基于双剪应力屈服准则的受内压管道爆破压力分析

采用双剪应力屈服准则,对在内压作用下的无缺陷管道进行了塑性极限分析,得到了管道爆破压力的计算公式;并且将结果与基于Tresca、Mises、平均剪应力屈服准则得到的爆破压力进行了比较.研究结果表明:爆破压力随着管道材料的应变硬化指数的增大而减小,随着管道厚径比的增大而增大;此外,基于双剪应力屈服准则得到的管道爆破压力为爆破压力的上限,而基于Tresca屈服准则得到的爆破压力为管道爆破压力的下限.     

组合荷载作用下腐蚀缺陷管道的极限承载力

腐蚀缺陷的存在会降低管道的承载力,影响管道的正常运行.考虑了管道轴向与环向材料强度的各向异性,提出了腐蚀缺陷压力管道在内压、轴力和弯矩组合荷载作用下极限承载力的一组广义解.推导了等深度腐蚀、椭圆腐蚀和抛物线三种形状腐蚀缺陷管道的解析解.通过算例验证了解析解与广义解结果具有很好的吻合性.腐蚀形状对极限承载力有显著影响,把...     

MY准则解析复合型裂尖塑性区

首次以MY(平均屈服)准则对I-II复合型裂纹在小范围屈服下的裂尖塑性区进行了分析,分别获得了平面应力和平面应变状态下塑性区尺寸的解析解。这两解表明,塑性区尺寸是材料屈服强度、应力强度因子、极角θ的函数。与Tresca准则、TSS屈服准则获得的解以及Mises解比较表明:Tresca准则预测塑性区上限,TSS屈服准则预测塑性区下限,MY准则预测的塑性区居于Tresca与TSS塑性区之间,逼近Mises解。另外,文中讨论了平面应力和平面应变状态下裂纹尖端的开裂问题,结果表明:当裂纹角β=π4时,平面应力状态下裂纹沿0-θ=0.2952π方向开裂;平面应变状态下裂纹沿0-θ=0.3188π方向开裂。     

受内压厚壁圆筒的塑性变形条件与脆断分析

基于弹性约束的概念,分析了受内压厚壁圆筒产生塑性变形的条件。发现厚壁圆筒发生脆性断裂的根本原因是,圆筒内壁高应力区因受到外壁低应力区的弹性约束,在应力达到材料的屈服条件时不能产生塑性变形。通过计算给出了受内压管道避免脆性断裂的壁厚设计和选材方法。研究结果表明,对外直径2b=300mm的不同管线钢,随屈强比从0.51增大到0.91,其临界壁厚由62.2mm降低至12.9mm,极限内压由225.2MPa降低至69.0MPa,即选用材料的屈强比越低,设计管道不发生脆断的壁厚尺寸范围越大,在临界壁厚尺寸范围内管道的极限承载能力也越高。因此使用较低屈强比的材料并控制合理的管道壁厚,能使管道在承受意外的冲击内压时,出现全面塑性变形,以吸收冲击能量,避免管道脆性断裂的发生。     

GM准则解析受线性荷载简支圆板的极限载荷

用GM(几何中线)屈服准则,对受线性荷载作用下的简支圆板进行塑性极限分析,求得极限载荷的解析解.该解为圆板半径a、切向应力最大点半径r0以及极限弯矩的函数.与Tresca、Mises和TSS(双剪应力)屈服准则预测的极限载荷比较表明,Tresca屈服准则预测极限载荷的下限,TSS屈服准则预测极限载荷的上限,GM准则预测的极限载荷恰居二者中间,并靠近Mises解.圆板半径a与切向应力最大点半径r0的变化关系为r0随着a的增加而增加,满足线性关系,r0分别出现在r0=0.7710a和r0=0.5472a的位置上.     

