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T N Chakherlou - One of the best experts on this subject based on the ideXlab platform.
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Numerical and experimental investigation of the effect of the Cold Expansion process on the fatigue behavior of hybrid (bonded-bolted) double shear lap aluminum joints
International Journal of Fatigue, 2019Co-Authors: Z. Emami Geiglou, T N ChakherlouAbstract:Abstract In this study, the effect of Cold Expansion process on the fatigue behavior of hybrid (bonded-bolted) double shear lap joints has been investigated, numerically and experimentally. Also the effects of Cold Expansion process and adhesive bonding process on the fatigue behavior of simple bolted double shear lap joint are studied, separately. For this purpose, six batches of specimens were made from 7075-T6 aluminum alloy sheet in Simple and Hybrid groups. Simple group consists of simple, 1.5% Cold expanded and 4.7% Cold expanded batches. Hybrid group consists of hybrid, 1.5% Cold expanded hybrid and 4.7% Cold expanded hybrid batches. All of the specimens after assembling were put under cyclic loading. The S-N curves of the experimental results show that the Cold Expansion process increases the fatigue lives of Hybrid and Simple group specimens. This increase is more appreciable by increasing the Cold Expansion percent. The adhesive bonding of Simple group specimens increases the fatigue life of these specimens. For all specimens the fatigue life enhancement is more appreciable at the lower loads. Also, the rate of crack growth in Hybrid group is slower than that of Simple group.
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Investigating the effect of Cold Expansion process on the fatigue behavior of aluminum alloy 7075-T6 in double-lap shear joints:
Proceedings of the Institution of Mechanical Engineers Part L: Journal of Materials: Design and Applications, 2018Co-Authors: Z. Emami Geiglou, T N ChakherlouAbstract:In this paper, the effect of Cold Expansion process on the fatigue behavior of 7075-T6 aluminum alloy has been investigated both by numerical modeling and conducting experimental tests. In the expe...
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Investigating the effect of Cold Expansion on frictional force evolution during fretting fatigue tests of AL2024-T3 plates
International Journal of Mechanical Sciences, 2018Co-Authors: P. Shahriary, T N ChakherlouAbstract:Abstract In this paper, fretting fatigue experiments are conducted on Cold expanded holed plates using fretting test configuration which is designed to simulate fretting fatigue condition around the holes. Two values of normal contact force and longitudinal cyclic load are applied on the specimens, and the evolution of friction force is measured during the tests. Finite element simulation is performed for better understanding of the Cold Expansion process and its effect on the contact configuration. The obtained results show that a high degree of Cold Expansion does not increase fretting fatigue life. Moreover, the value of frictional force is low at the early cycles of tests and increases to reach a stabilized value. The stabilized value of frictional force on the entrance and exit planes of low degree Cold expanded specimens is almost the same, while it is lower on the exit plane of high degree Cold expanded specimens in comparison to the entrance plane of the same specimen. It is revealed that the geometrical change that occurs on the plate during the high degree Cold Expansion process is the main cause of this phenomenon, while the increased hardness around the hole is the subsidiary factor.
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experimental and numerical comparison of Cold Expansion and interference fit methods in improving fatigue life of holed plate in double shear lap joints
Aerospace Science and Technology, 2013Co-Authors: T N Chakherlou, H Taghizadeh, A B AghdamAbstract:Abstract In this paper experimental and numerical investigations have been carried out on comparison of Cold Expansion and interference fit techniques in improving fatigue life of holed plates made from Al 2024-T3 in double shear lap joints. Fatigue tests were conducted on the specimens to study the role of Cold Expansion and interference fit on fatigue life and failure mode. Also to explain the experimental results and to obtain the residual stress and pre-stress distributions in the specimens due to these two techniques, finite element simulations were employed. The experimental results revealed that the interference fitted specimens exhibit much longer fatigue life, compared to Cold expanded specimens at lower amplitude cyclic load, but as the load increases the two techniques show almost the same fatigue life. The finite element simulations show that interference fit reduces the local stress amplitude around the fastener hole, whereas Cold Expansion reduces the local mean stress. The numerical simulations can clarify and explain the experimentally observed results.
