Optimization of a cold-working process for increasing fatigue life

This paper introduces a method which allows the calculation of the optimal radial interference and the optimal mandrel shape on a cold-expanded bushing–hole connection commonly used in aerospace structures, in order to obtain the desired values of the residual stresses on the hole surface. This method has been developed by an extended campaign of FE analysis, planned and evaluated with statistical techniques on the basis of a previous presented closed-form method to determine the residual stress field. The method will give the possibility to reduce the zone of the hole surface subject to negligible residual radial stresses, obtaining also compressive residual circumferential stresses on the entire hole surface.An experimental axial fatigue test plan on aeronautical components with optimized cold-expanded bushing–hole connections and subjected to cyclic loads showed a substantial improvement in fatigue life.     

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.     

An approach to modeling time-dependent creep and residual stress relaxation around cold worked holes in aluminium alloys at room temperature

Creep behaviour of aluminium alloys is also observed at room temperature. As a result, a relaxation occurs of deliberately introduced beneficial residual stresses around fastener holes, before the relevant structural component is subjected to exploitation. Therefore, to adequately asses the life-time of the component with cold worked holes, it is necessary to quantify this relaxation. In this paper a combined iterative approach for building a time-dependent creep constitutive model of aluminium alloys at room temperature has been developed in order to be used in finite element (FE) simulations of the cold hole working process. The approach is based on an experimental study of the change in diameters of cold worked holes through mandrel cold working method and a subsequent series of FE simulations of the cold working process and of the following creep behaviour to determine the necessary equivalent stresses in the constitutive model. The obtained creep constitutive model has been founded on the power-law model. The model parameters A, n and m have been determined on the basis of a developed by the authors algorithm. The approach has been illustrated on D16T aluminium alloy widely used in the airspace industry. The material behaviour in the plastic field has been described by the nonlinear kinematic hardening model, obtained through a uniaxial tensile test. Both constitutive models have been used in FE simulations of the cold working processes and of subsequent residual stress relaxation around the cold worked open holes due to creep at room temperature. On the base of the FE results, mathematical models describing the residual stress relaxation have been obtained. Thus, the residual stresses are adequately evaluated immediately before introducing the structural component in operation.     

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.     

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.     

Investigation the effect of tightening torque on the fatigue strength of double lap simple bolted and hybrid (bolted–bonded) joints using volumetric method

In this research, the effect of the tightening torque on the fatigue strength of 2024-T3 double lap simple bolted and hybrid (bolted–bonded) joints have been investigated experimentally by conducting fatigue tests and numerically by implementing finite element analysis. To do so, three sets of specimens were prepared and each of them subjected to tightening torque of 1, 2.5 and 5 Nm and then fatigue tests were carried out under different cyclic longitudinal load levels. In the numerical method, the effect of the tightening torque on the fatigue strength of the considered joints has been studied by means of volumetric method. To obtain stress distribution around the notch (bolt hole) which is required for the volumetric method, nonlinear finite element simulations were carried out. In order to estimate the fatigue life, the available smooth S–N curve of Al2024-T3 and the fatigue notch factors obtained from the volumetric method were used. The estimated fatigue life was compared with the available experimental test results. The investigation shows that there is a good agreement between the life predicted by the volumetric method and the experimental results for different specimens with a various amount of tightening torques. The results obtained from the experimental analysis showed that the hybrid joints have a better fatigue strength compared to the simple bolted joints. In addition, the volumetric method and experimental results revealed that the fatigue life of both kinds of the joints were improved by increasing the clamping force resulting from the torque tightening due to compressive stresses which appeared around the bolt hole.     

Effect of residual stresses on fatigue strength of high strength steel sheets with punched holes

The effect of residual stresses on the reverse bending fatigue strength of steel sheets with punched holes was studied for steels with tensile strength grades of 540 MPa and 780 MPa. Tensile and compressive residual stresses were induced around the punched holes. Heat treatment of the specimens with punched holes at 873 K for 1 h decreased the residual stresses around the holes and improved the fatigue strength of the sheets. This result means that the tensile residual stresses induced in the sidewalls of the holes and near the hole edges by punching reduced fatigue strength. The effect of the residual stresses on the fatigue limits of the edges was estimated by the modified Goodman relation using the residual stresses after cyclic loading and the ultimate tensile strength at the fatigue crack initiation sites.     

RELAXATION OF RESIDUAL STRESSES AT COLD-WORKED FASTENER HOLES DUE TO FATIGUE LOADING

Abstract— Cold-expansion of fastener holes is now commonly used within the aerospace industry to increase the fatigue endurance of airframes. Although a number of methods of cold expansion are possible, the split-sleeve cold-expansion process is the most widely accepted and is frequently used in the repair and manufacture stages of both military and civil aircraft. In the present work, the redistribution of residual hoop stresses due to the application of constant amplitude fatigue loading at 4% cold-expanded holes has been studied. A modified Sachs method was adopted to evaluate the residual stress profiles and a replication technique was used to quantify crack growth. It was found that the decay of the residual hoop stress profile near the bore of the hole was due to the initiation and growth of small fatigue cracks. Cracks were found to initiate both near and below the fatigue limit, but subsequently arrested so stabilising the overall residual stress profile.     

