonic fractures was affected by the distribution of stress intensity and the tectonic position of folds and faults, which resulted in some developed areas with level I and II. There are obvious differences in the development of tectonic fractures in the fold and fault zones and the anticline and syncline structure at the same fold zones. The tectonic fractures of the Shanxi Formation during the Himalayan period are more developed than those during the Indosinian and Yanshanian period due to the superposition of the late tectonic movement to the early tectonic movement and the differences in the magnitude and direction of stress intensity.

COUPLED NUMERICAL SIMULATION ON COLD ROLLER'S TEMPERATURE FIFLD-PHASE TRANSFORMATION - STRESS FIELD DURING ITS QUENCHING PSOCESS

Complicated changns occur inside the steel parts during quenching process. The abruptly changed boundary conditions make the temperature field,micro - structure and stress field change dramatically in very short time, and these variables take a contact interactions in the whole process. In this paper, a three dimensional non - linear mathematical model for queeching process has been founded and the numerical simulation on temperature field,microstructre and stress field has been realized.In the FEM analysis, the incremental iteration method is used to deal with such complicated nonlinear as boundary nonlinear, physical property nonlinear,transformation nonlinear etc.The effect of stress on transformation kinetics has been considered in the calculation of microstructure. In the stress field anal- ysis,a thermo- elasto - plastic model has been founded, which considers such factors as transforma- tion strain,transformation plastic strain, themal strain and the effect of temperature and transforma- tion on mechanical propertier etc. The transient temperature field, microstructure distribution and stress field of the roller on any time can be displayed vividly,and the cooling curve and the changes of stress on any position can also be given.

The Relationship between Fractures and Tectonic Stress Field in the Extra Low-Permeability Sandstone Reservoir at the South of Western Sichuan Depression

The formation and distribution of fractures are controlled by paleotectonic stress field, and their preservative status and effects on development are dominated by the modern stress field. Since Triassic, it has experienced four tectonic movements and developed four sets of tectonic fractures in the extra low-permeability sandstone reservoir at the south of western Sichuan depression. The strikes of fractures are in the S-N, NE-SW, E-W, and NW-SE directions respectively. At the end of Triassic, under the horizontal compression tectonic stress field, for which the maximum principal stress direction was NW.SE, the fractures were well developed near the S-N faults and at the end of NE-SW faults, because of their stress concentration. At the end of Cretaceous, in the horizontal compression stress fields of the NE-SW direction, the stress was obviously lower near the NE-SW faults, thus, fractures mainly developed near the S-N faults. At the end of Neogene-Early Pleistocene, under the horizontal compression tectonic stress fields of E-W direction, stress concentrated near the NE-SW faults and fractures developed at these places, especially at the end of the NE-SE faults, the cross positions of NE-SW, and S-N faults. Therefore, fractures developed mostly near S-N faults and NE-SW faults. At the cross positions of the above two sets of faults, the degree of development of the fractures was the highest. Under the modern stress field of the NW-SE direction, the NW-SE fractures were mainly the seepage ones with tensional state, the best connectivity, the widest aperture, the highest permeability, and the minimum opening pressure.

Evolution of residual stress field in 6N01 aluminum alloy friction stir welding joint

Based on the characteristics of friction stir welding( FSW) and Coulomb friction work theory,the residual stresses field of FSW joints of 6 N01 aluminum alloy( T5),which was used in high speed train,were calculated by using the ANSYS finite element software. During the FEM calculation,the dual heat source models namely the body heat source and surface heat source were used to explore the evolution law of the welding process to the residual stress field. The method of ultrasonic residual stress detecting was used to investigate the residual stresses field of the 6 N01 aluminum alloy FSW joints. The results show that the steady-state temperature of 6 N01 aluminum alloy during FSW is about 550 ℃,and the temperature mutates at the beginning and at end of welding. The longitudinal residual stress σ_x is the main stress,which fluctuates in the range of-25 to 242 MPa. Moreover,the stress in the range of shaft shoulder is tensile stress that the maximum tensile stress is 242 MPa,and the stress in the outside of shaft shoulder is compressive stress that the maximum compressive stress is 25 MPa. The distribution of the tensile stress in the welding nugget zone( WNZ) is obviously bimodal,and the residual stress on the advancing side is higher than that on the retreating side. With the increasing of the welding speed,the maximum temperature decreased and the maximum residual stress decreased when the pin-wheel speed kept constant. With the increasing of the pin-wheel speed,the maximum temperature of the joint increased and the maximum residual stress increased when the welding speed was constant. The experimental results were in good agreement with the finite element results.

