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.     

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.     

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。     

Experimental evaluation of the influence of macro circumferential residual stress on the wear resistance of some metals

To investigate the effect of residual stress on the wear resistance of metals, macro circumferential residual stresses σ^I were modelled as externally applied stress, below the yield stress of the material because residual stress cannot exceed yield stress, with a special apparatus. In order to compare the effect of residual stress on wear resistance, three different stress levels were applied to each specimen, 0 R_e, 0.5 R_e, and 0.8 R_e. A full programme of testing under all combinations of factors would be very expensive and time consuming, so, in the present case, all the other factors were fixed at constant values, while the chosen factor was varied in a controlled way in a series of tests. There has been no universally accepted theory or law on the effect of residual stress on wear resistance. In this study, the wear results for dry wear tests in terms of residual stress applied mechanically to specimens were very difficult to interpret.     

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.     

A gas-discharge plasma focuser

A device is proposed for the formation of a gas-discharge plasma stream with a sinusoidal distribution of the charged-particle density over the stream cross section, which is achieved by using wavy shapes of the anode and cathode surfaces that are placed coaxially relative to each other at the distance λ _e < h < 3λ _e , where λ _e is the mean free path of an electron in the gas-discharge plasma stream. The anode is a stainless steel grid with mesh dimensions of 1 × 1 mm. The aluminum cathode is 120 mm in diameter and 50-mm thick. The device provides a discharge current of up to 0.6 А at a controlled voltage at the electrodes in the range of 0.21–0.7 kV. In this case, plasma streams propagate to a distance of up to 50λ _e beyond the limits of the electrodes.     

Limit angular velocity of rotating disc with unified yield criterion

Plastic limit analysis of a rotating solid or annular disc with variable thickness is presented in terms of a unified yield criterion (UYC). Stress distributions of the discs in plastic limit state corresponding to different yield curves are deduced. Upper and lower bounds of the plastic limit solutions are derived by selecting a weighting coefficient in the unified yield criterion. Stress redistribution is solved when the stress field violates yield criterion locally. Limit angular velocity as well as the stress distributions with respect to three special criteria, namely the Tresca criterion, the Mises criterion (close form solution) and the Yu criterion are illustrated and compared. The influences of yield criterion as well as the thickness on plastic limit solution of a rotating disc are demonstrated and discussed.     

Elastic–plastic contact analysis of an ellipsoid and a rigid flat

The work presents a finite element model (FEM) of the equivalent von-Mises stress and displacements that are formed for the different ellipticity contact of an ellipsoid with a rigid flat. The material is modeled as elastic perfectly plastic and follows the von-Mises yield criterion. The smaller the ellipticity of the ellipsoid is, the larger the depth of the first yield point from the ellipsoid tip happens. The FEM produces contours for the normalized normal and radial displacement as functions of the different interference depths. The evolution of plastic region in the asperity tip for a sphere (k_e=1) and an ellipsoid with different ellipticities $(k_e=\frac{1}{2}\mathrm{and}\frac{1}{5})$ is shown with increasing interferences. It is interesting to note the behavior of the evolution of the plastic region in the ellipsoid tip for different ellipticities, k_e, is different. The developments of the plastic region on the contact surface are shown in more details in Fig. 7. When the dimensionless contact pressure is up to 2.5, the uniform contact pressure distribution is almost prevailing in the entire contact area. It can be observed clearly that the normalized contact pressure ascends slowly from the center to the edge of the contact area for a sphere (k_e=1), almost has uniform distribution prevailing the entire contact area for an ellipsoid $(k_e=\frac{1}{2})$, and descends slowly from the center to the edge of the contact area for an ellipsoid $(k_e=\frac{1}{5})$.     

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。     

热-机械载荷下厚壁圆筒自增强压力优化分析

理论上推导了厚壁圆筒在内压及热载荷共同作用下的最佳自增强压力,并基于ANSYS的优化分析结果对理论解进行了验证。结果表明最佳自增强压力的理论解与数值解一致,最大误差不超过1%;另外,不考虑热载荷进行自增强后,会增大工作状态下厚壁圆筒内外壁应力差,降低结构的疲劳强度;工程上可根据本文解析解进行自增强处理,以提高厚壁圆筒的承载能力。     

Maximum load for toruslike shells

Maximum loads for toruslike shells with constant thickness loaded with an axial force, internal pressure, and a bending torque are calculated. The rigid plastic body model, the Tresca yield condition, and the plastic yield law associated with it are used. Application of the finite element method for calculation of the maximum load on a shell is considered. A significant increase in the characteristic deformation of a shell is used as a criterion. The corresponding formulas for maximum loads are obtained based on the kinematic method of the limit equilibrium theory. The difference between the obtained results and the static solution does not exceed 3%.     