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effect of Cold Expansion and bolt clamping on fretting fatigue behavior of al 2024 t3 in double shear lap joints
Engineering Failure Analysis, 2012Co-Authors: T N Chakherlou, M Shakouri, Alireza Akbari, A B AghdamAbstract:Abstract In this paper the fatigue behavior of double shear lap joints treated by Cold Expansion and bolt clamping has been investigated. Fatigue tests and numerical simulations were conducted to study the combined effect of Cold Expansion and bolt clamping on the fatigue life and failure mode. The results showed significant changes on the fatigue behavior of the double shear lap joints at different load ranges. Depending on the degree of Cold Expansion and clamping torque, both plain fatigue and fretting fatigue failures were observed. The optimum degree of Cold Expansion in conjunction with the clamping force differs from those reported for joints that were Cold expanded only.
Jeffrey Vogwell - One of the best experts on this subject based on the ideXlab platform.
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The effect of Cold Expansion on fatigue resistance on fastener holes
2013Co-Authors: Jeffrey Vogwell, J. M. MinguezAbstract:Abstract It has long been known that Cold Expansion of fastener holes (as used on bolted or riveted metal joints) can be used as a means of improving the resistance of the hole to failure by fatigue. However, the fatigue resisting behaviour can be unpredictable as tensile fatigue tests carried out on batches of specimen made of aircraft grade aluminium alloy and containing a central hole has shown. Those subjected to the ballising method of Cold Expansion did not result in any noticeable improvement in fatigue life. This finding is partly supported by recently published research findings where finite element models have been used to predict residual stress distributions. Results have shown that sometimes positive, rather than negative, residual stresses can result at the edge of a hole after Cold forming under certain conditions and this helps explain why the anticipated improvement in fatigue strength sometimes does not materialise.
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Fatigue life of an aerospace aluminium alloy subjected to Cold Expansion and a cyclic temperature regime
Engineering Failure Analysis, 2006Co-Authors: J. M. Minguez, Jeffrey VogwellAbstract:Abstract This paper describes experimental work that was carried out to study the influence of cyclic temperature variation on the fatigue life of fastener holes in an aerospace aluminium alloy after they had been subjected to Cold Expansion. Three different batches of specimen were produced for fatigue testing. The first samples had the fastener hole left in the ‘as drilled’ state, the second and third batches had their drilled holes Cold expanded by directly force fitting an oversized pin through the hole. In addition, the third batch with Cold expanded holes was then subjected to a representative range flight cycle temperature variations. The results reveal that the cyclic temperature variation, rather than relaxing the residual stress and thus the Cold Expansion effect, as was feared, has actually extended the fatigue life of the Cold expanded holed specimens tested. It is believed that this is because the temperature changes have tended to neutralise the local peak residual stresses which can occur at the surface faces.
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a novel method of Cold Expansion which creates near uniform compressive tangential residual stress around a fastener hole
Fatigue & Fracture of Engineering Materials & Structures, 2004Co-Authors: T N Chakherlou, Jeffrey VogwellAbstract: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.
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A novel method of Cold Expansion which creates near‐uniform compressive tangential residual stress around a fastener hole
Fatigue Fracture of Engineering Materials and Structures, 2004Co-Authors: T N Chakherlou, Jeffrey VogwellAbstract: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.
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the effect of Cold Expansion on improving the fatigue life of fastener holes
Engineering Failure Analysis, 2003Co-Authors: T N Chakherlou, Jeffrey VogwellAbstract:Abstract An analytical and experimental study has been completed to assess the effectiveness of a direct Cold Expansion technique on the fatigue strength of fastener holes. Such methods are used in the aircraft construction industry to make holes more resistant to failure but recent research findings have reported that sometimes the anticipated benefits of Cold Expansion are not always achieved. This research work has sought to clarify the situation.
Abhay Sharma - One of the best experts on this subject based on the ideXlab platform.
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Combined Cold Expansion and Friction Stir Processing of Fastener Holes in Aluminum Alloy Al-2014-T6
Transactions of the Indian Institute of Metals, 2017Co-Authors: Nitin J. Panaskar, Abhay SharmaAbstract:Cold Expansion is used to induce compressive stress zone, by inserting a tapered mandrel/pin or ball into an undersized fastener hole in order to improve fatigue life. In this paper, combined Cold Expansion and friction stir processing of fastener holes in aluminium alloy Al-2014-T6 is presented wherein the Cold Expansion tool rotates and thus friction stirs the cylindrical surface of a fastener hole while expanding it. The residual stress, surface roughness and hardness of wall of fastener holes are measured and SEM images are captured. The combined Cold Expansion method is evaluated for three conditions at tool and fastener hole interface, namely wet (i.e., in presence of metal working fluid), solid lubricant (i.e., in presence of Al_2O_3 nanoparticles), and dry (i.e., without any external medium). The conventional Cold Expansion process is compared with combined Cold Expansion and friction stir processing. The results indicate efficacy of using nanoparticles as a medium in combined Cold Expansion and surface processing of Al-2014-T6 aluminium alloy to improve surface integrity and fatigue life.
