The spherical vessel with anisotropic creep properties considering large strains

The effect of material anisotropy on creep of pressurized thick-walled spherical vessel has been discussed considering the large strain theory. It is found that the creep strain varies with varying anisotropy of the material. The results obtained for the anisotropic case have been compared with those obtained for the isotropic case and it is observed that the stress and strain distribution in the wall of the vessel is strikingly different for the two cases.     

Creep of thick-walled cylinders subjected to internal pressure and axial load

A creep theory is presented to predict deformations at any specified time for a thick-walled cylinder subjected to internal pressure and axial load. The theory is based on the usual assumptions that the deformations are infinitestimal, that the material is incompressible and that the total strain theory is valid. The stress-strain-time relation for the material is assumed to be represented by an isochronous stress-strain diagram which is approximated by an arc hyperbolic sine function. The experimental part of the investigation included tests of thick-walled cylinders made of high-density poly-ethylene whose ratio of outside to inside radii were either 1.5 or 2.0. The test cylinders were either tested as closed-ented cylinders with internal pressure or subjected to a combination of internal pressure and axial load. Also, the application of the theory for varying load conditions was studied. Good agreement was found between theory and experiment.     

Limit analysis of viscoplastic thick-walled cylinder and spherical shell under internal pressure using a strain gradient plasticity theory

Plastic limit load of viscoplastic thick-walled cylinder and spherical shell subjected to internal pressure is investigated analytically using a strain gradient plasticity theory. As a result, the current solutions can capture the size effect at the micron scale. Numerical results show that the smaller the inner radius of the cylinder or spherical shell, the more significant the scale effects. Results also show that the size effect is more evident with increasing strain or strain-rate sensitivity index. The classical plastic-based solutions of the same problems are shown to be a special case of the present solution.     

柱状装药爆炸条件下厚壁圆筒爆室内 流场及结构动力响应分析

借助非线性动力有限元程序ANSYS/LS-DYNA,采用基于罚函数的流固耦合算法,对厚壁圆筒爆 室在柱状装药爆炸作用下的动态响应过程进行了数值模拟研究。分析了厚壁圆筒爆室内柱状装药爆炸非定 常流场的演化过程以及筒体的动力响应特征。给出了爆炸流场的压力云图、筒壁受到的爆炸压力峰值及冲量 的分布规律、筒体的等效应力云图以及等效应力的分布规律等。流场压力及筒体应变的计算结果与实测结果 吻合较好,并将动力响应的有限元计算结果与理论解进行了比较,证明轴对称平面应变假设下的理论解可以 给出问题的保守估算。分析表明,该厚壁圆筒爆室在柱状装药爆炸作用下在弹性范围内工作,爆室的强度设 计是安全的。     

Note on the Radial Deformation and Stresses in Anisotropic Nonhomogeneous Elastic Media

Abstract

In this paper we study the elasticity problem of a cylindrically anisotropic, elastic medium bounded by two axisymmetric cylindrical surfaces subjected to normal piessures (plane strain). The material of the structure is orthotropic with cylindrical anisotropy and, in addition, is continuously inhomogeneous with mechanical properties varying along the radius. General solutions in terms of Whittaker functions are presented. The results obtained by St. Venant for a homogeneous cylindrically anisotropic medium can be deduced from the general solutions. The problem of a solid cylinder of the same medium under the external pressure is also solved as a particular case of the above problem. Problems of the type covered in this paper are encountered in nuclear reactor design.     

A Study on Hydraulic Autofrettage of Thick-Walled Cylinders Incorporating Bauschinger Effect

Pressure vessels which are subjected to cyclic external or internal high pressure are used in many fields of industry and need to be sure of reliability and safety. To ensure of reliability and safety, thick-walled cylinder, such as a cannon or nuclear reactor, is autofrettaged to induce advantageous residual stresses. The compressive residual stress which was introduced by autofrettage process acts to offset the tensile residual stress induced by internal pressure. It increases operating pressure and restrains crack initiation and crack propagation. As the autofrettage level increases, the magnitude of compressive residual stress at the bore also increases. However, the Bauschinger effect reduces the compressive residual stresses with prior tensile plastic strain, and decreases the beneficial autofrettage effect. There are some differences between theoretical solution considering elastic-perfectly material behavior and real autofrettage process results. The purpose of the present paper is to predict the accurate residual stress of SNCM 8 high strength steel using the Kendall model which was adopted by ASME Code. The tensile and uniaxial Bauschinger effect tests of SNCM 8 were performed to evaluate Bauschinger effect factor(BEF), thereafter this constant was used in calculating the residual stress. The residual stress distribution which is considering the Bauschinger effect was profiled using Kendall model, and the results were compared with the analytical and Finite Element analysis. The results were found that residual stress incorporating the Bauschinger effect at bore was smaller than ideal calculation. These results should be considered in designing pressure vessels.     

