基于应变硬化模型的复合自增强圆筒的应力分析

自增强是通过提高压力容器的残余应力来增强他们的承载能力和疲劳寿命。自增强复合圆筒可以承受比一个具有相同尺寸的单层圆筒更高的压力。引入了应变硬化模型,对自增强复合圆筒的残余应力进行了分析,并对其分布进行了预测。研究表明:复合圆筒内壁的切向残余应力和应力幅随着超应变度的增大而增大。缩套是提高压缩残余应力的一个非常有效的方法。     

A residual stress analysis program using a Matlab GUI on an autofrettaged compound cylinder

A program for the residual stress analysis of an autofrettaged compound cylinder is designed using a Matlab graphical user interface (GUI) and program design technique. The high-pressure vessels are autofrettaged in order to increase their operating pressure and fatigue life. An autofrettage process causes plastic expansion of the inner section of the cylinder, adding residual compressive stress to the bore after relaxation. Such a compound cylinder is produced via a shrink-fit procedure that incorporates a monobloc tube that has previously undergone autofrettage. This paper presents a simple and visual tool to calculate the residual stress and describe the distribution of residual stress for both the elastic-perfectly plastic model and the strain-hardening model.     

基于三剪统一强度准则的厚壁圆筒自增强分析

基于三剪统一强度准则,考虑材料应变强化效应、包辛格效应、拉压异性及中间主应力的影响,采用双线性强化材料模型对厚壁圆筒进行自增强分析,得到了厚壁圆筒加载应力、残余应力和工作应力的解析解,提出了最佳自增强压力的计算方法,探讨了拉压比、强度准则变化参数的影响,比较了自增强处理和非自增强处理及双线性强化模型和理想弹塑性模型厚壁圆筒的应力分布差异。研究结果表明：厚壁圆筒的最佳自增强压力随半径比和强度准则参数的增大而增大;工作时的最大等效应力随半径比和强度理论参数的增大而减小,随拉压比的增大而增大;自增强等效应力的最大值在弹塑性分界面处,且应力沿壁厚的分布较均匀;与理想弹塑性模型相比,双线性强化模型所对应的弹塑性分界面半径和残余应力较小,且随着自增强压力的增大,两种模型的差值越来越大;等效应力随半径比的变化规律可为厚壁圆筒选择合理的壁厚提供一定的参考;自增强技术可改善厚壁圆筒工作时的实际应力分布,提高其极限承载能力。     

Effect of optimum plastic depth on stresses and load-bearing capacity of autofrettaged cylinder

Autofrettage is an effective measure to even distribution of stresses and raise load-bearing capacity for (ultra-)high pressure apparatus. Currently, the research on autofrettage has focused mostly on specific engineering problems, while general theoretical study is rarely done. To discover the general law contained in autofrettage theory, by the aid of the authors’ previous work and according to the third strength theory, theoretical problems about autofrettage are studied including residual stresses and their equivalent stress, total stresses and their equivalent stress, etc. Because of the equation of optimum depth of plastic zone which is presented in the authors’ previous work, the equations for the residual stresses and their equivalent stress as well as the total stress and their equivalent stress are simplified greatly. Thus the law of distribution of the residual stresses and their equivalent stress as well as the total stress and their equivalent stress and the varying tendency of these stresses are discovered. The relation among various parameters are revealed. The safe and optimum load-bearing conditions for cylinders are obtained. According to the results obtained by theoretical analysis, it is shown that if the two parameters, namely ratio of outside to inside radius, k, and depth of plastic zone, kj, meet the equation of optimum depth of plastic zone, when the pressure contained in an autofrettaged cylinder is lower than two times the initial yield pressure of the unautofrettaged cylinder, the equivalent residual stress and the equivalent total stress at the inside surface as well as the elastic-plastic juncture of a cylinder are lower than yield strength. When an autofrettaged cylinder is subjected to just two times the initial yield pressure of the unautofrettaged cylinder, the equivalent total stress within the whole plastic zone is just identically equal to the yield strength, or it is a constant. The proposed research theoretically depicts the stress state of ultra-)high pressure autofrettaged cylinder more accurately and more reasonably and provides the reference for design of (ultra-)high pressure apparatus.     

