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 strength reduction factors at rivet holes for aircraft fuselage lap joints

Fatigue test results to be utilized in a fatigue life prediction model for aircraft fuselage riveted lap joints are presented. A series of fatigue tests on aluminium alloy sheet coupons with an open hole and filled hole subjected to remote tension, pin loading and out-of-plane bending have been carried out. Such loading conditions were conceived to replicate local effects of the bypass load, transfer load and secondary bending respectively at the critical rivet row. It was shown that the fatigue response of the open hole specimens could be predicted with a satisfactory accuracy employing the Neuber fatigue notch factor. For the filled hole specimens considerably longer fatigue lives were observed than for the open hole specimens under the same type of loading; however, a reduction of the notch effect due to the hole filling was found to depend on the type of loading, interference magnitude and applied load level. A concept of utilizing the obtained results to quantitatively account in the fatigue life prediction model for filling the hole by the rivet shank, in addition to geometry parameters, is presented. Finally, consideration is given to load transmission by frictional forces and its implication for the fatigue properties of riveted lap joints.     

Some contraindications of hole expansion in riveted joints

Comparable fatigue tests were carried out on aluminium alloy 7475-T7351 double butt joints with untreated and with cold expanded holes. Surprisingly, the behaviour of the specimens having cold expanded holes was worse than that of specimens with untreated holes. This result was attributed to the surface upset which was present in cold expanded holes. Several hypotheses were formulated and experimentally verified to overcome this problem, such as deeper hole deburring, rivet diameter, joint design and grip material, steel instead of aluminium alloy.Additional tests demonstrated that the problem was not present in sealed joint as the surface upset was hidden in the sealant thickness. Sealants have detrimental effects in the fatigue resistance of riveted joints, as they increase the load transferred by rivet bearing. The hole expansion is beneficial in this condition, while in un-sealed joints its effect must be accurately evaluated.Other authors too highlighted possible problems due to surface upset, up to suggest to eliminate it. Only in a very few cases, a reduction of fatigue life as a consequence of hole expansion was observed.     

Reconstitution of fatigue crack growth in Al-alloy 2024-T3 open-hole specimens using microfractographic techniques

Fatigue is one of the main problems in the provision of service life and safety of aircraft structures. The menace of fatigue cracking is accentuated in areas of stress concentration, e.g., joints of structural components. An example is the fuselage where riveting is used. One of the techniques for improving the fatigue life of these connections is the cold expansion of the rivet hole. As part of a larger project on the fatigue behaviour of aeronautical structures, an experimental study of open-hole specimens in Al-alloy 2024-T3, with and without hole expansion, is presented. The residual stress field created by the cold expansion was experimentally assessed by using the X-ray technique and predicted by FEA. Fatigue tests were supplemented by SEM measurements of fatigue striation spacing along longitudinal and transverse directions in the crack surface of each specimen. Empirical models and fractographic techniques developed by Nedbal et al. are used for the analysis of the experimental data, and results of quantitative microfractography are presented. Crack tunnelling was quantified based on the reconstituted crack history and on the surface crack growth measurements.     

Fatigue crack growth and life prediction of a single interference fitted holed plate

To understand the different aspects of fatigue behaviour of complex structural joints it will be much helpful if the effects of different parameters are studied separately. In this article, to study the isolated effect of interference fit on fatigue life a pined hole specimen is investigated. This specimen is a single‐holed plate with an oversized pin which force fitted to the hole. The investigation was carried out both experimentally and numerically. In the experimental part, interference fitted specimens along with open hole specimens were fatigue tested to study the experimental effect of the interference fit. In the numerical part, three‐dimensional finite element (FE) simulations have been performed in order to obtain the created stresses due to interference fit and subsequent applied longitudinal load at the holed plate. The stress distribution obtained from FE simulation around the hole was used to predict crack initiation life using Smith–Watson–Topper method and fatigue crack growth life using the NASGRO equation with applying the AFGROW computer code. The predicted fatigue life obtained from the numerical methods show a good agreement with the experimental fatigue life.     

