Bifurcation and post bifurcation behaviour of internally pressurized elastic-plastic circular tubes under plane strain conditions

The nonaxisymmetric bifurcation and post bifurcation behaviours of circular tubes subjected to internal pressure are investigated numerically in terms of the finite element method. It is assumed that tubes are made of elastic-plastic strain hardening material with smooth yield surface and that they deform under plane strain condition. Hill's uniqueness theory along with the Prandtl-Reuss equation and the separation of the variables are employed to obtain the bifurcation point and corresponding mode. The results indicate that the mode with longest wave length is critical and always follows the maximum pressure point for all cases investigated here.

For thin to thick tubes, the post bifurcation behaviours are numerically investigated. The development of unloading region, stress and strain distributions, localization of the deformation and thinning of the tube are clarified.     

Stewart并联机构奇异性与工作空间分析

应用奇异性理论,分析了并联机构在奇异点处的分岔性态。讨论了机构分岔点、理论工作空间和稳定工作空间与静动平台半径比的关系,给出了机构分岔点随静动平台半径比值变化的曲线图,不同比值的机构工作路径跟踪图。研究表明,当静动平台半径比较小时,机构具有较大的工作空间,当静动平台半径比逐渐趋变大时,机构的理论工作空间和稳定工作空间逐渐减小,最后收缩为一个点。     

直动式溢流阀的分岔分析与实验

为了改善广泛应用的直动式溢流阀的颤振行为,考虑油液压缩性、管道弹性和阀芯碰撞阀座时的能量损失,建立了溢流阀无量纲形式的数学模型。以4种不同的弹簧预压缩量,作出了相位和向量场分布图,得到了系统的稳定平衡状态。应用非光滑动态系统理论和计算软件MATLAB,画出了单参数和双参数分岔图,发现系统存在Hopf分岔、极限环鞍结点分岔、广义Hopf分岔和尖点分岔等分岔现象。搭建了测试平台,得到了阀芯位移分岔图和频谱瀑布图,对数学模型进行了实验验证。结果表明,小流量时为混沌或周期碰撞震荡,增大流量可改善阀芯颤振行为,为周期非碰撞震荡或稳定平衡状态。此研究工作为直动式溢流阀的失稳机理和颤振行为提供了理论依据。     

Hydroforming of aluminum extrusion tubes for automotive applications. Part I: buckling, wrinkling and bursting analyses of aluminum tubes

Three possible failure modes have been identified in tube hydroforming: buckling, wrinkling and bursting. A general theoretical framework is proposed for analyzing these failure modes as an elastoplastic bifurcation problem. This framework enables advanced yield criteria and various strain-hardening laws to be readily incorporated into the analysis. The effect of plastic deformation on the geometric instability in tube hydroforming, such as global buckling, axisymmetric wrinkling and asymmetric wrinkling, is precisely treated by using the exact plane stress moduli tensor. A mathematical formulation for predicting the localized condition for bursting failure is established herein. Furthermore, the critical conditions governing the onset of buckling, axisymmetric wrinkling and asymmetric wrinkling are derived in closed-form expressions for the critical axial compressive stresses. Closed-form solutions for the critical stress are developed based on Neale–Hutchinson's constitutive equation and an assumed deformation theory of plasticity. It is demonstrated that the onset of asymmetric wrinkling always requires a higher critical axial compressive stress than the axisymmetric one under the context of tube hydroforming with applied internal pressure and hence the asymmetric wrinkling mode can be excluded in the analysis of tube hydroforming. Parametric studies show that buckling and axisymmetric wrinkling are strongly dependent on geometric parameters such as t₀/r₀ and r₀/ℓ₀, and that axisymmetric wrinkling is the predominant mode for short tubes while global buckling occurs for long slender tubes.     

Finite element analysis and experimental investigation on deformation mechanism of non-axisymmetric tube spinning

This paper developed 3D elastoplastic finite element analysis (FEA) models to investigate non-axisymmetric tubes neck spinning. The three-roller mandreless neck spinning process was simulated by commercial FEA software, MSC. Marc. The distribution of the transient von Mises stresses in the contact zone between the roller and the blank, and the equivalent plastic strains after spinning were obtained. The locations and causes of fractures were analyzed. The thickness distribution of the spun workpiece was investigated numerically and experimentally. It shows that during 3D non-axisymmetric tubes spinning, diametral elongation and fractures mostly occur at the opening end of workpiece, which considered as the primary location of defects. Fractures may also occur easily at the initial spinning area, which may be considered a secondary location of defects. The distributions of equivalent stresses and strains are non-uniform during both offset and oblique 3D non-axisymmetric tubes spinning. The maximum stress and strain values occur at the location where the biggest offset or inclination is induced, while the minimum values occur at the opposite location of 180° away from the maximum values. For the oblique tube, however, the strain distribution changes gradually along the axial direction, which is different from that of the offset tube. Thinning occurs during forward path spinning and thickening occurs during backward path spinning. Therefore, for multipath neck spinning processes, forward and backward paths should be applied alternately to avoid excessive thinning or thickening of workpiece.     