含缺陷自增强厚壁圆筒塑性极限载荷分析

基于有限元理论,建立内壁含椭球形凹坑的厚壁圆筒有限元模型,模拟厚壁圆筒自增强过程的应力应变。采用三种不同的方法计算含凹坑缺陷的自增强厚壁圆筒的结构极限载荷,给出不同尺寸缺陷对极限载荷的影响规律。通过对比自增强与非增强条件下的极限载荷,表明自增强技术不能有效提高厚壁圆筒的极限承载能力,但在结构极限载荷下,含凹坑缺陷的自增强厚壁圆筒存在一个缺陷尺寸相对不敏感区,对提高结构的安全性是有利的。     

The overstrain of Thick-Walled cylinders considering the bauschinger effect factor (BEF)

An independent kinematic hardening material model in which the reverse yielding point is defined by the Bauschinger effect factor (BEF), has been defined for stainless steel SUS 304. The material model and the BEF are obtained experimentally and represented mathematically as continuous functions of effective plastic strain. The material model has been incorporated in a non-linear stress analysis for the prediction of reverse yielding in thick-walled cylinders during the autofrettage process of these vessels. Residual stress distributions of the independent kinematic hardening material model at the onset of reverse yielding are compared with residual stresses of an isotropic hardening model showing the significant effect of the BEF on reverse yielding predictions. Critical pressures of direct and reverse yielding are obtained for the most commonly used cylinders and a range of permissible internal pressures for an efficient autofrettaged process is recommended.     

Autofrettage of thick-walled pipe bends

The bending of a thick-walled cylinder to a given radius involves an elastic–plastic deformation that results in a residual, axial stress distribution. The latter alternates from maximum tension to maximum compression between top and bottom halves of the cross-section. The residual stress levels depend upon the depth of plastic penetration and may be determined as a closed solution when they arise from a bending moment applied to either a non-hardening or linearly-hardening material. When the bent pipe receives an autofrettage treatment without an intermediate heat treatment, this produces a further residual, triaxial stress state. The interaction between the residual states from bending and autofrettage has an important effect upon the net axial stress and the equivalent stress. It is shown that large plastic penetrations arising from bending and autofrettage can residually stress the section beyond its yield point: in tension and in compression across both its halves. With the unloading from each process, a Bauschinger effect reduces the yield point to assist with the onset of reversed plasticity. The latter is far less beneficial than when unloading is elastic. It is shown how a nonlinear kinematic hardening model can be employed to avoid unloading plasticity at the inner and outer diameters. The consequence of interacting residual stresses is that axial stress can play as important a role as hoop stress when designing for safe service loadings. In general, an enhanced residual stress state is beneficial when compressive but detrimental when tensile. Pre-compression is often employed in practice to reduce tensile stress arising from internal pressure, axial force and self-weight. Here, the compressive residuals arising from an autofrettage treatment have long been exploited to enhance the fatigue life of process piping and weaponry.     

厚壁圆筒安定问题的统一解析解

采用双剪统一强度准则对理想弹塑性材料的厚壁圆筒进行安定性分析,得出了厚壁圆筒加载应力、残余应力及安定极限压力的统一解析解。所得的解不仅能包含以往基于Tresca准则、Mohr—Coulomb准则和广义双剪准则的结果,而且给出一系列新的结果。这些结果能考虑材料的拉压强度差效应及中间主应力效应,因而适应于多种材料。最后,利用所得的解研究了材料的中间主应力效应和拉压强度差效应对厚壁圆筒安定极限压力的影响。结果表明：当考虑材料的拉压强度差效应及中间主应力效应时,厚壁圆筒安定极限压力将明显提高。     

Elastic-plastic analysis of a rolling disk by finite elements

An elastic-plastic finite element method is employed to determine the stress distribution in a circular disk rolling on a rigid track and subjected to hub loads. This model can be assumed to represent a railroad wheel. Of particular interest are the stresses that exceed the initial yield limit near the point of contact. The material constitutive laws considered herein represent elastic-perfectly plastic and strain hardening materials that obey Mises' yield condition. It is shown that unloading of the previously yielded elements due to rotation can be easily handled by the direct stiffness tangent modulus approach. Total and plastic strains, and the plastic work in the disk model are given for the entire rolling history of the disk. It is also demonstrated that the disk will shake down to a purely elastic steady state for load values beyond the initial yield if the material of the disk exhibits even a small amount of strain hardening.     

