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.     

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.     

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.     

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.     

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.     

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.     

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.     

The stress distribution around holes in thermal barrier coatings

The residual stress distribution in the thermally grown oxide (TGO) around holes in thermal barrier coatings has been measured using luminescence piezospectroscopy. Far removed from the holes the residual stress field in the oxide is equi-biaxial and independent of position but in the vicinity of the holes, the mean stress decreases monotonically towards the edge of the hole. The characteristic distance over which the stresses vary is of the order of the half the hole radius, typically 10–100 times the thickness of the TGO, consistent with a shear-lag model for stress redistribution. The measurements also indicate that the stress distribution in the TGO is unaffected by the presence of an as-deposited thermal barrier coating.     

Failure behavior of quasi-isotropic laminates with three-pin loaded holes

This paper presents the effect of hole positions on the failure behavior of glass–epoxy laminated composite plates fabricated from stacking sequence [0/90/±45]_S subjected to a traction force by three-pins. Three different hole distance parameters, namely the ratio of free edge distance to the outer holes/pin diameter (E/D = 1, 2, 3, 4, 5), the ratio of longitudinal distance between the holes/pin diameter (F/D = 2, 4, 6) and the ratio of transverse distance between the parallel holes/pin diameter (G/D = 3, 4, 5) were used to investigate the effects of hole positions on failure load and failure mode. Shear out failure mode which is not the desired mode for a structure occurs around the first and second pin holes very close to the free edge of the specimen (E/D = 1). The other specimens were damaged in bearing mode which is the most desired mode.     

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.     

孔挤压过程中孔边应力应变演化规律的试验与模拟研究

该文采用挤压棒直接挤压的方法对LY12CZ铝合金进行孔挤压试验,测试了在不同过盈量、不同润滑条件下挤压时挤压力和孔边应变变化曲线。建立三维有限元模型,对挤压过程开展了数值模拟。结合试验和模拟结果,揭示了挤压过程中孔边应力应变的演化和分布规律;挤压力的变化特征以及摩擦系数和过盈量对挤压力的影响;孔的深度方向切向应力在挤压过程中的分布及孔边残余压应力的来源与演变。模拟值与试验测量值吻合良好,验证了有限元模拟的可靠性。     

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 SIMPLIFIED RESIDUAL STRESS MODEL FOR PREDICTING FATIGUE CRACK GROWTH BEHAVIOR AT COLDWORKED FASTENER HOLES

This paper presents an investigation of the fatigue crack growth (FCG) behavior at fastener holes in a high strength steel, 30CrMnSiNi2A, before and after a cold-expansion process. The fatigue life of coldworked specimens was significantly increased compared to non-coldworked ones and increased the lower applied stress level. From a study of the residual stress distribution near the edge of the hole, it was found that the experimental residual compressive stresses in absolute values were much less than the calculated values derived by previous analytical methods. Thus, a simplified residual stress model for describing the FCG behavior at coldworked fastener holes is proposed, from which, the δK_eff and fatigue lives of specimens after cold-expansion can be predicted satisfactorily for engineering applications.     

Investigation of cold expansion of short edge margin holes with pre‐existing cracks in 2024‐T351 aluminium alloy

The United States Air Force has requirements to inspect and cold expand potentially thousands of fastener holes for an aircraft fleet, and the presence of existing cracks at those fastener holes is expected. Fatigue experiments were performed to investigate the resulting fatigue crack growth life of a fastener hole that contained a representative ‘unknown’ crack at the time of inspection (approximately 0.050 in. in length) at a short edge margin hole that was then cold expanded and compare that to a non‐cold expanded hole and a cold expanded hole with no pre‐existing cracks. The United States Air Force analytical approach used to account for the benefit due to cold expansion was compared to the experimental data and does not consistently provide conservative predictions.     

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.     