扭曲管换热器管板的有限元分析

采用有限元分析软件ANSYS,对扭曲管换热器的管板在三种工况下的应力进行计算,分析了扭曲管轴向刚度削弱系数对管板应力强度及扭曲管轴向应力的影响。结果表明,扭曲管的轴向变形补偿能力优于普通直管,可以降低在温差载荷作用下管板中的应力,但会提高压力作用下的管板应力。在压力载荷作用下,扭曲管上的平均应力大小与普通直管差别不大,但扭曲管的轴向应力在管子横截面上的分布不均匀,局部的轴向应力远远高于平均应力水平,因此扭曲管抗疲劳和应力腐蚀开裂的能力不如直管。不同厚度的管板受扭曲管管束轴向刚度的影响不同,当管板厚度较小时,扭曲管管束轴向刚度的影响较大。     

三维非轴对称偏心类管件旋压成形时的变形力分析

采用主应力法建立了三维非轴对称偏心类薄壁管件旋压成形时的变形力的理论计算公式,并对旋轮公转角度γ、道次偏移量δ等成形工艺参数对旋压力变化的影响进行了理论分析。结果表明,在偏心类管件旋压过程中,旋压力随旋轮公转角度γ作周期性变化,其变化的幅度取决于道次偏移量δ的大小。对工件道次偏移量δ、旋轮进给比f和名义压下量Δ等主要成形工艺参数对最大旋压力的影响进行了理论分析和试验研究,理论计算结果与试验结果吻合较好。     

An elastoplastic analysis of flange wrinkling in deep drawing process

The onset of flange wrinkling of a deep drawing cup is analyzed as an elastoplastic bifurcation problem. The flange is modeled as an elastoplastic annular plate subject to axisymmetric radial tension along its inner edge. As observed in the laboratory as well as practical industrial applications, aluminum alloy sheets usually wrinkle in the plastic range. Therefore, the critical condition governing the onset of elastoplastic wrinkling is formulated within the context of the general bifurcation theory. A closed-form solution for the critical drawing stress is developed based on an assumed nonlinear plastic stress field and the deformation theory of plasticity. The theory properly accounts for the plastic anisotropy of the aluminum sheets and the critical drawing stress at the onset of wrinkling is also compared against the one employing the flow theory of plasticity. The predicted critical bifurcation stress and the wave numbers are compared to those obtained by Senior's one-dimensional theory. It is demonstrated that there is a strong dependency of the critical bifurcated stress at the onset of wrinkling on the shear stress induced on the flange. The effects of flange width, drawing ratios, material properties, strain hardening on the onset of wrinkling are investigated. The differences between the present theoretical approach and Senior's theory are emphasized.     

Reliability analysis of stainless steel/carbon steel double-layered tube on the basis of thermal deformation behavior

The thermal expansion of pipes depends on both the temperature of the pipe and the expansion coefficient of the piping material at the operating temperature. In the case of a double-layered tube consisting of two different tube materials, the thermal deformation behaviors are dependent on the relative tube sizes, thermal expansion coefficients, and the mechanical properties of the inner and outer tubes. For the safe and reliable application of double-layered tubes that are fabricated by hydroforming, the thermal stress in circumferential direction and the gap between the inner and outer tubes need to be analyzed over a wide range of temperatures (?50°C～200°C). As it is difficult to measure the thermal stress and the gap between tubes at operating temperature, this study has analytically investigated the thermal deformation behavior of a double-layered tube. From the analytical model, the effect of hydraulic pressure, residual stress, and the relative sizes of the inner and outer tubes on the resultant thermal deformation, such as the circumferential thermal stress and the gap between inner and outer tubes, has been analyzed. The analytical results provide a theoretical basis for determining the reliable operating temperature of double-layered tubes.     