屈强比对容器爆破压力计算公式精度的影响

借助于数理统计理论的F假设检验与t假设检验,建立了评价容器爆破压力计算公式精度的比较方法,分析了材料屈强比对福贝尔公式与流变应力公式精度的影响。通过对36组径比为1.3~4.71的钢制厚壁圆筒容器爆破压力实测值的研究,得到如下结论:福贝尔公式的合适应用范围是容器材料屈强比为0.4027~0.8852,主要精度指标为0.0866;流变应力公式的合适应用范围是容器材料屈强比为0.4997~0.8852,主要精度指标为0.0699;福贝尔公式的合适应用范围比流变应力公式广,流变应力公式在其合适应用范围的精度比福贝尔公式高。用流变应力公式设计材料屈强比为0.4027~0.8852的钢制厚壁圆筒,主要精度指标为0.0809,流变应力公式与福贝尔公式的精度无显著差异。     

西昌昔格达组粉砂岩动力特性研究

为西昌昔格达组地层场地地震安全性评价提供基础性数据,对西昌经久乡昔格达组粉砂岩进行了一系列动三轴试验.研究结果表明:西昌昔格达组粉砂岩在一定条件下(σ3c=100、200、400 kPa,kc=1.0、1.5、2.0)的骨干曲线符合幂函数模型;动剪应力随着固结围压σ3c或固结主压力比kc增大而增大;在偏压状态下产生相同动剪应变所需要的动剪应力比均压状态所需要的动剪应力大.不同固结应力条件下,动剪切模量随固结压力或固结主压力比增大而增大,随动剪应变增加而减小并趋于稳定;最大动剪切模量Gd0与σ3c/Pa、kc均有良好的幂函数关系.阻尼比随动剪应变增大而增大,但增大幅值随动剪应变增大而迅速减小;阻尼比随围压或固结主压力比增大而减小;不同固结应力条件下(λ/λmax)与(1-Gd/Gdo)有良好的幂函数关系并可归一化处理.西昌昔格达组饱和粉砂岩的动剪应力τd随固结围压σ3c或固结主压力比kc增大而增大,随振动次数增加而减小;τd/σm随固结围压σ3c增大而减小,随固结主压力比kc增大而增大;动剪应力τd与平均压力σm、固结主压力比kc有较好的线性关系.     

管道体积型缺陷复合材料补强的试验模拟研究

为分析管道体积型缺陷屈服前后复合材料缠绕层分担载荷的差异,在材质为X60钢、外径为508mm、壁厚为8.7mm的管件上预制深厚比约为70%的体积型缺陷,并进行低压水压试验,分析缺陷及完整管壁在弹性阶段的应力分布特点。采用玻璃纤维复合材料补强管道缺陷再次进行试验,分析试验压力上升时,管道缺陷发生塑性变形的水压值及应变响应趋势;采用水压试验结果验证有限元模型的准确性后,应用数值模拟分析管件缺陷屈服前后复合材料作用的差异。研究表明:对含体积型缺陷的管道,缺陷区域在内压作用下形成局部弯矩;复合材料缠绕层可以有效抑制这一弯矩,使弹性阶段局部弯矩的最大降幅超过50%,提高了缺陷发生屈服的压力;缺陷区域屈服之后,复合材料缠绕层分担环向载荷,对缺陷管壁的局部鼓胀具有约束作用,使补强管道沿剩余壁厚的应力分布不均匀度降低,约为未补强管道的一半,提高了管道的承载能力。     

考虑拉压强度差效应的厚壁圆筒承载能力分析

应用双剪统一强度理论，考虑材料的拉压异性和同性，推导了在内压力和轴力联合作用下的厚壁圆筒的塑性极限载荷表达式．在该表达式中，当反映中间主应力效应的系数取不同的值时，就能得到按Tresca屈服准则、线性逼近的Mises屈服准则和双剪应力屈服准则的计算结果，并且绘制了在相应准则下的极限应力线图．从而可知：在三维应力状态下，应用该理论，可以获得极限载荷分析的精确解；极限载荷线图与三种屈服准则的屈服曲线是相吻合的；计算的结果可以用于拉压异性和同性的材料，为工程应用提供了理论依据．     

瓦斯渗流场作用下煤层抽放钻孔弹塑性解

为研究瓦斯渗流场作用下的煤层抽放钻孔周围应力分布情况,假定钻孔周围煤体中瓦斯的流动为稳定径向流动状态,建立了渗流力学模型,给出了瓦斯径向稳定渗流方程;在考虑瓦斯渗流场作用下,推导了钻孔周围煤体的微元体力学平衡方程,并引入应力调整系数,求解出其弹性应力解析解;再应用Mohr-Coulomb屈服准则,求解出钻孔周围煤体的塑性应力和塑性半径的解析表达式。通过实例分析表明:钻孔内的抽放负压对钻孔周围煤体应力、塑性区的半径等参数影响较小;在一定的抽放负压(15k Pa)下,随着煤层原始瓦斯压力的增大,钻孔周围煤体的塑性区半径随之增大,距钻孔足够远处的弹性区煤体的应力也随之增大,这比不考虑瓦斯渗流场作用时的经典弹塑性解更加符合实际情况。     

