Autofrettage process analysis of a compound cylinder based on the elastic-perfectly plastic and strain hardening stress-strain curve

The autofrettage process enhances the carrying capacity and fatigue lifetime of pressure vessels by increasing their residual stress. A compound cylinder was introduced in order to increase residual stress. An autofrettaged compound cylinder can resist a higher pressure than a single cylinder having the same dimension. This residual stress can be measured through experimental or calculation processes. In this study, residual stress analysis of an autofrettaged compound cylinder was conducted. The elastic-perfectly plastic and strain hardening models were investigated. The residual stress distribution of the autofrettaged compound cylinder with shrink fit tolerance was predicted. Shrink fit is a very efficient way to extend compressive residual stress. The compressive residual stress of the strain-hardening model is smaller than that of the elastic-perfectly plastic model because of the Bauschinger effect. The compressive residual stress of the strain hardening model decreased by up to 80% overstrain level.     

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。     

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。     

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.     

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.     

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。     

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.     

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。     

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.     

Elastic-plastic stress analysis and fatigue lifetime prediction of cross-bores in autofrettaged pressure vessels

Elastic-plastic stress analysis has been performed to evaluate the fatigue life of an autofrettaged pressure vessel containing cross-bores subjected to pulsating internal pressure of 200 MPa. Finite element analyses were used to calculate the residual and operating stress distributions of the pressure vessel due to the autofrettage process and pulsating internal pressure, respectively. Theoretical stress concentration factors of 3.06, 2.58, and 2.64 were obtained at the cross-bore of the pressure vessel due to internal pressure, 50%, and 100% autofrettage loadings, respectively. Local stresses and local strains determined from the elastic-plastic finite element analysis were employed to calculate the failure location and fatigue life of the pressure vessel with radial cross-bores, incorporating the low-cycle fatigue properties of the pressure vessel steel and fatigue damage parameters. Increase in the amount of overstrain by autofrettage process moved the crack initiation location from the inner radius toward a mid-wall, and extended the crack initiation life, Predicted fatigue life of the fully autofrettaged pressure vessel with cross-bores increased about 50%, compared to the unautofrettaged pressure vessel. At the autofrettage level higher than 50%, the failure location and fatigue life of the pressure vessel were not significantly influenced by the autofrettage level.     

复合机械自紧技术研究

由于Bauschinger效应的影响，自紧厚壁管反向屈服现象普遍存在，使得内壁残余应力减少，厚壁管承载能力下降，因此，通过复合机械自紧技术，可消除Bauschinger效应，提高自紧厚壁管的弹性强度。本文在理论上和工艺上对复合自紧技术进行了研究，结果表明可大幅提高自紧 厚壁管的强度，这对自增强压力容器和管道设计具有指导意义。     

Plastic depth and load-bearing capacity of autofrettaged cylinders

Autofrettage technology is usually adopted to even out and reduce stresses as well as improve the load-bearing capacity of a variety of cylindrical ultra-high mechanical apparatuses. The autofrettage of cylinders is theoretically investigated based on maximum shear stress theory or the Tresca criterion to establish the general law for autofrettage theory. The equation for the optimum plastic depth for a certain load and radius ratio is derived to ensure that the equivalent stress of the total stress does not exceed the yield limit and the absolute value of the equivalent stress of the residual stress at the internal surface likewise does not exceed the yield limit. Through this equation, a set of concise equations for total stress and residual stresses are obtained. The safe and optimum load-bearing conditions for cylinders are presented. Results show that, provided the pressure contained in a cylinder is equal to the autofrettage pressure, irrespective of k _j, the equivalent total stress, σ_e, equals the yield limit everywhere in the entire plastic zone, that is, σ_e is a constant. In the elastic zone, σ_e is always lower than the yield limit, but if k _j is outside the quasi-infinite area enclosed by the curves of the sense and possible plastic depth, then either compressive yield occurs or k _j is meaningless. The results based on the Mises criterion and Tresca criteria are compared.     