Thermoelastoplastic deformation of a thick-walled cylinder with a radial crack

The thermoelastoplastic fracture mechanics problem of a thick-walled cylinder subjected to internal pressure and a nonuniform temperature field is solved by the method of elastic solutions combined with the finite-element method. The correctness of the solution is provided by using the Barenblatt crack model, in which the stress and strain fields are regular. The elastoplastic problem of a cracked cylinder subjected to internal pressure and a nonuniform temperature field are solved. The calculation results are compared with available data. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 173–183, May–June, 2008.     

One parameter model for creep in a whisker reinforced anisotropic rotating disc of Al–SiCw composite

Steady state creep in a rotating disc of anisotropic aluminum silicon carbide whisker composite has been studied in the present study. The creep behavior is described by Norton's power law. Stress and strain rate distributions for anisotropic discs have been calculated and compared with those obtained for isotropic disc. It is concluded that the radial strain rate which always remained compressive for the isotropic composite ($\alpha =1.0$) and anisotropic disc ($\alpha =1.3$), becomes tensile in the middle region of the disc when the anisotropy parameter $\alpha =0.7$. Also if α is reduced from 1.3 to 0.7 the variation of tensile strain rate in the tangential direction remains similar but the magnitude reduces by five orders of magnitude. The study revealed that anisotropy introduces significant change in the strain rates although its effect on the resulting stress distribution may be relatively small.     

Effects of initial anisotropy on the finite strain deformation behavior of glassy polymers

Solid phase deformation processing of glassy polymers produces highly anisotropic polymer components as a result of the massive reorientation of molecular chains during the large strain forming operation. Indeed, the polymer preform used as the starting materials is usually anisotropic owing to its prior deformation history. The process end product has often been fashioned for a particular application, i.e. to possess an increased flow strength along a particular axis, thereby exploiting the orientation induced anisotropy effects. The fully three-dimensional issues involved in the use of glassy polymer components include anisotropic flow strenghts, limiting extensibilities, and deformation patterns. These characteristics have been altered by the initial forming operation but are obviously not expected to be enhanced in all directions. The presence of anisotropy in structural components may also lead to premature failure or unexpected shear localization. In this report the effects of initial deformation and the associated anisotropies are investigated through uniaxial compression tests on preoriented polycarbonate (PC) and polymethylmethacrylate (PMMA) specimens. The evolving anisotropy is monitored by testing materials preoriented by various amounts of strain and under different states of deformation. The tensorial nature of the anisotropic material is characterized by examining the preoriented material response in three orthogonal directions. A model for the large strain deformation response of glassy polymers has been shown by Arruda and Boyce [in press] to be well predictive of the evolution of anisotropy during deformation in initially isotropic materials. Here the authors evaluate the ability of the model developed in Arruda and Boyce [in press] to predict several aspects of the anisotropic response of preoriented materials. Using material properties determined from the characterization of the isotropic material response and a knowledge of the anisotropic state of the preoriented material, model simulations are shown to accurately capture all aspects of the large strain anisotropic response including flow strengths, strain hardening characteristics, cross-sectional deformation patterns, and limiting extensibilities. Although anisotropy has been shown to evolve with temperature and strain rate in Boyce, Arruda and Jayachandran [in press] and also state of deformation in Arruda and Boyce [in press], we submit an experimental observation that the subsequent deformation response of preoriented polymers may be predicted using only a measure of optical anisotropy, and not the prior strain or thermal history. Optical anisotropy, as measured for example by birefringence, therefore represents a true internal variable indicative of the evolution of anisotropy with inelastic strain, state of strain, and temperature.     

Stress Singularity in an Elastic Cylinder of Cylindrically Anisotropic Materials

The issue of stress singularity in an elastic cylinder of cylindrically anisotropic materials is examined in the context of generalized plane strain and generalized torsion. With a viewpoint that the singularity may be attributed to a conflicting definition of anisotropy at r=0, we study the problem through a compound cylinder in which the outer cylinder is cylindrically anisotropic and the core is transversely isotropic. By letting the radius of the core go to zero, the cylinder becomes one with the central axis showing no conflict in the radial and tangential directions. Closed-form solutions are derived for the cylinder under pressure, extension, torsion, rotation and a uniform temperature change. It is found that the stress is bounded everywhere, and singularity does not occur if the anisotropy at r=0 is defined appropriately. This revised version was published online in July 2006 with corrections to the Cover Date.     

