A novel method of cold expansion which creates near-uniform compressive tangential residual stress around a fastener hole

A recognized way of improving the fatigue resistance of a fastener hole is to introduce compressive tangential residual stress around it. This can be achieved by using a cold expansion method in which an oversized pin or ball is forced through the hole to produce a local plastic region surrounded by an elastic one. Once the pin or ball is removed allowing the elastic region to spring back it results in compressive tangential residual stress around the hole. In practise, however, it is found that such a cold expansion method creates a non‐uniform residual stress distribution through the plate thickness and even tensile residual stress can be created at the entrance and exit faces. In this paper a new method of cold expansion is proposed. It uses a tapered pin with a mating tapered split sleeve and creates an almost uniform compressive residual stress around the hole as shown by FE method. Also, fatigue tests were carried out to verify that the method does significantly improve fatigue life. Finally the tangential residual stress distribution and fatigue life improvement of this new method were compared with those of a well‐established cold expansion method and it was shown that the new method is more efficient in improving fatigue life.     

开缝衬套孔挤压残余应力场数值计算研究

本文基于有限元技术模拟了开缝衬套挤压和直接芯棒挤压两种孔挤压工艺,对比研究了两种不同工艺导致的孔壁材料轴向流动和孔壁残余应力场。结果表明：开缝衬套挤压可有效抑制材料向挤出端流动,这在飞机夹层孔结构挤压中可减小夹层间隙尺寸;衬套开缝对应孔壁区域残余应力有突变,但仍然是对抗疲劳有利的压应力,而非拉应力;开缝衬套挤压挤入端孔边是压应力,而直接芯棒挤压是拉应力;相同干涉量条件下两种工艺引入的残余压应力峰值近似,但开缝衬套挤压残余压应力场域较直接芯棒挤压增大了约1 mm.     

Identifying the residual stress field developed by hole cold expansion using finite element analysis

The split sleeve cold expansion process is a cost effective method of enhancing the fatigue performance of aircraft fastener holes. However, the 3‐D nature of the induced residual stress fields is not fully understood. For this research, 2‐D and 3‐D models with uniform hole expansion and 3‐D models with expansion produced by contact with a rigid mandrel were developed. The models’ relative capabilities of capturing the residual stress fields were then evaluated. The residual stress profiles varied significantly through the thickness of the workpiece and were also strongly influenced by the direction of mandrel motion. Therefore the uniform expansion models were inadequate. The 3‐D contact models indicate that the mandrel entry face is the critical fatigue location, reporting the lowest circumferential compressive stresses adjacent to the hole. The effect of varying the frictional coefficient and plastic hardening laws were also investigated using the 3‐D contact models.     

Fatigue life of cold‐expanded fastener holes with interference‐fit fasteners at short edge margins

The fatigue life of 7075‐T6 aluminium specimens with countersunk fastener holes with cold expansion and interference‐fit fasteners with short edge margins was studied. The study was performed experimentally and through finite element analysis. The experiments measured the total fatigue life and crack growth. The results from the finite element analysis consisted of tangential residual stress profiles, which were combined with applied cyclic stresses for fatigue analysis. The experiments showed that the fatigue life improved with interference‐fit fasteners and cold expansion at all edge margins. The fatigue life also increased with increasing edge margin. The finite element results were used to make fatigue life predictions that corresponded reasonably well with the experimental results.     

Low cycle fatigue life prediction in shot‐peened components of different geometries—part I: residual stress relaxation

In this study, the residual stress relaxation behaviour occurring during low‐cycle fatigue in shot‐peened specimens with either a flat or a notched geometry has been studied. A representative low‐pressure steam turbine material, FV448, was used. The residual stress and strain hardening profiles caused by shot peening were measured experimentally and were then incorporated into a finite element model. By allowing for both effects of shot peening, the residual stress relaxation behaviour was successfully simulated using this model and correlated well with the experimental data. Although more modelling work may be required to simulate the interaction between shot peening effects and external loads in a range of notched geometries, the model predictions are consistent with the specimens tested in the current study. The novelty of this study lies in the development of such a modelling approach which can be used to effectively simulate the complex interaction between shot peening effects and external loads in notched regions. Compared with the un‐notched geometry, the notched geometry was found to be more effective in retaining the improvement in fatigue life resulting from shot peening, by restricting the compressive residual stress relaxation during fatigue loading.     