Extraction of ions from a plasma source and formation of beams

The current of ions extracted from a plasma source has been measured as a function of extraction voltage U _e . Comparison of the obtained characteristics to theoretical predictions has shown that the experimental data agree with the Child-Langmuir theory only within a certain range of U _e . The results of our measurements and computer simulation of the ion-beam profile allowed the assessment of the parameters of the ion-emitting surface and the average ion energy in the plasma of the source under study.     

Vibration response analysis caused by rubbing between rotating blade and casing

Two types of blade-tip rubbing due to the static misalignment of the bladed-disk center and casing center and casing deformation are simulated. By applying aerodynamic load in the blade lateral/flexural direction, vibration responses due to blade-casing rubbing are analyzed under the run-up process with constant angular acceleration and the steady-state process at 10000 rev/min. The effects of some parameters, such as the static misalignment e _c, casing stiffness k _c and casing deformation n _p, on the system vibration responses are also illustrated by spectrum cascades, time-domain waveforms of displacement, normal rubbing forces, amplitude spectra and the impulse P in a single blade-casing rubbing period. The results show that blade-tip rubbing will cause amplitude amplification and harmonic resonance phenomena when the multiple frequencies (nf _r) of rotational frequency (f _r) coincide with the first three flexural dynamic frequencies of the blade (f _n1, f _n2 and f _n3). For example, the displacement amplitudes at 3f _r, 14f _r and 38f _r are large and the vibration is dominant near f _n1. In addition, the casing deformation mainly excites the dominant Blade passing frequency (BPF), which is related to the casing deformation coefficient n _p. By comparing these impulse values, for the selected parameters in this paper, the casing stiffness has a greater effect on impulse than the static misalignment and casing deformation coefficient. The impulse shows a linear increase trend with the increasing static misalignment, and it decreases under the large n _p because the contact time decreases with the increase of n _p.     

Multi-color space threshold segmentation and self-learning <Emphasis Type="Italic">k</Emphasis>-NN algorithm for surge test EUT status identification

The identification of targets varies in different surge tests. A multi-color space threshold segmentation and self-learning k-nearest neighbor algorithm (k-NN) for equipment under test status identification was proposed after using feature matching to identify equipment status had to train new patterns every time before testing. First, color space (L*a*b*, hue saturation lightness (HSL), hue saturation value (HSV)) to segment was selected according to the high luminance points ratio and white luminance points ratio of the image. Second, the unknown class sample S _r was classified by the k-NN algorithm with training set T _z according to the feature vector, which was formed from number of pixels, eccentricity ratio, compactness ratio, and Euler’s numbers. Last, while the classification confidence coefficient equaled k, made S _r as one sample of pre-training set T _z ′. The training set T _z increased to T _z+1 by T _z ′ if T _z ′ was saturated. In nine series of illuminant, indicator light, screen, and disturbances samples (a total of 21600 frames), the algorithm had a 98.65%identification accuracy, also selected five groups of samples to enlarge the training set from T ₀ to T ₅ by itself.     

Plastic analysis of perforated plates for orthotropic yield criteria

The concept of an equivalent orthotropic material is used in evaluating the collapse loads for perforated plates. Uniformly loaded circular plates are investigated. Limit pressure solutions are obtained for both the simply supported and rigidly built-in edge conditions. Statically admissible radial and circumferential bending moment fields are found and the associated velocity fields are shown to be kinematically admissible. Numerical results are given in dimensionless form covering arbitrary plate geometries over the entire range of material orthotropy.These solutions are quite useful in the plastic analysis and design of perforated plates used as pressure vessel heads, tube sheets, reactor core support plates and the like. Perforated plates have considerably higher effective yield strengths when subjected to equi-biaxial loading than when subjected to loading of arbitrary biaxiality and orientation with respect to the penetration pattern. Thus, the equivalent orthotropic plastic material concept is ideally suited to the analysis of such plates. The resulting limit load pressures are substantially lower than the values obtained using isotropic Tresca yield criterion based on the yield strength for equi-biaxial loading. The results are substantially higher than the values obtained using the maximum isotropic Tresca yield condition falling entirely within the orthotropic yield surface.     

