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.

EXACT SOLUTIONS OF NEAR CRACK LINE FIELDS FOR MODE I CRACK UNDER PLANE STRESS CONDITION IN AN ELASTIC－PERFECTLY PLASTIC SOLID

The near crack line analysis method has been used in the present paper,The classical small scale yielding conditions have been completely abandoned in the analyses and one inappropriate matching condition used to be used at the elasticplastic boundary has been corrected.The reasonable solution of the plastic stresses near the crack line region has been established.By matching the plastic stresses with the exact elastic stresses at the elastic-plastic boundary,the plastic stresses the length of the plastic zone and the unit normal vector of the elastic-plastic boundary near the crock line region have been obtained for a mode I crack under uniaxial tension,as well as a mode I crack under biaxial tension,which shows that for both conditions the plastic stress componentsσy, and σsy.he length of the plastic zone and the unit normal vector of the elastic-plastic boundary are quite the same while the plastic stress σs is different.

The Plane Stress Crack-Tip Field for an Incompressible Rubber Material

The crack-tip field under plane stress condition for an incompressible rubbermaterial￣[1] is investigated by. the use of the fully nonlinear equilibrium theory. It isfound thai the crack-tip field is composed of two shrink sectors and one expansion se-ctor. At the crack-tip, stress and strain possess the singularity of R￣(-1) and R￣(-1n), respec-tively, (R is the distance to the crack-tip before deformation, n is the material const-ant). When the crack-tip is approached, the thickness of the sheet shrinks to zerowith the order of R￣(1.4n). The results obtained in this paper are consistent with that ob-tained in [8] when s→∞ .

Effect of Rotation, Magnetic Field and Initial Stresses on Propagation of Plane Waves in Transversely Isotropic Dissipative Half Space

The problem regarding the reflection of plane waves in a transversely isotropic dissipative medium is considered, in which we are studying about the reflection of incidence waves in initially stressed dissipative half space. After solving the governing equations, we find the two complex quasi-P (qP) and quasi-SV (qSV) waves. The occurrence of reflected waves is studied to calculate the reflection coefficient and the energy partition of incidence wave at the plane boundary of the dissipative medium. Numerical example is considered for the reflection coefficient and the partition of incident energy, in which we study about the effect of rotation, initial stresses and magnetic field.

SUPPLEMENTARY STUDY ON ANISOTROPIC PLASTIC STRESS FIELDS AT A STATIONARY PLANE-STRESS CRACK-TIP

Under the hypothesis that all the perfectly plastic stress components at a orach tip are the functions of θ only, making use of yield conditions and equilibrium equations. we derive the generally analytical expressions of the perfectly plastic stress field at a crack tip. Applying these generally analytical expressions to the concrete cracks, the analytical expressions of perfectly plastic stress fields at the tips of Mode Ⅰ Mode Ⅱ, Mode Ⅲ and Mixed Mode Ⅰ-Ⅱ cracks are obtained.

ANISOTROPIC PLASTIC FIELDS AT A RAPIDLY PROPAGATING PLANE-STRESS CRACK-TIP

Under the condition that all the stress components at a crack-tip are the functions of 0 only, making use of the equations of steady-state motion. Hill anisotropic yield condition and stress-strain relations, we obtain the general solution of anisotropic plastic field at a rapidly propagating plane-stress crack-tip. Applying this general solution to four particular cases of anisotropy, the general solutions of these four particular cases are derived. Finally, we give the anisotropic plastic field at the rapidly propagating plane-stress mode I crack-tip in the case of X=Y=Z

EFFECT OF THE POISSON RATIO ON THE PERFECTLY PLASTIC STRESS FIELD AT A STATIONARY PLANE-STRAIN CRACK TIP

Under the condition that all the perfectly plastic stress components at a crack tip are the functions of ? only, making use of equilibrium equations and Von-Mises yield condition containing Poisson ratio, in this paper, we derive the generally analytical expressions of perfectly plastic stress field at a stationary plane-strain crack tip. Applying these generally analytical expressions to the concrete cracks, the analytical expressions of perfectly plastic stress fields at the stationary tips of Mode I, Mode II and Mixed-Mode I-II plane-strain cracks are obtained. These analytical expressions contain Poisson ratio.