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Combined Cold Expansion and Friction Stir Processing of Fastener Holes in Aluminum Alloy Al-2014-T6
Transactions of the Indian Institute of Metals, 2017Co-Authors: Nitin J. Panaskar, Abhay SharmaAbstract:Cold Expansion is used to induce compressive stress zone, by inserting a tapered mandrel/pin or ball into an undersized fastener hole in order to improve fatigue life. In this paper, combined Cold Expansion and friction stir processing of fastener holes in aluminium alloy Al-2014-T6 is presented wherein the Cold Expansion tool rotates and thus friction stirs the cylindrical surface of a fastener hole while expanding it. The residual stress, surface roughness and hardness of wall of fastener holes are measured and SEM images are captured. The combined Cold Expansion method is evaluated for three conditions at tool and fastener hole interface, namely wet (i.e., in presence of metal working fluid), solid lubricant (i.e., in presence of Al_2O_3 nanoparticles), and dry (i.e., without any external medium). The conventional Cold Expansion process is compared with combined Cold Expansion and friction stir processing. The results indicate efficacy of using nanoparticles as a medium in combined Cold Expansion and surface processing of Al-2014-T6 aluminium alloy to improve surface integrity and fatigue life.
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A fundamental investigation on rotating tool Cold Expansion: numerical and experimental perspectives
The International Journal of Advanced Manufacturing Technology, 2014Co-Authors: Bhoopati M. Kumar, Nitin J. Panaskar, Abhay SharmaAbstract:In this study, we present the development of a novel technique for Cold Expansion using a rotating tapered mandrel that friction processes the cylindrical wall of the fastener hole and simultaneously Cold expands it. The developed technique, named as rotating tool Cold Expansion (RTCE), is experimentally and numerically investigated. A 3D thermomechanical finite element model for predicting the compressive residual stress, responsible for delaying crack propagation from the edges of the holes, is introduced. The efficacy is that RTCE is assessed for varying degrees of Cold Expansion under different lubricating conditions at the tool–workpiece interface, such as dry, metal working fluid, and nanopowder. The plastic deformation combined with friction stirring at the tool–workpiece interface helps the RTCE in controlling the surface damage at entry and exit of the hole that is most often observed with the conventional Cold Expansion technique. Enhanced friction due to the nanopowder at the tool–workpiece interface helps in sustaining efficacy of the RTCE even at a higher degree of Cold Expansion which otherwise leads to surface damage with other mediums.
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Rotating Tool Cold Expansion
2013Co-Authors: B K Motali, Abhay SharmaAbstract:Many engineering parts in industries are assembled by rivets, bolts, pins etc. These joints are more vulnerable to fatigue loadings and a crack is emanated. As structure is in use crack starts propagating over a period of time. Crack propagation can be obstructed by inducing a compressive residual stress zone around the vulnerable parts. Cold Expansion hole (CEH) is one of the techniques used to induce compressive stress zone, by inserting a tapered pin or a large diameter ball into an undersized hole. As the oversized object is inserted into the hole, the surrounding material is elastically deformed and when the object comes out from the other side, the expanded material springs back to form tangential compressive residual stress around the hole. In most of the cases the crack origins on the surface, a good surface finish is also an important parameter for increasing the strength at the surface and stop crack emanation. However, good surface finish is not achieved by CEH. A novel technique called rotating tool Cold Expansion (RTCE) technique is developed where a tapered mandrel is inserted into an undersized hole besides rotating it simultaneously. The tool rotation breaks down the coarse grains into fine grain structure achieving good surface finish. In this method, RTCE is performed with three undersized diameters, namely, 9.2, 9.5 and 9.9 mm diameters to a maximum of 10 mm diameter. The tool material is high speed steel and the work piece material is commercial aluminium. The induced residual stresses are measured using X-ray diffraction method and compared for three different Cold Expansion holes. Due to the rotation of the tool, heat is generated because of both friction at the interface and plastic deformation. A 3-D thermo-mechanical analysis is performed in ANSYS FEA for different values of coefficient of friction and plastic deformation rate and validated with experimental results. Compared to the degree of Cold Expansion through conventional techniques (upto 4%) the proposed technique is capable to produce good results up to 8.69% of Cold Expansion. Role of heat generated through friction and plastic deformation is critical to attain the best possible result, equal contributions of both are important.