Effect of local cold working on the fatigue life of 7475-T7351 aluminium alloy hole specimens

Different degrees of cold working (ranging from 0% to 5.58%) were applied to the hole of plate specimens of 7475-T7351 aluminium alloy. These specimens were then subjected to cyclic loading. In each test, the crack initiation was detected and subsequently the crack length was monitored, using a video camera system. The experimental results were analysed in order to determine the cold working effect on the fatigue initiation period, on the propagation life and finally on the overall fatigue life. It was found, for example, that the propagation life improvement factor for a degree of cold working of 5.58% is about 43.0 and 4.9 for applied nominal stresses of 191 and 300 MPa, respectively. For the same conditions, the fatigue life improvement factor is about 3.2 and 1.5. A numerical analysis was also performed, using three-dimensional finite element method to establish the stress and strain distributions resulting from the superposition of the cold working process and the fatigue loading. Then, the results were used in connection with the non-cold worked hole data for calculating the cold worked plate initiation period according to the strain-life concept; for determining the propagation life, the weight function technique was applied. The predictions are very close to the experimental results.     

Fatigue crack propagation from a cold-worked hole

The cold expansion process is widely used to enhance the fatigue life of structures with fastener holes. Various studies assert that the cold expansion improves the fatigue strength of fastener holes; however, the improvement of fatigue life is difficult to quantify. Therefore, the influence on fatigue life of cold-worked process was studied by numerical and experimental tests. Then, a parametric study on material hardening behavior and Bauschinger’s parameter was performed for several loading conditions in order to determine their effect on crack growth propagation. The results of the numerical tests have exhibited a good prediction of the fatigue life of the component.     

Analytical and experimental investigation of fatigue and fracture behaviors for anti-double dog-bone riveted joints

Load-transferred experiments and fatigue tests of the anti-double dog-bone riveted joints were carried out, and the fracture surfaces were observed by scanning electron microscopy (SEM) in this paper. Based on the finite element analysis (FEA), the multi-axial fatigue life of the anti-double dog-bone riveted joints has been predicted by Smith–Watson–Topper (S–W–T) method and Wang–Brown (W–B) method respectively. And the results of FEA were compared with the experiment results. The results show that because of the deformation of the rivets and the holes, the load transferred by the rivets decreases with external load increase. The fracture of joints all occur at rivet holes, and the crack initiates at the dog-bone specimen closed to the rivet head. Compared with the result of W–B method, the result of S–W–T method is more conservative and reliable.     

Fatigue testing of a shape-optimized circular hole in a plate under tensile and bending loads

With the help of the CAO method a plate with a shape-optimized circular hole has been developed. Its surface stresses have been drastically reduced by attaching material at places of high local stresses and reducing material at locations of low local stresses. Fatigue tests have been performed under tensile and bending loads (to ensure the prolongation of the crack initiation phase). The tests showed that the fatigue life of the shape-optimized specimen could be extended by a factor of at least 3 for tensile loading and at least 25 for bending loading compared to the non-optimized specimen type. This result validates the method used (as an effective method of structural shape optimization).     

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.     

EFFECTS OF COLD EXPANSION OF A HOLE ON FATIGUE CRACK INITIATION LOCATION AND LIFE OF AN LY12CZ ALLOY

Abstract— In the present study the effects of cold expansion of a hole on the location of fatigue crack initiation and life of LY12CZ alloy sheets are experimentally investigated and a quantitative expression of fatigue crack initiation life presented. Test results and analysis show that there may exist an optimum amount of cold expansion, for which both the coefficient of the resistance to fatigue crack initiation and the threshold are increased, and that the direction of cold expansion has no appreciable effect on fatigue crack initiation life. Observations show that, after cold expansion the fatigue crack nearly always initiates on the final entry face from which the mandrel is introduced into the hole during the final cold expansion process. Therefore it may be thought that the entry face is less resistant to fatigue crack initiation. In addition, the assumption of equivalence of residual stresses and also the strain hardening conditions on both the entry and exit faces may be questionable.     

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.     

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.     

Fracture Mechanics of cracks originating from holes treated for notch stress relieving

A tensile plate with a circular hole is investigated. The notch stresses are calculated, for an optimum notch arrangement as well as cold expansion of the notch. The stress-intensity factor is calculated for a crack originating at a single circular hole surrounded by two axially arranged circular stress-relieving notches. Furthermore, the influence of cold expansion of the main notch, which is to be relieved, and of the combination of cold expansion and stress-relieving notches on the stress intensity factor is investigated. The weight-function is given for all the cases above. It has been computed with good approximation by a Finite-Element-Method.     