A comparison of results of axial-tension,rotating-beam and pressurized-cylinder fatigue tests

In a previous paper by Davidson, Eisenstadt and Reiner, it was noted that, as the diameter ratio of an open-end, thick-walled cylinder approached unity, the stress state due to internal pressure approaches that of uniaxial tension. It was, therefore, proposed that the fatigue life of a cyclically pressurized thick-walled cylinder might be predicted from the results of axialtension fatigue tests. In this paper, the results of the thick-walled-cylinder fatigue tests, reported in Ref. 2, extrapolated to a diameter ratio of unity, are compared with the results of axial-tension fatigue tests on the same material. The effect of oil in contact with the surface of the axial fatigue specimens and that of varying the cyclic speed from 1800 cpm to 200 cpm are investigated. Rotating beam fatigue test results for the same material are also reported. The results of the axial-tension fatigue tests do not agree with the extrapolated thick-walled cylinder results in the range of fatigue lives from 10⁴ to 10⁶ cycles with the cylinder results showing the shorter lives. For less than 10⁴ cycles, the results converge. No effect of cyclic speed or of oil in contact with the surface was found. The results of the rotating-beam tests generally lie between the axial-tension and extrapolated cylinder results.     

不同拉压特性的厚壁圆筒极限内压统一解

厚壁圆筒在实际工程领域中应用广泛,若能精确计算出极限内压,对预防事故发生,降低风险有重要意义.工程中存在许多材料,其拉压强度和拉压模量均存在差异,这些差异对极限内压的大小有显著影响.以往研究表明,仅考虑拉压强度与拉压模量的一个方面,计算结果与实际情况存在一定的误差.本文基于双剪统一强度理论,综合考虑中间主应力效应及材料拉压强度和拉压模量的不同,推导了内压作用下厚壁圆筒的弹、塑性状态的应力分布及弹性极限内压、塑性极限内压与安定极限内压的统一解,通过与其他文献对比分析验证了本文计算结果的正确性,分析了半径比、统一强度理论参数、拉压强度比与拉压模量系数对弹性极限内压、塑性极限内压及安定极限内压的影响.结果表明:统一解均随半径比和统一强度理论参数的增大而增大,随拉压强度比的增大而减小,弹性极限内压随材料拉压模量系数的增大而减小,当壁厚增加到一定值后,安定极限内压随材料拉压模量系数的增大而减小;材料的拉压模量不同、拉压强度差异对厚壁圆筒的安定性影响显著,考虑中间主应力效应可使材料的潜能得到更充分发挥,极限内压随半径比的变化规律可为选择合理壁厚提供参考,该结论可为厚壁圆筒的工程应用提供理论依据.     

Stability of boreholes in a geologic medium including the effects of anisotropy

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he analytical solutions of thick-walled cylinder of softening material and its stability

将弹塑性材料的应力应变全过程曲线简化为三线性模型(弹性-线性软化-残余理想塑性), 并 假设材料服从Tresca屈服准则和关联流动法则,推导出受内压厚壁筒的解析解. 在这个解析解 的基础上,讨论了厚壁筒的平衡稳定性问题,内压达到临界载荷时,厚壁筒丧失稳定性,其 临界载荷就是软化塑性材料厚壁筒的承载能力.     

Simplified prediction of the creep buckling of cylinders under external pressure. Part 2: Experimental verification

In this paper, the simplified method, proposed in (Combescure, 1998), for the prediction of creep buckling is compared to experimental results. The model is applied to predict the buckling time of two sets of experiments on cylinders subjected to uniform external pressure. It is shown that the proposed model is satisfactory for this type of prediction: in all cases, the times up to failure predicted by the model are generally lower than the experimental failure times. The model is rather conservative for thicker cylinders. However, it appears that a very detailed geometrical imperfection survey would be necessary if a highly accurate assessement of the creep failure time were sought. It has been observed experimentally that creep buckling is a very dangerous failure mode: nothing seems to happen during a very long “incubation” period but, when the initial imperfection reaches some critical value, buckling then suddenly occurs. For thin cylinders, the level of creep strain at which the instability starts to develop is much lower than the strain at which the tertiary creep initiates; the instability is thus clearly generated from the interaction between the material and the geometrical nonlinearity.     

