Analysis of residual stresses in cylindrically anisotropic materials

Metal-forming operations leave residual stresses in formed parts due to nonuniform deformation occurring during the process. An exact method of determining the longitudinal, radial and circumferential (tangential) residual stresses in axisymmetric specimens was proposed by Mesnager¹ and further developed by Sachs². The boring-out technique can be complemented by a similar procedure in which strains are measured on the inner surface of the tube when material is removed from the outer surface.The work proposed in this paper extends previous analyses of residual stresses to the case where the material exhibits cylindrical elastic anisotropy, i.e., the principal axes of anisotropy correspond to the longitudinal, radial and circum-ferential directions of the tube. In addition, the present analysis considers the case in which a residual-shear stress, developed by twisting the tube about its axis, exists in the tube. When such shearing stresses are present, the principal axes of the residual-stress distribution are not parallel to the principal axes of the tube.     

冲击载荷下自增强身管残余应力变化规律

基于有限元分析方法,建立速射火炮身管截面的有限元模型,采用直接耦合的方法,模拟了承受热应力和火药燃气压力的自紧身管在先50连发、冷却后再连发10发过程中身管的残余应力,得到并分析了残余应力的变化规律,指出内壁薄层的塑性变形和残余应力的反复变化,不利于内壁的稳定,还提出了减小残余应力变化程度的策略.     

Residual stresses in squeeze-cast aluminum rods

The longitudinal slitting technique has been applied to determining and comparing the residual stresses in as-cast and squeeze-cast aluminum rods. Residual stresses in the squeeze-cast aluminum alloy rods are found to increase with applied punch pressures under a constant die-base thermocouple reference temperature. For the variations of residual stresses with varying die-base thermocouple reference temperatures, a peak residual stress is found to occur at a die-base thermocouple reference temperature of 100° C. A semi-empirical formula is derived for the determination of the maximum longitudinal residual stress in the tapered cylindrical as-cast aluminum alloy, from which the maximum longitudinal residual stresses for squeeze cast can be determined, using the residual-stress ratios obtained experimentally     

Residual-stress measurement in SS304 seamless tube

This paper involves the experimental measurement of residual stresses in a nonwelded nuclear-grade 304 stainless-steel seamless tube subjected to one-sided quenching of its outside surface. Because this grade of tube is used extensively in nuclear power plants, the residual stresses measured are of interest to the nuclear industry. The Sach's boring method was used to obtain residual stresses. The longitudinal and tangential residual stresses at the inner wall were found to be 69 MPa to 138 MPa compressive. The results indicate that the residual-stress distribution would allow the tube to be highly resistant to the formation and propagation of stress-corrosion cracks.     

General stress-velocity expressions in acoustoelasticity

The velocity of a transverse wave propagating in an elastic body depends on the stress field of the body. If transverse waves are sent through a body with a uniaxial stress field, there will be proportionality between the principal-stress difference and the relative velocity difference between the waves polarized in accordance with the two main directions. This technique is used for determining uniaxial residual-stress fields. The main object of the investigation described in this paper has been to investigate the usefulness of the method in the case of biaxial residual-stress fields. Both theoretically and experimentally, the investigation has shown that there is also proportionality between principal-stress difference and relative-velocity difference for a biaxial field. However, the tests have also shown that inaccuracies with this method, on account for example of preferred orientation in steel materials, are of such an order of magnitude that the method cannot, at the present stage of development, compete with the more traditional methods, such as the drilling method and the X-ray diffraction method.     

A New Procedure to Measure Near Yield Residual Stresses Using the Deep Hole Drilling Technique

Mechanical strain relief techniques for estimating the magnitude of residual stress work by measuring strains or displacements when part of the component is machined away. The underlying assumption is that such strain or displacement changes result from elastic unloading. Unfortunately, in components containing high levels of residual stress, elastic-plastic unloading may well occur, particularly when the residual stresses are highly triaxial. This paper examines the performance of one mechanical strain relief technique particularly suitable for large section components, the deep hole drilling (DHD) technique. The magnitude of error is calculated for different magnitudes of residual stress and can be substantial for residual stress states close to yield. A modification to the technique is described to allow large magnitudes of residual stress to be measured correctly. The new technique is validated using the case of a quenched cylinder where use of the standard DHD technique leads to unacceptable error. The measured residual stresses using the new technique are compared with the results obtained using the neutron diffraction technique and are shown to be in excellent agreement.     