Prediction of fatigue life in aircraft double lap bolted joints using several multiaxial fatigue criteria

In this research, the effects of torque tightening on the fatigue strength of 2024-T3 aluminium alloy double lap bolted joints have been studied via experimental and multiaxial fatigue analysis. To do so, three sets of the specimens were prepared and each subjected to different levels of torque i.e. 1, 2.5 and 5 N m and then fatigue tests were carried out at various cyclic longitudinal load levels. A non-linear finite element ANSYS code was used to obtain stress and strain distribution in the joint plates due to torque tightening of bolt and longitudinal applied loads. Fatigue lives of the specimens were estimated with six different multiaxial fatigue criteria by means of local stress and strain distribution obtained from finite element analysis. Multiaxial fatigue analysis and experimental results revealed that the fatigue life of double lap bolted joints were improved by increasing the clamping force due to compressive stresses which appeared around the hole.     

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.     

Investigation of the multiaxial fatigue behaviour of 316 stainless steel based on critical plane method

In this work, the multiaxial behaviour of 316 stainless steel is studied under the lens of critical plane approach. A series of experiments were developed on dog bone–shaped hollow cylindrical specimens made of type 316 stainless steel. Five different loading conditions were assessed with (a) only tensile axial stress, (b) only hoop stress, (c) combination of axial and hoop stresses with square shape, (d) combination of tensile axial and hoop stresses with L shape, and (e) combination of compressive axial and hoop stresses with L shape. The fatigue analysis is performed with four different critical plane theories, namely, Wang‐Brown, Fatemi‐Socie, Liu I, and Liu II. The efficiency of all four theories is studied in terms of the accuracy of their life predictions and crack failure plane angle. The best fatigue life predictions were obtained with Liu II model, and the best predictions of the failure plane were obtained with Liu I model.     

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.     

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.     

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.     

Investigation of residual stresses in a repair‐welded rail head considering solid‐state phase transformation

Repair welding for recovery from local damage of a rail head surface is known to cause high residual stress and can accelerate fatigue in the rail. This study examines repair‐welded rails by applying experimental and numerical approaches. In the former approach, two newly manufactured rail specimens and four repair‐welded rail specimens with two different weld depths were prepared, and their residual stresses were measured with a sectioning method. In the latter approach, a finite element repair welding simulation model was developed that adopted a prescribed temperature method with a moving block as an input heat source, and the thermal strain caused by the volume change due to solid‐state phase transformation was considered. Overall, the residual stresses correlated well between the experimental and numerical approaches. The measured high compressive residual stress of ?290 MPa seems to be beneficial to prevent a crack initiation in the rail surface.     

Analytical methodology for predicting fatigue life distribution of fuselage splices

Methodologies to predict fatigue life distribution of fuselage splices, measured as the number of cycles to visible cracks, were developed in this work. Modeling procedures using three dimensional nonlinear finite element (FE) analysis were developed to obtain the stress state at the rivet hole. Contact surfaces, which include friction effects, were used to simulate the rivet to hole and skin to skin interactions. The squeezing force (SF) resulting from the riveting process and the coefficient of friction (CF) used for the contact surfaces were taken as random variables. Analytical expressions for local stress as a function of the squeezing force and coefficient of friction were developed using a response surface technique along with limited FE analyses. Based on the calculated local stresses, a strain-life approach was employed to predict fretting fatigue crack nucleation at the rivet hole. A Monte Carlo simulation was developed, which integrated the two random variables into the models, to determine the fatigue life distribution to visible cracks. Results from the simulation showed that the predicted fatigue life distribution correlated very well with the existing test data. Further sensitivity studies indicated that the squeezing force has a stronger influence on the life distribution than the coefficient of friction.     

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.     

多孔复合材料机械连接件弹性接触内力和应力分析

本文用有限元混合法给出了多孔复合材料机械连接件弹性接触内力和应力分析。文中详细讨论了销钉弹性、层合板铺设方式和摩擦对各孔钉载分配及孔边应力的影响,并给出了多孔连接件向单孔连接件简化的条件。      

FATIGUE LIFE PREDICTION OF NOTCHED COMPOSITE COMPONENTS

Abstract— The local stress/strain approach has been used to predict the fatigue lives of notched composite components. The method was based on a microstress analysis and the application of a multiaxial fatigue parameter incorporating the alternating strain components on the critical plane. This parameter was able to correlate the fatigue lives obtained under a variety of multiaxial loading and geometrical configurations, enabling a generalized fatigue life curve to be determined on the basis of limited experimental data.
The ability of the multiaxial fatigue parameter to relate the fatigue behaviour of composites was illustrated by predicting the locations of crack initiation sites in a unidirectional silicon carbide fibre reinforced titanium plate containing a circular hole tested under constant amplitude cyclic loading. The same approach was also successfully employed to predict the fatigue lives of graphite reinforced epoxy composite tubes with circular holes tested under several combinations of cyclic tension and torsion.