Edge distance effects on residual stress distribution around a cold expanded hole in Al 2024 alloy

Cold expansion process is a well-known technique for improving the fatigue life of aerospace structures by introducing a compressive residual stress around the fastener holes. However, there are concerns about the residual stress distribution around those holes which are located near the free edges of structure. The purpose of this study is to investigate the influence of edge distance ratio (e/D) on the residual stress distribution around a cold expanded hole in Al 2024 alloy. A two-dimensional finite element simulation was carried out with various degrees of cold expansion and various values of e/D. It was found that for edge distance ratios less than e/D = 3, there are considerable effects on the residual stress profile. Also, the dependency of residual stress distribution on the degree of expansion was reduced significantly for small e/Ds. The results revealed that the bulging of the plate free edge increases with reduction of e/D but in worse cases the maximum bulging at the plate free edge was lower than 3% of the hole radius. The weight function method was then used for determining stress intensity factors for a crack emanating from a cold expanded hole.     

Strain ratcheting and stress relaxation around interference‐fitted single‐holed plates under cyclic loading: experimental and numerical investigations

Longitudinal strain ratcheting and stress relaxation in interference‐fitted single‐holed plates were investigated both experimentally and numerically. In the experimental part single‐holed plates made from Al‐alloy 7075‐T6 were force‐fitted with oversized pins to create 1% and 2% nominal interference fit sizes. Then these plates (specimens) were instrumented with dynamic strain gauges in longitudinal direction around the hole to measure the strain during interference fit and strain ratcheting during subsequent cyclic loading. In the numerical part, 2D finite element code has been written to simulate the interference fit process and subsequent cyclic loading to obtain strains and stresses around the force fitted hole. To predict the strain ratcheting, Ohno–Wang kinematic hardening model was applied for simulation of stress/strain path. The strain ratcheting predicted from the finite element code and experimental test results were compared. The results showed that there is a good agreement between the measured and numerically evaluated strains, and the strain ratcheting is bigger for higher cyclic load level, but it is smaller for larger interference size.     

FE analysis of residual stress relaxation in a girth-welded duplex stainless steel pipe under cyclic loading

This study intends to characterize the residual stress relaxation in a girth-welded duplex stainless steel pipe exposed to cyclic loading. FE thermal simulation of the girth welding process is first performed to identify the weld-induced residual stresses. 3-D elastic–plastic FE analyses incorporated with the cyclic plasticity constitutive model which can describe the cyclic stress relaxation are next carried out to evaluate reconstruction of the residual stresses under cyclic mechanical loading. The results unveils that considerable reduction of the residual stresses in and around the girth weld occur even after the initial few loading cycles and degree of the stress relaxation is dependent on the magnitude of applied cyclic loading.     

The residual stress intensity factors for cold‐worked cracked holes: a technical note

Cold‐working of riveted holes reduces the stress intensity factor associated with cracks that may develop at the hole boundary, by creating a compressive residual stress field. The residual stress field is determined using the finite‐element method and the reduction of the stress intensity factor for different values of the interference is evaluated with the weight function method, in the case of an infinite plate made from an elastic–perfectly plastic material, and having a hole with two symmetrical cracks. Once the weight function of the structure is known, further calculation of the stress intensity factors for different loadings such as a remote uniform stress, or a point load that simulates the action of the rivet can be performed without difficulty.     

Advances in analysis of total uncertainties in a semi‐invasive residual stress measurement method

The ability to characterise residual stress distribution accurately and over different length scales, particularly deep into an engineering part, plays a significant role in assessing structural integrity. Two most commonly used techniques to measure residual stress fields deep into engineering components include neutron diffraction (ND) and deep‐hole drilling (DHD). As the measurements depend on several physical quantities, they are susceptible to error. The error or uncertainties may turn substantial and compromise the suitability of the results. Although noninvasive, the neutron diffraction technique is neither readily available nor portable and is limited to approximately 60‐mm‐thick specimen; errors associated with results become unacceptable at greater flight paths. Moreover, a mock‐up representing the engineering component is normally used in the ND technique. In contrast, the DHD technique is portable and measures residual stresses with high spatial resolution. An error propagation technique was applied to develop an error analysis procedure taking into consideration various stages of the DHD method and successfully applied to different DHD measurements. An essential feature comprising the effect of plasticity due to the creation of reference hole in the DHD procedure has not yet been taken into account in the error analysis procedure. This paper briefly describes how the uncertainties due to the creation of the initial reference hole can be determined. The effect of plasticity in the drilling procedure is quantified in this study. This error is combined with other sources of error and formulated to determine the total error. An incremental DHD technique was used to measure the complex triaxial residual stress field in an as‐welded circular disc, and the measured data were used to illustrate the total error using the error analysis method developed in the study.     