On Pressurized Curvilinearly Orthotropic Circular Disk, Cylinder and Sphere Made of Radially Nonuniform Material

A unified analysis is presented for the elastic response of a pressurized cylindrically anisotropic hollow disk under assumed conditions of plane stress, or a hollow cylinder under plane strain conditions, and a spherically anisotropic hollow sphere, made of material which is nonuniform in the radial direction according to the power law relationship. The solution for a cylinder under generalized plane strain is also presented. Two parameters play a prominent role in the analysis: the material nonuniformity parameter m, and the parameter ?? which accounts for the combined effects of material anisotropy, represented by the specified parameters (??, ??, ??), and material nonuniformity, represented by the parameter m. The radial and circumferential stresses are the linear combinations of two power functions of the radial coordinate, whose exponents (n ₁ and n ₂) depend on the parameters m and ??. New light is added to the stress amplification and shielding under combined effects of curvilinear anisotropy and radial nonuniformity. Different loading combinations are considered, including the equal pressure at both boundaries, and the uniform pressure at the inner or the outer boundary. While the stress state for the equal pressure loading is uniform in the case of isotropic uniform material (m=0, ??=1), and for one particular radially nonuniform and anisotropic material, it is strongly nonuniform for a general anisotropic or nonuniform material. If the aspect ratio of the inner and outer radii decreases (small hole in a large disk/cylinder or sphere), the magnitude of the circumferential stress at the inner radius increases for n ₁>0 (stress amplification), and decreases for n ₁<0 (stress shielding). Both can be achieved by various combinations of the material parameters m, ??, ??, and ??. While the stress amplification in the case of a pressurized external boundary occurs readily, it occurs only exceptionally in the case of a pressurized internal boundary. The effects of material parameters on the displacement response are also analyzed. The approximate character of the plane stress solution of a pressurized thin disk is discussed and the results are compared with those obtained by numerical solution of the exact three-dimensional disk model.     

Creep analysis with a stress range dependent constitutive model

Many materials exhibit the stress range dependent creep behavior. The power law creep observed for a certain stress range changes to the viscous type creep as the stress value decreases. Recently published experimental data for advanced heat resistant steels indicate that the high creep exponent (in the range 7–12) may decrease to the low value of approximately unity within the stress range relevant for engineering structures. The aim of this paper is to analyze the influence of the stress range dependent power-law-viscous creep transition on the behavior of structures at elevated temperature. A constitutive model for the minimum creep rate is introduced to describe both the linear and the power law creep depending upon the stress level. To demonstrate basic features of the stress range dependent creep modeling, several elementary examples from structural mechanics are presented. They include a stress relaxation problem, a beam subjected to pure bending and a pressurized thick-walled cylinder. Based on the uni-axial transition stress the transition value of the external load is estimated such that above this value the power law can be applied. For the loading levels below this value the character of the stress distribution as well as the stress values are essentially influenced by the viscous creep.     

Damage induced structural instability

Multiaxial stress-strain damage relations, describing both time-independent and time-dependent strain and damage creation are postulated. The influence of damage creation on the load carrying capacity of simple structures is discussed. The time-independent deformation, and loss of stability, of a thick-walled cylinder under torque and internal pressure are analysed. The results are shown to be similar to previously found results for a beam under tension and bending.     

Creep transition in torsion

Stresses for a circular cylinder of compressible material subjected to torsion are derived in closed form for steady state creep. It is shown that the asymptotic solution through stress leads from elastic state to plastic and then to creep and through stress difference leads to the creep state. The effect of compressibility is presented graphically. The results indicate that the value of maximum shear stress for a cylinder of compressible material is greater than that for an incompressible material and increases with the increase in a measure index n. For an incompressible material, as a particular case, the results obtained are the same as given by Marin [9].     

散体介质SHPB被动围压试验体应力计算的理论修正方法

SHPB被动围压试验为探究散体介质在爆炸和冲击荷载作用下的力学行为提供了一个行之有效的方法。针对相关试验设计和计算中存在的弊端和不足,借助经典板壳理论将SHPB被动围压试验中用于约束散体介质的刚性套筒简化为受均匀带状内压作用的圆柱形壳体。理论计算了套筒径向位移、环向应变与均匀带状内压及套筒几何、力学参数的关系,得到了套筒径向位移、环向应变沿其轴向的分布规律;分析了套筒长度、厚度、内外径以及均匀带状内压宽度之间等无量纲几何参数对计算结果的影响;将理论计算结果与试验和数值模拟结果进行对比,验证了理论计算结果的正确性。本文中提出的理论修正方法可为指导散体介质SHPB被动围压试验提供参考。