封闭应力方向对巴西圆盘试验影响的数值模拟

为揭示封闭应力对巴西圆盘应力分布和破裂演化过程的影响,开展不同方向封闭应力对巴西圆盘破裂二维数值模拟研究。将封闭应力的区域等效成一个封闭的包裹体分布在岩体中,探究不同方向封闭应力对圆盘应力分布和裂纹扩展的影响。结果表明,施加封闭应力的部位出现局部应力变化明显高于未施加的区域,随着加载的进行,施加封闭应力区域的局部应力小于周围未施加封闭应力的区域;对比有无封闭应力存在时加载过程中最大米塞斯应力,得出当封闭应力与加载方向夹角为0°时最大,为20.78 MPa;当无封闭应力和封闭应力方向为0°时,圆盘中心起裂,封闭应力方向为30°,60°,90°时,圆盘的裂纹带发生倾斜并出现多条倾斜短裂纹,圆盘未中心起裂。

     

基于X射线衍射法的含石英脉硅质板岩封闭应力测量

岩石在冷却和漫长的地质演化过程中会有应力被封闭其中,岩石中存在封闭应力的现象逐渐被人们所认识。为揭示岩石封闭应力的存在形式,利用X射线衍射仪,对含石英脉硅质板岩样品采用侧倾固ψ法测量并计算了封闭应力的量值,确定了封闭应力的主应力。研究发现：含石英脉板岩样品测试石英脉区域石英粒径约40 μm;在衍射角152°~156°扫描范围具有良好的独立衍射峰,获得的不同ψ时的（324）晶面衍射图谱,其衍射峰偏移方向具有一致性,证明了封闭应力的存在;石英脉测量点的封闭应力为压应力,最大主应力平行脉体走向（22.71 MPa）,最小主应力垂直脉体走向（12.97 MPa）;基体测点中未测得2θ–sin²ψ线性相关规律。本文所提出的封闭应力的测量方法可为后续开展不同类型岩石封闭应力的观测和相关研究提供参考。

     

The solid phase stress tensor in porous media mechanics and the Hill-Mandel condition

An assessment of the stress tensors used currently for the modeling of partially saturated porous media is made which includes concepts like total stress, solid phase stress, and solid pressure. Thermodynamically constrained averaging theory is used to derive the solid phase stress tensor. It is shown that in the upscaling procedure the Hill conditions are satisfied, which is not trivial. The stress tensor is then compared to traditional stress measures. The physical meaning of two forms of solid pressure and of the Biot coefficient is clarified. Finally, a Bishop-Skempton like form of the stress tensor is obtained and a form of the total stress tensor that does not make use of the effective stress concept.     

一种新的应力率定义

本文研究客观应力率的定义及表示,在放弃了客观应力率形式上的对称性以后定义了一类广义的非对称的客观应力率。从Cauchy应力原理出发,通过构造应力向量形式上和变形及变形率无关的客观导数,得到两种形式的应力率;它们表示作用在参考构形中单位物质面元应力向量的真实变化,这样就消除了应力率定义中的不确定性。用新应力率对次弹性体简单剪切进行了计算,得到的应力不振荡,且满足超弹性正应力-剪应力普适关系。     

边坡下伏地下圆形洞室的弹性应力解析

根据洞室与边坡的相对位置,将其分为深埋地下洞室与浅埋地下洞室,并分别建立了计算模型。将浅埋圆形洞室视为分布荷载作用下半无限体表面附近的孔洞的应力分析问题,采取复变函数的保角映射得到了浅埋洞室的应力解析解。将深埋洞室视为一个双向受压无限板孔应力集中问题,得到了边坡下伏深埋圆形洞室的应力解析解。以某填筑边坡下地下圆形洞室为例,计算得到了浅埋圆形洞室周边的径向应力与环向应力分布,计算结果表明洞室圆心水平线上的环向压应力随着与洞周距离的增加逐渐减小,但径向压应力却是首先增加,然后才逐步减小。洞顶圆周出现环向拉应力,随着越来越接近地表,环向应力逐步转变为压应力并且越来越大,而径向应力逐渐变大。洞周环向拉应力在洞顶与洞底数值最大,洞室左右两端洞周环向压应力数值最大;洞周径向应力在洞顶、洞底数值较小,左右两端洞周应力最大。     

偶应力理论下拉力型锚固体的受力特性

锚固体的受力特征及其影响因素是锚固体设计的重要依据,直接影响锚固效果。传统的经典弹性理论没有考虑应变梯度的影响。偶应力理论引进弯曲曲率,考虑了弯曲效应对介质变形特性的影响。基于偶应力理论,建立了平面应变问题的有限元计算模型,研究锚固体锚固段界面上的剪应力分布、锚固体轴力分布、偶应力的尺度效应以及弹性模量和围压对锚固力的影响,并将偶应力理论的计算结果和经典弹性理论的计算结果进行了比较。结果表明,在偶应力理论下,锚固体锚固段界面的剪应力有所减小,特别是峰值处的剪应力减小明显;岩土的弹性模量越大,锚固界面局部剪应力越大;锚固力随着围压的增大而增大,偶应力尺度效应明显。     