Measurement of length-scale and solution of cantilever beam in couple stress elasto-plasticity

Owing to the absence of proper analytical solution of cantilever beams for couple stress/strain gradient elasto-plastic theory, experimental studies of the cantilever beam in the micro-scale are not suitable for the determination of material length-scale. Based on the couple stress elasto-plasticity, an analytical solution of thin cantilever beams is firstly presented, and the solution can be regarded as an extension of the elastic and rigid-plastic solutions of pure bending beam. A comparison with numerical results shows that the current analytical solution is reliable for the case of σ0 〈〈 H 〈〈 E, where σ0 is the initial yield strength, H is the hardening modulus and E is the elastic modulus. Fortunately, the above mentioned condition can be satisfied for many metal materials, and thus the solution can be used to determine the material length-scale of micro-structures in conjunction with the experiment of cantilever beams in the micro-scale.     

Strength differential effect and influence of strength criterion on burst pressure of thin-walled pipelines

In the framework of the finite deformation theory, the plastic collapse analysis of thin-walled pipes subjected to the internal pressure is conducted on the basis of the unified strength criterion (USC). An analytical solution of the burst pressure for pipes with capped ends is derived, which includes the strength differential effect and takes the influence of strength criterion on the burst pressure into account. In addition, a USC-based analytical solution of the burst pressure for end-opened pipes under the internal pressure is obtained. By discussion, it is found that for the end-capped pipes, the influence of different yield criteria and the strength differential effect on the burst pressure are significant, while for the end-opened pipes, the burst pressure is independent of the specific form of the strength criterion and strength difference in tension and compression.     

Bifurcation From Stability to Instability for a Free Boundary Problem Arising in a Tumor Model

We consider a time-dependent free boundary problem with radially symmetric initial data: σ_t − Δσ + σ = 0 if and σ(r,0)=σ₀(r) in {r < R(0)} where R(0) is given. This is a model for tumor growth, with nutrient concentration (or tumor cells density) σ(r,t) and proliferation rate then there exists a unique stationary solution (σ_S(r), R_S), where R_S depends only on the number . We prove that there exists a number μ_*, such that if μ < μ_* . . . then the stationary solution is stable with respect to non-radially symmetric perturbations, whereas if μ > μ_* then the stationary solution is unstable.     

Euler–Poisson Systems as Action-Minimizing Paths in the Wasserstein Space

This paper uses a variational approach to establish existence of solutions (σ _t , v _t ) for the 1-d Euler–Poisson system by minimizing an action. We assume that the initial and terminal points σ ₀, σ _T are prescribed in , the set of Borel probability measures on the real line, of finite second-order moments. We show existence of a unique minimizer of the action when the time interval [0,T] satisfies T < π. These solutions conserve the Hamiltonian and they yield a path t → σ _t in . When σ _t  = δ _y(t) is a Dirac mass, the Euler–Poisson system reduces to . The kinetic version of the Euler–Poisson, that is the Vlasov–Poisson system was studied in Ambrosio and Gangbo (Comm Pure Appl Math, to appear) as a Hamiltonian system. WG gratefully acknowledges the support provided by NSF grants DMS-02-00267, DMS-03-54729 and DMS-06-00791. TN gratefully acknowledges the postdoctoral support provided by NSF grants DMS-03- 54729 and the School of Mathematics. AT gratefully acknowledges the support provided by the School of Mathematics.     

Prediction of mixed-mode fracture based on an elasto–plastic energy balance criterion

The maximum energy release rate criterion, i.e., G _max criterion, is commonly used for crack propagation analysis. This fracture criterion is based on the elastic macroscopic strength of materials. In the present investigation, however, the G _max criterion has been modified in order to accommodate the consideration of plastic strain energy. This modified criterion is extended to study the fatigue crack growth characteristics of mixed-mode cracks. To predict crack propagation due to fatigue loads, a new elasto–plastic energy model is presented. This new model includes the effects of material properties such as strain hardening exponent n, yield strength σ _y , and fracture toughness and stress intensity factor ranges. The results obtained are compared with those obtained using the commonly employed crack growth law and the experimental data.     