Numerical simulation study on the influence of the ground stress field on the stability of roadways

We adopt the concept of generalized plane strain to model a roadway in a stress field.This can avoid limitations caused by simplifying the stress analysis as plane strain.FLAC3D was used to investigate the maximum tensile stress and displacement of a roadway in a known stress field for angles,α,between the roadway axial direction and the maximum principal stress of 0°,30°,45°,60° and 90°.This theory was applied to the analysis of an engineering case.The results indicate that stress and displacement of the surrounding rock increase as the angle,α,increases.This provides some significant guidance for a reasonable layout of roadways in a known stress field.

Three dimensional K-Tz stress fields around the embedded center elliptical crack front in elastic plates

Through detailed three-dimensional （3D） finite element （FE） calculations, the out-of-plane constraints Tz along embedded center-elliptical cracks in mode I elastic plates are studied. The distributions of Tz are obtained near the crack front with aspect ratios （a/c） of 0.2, 0.4, 0.5, 0.6, 0.8 and 1.0. Tz decreases from an approximate value of Poisson ratio v at the crack tip to zero with increasing normalized radial distances （r/a） in the normal plane of the crack front line, and increases gradually when the elliptical parameter angle φ changes from 0° to 90°at the same r/a. With a/c rising to 1.0, Tz is getting nearly independent of φ and is only related to r/a. Based on the present FE calculations for Tz, empirical formulas for Tz are obtained to describe the 3D distribution of Tz for embedded center-elliptical cracks using the least squares method in the range of 0.2 ≤ a/c ≤ 1.0. These Tz results together with the corresponding stress intensity factor K are well suitable for the analysis of the 3D embedded centerelliptical crack from field, and a two-parameter K-Tz principle is proposed.

Three-Dimensional Stress Fields in Finite Thickness Plate with Hole Under Shear Load

The theoretical solutions are obtained for the three-dimensional(3-D)stress field in an infinite isotropic elastic plate with a through-the-thickness circular hole subjected to shear load at far field by using Kane and Mindlin′s assumption based on the stress function method.Based on the present solutions,the characteristics of 3-D stress field are analyzed and the emphasis is placed on the effects of the plate thickness and Poisson′s ratio on the deviation of the present 3-D in-plane stress from the related plane stress solutions,the stress concentration and the out-of-plane constraint.The present solutions show that the stress concentration factor reaches its peak value of about 8.9% which is higher than that of the plane stress solutions.As expected,the out-of-plane stress constraint factor can reach 1on the surface of the hole when the plate is a very thick one.

盖州青石岭震群断层面参数的确定及构造应力场特征研究

根据之前学者的双差定位结果,使用Fit_Fault软件包计算盖州青石岭震群发震断层面走向为114.30°,倾角74.67°。收集2001年至2011年辽宁地区的震源机制解资料,采用全局网格搜索算法,反演该地区的构造应力场,其主压应力轴为NEE向,主张应力轴为NNW向,整体呈现拉张的应力状态。并据此确定出青石岭震群发震断层的滑动角是35.49°,为左旋走滑性质。模拟在辽宁地区构造应力体系下各种产状的断层面上可产生的相对剪应力和相对正应力分布情况,发现该震群发震断层面上的相对剪应力和相对正应力分别为0.513和0.576。分析认为盖州青石岭震群是一处地质薄弱带,背景构造应力场在其最近一期的活动中未起主导作用。

从震源机制中准确识别发震断层面对重构应力场的意义

基于震源机制的应力场反演,需要从震源机制的两个节面中准确地识别出发震断层面,然后通过拟合发震断层面的滑动方向获得应力场.然而,目前的技术和方法不能保证能够从所有的震源机制中准确地识别出发震断层面.因此,用于应力场反演的断层数据中会参入小部分辅助断层面,这部分假断层的存在会造成重构的应力场与实际应力场产生多大程度的偏离?本文通过合成实验揭示出,从部分震源机制中错误地选择断层面可能会造成重构的应力场方向和主应力相对大小(R)与实际产生较大偏离,重构应力场的偏离程度主要与实际的应力R值、错误选择断层面的震源机制所占的比例以及震源机制中包含的噪声大小这三个因素有关.当实际的应力R值为中间值附近时,只有准确地选择断层面才能准确地重构R值,当实际的应力R值较小时,准确地选择断层面有助于准确地重构应力方向,故准确地从震源机制中选择断层面可以保证在不同的背景应力场下都能准确地重构应力场方向和R值,这对于根据重构的应力场合理解释构造运动具有重要意义.