Characteristics of evolution of mining-induced stress field in the longwall panel:insights from physical modeling

The evolution of mining-induced stress field in longwall panel is closely related to the fracture field and the breaking characteristics of strata.Few laboratory experiments have been conducted to investigate the stress field.This study investigated its evolution by constructing a large-scale physical model according to the in situ conditions of the longwall panel.Theoretical analysis was used to reveal the mechanism of stress distribution in the overburden.The modelling results showed that:(1)The major principal stress field is arch-shaped,and the strata overlying both the solid zones and gob constitute a series of coordinated load-bearing structures.The stress increasing zone is like a macro stress arch.High stress is especially concentrated on both shoulders of the arch-shaped structure.The stress concentration of the solid zone in front of the gob is higher than the rear solid zone.(2)The characteristics of the vertical stress field in different regions are significantly different.Stress decreases in the zone above the gob and increases in solid zones on both sides of it.The mechanical analysis show that for a given stratum,the trajectories of principal stress are arch-shaped or inverselyarched,referred to as the‘‘principal stress arch’’,irrespective of its initial breaking or periodic breaking,and determines the fracture morphology.That is,the trajectories of tensile principal stress are inversely arched before the first breaking of the strata,and cause the breaking lines to resemble an inverted funnel.In case of periodic breaking,the breaking line forms an obtuse angle with the advancing direction of the panel.Good agreement was obtained between the results of physical modeling and the theoretical analysis.

Three dimensional tectonic stress field in North China

According to the latest data of geological structure, geophysics, in-situ stress measurement and focal mechanism,3-D tectonic stress field model in North China is built and 3-D tectonic stress field pattern of North China aresimulated by finite element method. Then the overall characteristics and regional specific feature of North Chinaare studied. Finally, the influences of the valid dynamic boundary conditions of North China Block, active faultsand the inhomogeneity of crustal medium on tectonic stress field of North China are investigated.

End Late Paleozoic tectonic stress field in the southern edge of Junggar Basin

This paper presents the end Late Paleozoic tectonic stress field in the southern edge of Junggar Basin by interpreting stress-response structures （dykes, folds, faults with slickenside and conjugate joints）. The direction of the maximum principal stress axes is interpreted to be NW-SE （about 325°）, and the accommodated motion among plates is assigned as the driving force of this tectonic stress field. The average value of the stress index Rt is about 2.09, which indicates a variation from strike-slip to compressive tectonic stress regime in the study area during the end Late Paleozoic period. The reconstruction of the tectonic field in the southern edge of Junggar Basin provides insights into the tectonic deformation processes around the southern Junggar Basin and contributes to the further understanding of basin evolution and tectonic settings during the culmination of the Paleo- zoic.

Petrel2ANSYS: Accessible software for simulation of crustal stress fields using constraints provided by multiple 3D models employing different types of grids

Crustal stresses play an important role in both exploration and development in the oil and gas industry.However,it is difficult to simulate crustal stress distributions accurately,because of the incompatibilities that exist among different software.Here,a series of algorithms is developed and integrated in the Petrel2ANSYS to carry out two-way conversions between the 3D attribute models that employ corner-point grids used in Petrel and the 3D finite-element grids used in ANSYS.Furthermore,a modified method of simulating stress characteristics and analyzing stress fields using the finite-element method and multiple finely resolved 3D models is proposed.Compared to the traditional finite-element simulation-based approach,which involves describing the heterogeneous within a rock body or sedimentary facies in detail and simulating the stress distribution,the single grid cell-based approach focuses on a greater degree on combining the rock mechanics described by 3D corner-point grid models with the finely resolved material characteristics of 3D finite-element models.Different models that use structured and unstructured grids are verified in Petrel2ANSYS to assess the feasibility.In addition,with minor modifications,platforms based on the present algorithms can be extended to other models to convert corner-point grids to the finite-element grids constructed by other software.