Analysis on autofrettage of cylinders

Autofrettage is an effective technique to improve load-bearing capacity and safety for pressure vessels.For autofrettaged cylinder,the depth of plastic zone,or overstrain is a key factor which affects load-bearing capacity and safety.The previous research on overstrain was not done in terms of the point of view of raising load-bearing capacity as far as possible and simultaneously avoiding compressive yield for cylinders experiencing autofrettage handling,and there were no analytic solutions of autofrettage in the above view point presented,the 3rd and 4th strength theories were not applied synthetically in the research to compare the results from these two theories.In this paper,with the aid of the analytic method,based on summing up the authors’ previous research,results from autofrettage of a cylinder based on the 3rd and 4th strength theories are studied and compared,and the laws contained in the results are looked into.Then,the essential cause and reason for the obtained laws are analyzed and the inherent and meaning relations between various parameters in autofrettage theory are revealed.It is shown that the maximum radius ratio for equivalent residual stress at inside surface never exceeds the yield strength even for a cylinder experiencing wholly yielded autofrettage,or the critical radius ratio is kc=2.218 457 489 916 7…,irrespective of the 3rd or 4th strength theories.The equation relating the depth of plastic zone with the thickness of a cylinder is identical for the 3rd and 4th strength theories.In form,the optimum load-bearing capacity of an autofrettaged cylinder is two times the initial yield pressure of the unautofrettaged cylinder irrespective of the 3rd or 4th strength theory.The revealed inherent relations between various parameters and varying laws of the parameters as well as the forms of the relations under the 3rd and 4th strength theories not only have theoretical meanings but also have prospects in engineering application.     

自增强内锥圆筒压力容器的弹塑性应力分析

根据材料的实际性能实验得出了高强度的混合硬化模型,对自增强厚壁内锥圆筒组合式压力容器加载时的应力奕变和卸载后的残余应力应变,建立了非线性边界无限制的计算格式,得到了这种类型的压力容器沿径向和轴向的应力场,并通过超高压自增强实验与有限元计算进行了验证。     

Stress analysis of the strain rate hardening materials in axially symmetric field

This paper presents an analysis of a circular hollow cylinder composed of strain rate hardening plastic material subjected to a sudden internal pressure loading. Materials satisfying the constitutive relation, and Levy-Mises equation are considered in the analysis. Dynamic and static analyses of axially symmetric material loaded under plane strain condition are described. The paper discusses the effect of strain rate hardening exponent, m, on the dynamic and static plastic response in the axially symmetric medium. A method is presented for the determination of the strain rate hardening exponent by measuring the hoop stress on the outer surface of a thin cylindrical specimen using the static solution.     

自增强疲劳寿命的理论分析

自增强处理是化工、石油行业提高高压设备承载能力和疲劳寿命的重要举措。文中利用断裂力学理论和疲劳损伤理论,探讨研究了自增强处理后残余应力对高压设备寿命的影响,得出引入残余压应力能提高高压设备寿命的结论,对今后在自增强处理方面的实验与理论研究具有指导意义。     

An analysis of the can effect in an isostatic pressing of copper powder

Based on an elastic-plastic analysis of the can deformation, experimental data from Wadley et al. (1991, Acta Metall. Mater.39, 979) are used to evaluate the shielding effect of the can in an isostatic pressing of copper powder. The calculation indicates that the consolidation of the powder compact is preceded by a stage of powder rearrangement. Thereafter, during consolidation, it is found that in this particular case, compressive stresses in the powder are about 20 MPa less than the pressure applied to the exterior of the can. Furthermore, the powder is not in a state of hydrostatic pressure. The axial compressive stress in the powder is less than the transverse compressive stress. This effect is due to the can which supports a larger load in the axial direction compared to the radial direction during plastic deformation. A model for the nonisostatic yielding of metal powder is compared to the data. It is found that strain hardening must be allowed for to get agreement between the model and the experiment for cold pressing.     