Experimental and numerical analyses of mean stress relaxation in cold expanded plate of Al‐alloy 2024‐T3 in double shear lap joints

In this paper, the mean stress relaxation behavior of simple Al‐alloy 2024‐T3 specimens and also the mean stress relaxation around the hole of cold expanded specimen are studied. The analyses are performed through the combination of the nonlinear isotropic hardening and Chaboche nonlinear kinematic hardening model accompanied by the results of experimental tests. The strain‐controlled axial tests are performed at two different strain amplitudes, while the stress‐controlled tests of cold expanded specimens are performed for three different imposed load amplitudes. The constitutive equations of the hardening model are coded as a UMAT subroutine in FORTRAN programming language and implemented in the commercial finite element code of ABAQUS. The accuracy of the hardening model has been proved in two steps: first by simulations of mean stress relaxation during the uniaxial strain‐controlled cyclic tests and second by simulation of strain ratcheting during the stress‐controlled cyclic loading. The stress and strain distributions after cold expansion process are examined as well as the mean stress relaxation due to cyclic loading. The results show the influences of imposed stress amplitude on increasing mean stress relaxation and also the effect of cold expansion level on reducing the mean stress relaxation.     

Implementation of cyclic plasticity models based on a general form of kinematic hardening

This paper deals with implementation of cyclic plastic constitutive models in which a general form of strain hardening and dynamic recovery is employed to represent the multilinear, as well as non‐linear, evolution of back stress. First, in order to incorporate such a general form of kinematic hardening in finite element methods, successive substitution and its convergence are discussed for implicitly integrating stress; moreover, a new expression of consistent tangent modulus is derived by introducing a set of fourth‐rank constitutive parameters into discretized kinematic hardening. Then, the constitutive parameters introduced are specified in three cases of the general form of kinematic hardening; the three cases have distinct capabilities of simulating ratcheting and cyclic stress relaxation. Numerical examples are given to verify the convergence in successive substitution and the new expression of consistent tangent stiffness. Error maps for implicitly integrating stress under non‐proportional as well as proportional loading are also given to show that the multilinear case of the general form provides high accuracy even if strain increment is very large. Copyright © 2002 John Wiley & Sons, Ltd.     

Numerical integration of a pressure‐dependent,non‐linear kinematic hardening constitutive model for large strain cyclic plasticity of metals

A Gurson‐based constitutive model is presented, which includes non‐linear mixed isotropic–kinematic hardening and creep, and allows the analysis of problems involving arbitrarily large plastic strains. This model was developed with the main objective of allowing, on the basis of a single set of material parameters, the numerical simulation of all the main features of cold metal forming processes, which usually imply severe loading–unloading cycles with very large plastic strains, difficult to be correctly reproduced numerically. A suitable integration scheme of the rate equations is described and implemented into a finite element code. The results obtained are compared with some reference experimental ones; an application of the model for the simulation of wire drawing processes is also presented. Copyright © 2011 John Wiley & Sons, Ltd.     

Contact stress and residual stress in the nose rail of a high manganese steel crossing due to wheel contact loading

Fatigue failure of a high manganese steel crossing is related to its internal crack initiation and growth, which is affected significantly by the magnitude and distribution pattern of contact stress and residual stress in the crossing. Considering the actual service conditions of a crossing and the accuracy requirement for numerical calculation, a whole model of wheel/crossing/ties and a partial model of wheel/crossing are established using elastic‐plastic finite element method. The distributions of contact stress fields and residual stress fields due to wheel contact loading are studied. The effect of train speed on the residual stress in the nose rail is discussed. The contact stress field shows regular contours in the cross‐section of nose rail and decreases remarkably with increasing distance of the wheel‐crossing contact position. The maximum contact stress is located at the contact surface between wheel and crossing. The maximum residual stress is located at a position of 1.5‐2.0 mm below the surface of the nose rail, rather than at the contact surface of wheel and crossing. In a failed high manganese steel crossing, the dense cracks mainly were observed neither at the position of maximum contact stress (the contact surface between the wheel and the crossing), nor at the position of maximum residual stress (1.5‐2.0 mm below the surface of the nose rail), but around the depth of 0.8‐1.0 mm from the worn surface, which is between the position of maximum contact stress and the position of maximum residual stress. It indicates that the combined effects of the maximum contact stress and the maximum residual stress play important roles in fatigue crack initiation in the nose rail. The size of high residual stress region increases with the increase of the train speed. The maximum residual stress in the nose rail increases remarkably with the increase of the train speed.     

Numerical simulation of fatigue crack propagation in compressive residual stress fields of notched round bars

In this paper, the influence of the residual compressive stresses induced by roller burnishing on fatigue crack propagation in the fillet of notched round bar is investigated. A 3D finite element simulation model of rolling has allowed to introduce a residual stress profile as an initial condition. After the rolling process, fatigue loading has been applied to three‐point bending specimens in which an initial crack has been introduced. A numerical predictive method of crack propagation in roller burnished specimens has also been implemented. It is based on a step‐by‐step process of stress intensity factor calculations by elastic finite element analyses. These stress intensity factor results are combined with the Paris law to estimate the fatigue crack growth rate. In the case of roller burnished specimens, a numerical modification concerning experimental crack closure has to be considered. This method is applied to three specimens: without roller burnishing, and with two levels of roller burnishing (type A and type B). In all these cases, the computational finite element predictions of fatigue crack growth rate agree well with the experimental measurements. The developed model can be easily extended to crankshafts in real operating conditions.     