Numerical simulation of flows of non-Newtonian fluids in the stenotic and bifurcated tubes

Steady flows of Newtonian and non-Newtonian fluids in the stenotic and bifurcated tubes are numerically simulated. Four rheologically different fluids such as water, aqueous sugar solution, aqueous Carbopol solution and blood are selected for the namerical simulation and the modified power-law model is used for the numerical simulation of non-Newtonian fluids in the stenotic and bifurcated tubes. Apparent viscosity of a non-Newtonian fluid in the modified power-law model is expressed as a function of the shear rate. Flows in the circular tube with sudden contraction-sudden expansion and gradual contraction-gradual expansion are studied numerically. Analyses in the stenotic tubes are concentrated on the effects of rheological properties, the stenotic geometry and Reynolds number. Flow characteristics of Carbopol solution in the stenotic tubes are compared with those of blood. Effects of the bifurcation geometry on the flow behaviors of Newtonian and non-Newtonian fluids are numerically investigated. Numerical analyses are focused on the flow patterns in the branch tubes of which angles are 30°, 60° and 90° and on the diameter ratios for Newtonian and non-Newtonian fluids. Variations of the axial velocity and pressure drop along the bifurcated tubes for various flow parameters are presented for Newtonian and non-Newtonian fluids.     

Maximum load factors corresponding to a slightly asymmetric bifurcation point

Explicit formulations are derived for quantitative evaluation of imperfection sensitivity of critical load factors corresponding to a slightly asymmetric bifurcation point; i.e. the perfect system itself has slight asymmetry. The load factor corresponding to local minimum or maximum along the fundamental equilibrium path and the complementary path are simultaneously obtained as functions of the imperfection parameter. The upper bound of the imperfection parameter is also derived for existence of critical points along the fundamental equilibrium path. This way, interpolation formulas are presented between symmetric and asymmetric systems. The accuracy of the proposed formulas is verified by the examples of rods supported by translational and rotational springs.     

花键管挤压成形研究

分析了冷挤压成形花键管的可行性，包括挤压成形的力学计算、摩擦力分析和模具的初步设计。应用模拟分析软件，根据初步的设计结果，模拟花键管冷挤压成形的挤压变形过程，受力状况及应力分布。并根据模拟结果适当改进模具结构。最终进行模具的设计加工和表面磷化皂化处理，有效减小挤压加工过程中的摩擦，在压力机上完成花键管的挤压成形。     

Prediction of limit strain in sheet metal-forming processes by 3D analysis of localized necking

Theoretical prediction of forming limit strain of sheet metal is developed in the framework of the three-dimensional general bifurcation theory. The onset of the three-dimensional discontinuous velocity field in the biaxially stretched uniform sheet is predicted. Three fundamental mode vectors, i.e. shear horizontal, shear vertical and normal modes are introduced and it is demonstrated that any bifurcation mode is represented by the linear combination of them. The onset of the bifurcation is numerically analyzed in terms of the modes by the use of the linear comparison solid originally introduced by Hill in 1959. In this study, a linear constitutive relation is adopted for the linear comparison solid, which is developed based on the constitutive theory proposed by Goya and Ito and is capable of incorporating the directional dependence of the plastic strain rate on the stress rate. The numerical results show that forming limit strains predicted by the three-dimensional mode theory is much higher in general than that given by Stören and Rice in 1975. Then, it is revealed from the three-dimensional mode analysis that the bifurcation mode that arises can be changed from one type to another according to the sign of stress ratio. It is also shown that the strain limit predicted by the three-dimensional mode analysis gives upper limit lines for the bifurcation lines proposed in the past for any linear strain-path directions.     

内压作用下波纹换热管应力分析

用有限元法和实验应力分析法对波纹换热管在内压作用下的应力分布规律进行探讨。结果表明,光管加工成波纹换热管后,在波峰过渡处与波谷过渡处均产生了较严重的应力集中现象,最大应力出现在波谷过渡处附近,比相应条件下光管中的应力大许多,且在管的厚度方向有应力梯度存在。通过分析指出影响波纹管上最大应力强度值的因素,并得出最大应力强度值最小时的优化波形。     

国产乙烯裂解炉管抽样检测状况

总结了两年多来中国石化炉管质量检测检验与评估中心对乙烯裂解炉管抽样检测的状况。对国产乙烯裂解炉141根离心铸造炉管、24根炉管焊接件以及27根静态铸造管件开展了化学成分、室温拉伸性能、高温持久性能试验和低倍组织酸蚀试验,给出了当前国产离心铸造炉管行业对杂质元素含量的控制情况、国产离心铸造炉管和静态铸造管件的室温拉伸性能与高温持久寿命状况,以及柱状晶与等轴晶比例。结果表明,当前国产乙烯裂解炉管合格率在80%~90%左右,炉管焊接件和静态铸造管件的高温持久寿命基本不合格,凸显出了国产乙烯裂解炉管行业存在的严峻问题。还就离心铸造炉管和管件杂质元素、新制造炉管性能与服役炉管失效模式的关系等问题开展了讨论。     

Inelastic wrinkling and collapse of tubes under combined bending and internal pressure

