Numerical simulation of residual stress relaxation around a cold‐expanded fastener hole under longitudinal cyclic loading using different kinematic hardening models

Cold expansion of fastener holes creates compressive residual stresses around the hole. This well‐known technique improves fatigue life by reducing tensile stress around the holes. However, cyclic loading causes these compressive residual stresses to relax, thus reducing their beneficial effect. Estimation of the fatigue life without considering the residual stress relaxation might lead to inaccurate results. In this research, numerical studies were carried out using 2D finite element (FE) models to determine the initial tangential and radial residual stress distributions generated by cold expansion and their relaxation under cyclic loading. To predict the stress relaxation, four nonlinear kinematic hardening models were applied in simulation of stress/strain path. The results obtained from the FE analysis were compared with available experimental results. A good agreement between the numerical and experimental results was observed.     

Cold expansion of holes and resulting fatigue life enhancement and residual stresses in Al 2024 T3 alloy – An experimental study

This paper presents the experimental results of fatigue life enhancement and the residual stresses around the cold expanded holes in Al 2024, a widely used aerospace alloy. Two techniques for cold expansion of holes, namely split-sleeve with taper pin technique and split-sleeve with ball technique were considered for comparison, as the former involves surface contact and the latter has line contact during expansion. The techniques were compared based on the fatigue life enhancement in the expanded holes, the induced and the residual stresses due to expansion. The holes were expanded by 2%, 3%, 4%, 5%, and 6% using INSTRON machine in both the techniques. While both the techniques resulted in improvement in fatigue life of the expanded holes, the taper pin technique yielded 200% higher fatigue life improvement than that obtained by ball technique. The induced residual stresses were measured by mounting strain gages of 0.2 mm gage length. These are drawn as a function of induced strain. In both the techniques residual stresses increased with increase in percentage of expansion until 5% and then decreased for 6% expansion. The increase in fatigue life at 5% expansion was 1.88 times and 5.3 times higher than that of the non-expanded holes for ball and tapered method, respectively. The corresponding improvement in taper method was greater than the non-expanded holes. While, it was observed that the residual stresses decreased with respect to the distance from the hole in both the techniques, the ball technique resulted in lower residual stresses than that of taper pin technique.     

The effect of hole shape on the extent of fatigue life improvement by cold expansions

The cold expansion of circular holes is known to improve resistance to fatigue. In this study the effect of the cold expansion of a circular hole on fatigue life by means of a quasi-elliptical pin was investigated. Additional evaluations were conducted, including determinations of the effects of crack propagation from the hole. The major life extension was obtained through slower crack growth in the short-crack stage. The decrease in fatigue crack growth in cold-expanded specimens was related to higher crack-opening stresses which are a consequence of the presence of compressive residual stresses arising from cold expansion. In this study, an experimental investigation was carried out to quantify the effect of the cold expansion on the initiation and the propagation of the fatigue crack and was discussed. Fatigue life improvement of the cold-worked hole specimen was explained by determining the hardness results around the cold-worked hole. The results indicate that significant life improvements can be obtained through cold expansion applied with a quasi-elliptical pin in this work with the optimum results being obtained when the pin diameter is 4% larger than the diameter of the specimen hole. Also, a brief examination of the effect of the rivet shape on the fatigue life of a riveted specimen was carried out. To lengthen the fatigue life of a riveted plate which uses countersunk head rivets, the shape of the countersink and the rivet head were improved. The experimental results showed that the fatigue life of the riveted plate was improved where the improved rivet was used.     

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.     

Finite element method and experimental investigation on the residual stress fields and fatigue performance of cold expansion hole

Cold expansion is an efficient way to improve the fatigue life of an open hole. The residual stress fields of cold expansion holes are vital for key components designing, manufacturing and fatigue properties assessment. In this paper, three finite element models have been established to study the residual stress fields of cold expansion hole, experiments were carried out to measure the residual stress of cold expansion hole and verify simulation results. Three groups of specimens with different cold expansion levels are examined by fatigue test. The fracture surfaces of specimens are observed by scanning electron microscope. The finite element method (FEM) results show, with interference values develop, the maximum values of circumferential residual compressive/tensile stresses increase in “infinite” and “finite” domain, and a higher positive stress values are obtained at the boundary of “finite” domain. The effects of the friction between the mandrel and the hole’s surface and two cold expansion techniques on the distribution of residual stress is local, which only affects the radial residual stress around the maximum value and the circumferential residual stress near the hole’s edge. Crack always initiates near entrance face and the crack propagation speed along transverse direction is faster than that along axial direction.     