热预应力自增强厚壁圆筒研究

厚壁圆筒自增强处理技术的关键在于预应力。传统的自增强处理技术采用的是机械预应力方法,即在圆筒投入使用前,对其施加超过操作压力的自增强压力,使之获得残余预应力。考虑到厚壁圆筒内、外壁存在温差时,筒壁中有热应力产生,因此针对厚壁圆筒自增强问题,提出了以热应力作为预应力的自增强技术。具体研究了圆筒壁厚、温差等对热应力与总应力(热应力与操作应力的叠加)的影响、热应力与总应力的变化趋势、各种参数间的约束条件;在分析热应力与总应力特性的基础上,得出最佳设计条件,提出了基于第四强度理论的热预应力自增强厚壁圆筒的设计方法。结果表明,热预应力能有效地降低和均化厚壁圆筒的操作应力;按照所提出的设计方法,在确保圆筒安全的前提下,可使圆筒获得最大的承载能力和最小的壁厚。     

残余应力松弛和自增强处理压力对在役高压容器的安全影响

为了确定残余应力松弛和自增强处理压力对在役高压容器安全性能的影响,通过分析测试结果获得了残余应力的松弛规律,计算了在工作压力、残余应力作用下的当量等效应力沿壁厚分布情况,模拟计算出了不同的工作压力、自增强处理压力下的安全系数,推导出了最佳自增强处理压力。结果表明所研究的高压聚乙烯反应管在使用10年后,环向应力在近内壁区衰减最快,从-600MPa衰减到-333MPa,衰减率达45%;在弹性区衰减较小,残余应力峰值位置外移,但其峰值大小变化不大。对于自增强处理后的压力容器,在工作压力作用下,随着残余应力的松弛,内壁面当量等效应力增大,当量等效应力在弹塑性交界处最大,应该按此处的当量等效应力计算安全系数。依据示例聚乙烯反应管尺寸,模拟计算出在工作压力分别为180、280、380MPa时,经过自增强处理压力分别为606、677、743MPa的最佳自增强处理后,其安全系数比残余应力全部衰减为0时分别高16%、26%、37%。压力容器工作压力越大,经最佳自增强处理后安全系数增大得越多,但残余应力衰减对其安全影响越大。     

A comparative study of thermal and hydraulic autofrettage

Thermal autofrettage is a potential process to generate beneficial compressive residual stresses at and around the inner wall of a thickwalled cylinder for increasing its pressure carrying capacity. Due to its simplicity and inexpensive arrangement, it can compete with the conventional hydraulic autofrettage process. In this work, a comparative study of the thermal autofrettage and the hydraulic autofrettage is carried out. As the thermal autofrettage does not require hydraulic power pack, the process is more economical than the hydraulic autofrettage. The thermal autofrettage process is also studied for the thick-walled cylindrical vessels subjected to high thermal gradient with or without pressure and is compared with the hydraulic autofrettage. Comparison shows that for cylinders subjected to high thermal gradient without pressure, the thermal autofrettage is superior to the hydraulic autofrettage.     

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。     

双层缩套厚壁筒自增强残余应力分析

基于ANSYS平台,使用APDL语言开发了双层缩套厚壁筒自增强残余应力求解参数化有限元接触模型。考虑缩套预应力的影响,基于理想弹塑性材料模型和Mises屈服准则,推导出了双层缩套厚壁筒自增强残余应力解析解,并将其有限元分析值和解析解进行了比较,有限元分析值与解析解在屈服区结果一致,而在弹性区略有差别,与已有的解析解相比,由于考虑了缩套初始预应力对自增强处理过程应力状态的影响,其残余应力有限元模型的仿真结果和解析解都具有更高的精度。     

厚壁圆筒自增强压力的优化分析

采用考虑材料应变强化效应和包辛格效应的双线性材料模型,建立了厚壁圆筒自增强理论模型。基于工作时的等效应力及周向应力,提出了最佳自增强压力的评定方法并给出了理论求解过程。采用有限元软件对自增强厚壁圆筒涉及的三个加载过程进行模拟分析,模拟结果与理论计算结果相吻合。由模拟结果得到了厚壁圆筒工作时的最大等效应力和最大周向应力与自增强压力的关系曲线,并采用直接加权组合法进行优化,得到了最佳自增强压力。研究结果为厚壁圆筒最佳自增强压力的求解提供了新思路,具有一定的工程意义。     

Influence of reverse yielding on residual stresses induced by autofrettage

The paper investigates the influence of reverse yielding on residual stresses induced by autofrettage. On the basis of reverse loading tests, a material model is developed and implemented into analytical procedures capable of treating the elasto-plastic deformation behaviour of thick-walled tubes during both loading and unloading phases. The results show that residual hoop stresses are drastically reduced near the tube bore as compared with residual stresses obtained from conventional isotropic hardening analysis. Pure kinematic hardening analysis is also shown to overestimate residual hoop stress induced by autofrettage.