曲轴弯曲疲劳试验裂纹研究与失效判定

通过对疲劳裂纹的产生、扩展机理研究和试验,结合疲劳试验数据分析了疲劳裂纹扩展与疲劳寿命的关系。试验结果及分析表明,大量经圆角滚压强化的球墨铸铁曲轴,疲劳试验运行107次在连杆颈与曲柄臂过度圆角产生微裂纹,该裂纹属于非扩展裂纹,继续试验时裂纹不扩展,试样在该载荷下具有无限疲劳寿命。     

Effect of Cold-Working by hole expansion on fatigue life of 7075-T7351 and 7475-T761 Aluminum lugs with and without initial flaws under maneuver loading spectrum

The effect of cold working by hole expansion on fatigue life of aircraft lugs under maneuver and constant amplitude laoding was investigated. Of the two nominal expansion levels used, 2% expansion resulted in greater life improvement than the larger expansion of 3.3%. The reason for this was the relatively small w/d ratio and lug head shape distortion caused by the larger expansion. The hole expansion had a more beneficial effect in the case of lugs with 1 mm deep initial flaws than lugs without flaws. Hole expansion considerably improved the damage tolerance of the lugs investigated.     

Experimental investigation on low cycle fatigue and fracture behaviour of a notched Ni‐based superalloy at elevated temperature

In order to investigate the effects of stress concentration on low cycle fatigue properties and fracture behaviour of a nickel‐based powder metallurgy superalloy, FGH97, at elevated temperature, the low cycle fatigue tests have been conducted with semi‐circular and semi‐elliptical single‐edge notched plate specimens at 550 and 700 °C. The results show that the fatigue life of the notched specimen decreases with the increase of stress concentration factor and the fatigue crack initiation life evidently decreases because of the defect located in the stress concentration zone. Moreover, the plastic deformation induced by notch stress concentration affects the initial crack occurrence zone. The angle α of the crack occurrence zone is within ±10° of notch bisector for semi‐circular notched specimens and ±20° for semi‐elliptical notched specimens. The crack propagation rate decreases to a minimum at a certain length, D, and then increases with the growth of the crack. The crack propagation rate of the semi‐elliptical notched specimen decelerates at a faster rate than that of the semi‐circular notched specimen because of the increase of the notch plasticity gradient. The crack length, D, is affected by both the applied load and the notch plasticity gradient. In addition, the fracture mechanism is shown to transition from transgranular to intergranular as temperature increases from 550 to 700 °C, which would accelerate crack propagation and reduce the fatigue life.     

应用局部应力-应变法计算联轴器膜片疲劳寿命

由于轴线间的角向不对中,联轴器旋转时膜片中产生交变应力,引起疲劳问题。使用中需要考虑其疲劳寿命。本文对六孔圆环形和束腰形膜片,利用有限元方法和薄板弯曲理论建立膜片应力计算模型。引入改进的局部应力－应变法,建立计算膜片联轴器膜片疲劳裂纹形成寿命的模型和方法。定量分析两种形式膜片的应力、附加载荷和疲劳寿命,最后,得出对膜片组设计有参考价值的结论。结论表明,对于设计合理的膜片,其疲劳寿命能满足机组工作要求。     

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.     

S‐N curve for riveted details in corrosive environment and its application to a bridge

A formula for stress‐life curve is proposed to predict the fatigue life of riveted bridges located in corrosive environments. The corrosive environment‐dependent parameters of the S‐N curve are determined based on the corrosion fatigue testing results of different types of steel specimens in air, fresh water, and seawater. Eurocode detail category 71 and UK WI‐rivet detail category represent the fatigue strength of riveted members. The proposed S‐N curve formula is compared with full‐scale fatigue test results of riveted joints, plate girders, and truss girders, which were tested in a corrosive environment. Thus, the validity of the formula is confirmed. The formula does not require any material parameter other than the code‐given fatigue curve of riveted details. The fatigue life of a riveted railway bridge is estimated by using the proposed formula, and the results are compared with conventional approaches. The applicability and significance of the proposed curve are confirmed.