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.     

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.     

Interference fit effect on improving fatigue life of a holed single plate

This paper deals with the influence of interference fit coupling on the fatigue strength of holed plates made of a medium‐carbon forging steel (35 KB2), heat treated by quenching followed by tempering, up to a hardness of about 350 BH, obtaining a sorbitic microstructure. Tensile and impact tests showed an ultimate tensile strength of about 1100 MPa, a yield strength of about 1000 MPa, an elongation to failure of 15% and an impact toughness KV of 43 J at room temperature. Axial fatigue tests were performed on holed specimens with or without a pin, made of the same material, press fitted and still left into their central hole. The tension–tension fatigue tests have been performed with a stress ratio R = 0.1. The effect on fatigue strength was investigated both experimentally and numerically. Three different conditions were investigated by using open hole specimens, specimens with 0.6% of nominal specific interference and specimens with 2% of nominal specific interference. The experimental stress‐life (S–N) curves pointed out an increased fatigue life of the interference fit specimens, compared with the open hole ones. The numerical investigation was performed in order to analyse the stress field by applying an elastic plastic 2D simulation, with commercial finite element software. The stress history and distribution around the interference‐fitted hole indicate a significant reduction of the stress amplitude produced by the external loading (remote stress) because a residual and compressive stress field is generated by the pin insertion.     

芯棒锥面结构对孔冷挤压强化残余应力场的影响

为了在紧固孔周引入均匀的残余压应力,以延长紧固孔构件的疲劳寿命、提高其抗应力腐蚀性能,利用ANSYS有限元软件,建立了轴对称弹塑性有限元模型,对直接芯棒冷挤压强化过程进行了仿真,特别是对芯棒的前锥段曲线结构形式进行了设计与分析,研究了前锥段曲线形式对残余应力场分布的影响.结果表明:孔壁表面的周向残余应力分布复杂且不均匀,比较而言,外凸型正弦曲线型芯棒所产生的残余压应力沿孔壁深度方向分布更加均匀;几种曲线形式的芯棒在上表面近孔边区域均产生了径向残余拉应力,在孔的挤入段产生了轴向残余拉应力,但外凸型正弦曲线型芯棒在上述区域所产生的残余拉应力较小,且分布区域也较小.     

A new conception for enhancement of fatigue life of large number of fastener holes in aircraft structures

A new conception for increasing fatigue life of large number of fastener holes in aircraft structures is developed. It is accomplished by a new method, called friction stir hole expansion (FSHE). This method not only reduces labour and time consumption, but it also decreases the overall cost for processing a large number of holes in structures made of aerospace grade 2024‐T3 aluminium alloy. FSHE combines the advantages of friction stir processing with these of mandrel cold working methods in two ways: a micro effect, expressed in hole surface modification, and a macro effect, expressed by the introduction of beneficial compressive residual macro stresses. The effectiveness of the method has been assessed by fatigue tests. Finite element simulations have been carried out. It has been proven that the greater fatigue life of fastener holes, processed by FSHE, is a consequence of the obtained micro effect.     

Numerical and experimental investigation of the cold expansion process with split sleeve in titanium alloy TC4

A series of uniaxial fatigue tests were carried out using specimens containing non-cold expanded and cold expanded holes to assess the effect of split sleeve cold expansion on fatigue behavior of titanium alloy TC4. The fracture surfaces of specimens were observed by scanning electron microscope (SEM). 3D finite element models were also used to analyze the residual stress fields around cold expanded holes. Based on the qualitative finite element analysis (FEA), the multi-axial fatigue lives of the non-cold and cold expanded holes have been predicted by Smith–Watson–Topper (SWT) method and Wang–Brown (WB) method respectively. The effects of the friction between the split sleeve and the hole’s surface were also considered. The results reveal that crack of cold expanded specimen always initiates near entrance face and the crack propagation speed along transverse direction is faster than along axial direction. The lowest compressive stress occurs at the entrance face where crack is preferentially initiated. The mandrel entrance face is the most sensitive region to friction between the split sleeve outer surface and the hole. After cold expansion, fatigue life of TC4 open hole was increased to 1.7–2.2 times. Compared with the result of SWT theory, the result of WB theory is more conservative and reliable.     