Magneto-elastic stress in a thin infinite plate with an elliptical hole under uniform magnetic field

Two-dimensional magnetic field and magneto-elastic stress solutions are presented for a magnetic material of a thin infinite plate with an elliptical hole under uniform magnetic field. The linear constitutive equation is used for the magnetic field and the stress analyses. The magneto-elastic stress is analyzed using Maxwell stress since only Maxwell stress is caused as a body force according to the electro magneto theory. Except the approximation of the plane stress state in which the plate is thin, no further assumption is made for the stress analysis, though Maxwell stress components are expressed by nonlinear terms. The rigorous boundary condition expressed by Maxwell stress is completely satisfied without any linear assumptions on the boundary. First, magnetic field and stress for soft ferromagnetic material is analyzed and then those for paramagnetic and diamagnetic materials are analyzed. It is stated that the stress components are the same expressions for those materials and the difference is only the magnitude of the permeability, though the magnetic fields are different each other in the plates. If the analysis of magnetic field of paramagnetic materials is easier than that of soft ferromagnetic material, the stress analysis may be carried out using the magnetic field for paramagnetic material. Shear deflection as well as stress in the direction of the plate thickness arises and the solutions are also obtained. Figures of the magnetic field and stress distribution are shown. Stress intensity factors are also derived.     

考虑夹杂相互作用的复合陶瓷夹杂界面的断裂分析

复合材料中夹杂含量较高时,夹杂间的相互作用能显著改变材料细观应力应变场分布,基体和夹杂中的平均应力应变水平也会发生较大变化,导致复合材料强度等力学性能发生显著变化. 为修正单一夹杂模型运用在实际材料中的误差,基于相互作用直推估计法,建立一种考虑含夹杂相互作用的夹杂界面裂纹开裂模型. 首先根据相互作用直推估计法,得到残余应力和外载应力共同作用下夹杂中的平均应力,再计算无限大基体中相同的夹杂达到相同应力场时的等效加载应力,将此加载应力作为含界面裂纹夹杂的等效应力边界条件,在此边界条件下求得界面裂纹尖端的应力强度因子,进而得到界面裂纹开裂的极限加载条件,并分析了夹杂弹性性能、含量、热残余应力、夹杂尺寸等因素对界面裂纹开裂条件的影响. 结果表明,方法能够有效修正单夹杂模型运用在实际材料中的误差,较大的残余应力对界面裂纹开裂有重要的影响,夹杂刚度的影响并非单调且比较复杂;在残余应力较小时,降低柔性夹杂刚度或者增大刚性夹杂刚度都有利于提高材料强度;扩大夹杂尺寸将导致裂纹开裂极限应力显著降低,从而降低材料强度.      

Global material constraints and their associated reactive stresses

The stress field in a material subject to a global material constraint is composed of a reactive stress and an active stress. The active stress is determined by the deformation while the reactive stress arises because of the constraint. The static equilibrium equations can be reduced to equations involving only the active stress. The resulting equations may then be solved to determine the deformation. Although the reactive stress is not needed in order to find the deformation, it is needed to satisfy traction boundary conditions. Rod, shell, and finite element theories can therefore be developed in an unambiguous way. As an example, one can calculate explicitly a reactive stress in a rod-like body subjected to a compressive end load.     

The effect of biaxial loading on the critical resolved shear stress of zinc single crystals

This paper reports an experimental investigation to test the hypothesis that the critical resolved shear stress is independent of the resolved normal stress on the active slip system plane. The resolved normal stress is varied independently for crystals of constant orientation by applying a uniform biaxial tension stress through slitted rubber strips glued to a flat tension sample. It is found that the critical resolved shear stress is constant until the resolved normal stress on the active slip system becomes twice the resolved shear stress; and then, for further increases in the resolved normal stress, the critical resolved shear stress begins to decrease.     

三向应力Mohr圆的真实构成及剪应力作用方向的确定

三向应力Mohr圆的构成在传统上是借助公式推证而得，并以平面图形来表示，缺乏三维的真实感和直观性。在应力应变分析中，对于平面应力问题，可以通过平面应力摩尔圆确定过一点不同斜面上的应力分量及其作用方向。对于三维问题，利用摩尔圆图解法可以确定某一斜面上的正应力和剪应力的数值，但不能表示剪应力的作用方向。剪应力的作用方向需要通过另外的图解方法来确定。本文分别从坐标系旋转和数值计算的角度解释了三向应力Mohr圆的构成过程，形象地说明了Mohr圆的物理本质。针对三向应力Mohr圆不能表示剪应力作用方向的问题，通过矢量运算，给出了剪应力作用方向的确定公式。     

Stress concentration around a hole in a radially inhomogeneous plate

The stress concentration factor around a circular hole in an infinite plate subjected to uniform biaxial tension and pure shear is considered. The plate is made of a functionally graded material where both Young’s modulus and Poisson’s ratio vary in the radial direction. For plane stress conditions, the governing differential equation for the stress function is derived and solved. A general form for the stress concentration factor in case of biaxial tension is presented. Using a Frobenius series solution, the stress concentration factor is calculated for pure shear case. The stress concentration factor for uniaxial tension is then obtained by superposition of these two modes. The effect of nonhomogeneous stiffness and varying Poisson’s ratio upon the stress concentration factors are analyzed. A reasonable approximation in the practical range of Young’s modulus is obtained for the stress concentration factor in pure shear loading.     