双金属复合管液压成形压力的计算

根据基本假设，建立双金属复合管的材料模型及力学模型。采用弹塑性理论，分析双金属复合管液压成形过程中内管及外管的应力应变状态。利用变形协调条件，得出液压力Pi与复合管内外管之间残余接触压力Pe^*的计算公式，给出液压成型压力的最大值与最小值，并通过试验验证理论公式的准确性。双金属复合管复合成形时要想获得残余接触压力，外层管材料屈服强度必须大于内层管材料屈服强度或强化后的应力值。     

泵阀箱材质自增强与疲劳强度研究

以内壁带“Ｖ”型缺口的厚壁圆环为对象,对两种高压泵阀箱常用钢４３ＣｒＮｉ２ＭｏＶａ、４２ＣｒＭｏＡ在自增强处理前后的疲劳寿命进行了理论分析与实验研究。首先用弹塑性有限元法计算了自增强后所形成的残余应力,发现自增强处理后在缺口根部所形成的残余应力有一最大值,有明显的残余应集中现象。     

A Finite Element Study of an Elasto-Plastic Disk or Cylindrical Contact Against a Rigid Flat in Plane Stress with Bilinear Hardening

This work presents a finite element study of elasto-plastic cylindrical contact. The geometry could also be described as a vertically aligned disk whose axis of symmetry is parallel to the contact surface. The cylinder is considered to be in the plane stress state. The material of the cylinder is modeled as elasto-plastic with bilinear hardening (also known as linear hardening). Simulations for a range of material properties and deflections typical to engineering applications are carried out. A mesh convergence study has also been performed. By employing symmetry, the cylinder has been modeled as a quarter circle and a straight line is used to model the opposing rigid flat surface. The finite element results for the elastic and fully plastic cylindrical contact cases are compared to other existing models such as Hertz contact and spherical elasto-plastic models. Since the case considered is plane stress, the stress distribution is significantly different from elasto-plastic spherical contacts, which would be closer to a plane strain case. An empirical relationship is fit to the results to allow for prediction of the contact width as a function of displacement and force.     

Fretting Wear Behavior of Laser Peened Ti-6Al-4V

This work deals with the influence of laser peening on the fretting wear behavior of Ti-6Al-4V. Laser peening was carried out on Ti-6Al-4V. The laser-peened surface was characterized by transmission electron microscopy. Surface roughness, nanoindentation hardness, residual stress, and tensile properties of the material in both laser-peened and unpeened conditions were determined. Fretting wear tests were conducted at different normal loads using a ball-on-flat contact geometry. Laser peening resulted in the formation of nanocrystallites on the surface and near-surface regions, increased hardness, and compressive residual stress. Laser peening did not affect the tensile properties and surface roughness significantly. There was no considerable difference between the values of the tangential force coefficient of laser-peened and unpeened samples. The fretting scar size, wear volume, and wear rate of laser-peened specimens were lower than those of unpeened samples. This may be attributed to an increase in surface hardness due to strain hardening and grain refinement at the surface and near-surface regions, higher compressive residual stress, and higher resistance to plastic deformation of laser-peened samples.     

高压聚乙烯反应管自增强残余应力的无损检测

针对超高压聚乙烯反应管内径小,壁厚大,内部介质压力为超高压等特点,。开发出一套管内壁应变片粘贴装置和引线密封装置,从而保证了内压达550MPa以上时应变片及引线的密封与绝缘性,基于内壁应变－压力关系曲线与残余应力之间的对应关系,成功地测取了反应管内壁残余应力。本方法可推广应用于小管径管道内壁应变和自增强残余应力的测试。     

Residual stress analysis of an external grooved thick-walled pressure vessel

Residual stress analysis of an autofrettaged thick-walled pressure vessel containing an external groove was described in order to calculate the stress concentration at the external groove. The autofrettage residual stress distributions of the external grooved thick-walled pressure vessel were simulated using an equivalent thermal loading from the analogy of thermal and autofrettage residual stress fields. Thermal stresses due to the simulated thermal loadings for various degrees of autofrettage overstrain level were computed using finite element methods. Very high stress concentration factors due to autofrettage loadings were obtained at the external groove root that contained a sharp root radius. Experimental measurement of residual stresses for a fully autofrettaged smooth thick-walled pressure vessel using an equivalent saw cut method resulted in very close agreement with the theoretical autofrettage residual stress distributions. The stress analysis results implied that the autofrettage residual stress concentration might cause a cracking problem at the external groove root of the thick-walled pressure vessel, indicating that lower autofrettage overstrain and a groove geometry change were desirable for enhanced durability.