Direct simulation of isolated elliptic vortices and of their radiated noise

The aerodynamic evolution and the acoustic radiation of elliptic vortices with various aspect ratios and moderate Mach numbers are investigated by solving numerically the full compressible Navier–Stokes equations. Three behaviours are observed according to the aspect ratio σ = a/b where a and b are the major and minor semi-axes of the vortices. At the small aspect ratio σ = 1.2, the vortex rotates at a constant angular velocity and radiates like a rotating quadrupole. At the moderate aspect ratio σ = 5, the vortex is initially unstable. However the growth of instability waves is inhibited by the return to axisymmetry which decreases its aspect ratio. The noise level becomes lower with time and the radiation frequency increases. For vortices with larger aspect ratios σ ≥ 6, the return to axisymmetry does not occur quickly enough to stop the growth of instabilities, which splits the vortices. Various mergers are then found to occur. For instance in the case σ = 6, several successive switches between an elliptic state and a configuration of two co-rotating vortices are observed. The present results show that the initial value of the aspect ratio yields the relative weight between the return to axisymmetry which stabilizes the vortex and the growth of instabilities which tends to split it. Moreover the noise generated by the vortices is also calculated using the analytical solution derived by Howe (J. Fluid Mech. 71:625–673, 1975) and is compared with the reference solution provided by the direct computation. This solution is found to be valid for σ = 1.2. An extended solution is proposed for higher aspect ratios. Finally, the pressure field appears weakly affected by the switches between the two unstable configurations in the case σ = 6, which underlines the difficulty to detect the split or the merger of vortices from the radiated pressure. This study also shows that elliptic vortices can be used as a basic configuration of aerodynamic noise generation.      

The leakage criterions of thin-wall pressure vessels,materials of missile and spacecraft

This paper presents the development of three leadage criterions to predict fracture in thin-wall pressure vessels, materials of missile and spaceraft. Experimental results show that the criterions are successful.I. Notation P internal pressure kg/mm² - _b critical stress kg/mm² - t wall thickness mm - r internal radius mm - t _o wall thickness at crack tip mm - r _o internal radius at crack tip mm - _B yield strength kg/mm² - _H circumferential stress at the yield tange of the crack tip kg/mm² - n rate of strain gardening - 2c length of surface-crack mm - a depth of surface-crack mm - L length of testing piece mm - K, C, B, aA constant     

Analytical evaluation of stress-strain test data

An analytical model for deducing the actual stress-strain properties from laboratory test results is discussed. As an illustration, an elastic bilinear material is used for unconfined cylindrical compression test conditions, as simulated with a finite element analysis. The results obtained are applicable for assisting in evaluating measured strength and stiffness properties of some clay soils, concrete test cylinders, concrete cores, and rock cores.The quantitative results of this study can be used for interpreting measured stress-strain data for unconfined compression test conditions. The error in measured results is shown to be influenced by Poisson's ratio, length-to-diameter ratio of the specimen, end condition, and ratio of inelastic modulus to initial elastic modulus. Curves for adjusting the measured results to the theoretical results are presented.Nomenclature D specimen diameter - E _i initial elastic stiffness modulus - E _y elastic stiffness modulus beyond the yield stress, plastic or inelastic modulus - L specimen length - axial strain - _av average strain - _g gage length strain - _y yield strain - Poisson's ratio - compressive stress - _av average stress - _t theoretical compressive stress - _y yield stress - _ym measured stress at the yield strain     

Long-term strength of metals in complex stress state (a survey)

An analytic survey of experimental data and theoretical approaches characterizing the long-term strength of metals in complex stress state is given. In Sections 2 and 3, the results of plane stress tests (with opposite and equal signs of the nonzero principal stresses, respectively) are analyzed. In Section 4, the results of inhomogeneous stress tests (thick-walled tubes under the action of internal pressures and tensile forces) are considered. All known experimental data (35 test series) are analyzed by a criterion approach. An equivalent stress σ _e is introduced as a characteristic of the stress state. Attention is mainly paid to the dependence of σ _e on the principal stresses. Statistical methods are used to obtain an expression for σ _e, which can be used to study various types of the complex stress state. It is shown that for the long-term strength criterion one can use the power or power-fractional dependence of the time to rupture on the equivalent stress. The methods proposed to describe the test results give a good correspondence between the experimental and theoretical values of the time to rupture. In Section 5, the possibilities of complicating the expressions for σ _e by using additional material constants are considered.