复杂应力场中圆形隧洞偏应力场分布规律

为了厘清深部圆形中导洞(设置于双向隧洞中间)围岩偏应力分布问题,结合岩石力学与摩尔-库仑屈服准则,推导平面三向应力场中圆形隧洞围岩主偏应力与塑性区半径解析解,研究不同工况下圆形隧洞围岩主偏应力的分布规律及塑性区边界处主偏应力的几何形态分布特征。结果表明:当隧洞所处的斜向应力场为竖向应力场0.5~1.0倍时,随着斜向应力场水平方位角α_(1)=α_(2)增加,径向1.0倍隧洞半径范围内顶底主偏应力在快速降低,腰部主偏应力在快速增加,径向1.0倍隧洞半径范围外隧洞围岩主偏应力先小幅下降后又逐渐增大,最终在围岩深部趋于某定值;隧洞围岩主偏应力对其塑性区形态分布影响显著,当斜向应力场水平方位角α_(1)=α_(2)为30°时,围岩塑性区形态分布较优,为圆形或椭圆形。

MODE Ⅰ AND MODE Ⅱ CRACK TIP ASYMPTOTIC FIELDS WITH STRAIN GRADIENT EFFECTS

The strain gradient effect becomes significant when the size of frac- ture process zone around a crack tip is comparable to the intrinsic material length l, typically of the order of microns. Using the new strain gradient deformation theory given by Chen and Wang, the asymptotic fields near a crack tip in an elastic-plastic material with strain gradient effects are investigated. It is established that the dom- inant strain field is irrotational. For mode Ⅰ plane stress crack tip asymptotic field, the stress asymptotic field and the couple stress asymptotic field can not exist si- multaneously. In the stress dominated asymptotic field, the angular distributions of stresses are consistent with the classical plane stress HRR field; In the couple stress dominated asymptotic field, the angular distributions of couple stresses are consistent with that obtained by Huang et al. For mode Ⅱ plane stress and plane strain crack tip asymptotic fields, only the stress-dominated asymptotic fields exist. The couple stress asymptotic field is less singular than the stress asymptotic fields. The stress asymptotic fields are the same as mode Ⅱ plane stress and plane strain HRR fields, respectively. The increase in stresses is not observed in strain gradient plasticity for mode Ⅰ and mode Ⅱ, because the present theory is based only on the rotational gradi- ent of deformation and the crack tip asymptotic fields are irrotational and dominated by the stretching gradient.

Stress value in 2003 Dayao Ms6.1 earthquake source region

The Ms6.2 Dayao, Yunnan, earthquake occurred on July 21, 2003, followed by a major Ms6.1 earthquake about 88 days later in the same region. Hypocenters of the two earthquakes are almost in the same place. Based on the P wave first motion polarities of the two aftershock sequences recorded by temporary stations, we have studied the stress field in the aftershock zone and obtained the two stress field directions in Dayao region using the new version of PKU_Grid^Test Software provided by Chunquan Yu. Assuming that the rotation of the stress field is caused by the second main shock, we estimated the crustal stress value in the focal region by using the stress value calculation method proposed by Yongge Wan. The estimated maximum, intermediate and minimum principal stresses are 166.3 MPa, 158.7 MPa and 151 MPa, respectively, before the second main shock. The normal and shear stresses projected on the fault plane of the second main shock before it occurred are 157.3 MPa, 7.4 MPa, and are 158.8 MPa, 0.2 MPa after it occurred, respectively. The perturbed input parameters experiments attest the stability of the solution. The result shows that the preseismic shear stress is larger than the post-seismic one, and their difference corresponds to the stress drop approximately. The estimated compressive stress level is very high, but the differential stress is low. The result is helpful for friction coefficient estimation, plate motion simulation and related studies.