Residual stress/strain evolution due to low‐cycle fatigue by removing local material volume and optical interferometric data

Three experimental methods, based on optical interferometric measurements of deformation response to local material removing, have been implemented for residual stresses determination. Two first techniques are employed to characterize initial residual stress values and their evolution near welded joints of aluminium plates under low‐cycle fatigue. The hole‐drilling method gives high‐accurate dependencies between residual stress components and number of cycles. The second approach comprises cracks modelling by narrow notches to describe residual stress distributions in more wide spatial range near the weld. The results demonstrate residual stress evolution is of complex character and cannot be uniquely qualified as a gradual relaxation. Besides, the secondary hole drilling method is developed and used as a fast and reliable tool to quantify the redistribution of residual strains near cold‐expanded holes due to low‐cycle fatigue. Dependencies of circumferential residual strains along the secondary hole edge versus number of cycles are constructed.     

The effect of cold expansion on fatigue crack growth from open holes at room and high temperature

In this paper a series of residual stress measurements and fatigue crack growth tests have been carried out using aluminium alloy 2650 specimens containing cold expanded and non cold expanded holes. Residual stress measurements have been done after cold expansion and after various loading and temperature conditions. In order to measure an angular variation of residual stresses, X-ray and a new technique called the Garcia–Sachs method have been employed. Results revealed that residual stress relaxation occurred as a result of exposure at 150°C. The magnitude of relaxation was shown to be dependent on the level and the sign of externally applied load. Fatigue crack growth tests have been carried out at 20°C and 150°C for both cold expanded and non-cold expanded conditions. Fatigue crack growth rates in specimens containing cold expanded fastener holes were affected significantly by elevated temperature exposure. Depending on the exposure time and loading conditions the fatigue life improvement was found to be between one and greater than 10 for tests at 20°C.     

Analytical and numerical modelling of plasticity-induced crack closure in cold-expanded holes

The aim of this research was the development of an analytical model for plasticity-induced fatigue crack closure for cold expanded holes. This paper extends Nowell's plane stress model of plasticity-induced crack closure for a plate with a circular hole and two radial symmetric cracks. The possibility of existence of an initial residual stress field is also taken into account. This model has potential to be applied to other cracked geometries and arbitrary residual stress fields, although the paper is focused on the study of cold-expanded holes. Hole cold-expansion is widely used in aircraft industry, for improving the fatigue performance of rivet holes by delaying fatigue crack propagation. This paper shows that the residual stress field due to cold-expansion has a strong influence on the closure behaviour and therefore on fatigue crack propagation. The analytical model developed, was compared with finite element analyses of plasticity-induced crack closure with and without residual stresses. Finally, the model was used to predict fatigue lives for some experiments recently reported in the literature for fatigue crack propagation from cold-expanded holes. Predicted fatigue lives correlate well with experimental data.     

Fatigue life estimation after crack repair in 6005 A-T6 aluminium alloy using the cold expansion hole technique

In this paper, the hole drilling (HD) and the cold expansion (CE) processes, which were used as a technique for crack repair, were investigated in order to estimate the beneficial effects on fatigue crack initiation (FCI). The FCI life is defined as the number of cycles to initiate a new crack of 0.2 mm on the surface of the specimen. Three hole radii and three degrees of cold expansion (DCE%) values were tested after a crack propagation period. Crack retardation after the CE process was observed. This phenomenon is due to two mechanisms: retardation owing to both geometric and mechanical effects, which is produced by the stress concentration at the drilled hole, and the large strain‐induced compressive residual stresses around the hole. In this report, the influence of the loading conditions was studied. For high values of the stress intensity factor range ΔK_ρ around the hole (based on the pseudo crack length a + ρ), the number of cycles corresponding to crack initiation N_i is low. At the edge of the hole, the maximum stress range can be approximated by the following formula: Δσ_max = 2ΔK_ρ /√πρ , where ρ is the hole radius and ΔK_ρ is the related stress intensity factor range.The FCI life extension, defined by the number of cycles corresponding to crack re‐initiation N_i , is related to the relative maximum stress range ratio R_σ = [(Δσ_max )/(Δσ_max )_th ] where (Δσ_max )_th is the value of the threshold maximum stress range obtained when N_i = 2 × 10⁶ cycles. The relationship between N_i and R_σ may be written as a power function.     

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.