Exact solutions for plastic responses of orthotropic strain-hardening rotating hollow cylinders

This paper presents exact solutions for plastic responses of plastically orthotropic strain-hardening rotating hollow cylinders. Hill’s yield criterion and the Voce hardening law were adopted. The concept of sequential limit analysis was employed to deal with the strain-hardening behavior by updating the yield criterion and the deformed configuration sequentially. First, exact solutions of the plastic angular velocity were acquired by solving both static and kinematic limit analysis problems. The existence of closed-form exact solutions for some cases was also illustrated. Moreover, the global hardening behavior was analytically evaluated. The corresponding distributions of plastic stress components and equivalent plastic strain were also developed. Second, the elastic–plastic capability of the commercial finite-element code ABAQUS was employed for rigorous validations of analytical solutions. Finally, good agreement is observed between analytical solutions and numerical results.     

Sustainability analyses of cutting edge radius on specific cutting energy and surface finish in side milling processes

The aim of this work is to determine the influence of cutting edge radius on the specific cutting energy and surface finish in a mechanical machining process. This was achieved by assessing the direct electrical energy demand during side milling of aluminium AW6082-T6 alloy and AISI 1018 steel in a dry cutting environment using three different cutting tool inserts. The specific energy coefficient was evaluated as an index of the sustainable milling process. The surface finish of the machined parts was also investigated after machining. It was observed that machining with the 48.50-μm cutting edge radius insert resulted in lower specific cutting energy requirements when compared with the 68.50 and 98.72-μm cutting edge radii inserts, respectively. However, as the ratio of the undeformed chip thickness to cutting edge radius is less than 1, the surface roughness increases. The surface roughness values gradually decrease as the ratio of undeformed chip thickness to cutting edge radius (h/r _e) tends to be 1 and at minimum surface roughness values when the ratio of h/r _e equalled to 1. However, the surface roughness values increased as h/r _e becomes higher than 1. This machining strategy further elucidates the black box and trade-offs of ploughing and rubbing characteristics of micro machining and optimization strategy for minimum energy and sustainable manufacture.     

A Neutron Spectrometer for Experiments with Radioactive Beams on the ACCULINNA-2 Fragment Separator

A neutron spectrometer based on stilbene crystals has been developed by the Flerov Laboratory of Nuclear Reactions at the Joint Institute for Nuclear Research (Dubna, Russia). The timing resolution is determined as a function of the signal amplitude (σT = 0.18 ns at an amplitude of 1 MeV in the electron equivalent). The measured energy resolution of the detecting modules for γ rays is σE/E = 4.5% at E = 1 MeV. The quality of the n–γ discrimination is investigated. It is shown that reliable discrimination is possible, beginning with a deposited energy of 100 keV in the electron equivalent, which corresponds to the kinetic energy of recoil protons of ～700 keV. The neutron spectrometer helps to significantly expand the experimental capabilities and to carry out correlation experiments with radioactive beams on the ACCULINNA-2 fragment separator at a new level of quality.     

基于AWB的驱动桥疲劳强度及寿命有限元分析

针对某型号整体式铸造驱动桥,在ANSYS WORKBENCH中建立起桥壳的有限元模型。最大垂直载荷作用下驱动桥的刚-强度分析结果表明,该驱动桥的刚度满足国家标准要求,圆弧过渡区及阶梯轴直径过渡区域应力较大,最大等效应力没有超过材料的屈服极限,桥壳不会出现断裂和塑性变形。驱动桥的疲劳寿命分析发现,该桥壳的疲劳寿命偏安全。     

Data recording system of a dispersion interferometer based on a CO<Subscript>2</Subscript> laser

The data recording system of a multichannel double-pass dispersion interferometer based on a CO₂ laser is described. This system has been designed to record the linear density of plasmas in a real-time mode with a time discreteness of 4 μs and resolution 〈N _e L〉 ～ 0.34 × 10¹³ cm^?2 (N _e is the electron component of the plasma density, and L is the plasma size in the wave propagation direction) in the range of linear density variations of up to 10¹⁷ cm^?2. The system is built from unified recording modules that use fast ADCs to record the shape of photodetector and modulator signals and FPGA-based digital units of dataflow processing to form results of measurements. The single-channel recording module of the dispersion interferometer has been tested under actual experimental conditions of the GDL gas-dynamic trap and the TEXTOR tokamak (Julich, Germany).