PLANE PROBLEMS OF A FINITE DISC CONTAINING AN INTERNAL CRACK

Using complex variable methods in elasticity, this paper deals with the plane problems ot a finite disc containing an internal linear crack at any position under general loads, obtains the general forms of Complex stress functions and stress-intensity tactors expressed in terms of series, and to these problems disiusses three sposial cases,i.e.the cases of the crack under a uniform pressure, a uniform shear stress and the use of the dise rotating uniformly. In these cases the approximate formulas calcidating the stress-intensity factors are also presented. The calculated results shun that for the middle and.small orachs situated inside the disc and not near the external boundary,these approximate formulas give good or better approximation.

基于震源机制解分析邢台地震的发震构造

活动断层几何形状的确定为评估一个地区的地震危险性提供重要的理论依据,邢台老震区内构造背景复杂,前人对邢台地震的发震构造展开大量研究,取得丰富成果。通过震源机制节面聚类得到邢台地震发震断层的走向、倾角及其标准差,综合前人研究结果求取发震断层面的平均解;结合区域地壳应力张量,估计该断层的滑动方向及其误差,分析该区域的地震活动危险性。结果表明:邢台地震发震断层的走向为32.45°,倾角为79.44°,滑动角-153.96°,标准差为4.55°。该断层为走向NNE、倾向NWW的高倾角走滑型断层,而非正断性质的新河断裂。区域地壳应力场在断层面上产生的相对剪应力为0.83,相对正应力为0.59。该断层不是最大剪应力的断层面形状,但剪应力强度仍较大,表明该断层在地震能量积累和释放过程中仍起到必不可少的作用。

平面幂律塑性Ⅰ型裂纹尖端应力场全解

在航空航天、船舶、石油管道和核电等领域,服役结构或部件在长期极端条件下运行,不可避免地会产生裂纹,因此,为研究含裂纹结构的准静态断裂行为,必须了解裂纹尖端附近区域的应力应变场特点.对于幂律材料裂纹构元,研究平面应变和平面应力条件下Ⅰ型裂纹尖端应力场的解析分布.基于能量密度等效和量纲分析,推导了能量密度中值点代表性体积单元(representative volume element,RVE)的等效应力解析方程,并定义其为应力因子,进而针对有限平面应变和平面应力紧凑拉伸(compact tension,CT)试样和单边裂纹弯曲(single edge bend,SEB)试样,以应力因子作为应力特征量,并构造用于表征裂尖等效应力等值线的蝶翅轮廓式和扇贝轮廓式三角特殊函数,提出描述幂律塑性条件下平面I型裂纹尖端应力场的半解析模型.该半解析模型形式简单,对CT和SEB试样的裂尖应力场的预测结果与有限元分析的结果比较表明,两者之间均密切吻合,模型公式可直接用于预测Ⅰ型裂纹尖端应力分布,方便于断裂安全评价和理论发展.

华胜煤矿房柱群下巷道非对称变形破坏机理及控制技术

在近距离煤层开采中,下煤层巷道的稳定性对于整个矿井的安全生产至关重要。因此,本文以兼并重组矿井华胜煤矿为工程案例,基于上煤层巷道房柱群采空区底板应力分布规律,研究了下煤层巷道的变形破坏机理及控制技术。首先,详细分析了华胜煤矿下煤层巷道的地质概况、围岩力学参数和原有支护方案,并基于现场钻孔窥视结果得到了下煤层巷道顶板房柱的具体位置,分析了下煤层巷道的非对称变形机理。然后,运用半无限平面理论计算得到了上煤层巷道房柱群采空区底板的应力分布规律。结果表明,上煤层中房柱群的不对称分布导致下煤层巷道顶板应力分布不均匀,从而引发了下煤层巷道的非对称变形,且越靠近上煤层房柱群中的煤柱,变形越大。基于此,进一步通过数值分析和现场应用对下煤层巷道位置及支护方案进行了优化和验证。华胜煤矿下煤层巷道在优化后的巷道位置及支护方案控制下整体并未出现非对称大变形。本研究结果对类似工程地质条件的下煤层巷道支护方案设计具有指导意义。

High Order Asymptotic Field for Plane Stress Crack Problem

This paper presents an exact analysis for high order asymptotic field of theplane stress crack problem.It has been shown that the second order asymptotic field is notan independent eigen field and should be matched with the elastic strain term of the firstorder asymptotic field.The second order stress field ahead of the crack tip is quite smallcompared with the first order stress field.The stress field ahead of crack tip is character-ized by the HRR field.Hence the J integral can be used as a criterion for crack initiation.