斜面应力公式的适用条件 1)

斜面应力公式,即一点应力的坐标旋转变换公式,是材料力学和弹性力学里最常用的公式之一,并广泛用于固体力学和工程设计中。一个让学生感觉例外的典型例子是含V 形切口的薄板在切口尖端的应力情况,如果利用斜面应力公式和切口面的自由面条件,就会得出切口尖点处于零应力状态的结果,而这与线弹性断裂力学给出切口处应力趋于无限大的结果不符。为消除这一疑虑,考察了尖端应力的特性,指出：只有在过一点的各个斜面上的应力是单值连续的情况下,斜面应力公式才能适用,此时,该点的全部应力分量组成应力张量。在V形切口的尖端、裂纹尖端,自由面与顺其延伸至介质内侧的面上的应力不同,应力在该面上就不是单值连续的,该点的应力状态就不能用张量表示,斜面应力公式在切口或裂纹尖端就不适用了。     

Multi-scale analysis of subgrid stress and energy dissipation in turbulent channel flow

In present study, the subgrid scale （SGS） stress and dissipation for multiscale formulation of large eddy simulation are analyzed using the data of turbulent channel flow at Ret = 180 obtained by direct numerical simulation. It is found that the small scale SGS stress is much smaller than the large scale SGS stress for all the stress components. The dominant contributor to large scale SGS stress is the cross stress between small scale and subgrid scale motions, while the cross stress between large scale and subgrid scale motions make major contributions to small scale SGS stress. The energy transfer from resolved large scales to subgrid scales is mainly caused by SGS Reynolds stress, while that between resolved small scales and subgrid scales are mainly due to the cross stress. The multiscale formulation of SGS models are evaluated a priori, and it is found that the small- small model is superior to other variants in terms of SGS dissipation.     

THE STRESS SUBSPACE OF HYBRID STRESS ELEMENT AND THE DIAGONALIZATION METHOD FOR FLEXIBILITY MATRIX H

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新的一个求解带孔薄板弹性问题的二维杂交应力单元

建立了一个新的求解带圆孔薄板弹性问题的二维杂交应力单元,该单元为四节点四边形平面单元,名为P-HS4-8β。由极坐标系下的物理方程和几何方程求解出了一个极坐标方向的应力,通过将这个应力带入由Hellinger-Reissner原理推导的极坐标系下平面应力问题的能量方程中,得到了消除了该应力的能量方程,基于这个能量方程建立了杂交应力单元列式。根据圆孔边无外力条件和相容方程,推导了适用于求解带圆孔薄板问题的极坐标系下的二应力插值矩阵,并将此矩阵应用于新的有限单元列式中。数值算例表明新单元在求解孔边附近的应力时具有较高的精度。     

界面对应力波作用的动光弹试验研究

用动光弹法分析研究了在冲击载荷作用下界面上应力波的传播过程,利用应力波理论分析了界面上应力波的作用机理,证实了界面上存在着能量累积和阻滞能量传递的作用,并结合弹性波动理论和应力 光学定律导出了波动方程与条纹级数之间的关系式。     

螺旋压缩弹簧应力松弛特性试验分析及其应用

本文通过应力松弛试验、理论推导及数值模拟研究了高温下螺旋压缩弹簧的应力松弛规律,并利用加速模型对工况下弹簧应力松弛服役寿命做出预测.首先,根据螺旋压缩弹簧的结构特点搭建了弹簧应力松弛连续动态测试装置,该装置不仅避免了传统测试方法存在的缺陷,而且能够保证试验过程中位移载荷恒定,并实时监测载荷变化.本文以某飞机舱门单锁机构...     

煤体中爆炸应力波传播与衰减规律模拟实验研究

在岩石爆破理论的基础上分析了煤体中爆炸应力波的作用机理,借助损伤力学理论探讨了煤体在 爆炸应力波作用下的损伤断裂准则。煤体中爆炸应力波传播与衰减规律模拟实验结果表明:煤体中爆炸应力 波一般包含2段波形,第1段由压缩相和拉伸相组成简单波形,第2段是由多种作用形成的复杂波形;爆炸应 力波作用下,煤体首先承受压应力,而后承受拉应力,且压缩相的作用时间较拉伸相作用时间短;煤体中爆炸 应力波的衰减速度较一般岩体中的快,实验条件下应力波衰减因数符合=3-/(1-),爆炸应力波的主要 作用是在煤体中形成少量新裂隙、激活煤体中原生裂隙并打破煤体中瓦斯气体的平衡状态。