Residual stresses in thick-walled cylinders resulting from mechanically induced overstrain

Autofrettage is a process for inducing elastic response in thick-walled cylinders subjected to internal pressures which otherwise cause plastic strains. To extend the use of autofrettage to higher pressure applications and to elminate many of the problems encountered in the use of the conventional process based on the use of direct internal hydrostatic pressure, a new technique has been developed which utilizes the mechanical advantage of a sliding wedge to produce the desired bore enlargement. Since the use of a sliding wedge or mandrel will induce shearing forces at the mandrel-cylinder interface, the resultant residual-stress distribution will differ from that theoretically predicted as characteristic of the direct hydrostatic process. It is the purpose of this work to determine the residual-stress distribution as a function of magnitude of overstrain and diameter ratio, and how it affects the reyielding characteristics of cylinders autofrettaged by this technique. Residual-stress distributions, determined by the Sachs boring-out technique for diameter ratios ranging from 1.5 to 2.3 and for several different magnitudes of overstrain, are shown. The shearing force associated with this technique induces substantial longitudinal residual stresses. The increase in the magnitude of this longitudinal residual stress with overstrain and the resultant decrease in the tangential residual stress are shown and discussed. Hydrostatic reyielding tests of autofrettaged cylinders are used to substantiate the decrease of tangential residual stress with increased overstrain. The substantially lower optimum overstrain as compared to the direct hydrostatic technique is shown and discussed. For optimum overstrain, the elastic strength of cylinders autofrettaged by swaging is comparable to that characteristic of the conventional process.     

New approach to the autofrettage of high-strength cylinders

The usual method of autofrettage (cold working) for gun tubes utilizes hydraulic pressure applied directly to the bore in order to plastically deform the wall of the tube so that favorable residual-stress patterns are produced. The strength of the tube is effectively increased, providing many associated benefits; however, ultra-high hydraulic pressures are required for high-strength steels since plastic-flow pressure is directly proportional to the yield strength of the material. A new method for the autofrettage of high-strength steel cylinders requiring greatly reduced pressures is developed and described herein. An oversize mandrel is forced through the tube to plastically deform the walls. Three methods of forcing the mandrel are investigated. Mechanical-push swaging is used in the autofrettage of short 5-in. long specimens with pull swaging and hydraulic-push swaging being used on specimens 40 in. long. All specimens are made from 4340 steel heat treated to various strengths. Cylinders with wall ratios ranging from 1.5 to 2.8, yield strengths ranging from 90,000 to 180,000 psi, and percent enlargements at the bore ranging from 1.0 to 5.0 are utilized. An engineering analysis is made investigating such factors as percent enlargement and elastic recovery at the bore, the ratio of pressure required for pushing the mandrel to the yield strength of the material, the effects of various lubricants on the frictional forces involved, and the induced three-dimensional stresses in the cylinder walls. Sach's boring-out technique is used to evaluate induced residual-stress patterns. Strains are recorded with electric-resistance strain gages and the associated dynamic and static instrumentation is described. Results are presented in graph form.     

Maximizing working pressure of autofrettaged three layer compound cylinders with considering Bauschinger effect and reverse yielding

One of the most effective methods for increasing capacity of thick-walled cylindrical pressure vessels is creating compressive residual stress in their walls. This can be applied by using multilayer shrink fitted or autofrettaged cylinders or combination of these methods. In this study, for a three layer compound cylinder, effects of interference fit values and their locations and autofrettage pressure were studied on the working pressure. Analytical and numerical results show that proper values and locations of the applied interferences can increase the capacity up to two times versus simple cylinder. Applying low-pressure autofrettage (less than one quarter of full autofrettage) on the compound cylinder can more increase the working pressure.     

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.     