Effect of expansion technique and plate thickness on near-hole residual stresses and fatigue life of cold expanded holes

Cold expansion of fastener holes is a common way of improving fatigue performance of airframes. Among the several techniques applicable, the split-sleeve method is the most accepted in creating beneficial compressive residual stresses around expanded holes. In the present work, residual stresses at expanded holes in several types of aluminium plates produced by two different techniques, split-sleeve and roller burnishing, have been evaluated by the novel destructive Sachs method and then compared. It was found that stress distribution particularly at the vicinity of the hole was sensitive to the method of expansion and plate thickness, due to differing characteristics of the plastic material flow. Thus, secondary reverse yielding after cold expansion found to reduce residual hoop stresses at the edge of the hole, and excessive expansion above a limit, was thought to increase reverse yielding. S–N data revealed that no benefit was gained from expanding beyond this limit. It was suggested that the reduction in the number of cycles to crack initiation or more often to crack growth was due to increased reverse yielding at the vicinity of the expanded hole.     

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.     

Characterization of residual stresses from cold expansion using spatial statistics

Residual stress fields from cold expansion have been widely used to extend the fatigue life of aircraft structures. However, the spatial statistical character of these residual stress fields has not been established and has not been incorporated in current analysis methods. The objective of this study was to establish a spatial statistical method to quantify the residual stress field around a cold expanded hole. A framework called the Spatial Analysis of Residual Stress (SpARS) was developed utilizing spatial correlation, response surface modelling techniques and statistical resampling methods to characterize the residual stress field. Our results showed that tolerance bounds on residual stress can be quantified using this method. We also demonstrated the SpARS method using recently published round robin case studies. The newly developed model will be useful for aircraft structural fatigue crack growth analyses to incorporate residual stress fields for extending inspection intervals for fatigue and fracture critical structures.     

冷胀孔裂纹寿命增长效果估算模型

本文用含孔边穿透裂纹的冷胀孔、未胀孔剩余寿命之比来评价孔冷胀强化工艺延长裂纹扩展寿命的效果。本文提出把理论计算方法与实验测试结果相结合来确定残余应力场:根据实验测量结果确定冷胀孔塑性区半径:把塑性区半径代入残余应力场的理论计算式中求出残余应力场初形;根据最大残余应力值与材料屈服应力之间的规律关系(由冷胀孔残余应力测试结果得出的)修正已计算出的残余应力场。本文用冷胀孔单边穿透裂纹在等幅循环载荷作用下的裂纹扩展寿命试验结果检验了所提出的模型,此估算模型可较保守而又较充分反映孔冷胀强化工艺对孔边裂纹的增寿作用。     

A new approach to enhancement of fatigue life of rail-end-bolt holes

The object of this paper is bolted joint railroads as the accent is put on the material behaviour around the bolted holes. The fatigue failure around rail-end-bolt holes is particularly dangerous, since it leads to derailment of trains and consequently, to inevitable accidents. Moreover, the cracking at rail-ends, which starts from bolt hole surface, causes premature rails replacement. It is well-known that the presence of residual compressive hoop stresses around the bolted holes closes the existing first mode cracks and impedes the formation of new ones and thereby extends the fatigue life of the holed components. In this article a new approach to enhancement of fatigue life of rail-end-bolt holes has been developed on the basis of a novel method and tool for cold expansion (CE) of holes, patented by the authors. The major advantage of the method is in imparting around the holes of beneficial residual compressive hoop stresses which are symmetric toward the middle longitudinal plane of the rail and thus the axial stress gradient is minimum. The developed approach consists in setting and solving a multi-objective optimization task of the CE of the rail-end-bolt holes. Because of the specificity of the studied problem, the optimal solution has been found by finite element (FE) simulations. For that purpose generalized FE model of the object has been developed. Through this model the critical point around the outside holes has been localized and the cycle of variation of hoop stresses has been determined taking into consideration assembly stresses. On the basis of adapting the generalized FE model of the rail joint to simulating the CE process, a comparison between the cases with and without CE of rail-end-bolt holes has been made. On this basis the optimal degree of CE and the successive hole treatment have been found. After simulating the CE process by the determined optimal degree of CE, the beneficial effect of implementing the new approach has been proved.     