应用增量理论考虑应变硬化效应包辛格效应和温度对机械性质影响的自增强厚壁圆筒分析

本文提出的采用增量理论的分析模型和方法可以定量分析应变硬化、包辛格效应和材料机械性质随温度变化等因素对自增强厚壁圆筒中残余应力和操作应力分布的影响.厚壁圆筒看成由N个同轴薄壁圆筒套在一起组成的构件;采用包括弹性、塑性和温度应变的增量型本构关系和相容条件导出了自增强圆筒的基本方程;设计了计算机程序并给出了分析实例。分析结果表明,应变硬化会减小塑性区并降低残余应力;包辛格效应使反向屈服容易出现;温度升高将使残余应力和热应力松驰.     

颗粒增强复合材料中微观热应力和残余应力分析

运用空间配位体密堆模型和球对称分析单元，分析计算了颗粒增强复合材料经历温度变化后产生的微观热应力和残余应力。分析结果表明，温度升高时界面产生径向张应力，降温时产生压应力。存在一个基体开始发生塑性变形的临界温差ｔ＿ｐ，其值随增强体体积分数Ｖ＿ｐ增加而降低。除组元间热膨胀系数差和弹性常数外，基体材料本构关系和屈服强度对热应力和残余应力均有很大影响。随Ｖ＿ｐ增加，微观应力和水静宏观应力幅值上升。但粒子周围塑性区尺寸近似与Ｖ＿ｐ无关。给出了不同变温条件下残余应力的确定方法。     

自紧身管临界裂纹尺寸的概率断裂力学研究

基于概率断裂力学理论和Mome Caflo模拟方法，本文进行了自紧身管临界裂纹尺寸的可靠性研究。自紧身管内表面的疲劳裂纹考虑为半椭圆形式。裂纹尖端处的应力强度因子由内压和自紧残余应力共同产生。自紧残余应力采用了符合身管材料具有强化和包辛格效应性能推导的公式计算，它产生的应力强度因子通过权函数方法得到。根据断裂准则，可计算出自紧身管的临界裂纹尺寸。实例分析表明，对数正态分布为临界裂纹尺寸的最佳分布，同时给出了在各种置信度和可靠度下自紧身管的临界裂纹尺寸。     

Analytical and numerical solution for a elastic pipe bend at in-plane bending with consideration for the end effect

The authors proposed an analytical method for the analysis of the end effect in a pipe bend loaded by a bending moment with consideration for the action of internal pressure. The method is based on the use of simplifying hypotheses and is reduced to the solution of a system of fourth-order differential equations along the axial coordinate with respect to unknown coefficients in the expansion for tangential displacements. An approximate analytical solution, which has a trapezoidal structure and is written in terms of Krylov’s functions, has been obtained. Boundary conditions are formulated in terms of the tangential and longitudinal displacements and axial and shearing stress resultant. For the flexibility factor, analytical solutions are presented in the case where a bend is approximated by a rigid restraint on both ends. To verify the analytical solution and its applicability limits, two numerical procedures were developed, which are based on the finite difference method and the reduction to the Kochi problem by the expansion of the unknowns in the Fourier series over the circumferential coordinate. The authors compare the results obtained with data from the literature, discuss the advantages and disadvantages of the methods, and present recommendations for their practical application.     

Extension,inflation and torsion of a residually stressed circular cylindrical tube

In this paper, we provide a new example of the solution of a finite deformation boundary-value problem for a residually stressed elastic body. Specifically, we analyse the problem of the combined extension, inflation and torsion of a circular cylindrical tube subject to radial and circumferential residual stresses and governed by a residual-stress dependent nonlinear elastic constitutive law. The problem is first of all formulated for a general elastic strain-energy function, and compact expressions in the form of integrals are obtained for the pressure, axial load and torsional moment required to maintain the given deformation. For two specific simple prototype strain-energy functions that include residual stress, the integrals are evaluated to give explicit closed-form expressions for the pressure, axial load and torsional moment. The dependence of these quantities on a measure of the radial strain is illustrated graphically for different values of the parameters (in dimensionless form) involved, in particular the tube thickness, the amount of torsion and the strength of the residual stress. The results for the two strain-energy functions are compared and also compared with results when there is no residual stress.     

Residual Stresses in a Shaft after Weld Repair and Subsequent Stress Relief

To evaluate the possibility of repairing and/or modifying shaft surfaces by welding, remachining, and low-temperature stress relieving without introducing high residual stresses, residual-stress measurements were made on an 8.0 in. diameter shaft of Type 347 stainless steel. The measurements were made on the shaft surface before welding, after welding and remachining, and after a 750°F stress relief. This report shows the residual-stress patterns in and near the weld area at the various stages of the investigation. Measurements were made using the hole-drilling method. The holes were 0.060 in. diameter and 0.06 in. deep. They were made using a unique, stress free abrasive jet machining technique.*     

Effects ofR-ratio on crack initiation at external discontinuities in autofrettaged cylinders

Experimental work shows the effects of positive-stress ratios, or tensile-minimum stress during the fatigue cycle on the fatigue-crack initiation from holes. This simulates the effect of the residual-tensile stresses at the outside surface of autofrettaged cylinders. S-N curves and modified Goodman diagrams are shown for fatigue-crack initiation.Paper was presented at 1982 SESA/JSME Spring Meeting held in Oahu and Maui, HI on May 23–28, 1982.     