Experimental determination of stress-concentration factors in thick-walled cylinders with crossholes and sideholes

In a companion paper¹ submitted to ASME, the theoretical determination of stress-concentration factors in thick-walled cylinders was reported. The present paper reports the results of experiments conducted to check the predictions of the theory. The configuration is a thick-walled cylinder with crossholes or sideholes oriented perpendicular to the bore. Stress concentrations occur at the “tee” intersections of the holes with the bore. The loadings considered are internal pressure and external pressure. Both steel and plastic models were tested. Experiments were also conducted to determine the reduction of the stress-concentration factor by intersection radii at the crosshole intersection. Experimental results were found to agree well with theory. The best configuration was found to be one with crosshole (or sidehole) diameter equal to the bore diameter, and with an intersection radius at the tee intersection equal to the bore radius.     

Inelastic behavior of thick-walled cylinders subjected to nonproportionate loading

Inelastic behavior of thick-walled cylinders subjected to nonproportionate loading was studied by the testing of specimens made of C1045 steel and of annealed copper. Several theories were reviewed. A closed-form solution proposed by Mendelson¹² was used to predict external strains for open-end and closed-end thick-walled cylinders. An incremental theory proposed by Chu¹³ was used to provide incremental solutions for open-end thick-walled cylinders, and for cylinders subjected to nonproportionate loading. Test data for open-end and closed-end thick-walled cylinders made of C1045 steel and of annealed copper were in excellent agreement with the incremental theory. Larger values were predicted by use of the closed-form solution for circumferential strains than actual test data for open-end thick-walled cylinders at large depth of yielding. For cylinders subjected to nonproportionate loading, excellent agreement was indicated between the incremental theory and the experiments for the plot of axial load vs. circumferential strain for specimens made of both metals. Agreement between the incremental theory prediction of axial strains for the specimens made of annealed copper and test data is quite satisfactory. Larger values were predicted by the incremental theory for axial strain than experimental data for specimens made of C1045 steel. The error was conservative.     

自增强厚壁圆筒疲劳裂纹扩展寿命的可靠性分析

本文提供了自增强厚壁圆筒疲劳裂纹扩展寿命的可靠性分析的方法和公式,自增强残余应力用符合厚壁筒用钢具有强化和包辛格效应实际性能推得的公式进行计算,残余应力对应的应力强度因子的计算采用了有限元法,得到了工作内压与自增强残余应力共同作用下的厚壁筒应力强度因子公式,通过实验测定了厚壁筒用钢的断裂韧度和疲劳裂纹扩展速率等性能。     

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.     

Large strain creep analysis of thick-walled cylinders

The finite-strain theory has been used to study the creep behaviour of a thick-walled cylinder under large strains. The analysis is divided into two parts. In part 1 the creep deformation of a thick-walled cylinder of an anisotropic material subjected to internal pressure has been discussed. The effect of the anisotropy has been depicted graphically. It is found that the anisotropy of the material has a significant effect on the axial stress, strain and strain rate. Part 2 of the paper deals with the creep analysis of cylinders of either isotropic or anisotropic materials subjected to combined internal and external pressures. The effect of the anisotropy is found to be similar to that found in part 1. It is seen, however, that the introduction of external pressure results in decreasing the strain rate and thus increasing the life of the cylinder.     

双线性材料模型机械自紧厚壁圆筒的弹塑性分析

考虑了实际材料的应变硬化和Ｂａｕｓｃｈｉｎｇｅｒ效应，利用合理的简化假设、通过弹塑性分析，得到了计算机械自紧厚壁圆筒的应力、位移、过盈量与自紧度、残余胀大量和冲头推力等机械自紧技术的关键计算公式。本文的理论计算结果与实验值相符合。     

Unloading of thick-walled cylinders that have been plastically deformed

Two analytical solutions are used to predict load-strain relations for unloading of thick-walled cylinders. The solutions assume that the material is an isotropic-hardening material that obeys the von Mises yield condition. The loading function for the material for the unloading of the cylinders was obtained from tension-compression specimens that were unloaded and reverse loaded from several points along the tension stress-strain diagram. Good agreement is indicated between the unloading load-strain curves obtained from two thick-walled cylinders made of SAE 1045 steel and the curves predicted by the analytical solutions. The analytical solutions predict that the beneficial circumferential compressive residual stresses at the inside of the cylinders decrease by about 50 percent during the unloading.     