Analysis of singular stress fields at multi‐material corners under thermal loading

The scaled boundary finite‐element method is extended to the modelling of thermal stresses. The particular solution for the non‐homogeneous term caused by thermal loading is expressed as integrals in the radial direction, which are evaluated analytically for temperature changes varying as power functions of the radial coordinate. When applied to model a multi‐material corner, only the boundary of the problem domain is discretized. The boundary conditions on the straight material interfaces and the side‐faces forming the corner are satisfied analytically without discretization. The stress field is expressed semi‐analytically as a series solution. The stress distribution along the radial direction, including both the real and complex power singularity and the power‐logarithmic singularity, is represented analytically. The stress intensity factors are determined directly from their definitions in stresses. No knowledge on asymptotic expansions is required. Numerical examples are calculated to evaluate the accuracy of the scaled boundary finite‐element method. Copyright © 2005 John Wiley & Sons, Ltd.     

Numerical and experimental validation of residual stresses of laser‐welded joints and their influence on the fatigue behaviour

In this work laser‐welded tube‐tube specimens made of aluminium alloys AlMg3.5Mn and AlSi1MgMn T6 were experimentally tested under constant and variable amplitude loading, under pure axial and pure torsion loading. In order to evaluate the influence on fatigue behaviour of the residual stresses, because of the welding process, some specimens were subjected to postweld heat treatment and then were tested. The numerical analyses, using finite element (FE), were carried out to obtain a reliable estimation of the residual stress in the specimen. The numerical results were in a good agreement with experimental ones obtained by means of hole‐drilling method. Finally, the residual stress distribution was superimposed to stress distribution because of fatigue loads obtained by FE analyses applying local concept, to calculate the stresses in the crack initiation zone and to understand the different types of failure that occurred in as‐welded and relieved specimens.     

Ductile tearing simulation of Battelle pipe test using simplified stress‐modified fracture strain concept

In this paper, numerical ductile tearing simulation results are compared with six circumferential through‐wall and surface cracked pipes made of two materials (SA‐333 Gr. 6 and A106 Gr. B carbon steels), performed at Battelle. For simulation, a model using a simplified fracture strain model is employed, by analysing tensile data of the material. By comparing experimental J‐R data with FE simulation results, the damage model dependent on the element size is determined based on the ductility exhaustion concept. The model is used to simulate ductile tearing behaviour of six circumferential through‐wall and surface cracked pipes. In all cases, simulated results agree well with experimental load, crack length and crack mouth opening displacement versus load line displacement data.     

SiC/Ti-6Al-4V复合材料在横向拉伸载荷下界面失效行为的数值模拟

采用有限元模拟了SiC/Ti-6Al-4V复合材料冷却过程和横向拉伸试验过程, 横向拉伸试样采用十字形试样。分别建立了平面应力和轴对称有限元模型, 采用平面应力有限元模型计算环绕纤维圆周的界面微区应力分布, 预测界面失效机制。采用轴对称有限元模型分析复合材料界面脱粘过程以及残余应力对界面径向应力分布的影响。结果表明: 对于SiC/Ti-6Al-4V复合材料十字形试样,在横向拉伸载荷下的界面失效由径向应力导致,界面失效模式为法向失效, 剪切失效模式未发生; 十字形试样在横向拉伸载荷下界面初始脱粘位置处于界面中间; 随横向拉伸应力增加, 十字形试样的界面脱粘对称向两边扩展; 界面径向应力随残余应力降低而升高。     

Extraction of the generalized stress intensity factor in gross sliding complete contacts using a path‐independent integral*

A new procedure to extract the generalized stress intensity factor (GSIF) in full sliding complete contact problems is proposed. It is based on a path‐independent integral derived from the reciprocal theorem of Maxwell‐Betti and on a specially conceived extraction field. This extraction field avoids the computation of path integrals along the contact plane that start from the singular point. The methodology presented here is also applicable to configurations with large relative displacements of the indenter (gross sliding). The procedure overcomes the problems that arise when extracting the GSIF via the stress extrapolation technique, because it does not need highly refined meshes, and it can be applied far from the singularity‐dominated zone and with much less user intervention. The robustness of the method has been verified with numerical examples, studying the effect of large displacements of the indenter and different discretizations.