船用液压联轴器外套线性强化自增强应力分析

为了提高船用液压联轴器的承载能力,需对联轴器外套进行自增强处理．采用线性强化模型,得到了液压联轴器外套自增强卸载后的残余应力、自增强压力和安装后的应力公式、公式表明最佳径比不仅与材料的屈服极限、弹性模量、线性强化弹性模量有关,还与鲍辛格效应系数有关、结合《船标》中规定尺寸进行了自增强分析,结果表明自增强外套的承载能力与非自增强外套的相比提高近50％．     

Nondestructive residual-stress measurement in a wide-flanged rolled beam by acoustoelasticity

X-ray stress analysis is a standard nondestructive stress-measurement technique, but its use is limited in the sense that only a surface layer is surveyed. Recently, acoustoelasticity has emerged as a technique for nondestructive stress analysis. Acoustoelasticity makes use of stress-induced acoustic-birefringent effects. It gives stress distributions averaged through the thickness of a specimen. This technique is attractive because it does not require a transparent plastic model as photoelasticity does. However, much should be done before this method is established as a standard nondestructive technique of stress analysis. The most important among them is to separate stress-induced birefringence from that introduced by texture structure. For special cases, such as axisymmetric stress distributions and when a stress-free region is knowna priori, residual-stress distributions can be evaluated nondestructively. In this paper, we measured residual-stress distribution in a wide-flanged rolled beam by using a recently developed T-type transducer. The results were compared to those obtained from conventional destructive methods.     

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.     

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.     

On indentation of a pair of rigid punches connected by an elastic beam into an elastic half-plane with regard to the friction and adhesion forces in the contact region

The contact problem of indentation of a pair of rigid punches with plane bases connected by an elastic beam into the boundary of an elastic half-plane is considered under the conditions of plane strain state. The external load is generated by lumped forces applied to the punches and a uniformly distributed normal load acting on the beam.It is assumed that the contact between the punch and the elastic half-plane can be described by L. A. Galin’s statement, i.e., it is assumed that the adhesion acts in the interior part of each of the contact regions and the tangential stresses obeying the Coulomb law act on their boundaries.With the symmetry taken into account, the problem is stated only for a single punch, and solving this problem is reduced to a system of four singular integral equations for the tangential and normal stresses in the adhesion region and the contact pressure in the sliding zones. The solution of the constitutive system together with three conditions of equilibrium of the system of punches connected by a beam is constructed by direct numerical integration by the method of mechanical quadratures.As a result of the numerical analysis, the contact stress distribution functions were constructed and the values of the sliding zones and the punch rotation angle were determined for various values of the geometric, elastic, and force characteristics.     

Residual stresses in thick electrodeposits of a nickel-cobalt alloy

Some electroplated metals contain residual stresses which can cause warpage or premature failure of parts plated or electrofomed with these materials. Noticeably absent from the literature are residual-stress data for finished parts. Typically for plated or electroformed parts, residual stresses are determined independently on thin strips and then piece parts are plated. This research describes a technique which can be used to measure stress on finished parts. The method involves drilling a hole in the part and measuring the resulting change of strain in the vicinity of the hole. Viability of this technique was demonstrated by measuring the stress in a nickel-cobalt deposit plated on an aluminum cylinder. Two separate runs, one 50 deg removed from the other, provided almost identical results; stress was 160 MN/m² (23,200 psi). Two other runs in a region where plating was somewhat thinner provided slightly lower results probably because all boundary-condition requirements were not met. The computed residual-stress values compared quite favorably with independent rigid-strip measurements of 131 MN/m² (19,000 psi) obtained for the solution before and after plating of the cylinder.     

Plane steady vibration of an elastic wedge

The problem of plane steady vibration of an elastic wedge of arbitrary angle (less than 180 degrees) subject to harmonic normal and shearing tractions on its faces is reduced to a system of singular integral equations by the superposition of two half-plane solutions. The integral equations have kernels with Cauchy singularities of a non-translation type, except for the 90 degree wedge. The locations of these singularity lines are shown graphically as a function of wedge angle.