A semi-analytic analysis of shape memory alloy thick-walled cylinders under internal pressure

In this paper, a new method for analysis of the pseudoelastic response of shape memory alloy thick-walled cylinders subjected to internal pressure is proposed. Two cases of short and long cylinders are considered by assuming the plane stress and plane strain conditions. In each case, a three-dimensional phenomenological SMA constitutive model is simplified to obtain the corresponding two-dimensional constitutive relations. The cylinder is partitioned into a finite number of narrow annular regions, and appropriate assumptions are made in order to find a closed-form solution for the equilibrium equations in each annular region. The global solution is obtained by enforcing the stress continuity condition at the interface of the annular regions and imposing the boundary conditions. Several numerical examples are presented to demonstrate the efficiency of the proposed method, and the results are compared with three-dimensional finite element simulations.     

残余应力下厚壁筒表面裂纹的应力强度因子计算

本文首先介绍了边界元法计算裂纹尖端应力强度因子的基本理论,接着利用边界元法计算了在残余应力下不同厚壁筒内表面椭圆裂纹的应力强度因子,研究了其大不随椭圆裂纹不同而变化的规律,为厚壁筒结构的设计,制造以及疲劳寿命分析提供了许多有价值的参考资料。     

The symmetrical adhesive contact problem for circular elastic cylinders

The rolling contact problem involving circular cylinders is at the heart of numerous industrial processes, and critical to any elastohydrodynamic lubrication analysis is an accurate knowledge of the associated contact pressure for the static dry problem. In a recent article [1] the authors have obtained new horizontal pressure distributions, both exact and approximate for various problems involving the symmetrical contact of circular elastic cylinders. In [1] it is assumed that only the circumferential horizontal displacement is prescribed in the contact region while the vertical circumferential displacement is left arbitrary and is assumed to take on whatever value is predicted by the deformation. The advantage of this assumption is that the problem reduces to a single singular integral equation which by transformations can be simplified to an integral equation involving the standard finite Hilbert transform. Here we consider the more general displacement boundary value problem within the contact region, and to be specific we examine the problem with zero vertical circumferential displacement and prescribed horizontal circumferential displacement. The solution of this problem involves two coupled singular integral equations for the horizontal and vertical pressure distributions. Basic equations and some approximate analytical solutions are obtained for symmetrical contact of circular elastic cylinders by both parallel plates and circular cylinders which are either rigid or elastic. Numerical results for the approximate analytical solutions are given for contact by rigid parallel plates and rigid circular cylinders.     

基于SHPB装置的膨胀圆柱管实验技术

采用改进的SHPB实验装置对45钢薄壁金属圆柱管进行了膨胀断裂加载,完成了不同变形程度 (覆盖圆柱管整个变形及断裂过程)圆柱管的冻结回收实验。回收样品可用于断裂机理研究分析,通过数值模 拟辅助分析和实验数据拟合得到了圆柱管凸起处的径向应变、应变率和环向拉伸应力。通过在圆柱管端粘贴 应变片监测断裂信号的方式,准确判断了圆柱管凸起处发生断裂的时间,以及径向断裂应变、应变率和环向拉 伸断裂应力,在102~104s-1应变率范围内,SHPB实验装置可用于研究金属圆柱管膨胀断裂。     

The effect of a wake-mounted splitter plate on the flow around a surface-mounted finite-height circular cylinder