The problem of inelastic bending and collapse of tubes in the presence of internal pressure is investigated using experiments and analyses. The experiments involve 1.5-inch diameter, D/t=52 stainless steel tubes bent to failure at fixed values of pressure. The moment-curvature response is governed by the inelastic characteristics of the material. Bending induces some ovalization to the tube cross section while, simultaneously, the internal pressure causes the circumference to grow. Following some inelastic deformation, small amplitude axial wrinkles appear on the compressed side of the tube, and their amplitude grows stably as bending progresses. Eventually, wrinkling localizes, causing catastrophic failure usually in the form of an outward bulge. Internal pressure stabilizes the structure, it increases the wavelength of the wrinkles and can increase significantly the curvature at collapse. The onset of wrinkling is established by a custom bifurcation buckling formulation. The evolution of wrinkling and its eventual localization are simulated successfully using a FE shell model. The material is represented as an anisotropic elastic-plastic solid using the flow theory, while the models are assigned initial geometric imperfections with the wavelength of the wrinkling bifurcation mode. It is demonstrated that successful prediction of collapse requires very accurate representation of the material inelastic properties including yield anisotropies, and that as expected, the collapse curvature is sensitive to the imperfection amplitude and wavelength imposed.     

金属材料的平面应力非连续分叉

对已有弹塑性体非连续分叉结果进行了修正 ,使其更为合理。在此基础上 ,基于统一屈服准则 ,得出了金属材料非连续分叉的起始方位角以及相应的硬化模量的统一解析解 ,并且分析了不同程度的中间主应力对结果的影响。进而发现所得的结果与屈服准则的选取有关 ,揭示了在分叉研究中正确选取符合金属材料特性的强度准则的重要性。     

Transient and residual thermal stresses in quenched cylindrical bodies

To predict residual and thermal stresses which occur during water quenching of solid cylindrical rod and ring cross-sectioned steel tubes, a finite element technique has been used. The variations of residual stresses on different surfaces and cross-sections, e.g. in the radial, axial and tangential directions have been examined, and the effect of internal diameter of tubes on residual stress was investigated. The results show that the residual stresses act as a compressive force along the cooling surface and then by moving away from the surface begin to decrease and reverse their sign, near the centre of the cylinder are subjected to tensile stresses. Because of the reversal of the sign of stress, the effective stress goes to a minimum at some distance from the frontal surface and this may be vital since lower plastic deformation may cause cracking failure. As in solid cylinder, in cylindrical tubes also, the frontal and the upper cooling surface has significant effect on the stress distribution. From the comparison of the residual stress distributions of solid cylinder and cylindrical tubes and using their individual stress maps it was seen that they vary considerably along different cooling surfaces, especially at the frontal surface.     

Formability evaluation of dimple forming process based on numerical and experimental approach

Exhaust gas recirculation (EGR) cooler consists of a number of heat transfer tubes that have relatively larger net area than that of flat type tubes. The surface of the tubes is made up with lots of grooves and protrusions for enlarging the net heat transfer area. Most tubes are manufactured through forming processes, such as bending, spinning, roll forming, stamping and so on. Therefore, a series of fracture or defect can occur during the various forming processes. In this study, the manufacturing process of a dimple-type rectangular heat transfer tube used for an EGR cooler system is investigated based on the numerical simulation and the experimental approach. A prototype of the tube is designed and modified to a newly designed tube considering the conservation of the net heat transfer area based on the numerical and analytical approach. Formability evaluation of the tube sheet is carried out by using forming limit curves based on the plastic instability conditions. Strain- and stress-based forming limit curves are utilized to ensure the strain path independence. The newly designed tube having a number of dimples on the both sides are manufactured by the press forming process. Thickness distributions for the principal cross-sections are observed from both the simulation and the experiment and compared each other. From the results, it is confirmed that the forming process is robust to manufacture the dimple type rectangular tubes with the comparison of thickness, and application of the forming limit curves.     

广义Waterbomb折纸管的刚性折叠运动特性

对折叠模式的精确描述是折纸结构工程应用的前提,但现有的理论和方法无法全面地分析大多数折纸结构的刚性折叠过程。以广义Waterbomb折纸管为研究对象,基于球面机构运动学理论系统地分析了其折叠行为与运动协调条件,推导了折叠管刚性收缩和扭转运动的两套解析运动学方程。研究了各种几何设计参数对Waterbomb折纸管刚性折叠行为的影响,并讨论了该折纸结构折叠过程中的分岔行为与可能的物理干涉,及其引起的刚性折叠与结构形变的转化。此工作为基于广义Waterbomb折纸管的可编程超材料、可变形结构和机器人的设计与控制奠定了理论基础和设计依据,同时为复杂折纸结构的运动学分析提供了有效的手段。