Effect of residual stress around cold worked holes on fracture under superimposed mechanical load

Cold working is one method used to enhance the fatigue life of holes in aerospace structures. The method introduces a compressive stress field in the material around the hole and this reduces the tendency for fatigue cracks to initiate and grow under superimposed cyclic mechanical load. To include the benefit of cold working in design the stress intensity factors must be evaluated for cracks growing from the hole edge. Two-dimensional (2D) finite element analyses have been carried out to quantify the residual stresses surrounding the cold worked hole. These residual stresses have been used in a finite element calculation of the effective stress intensity factor for cracks emanating from the hole edge normal to the loading direction. The results of the 2D analysis have been compared with those derived using a weight function method. The weight function results have been shown always to underestimate the stress intensity factor. A three-dimensional (3D) FEA has been carried out using the same technique for stress intensity factor evaluation to investigate the effect of through thickness variation of residual stress. Stress intensity factors calculated with the 3D analysis are generally higher than those calculated using the 2D analysis.     

Experimental and numerical investigations on fatigue behavior of aluminum alloy 7050-T7451 single lap four-bolted joints

The fatigue behavior of aluminum alloy 7050-T7451 single lap four-bolted joints was studied by high-frequency fatigue test and finite element (FE) methods. The fatigue test results showed that a better enhancement of fatigue life was achieved for the joints with high-locked bolts by employing the combinations of cold expansion, interference fit, and clamping force. The fractography revealed that fatigue cracks propagated tortuously; more fatigue micro-cliffs, tearing ridges, lamellar structure were observed, and fatigue striation spacing was simultaneously reduced. The evaluation of residual stress conducted by FE methods confirmed the experimental results and locations of fatigue crack initiation. The extension of fatigue lives can be attributed to the evolution of fatigue damage and effect of beneficial compressive residual stresses around the hole, resulting in the delay of crack initiation, crack deflection, and plasticity-induced crack closure.     

Analysis of cold expanded fastener holes subjected to short time creep: Finite element modelling and fatigue tests

The beneficial effects of cold expansion have been well documented in previous studies, yet the performance of cold expanded plates exposed to elevated temperatures is an area of technical interest. In this research, finite element (FE) simulations along with experimental fatigue tests have been carried out to investigate the effect of exposure to elevated temperature on residual stress distribution and subsequent fatigue life of cold expanded fastener holes. According to the obtained results, creep stress relaxation occurs due to exposure to 120 °C for 50 h. FE results demonstrate a non-uniform residual stress relaxation regime through the plate thickness around the cold expanded hole and the fatigue test results show that the subsequent fatigue lives have significantly decreased.     

A comparative numerical study of combined cold expansion and local torsion on fastener holes

Cold expansion and local torsion processes provide controllable strengthening mechanisms for a fastener hole and therefore have engineering significance. They rely on the residual stress and the accumulated shearing strain, respectively, which are difficult to measure. Due to the complex closed form solutions for these mechanisms, their numerical study is of great importance. In this work, a combination of the cold expansion and the local torsion on a fastener hole has been investigated numerically to evaluate the amount and nature of the total accumulated residual stresses around a fastener hole. Different cases of the cold expansion and the local torsion processes were modelled and studied by finite element simulation to investigate the existence of a loading case which produces a beneficial compressive residual stress field in the vicinity of a hole. Sensitivity of the final residual stress with respect to a range of process parameters including adequate diametral interference and angle of rotation was investigated.