The influence of a wake-mounted splitter plate on the flow around a surface-mounted circular cylinder of finite height was investigated experimentally using a low-speed wind tunnel. The experiments were conducted at a Reynolds number of Re=7.4×10⁴ for cylinder aspect ratios of AR=9, 7, 5 and 3. The thickness of the boundary layer on the ground plane relative to the cylinder diameter was δ/D=1.5. The splitter plates were mounted on the wake centreline with negligible gap between the base of the cylinder and the leading edge of the plate. The lengths of the splitter plates, relative to the cylinder diameter, ranged from L/D=1 to 7, and the plate height was always equal to the cylinder height. Measurements of the mean drag force coefficient were obtained with a force balance, and measurements of the vortex shedding frequency were obtained with a single-component hot-wire probe situated in the wake of the cylinder–plate combination. Compared to the well-studied case involving an infinite circular cylinder, the splitter plate was found to be a less effective drag-reduction device for finite circular cylinders. Significant reduction in the mean drag coefficient was realized only for the finite circular cylinder of AR=9 with intermediate-length splitter plates of L/D=1–3. The mean drag coefficients of the other cylinders were almost unchanged. In terms of its effect on vortex shedding, a splitter plate of sufficient length was able to suppress Kármán vortex shedding for all of the finite circular cylinders tested. For AR=9, vortex shedding suppression occurred for L/D≥5, which is similar to the case of the infinite circular cylinder. For the smaller-aspect-ratio cylinders, however, the splitter plate was more effective than what occurs for the infinite circular cylinder: for AR=3, vortex shedding suppression occurred for all of the splitter plates tested (L/D≥1); for AR=5 and 7, vortex shedding suppression occurred for L/D≥1.5.     

Free surface ductility in upsetting

Cold upsetting of a circular cylinder is often used to evaluate the cold forgeability of forming materials. The index of the forgeability is the critical strain at which a crack occurs on the expanding free surface of the upsetting cylinder. The forming limit due to the cracking is analyzed by a method based on the sufficient condition for the collapse of the unique solution. The modes of cracking are determined by comparing the stabilities of deformation from the forming limit to the two modes able to permit strain rate discontinuityon the plane of localized necking. Numerous experiments published in the literature have shown a linear relationship with a slope of −0.5 in circumferential strain vs axial strain at the forming limit. The forming limit and the mode predicted are in very good agreement with the experimental results.     

Residual surface stresses in laminated cross-ply fiber-epoxy composite materials

Residual (curing) stresses in a cross-ply laminated plate are related to the strains released when individual plies are separated. Released displacements are determined using high-sensitivity moiré interferometry and linearized strain-displacement equations are used to determine residual strains. Elastic orthotropic stress-strain relations are used to calculate residual stresses remote from free-edges of a [90₂₀/0₂₀/90₂₀] graphite-epoxy cross-ply panel. The measured strains compare favorably with those predicted by laminated plate theory. In a second example, the circumferential and radial residual strains and stresses at the end-section of a thick-walled cross-ply graphite-epoxy cylinder are determined. Paper was presented at the 1992 SEM Spring Conference on Experimental Mechanics held in Las Vegas NV on June 8–11.     

Elastic Equilibrium of Circumferentially Inhomogeneous Orthotropic Cylindrical Shells of Arbitrary Thickness

An approach is proposed to determine the three-dimensional stress–strain state of hollow orthotropic cylinders with elastic characteristics variable in the circumferential direction. The solution of the problem is represented as a double Fourier series in the axial and circumferential coordinates. A resolving system of ordinary differential equations of high order is derived. An analysis is made of the stress state of a cylinder made of a composite with reinforcement density variable in the circumferential direction     

Analysis of dynamic stress intensity factors of thick-walled cylinder under internal impulsive pressure

Dynamic stress intensity factors are evaluated for thick-walled cylinder with a radial edge crack under internal impulsive pressure. Firstly, the equation for stress intensity factors under static uniform pressure is used as the reference case, and then the weight function for a thick-walled cylinder containing a radial edge crack can be worked out. Secondly, the dynamic stresses in uncracked thick-walled cylinders are solved under internal impulsive pressure by using mode shape function method. The solution consists of a quasi-static solution satisfying inhomogeneous boundary conditions and a dynamic solution satisfying homogeneous boundary condi- tions, and the history and distribution of dynamic stresses in thick-walled cylinders are derived in terms of Fourier-Bessel series. Finally, the dynamic stress intensity factor equations for thick-walled cylinder containing a radial edge crack sub- jected to internal impulsive pressure are given by dynamic weight function method. The finite element method is utilized to verify the results of numerical examples, showing the validity and feasibility of the proposed method.