Clément Chirol - One of the best experts on this subject based on the ideXlab platform.
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Numerical simulation of the out-of-plane displacement during Cold-Expansion of Titanium plate
2017Co-Authors: Julien Cochet, Clément Chirol, Alain DaidiéAbstract:This study deals with the Cold-Expansion process of a Ti-6Al-4V plate, investigated with the use of finite element simulation. Widely used in the aerospace industry, Cold Expansion of metallic holes aims towards improving the fatigue performance of metallic holes. Indeed, by providing compressive residual stresses in the hole surrounding, crack growth rate can be significantly decreased resulting in fatigue life improvements. However, little attention has been devoted to the prediction of the out-of-plane displacement near the hole wall. Perceived as problematic, further machining and surfacing are carried out upon Cold-Expansion in order to avoid material bump while maintaining the fatigue life as high as possible. Thus, in order to anticipate the depth of the removed layer, the Cold-Expansion process was simulated in 3D using Abaqus FEA software. The mechanical properties of the Ti-6Al-4V have been obtained from compression experiments at ambient temperature and at strain rates ranging from 0.1 to 10 s-1. To describe the compression behaviour, the Johnson-Cook flow stress model has been used. Carried out implicitly, the effects of tool velocity, lubrication, plate thickness and degree of Cold Expansion have also been studied. Combined with experimental measurements, the predictions of out-of-plane displacement have shown good geometric agreement. In the future, prediction of distortions and fatigue life is necessary. This will be accomplished by combining the present model with a damage model in order to establish a relationship between Cold-Expansion and fatigue life.
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Optimization of the Cold Expansion Process for Titanium Holes
Advanced Engineering Materials, 2016Co-Authors: Victor Achard, Alain Daidié, Manuel Paredes, Clément ChirolAbstract:Cold Expansion of metallic holes is widely used in the aerospace industry for improving the fatigue performance of mechanical assemblies. To increase the efficiency of the process, it is worth considering the possibility of carrying out the Expansion twice in succession in the same hole. This paper discusses the consequences of such an operation on a single titanium hole through a numerical and experimental study. More precisely, numerical modeling is developed in order to simulate cases where the Expansion is carried out twice: in the same direction and in opposite directions. The residual fields are analyzed and the results compared with experimental results using incremental hole-drilling technique. Results show that double Expansion may have a very positive impact on the homogeneity of the compressive fields.
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Cold Expansion process on hard alloy holes-experimental and numerical evaluation
Mechanics & Industry, 2016Co-Authors: Victor Achard, Alain Daidié, Manuel Paredes, Clément ChirolAbstract:This paper presents an evaluation of the influence of the Cold Expansion process on the fatigue performance of holes in hard alloys, as such materials are involved in an increasing number of aeronautical applications. Fatigue enhancement could bring significant savings for numerous possible industrial applications. However, although the Cold Expansion of aluminium holes has been studied widely, there have been few publications concerning this process in hard alloys and there is currently very few research activities on technique dedicated to high strength metallic holes. Thus, this work aims to define an approach to understand why processes and methodologies are suitable for obtaining effective Expansion of these materials. In this article, the response of expanded holes is studied, considering various experimental parameters and for a wide range of Expansion ratios. The influence on the fatigue strength of Ti-6Al-4V tensile specimens is also reported for various Expansion ratios, more precisely \textquotedblleftstandard\textquotedblright Expansion ratios and high Expansion ratios. Then, a specific numerical modelling of the process is presented, which enables us to understand the impact of high Expansion ratios in titanium holes and the influence on fatigue performance. A very good correlation between experimental and numerical results is observed.
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Numerical modelling of the Cold Expansion process in mechanical stacked assemblies
2016Co-Authors: Victor Achard, Alain Daidié, Manuel Paredes, Clément ChirolAbstract:The Cold Expansion process is a technology that is widely used to enhance the fatigue resistance of aircraft metallic parts. The issue analysed in this paper concerns the case when the Expansion is carried out through an assembly composed of several sheets. The numerical work conducted was intended to understand the phenomenology of the process within a stiff assembly. In particular, it aimed to analyse the deformation of the sheets and the residual stress fields generated by the process. For this purpose, an axisymmetric finite element model of the split sleeve process was developed, simulating a single Expansion performed through a stack of two titanium holes (Ti-6Al-4V). The sheets to be expanded were positioned between two steel plates to simulate the assembly. The model could predict the shape and intensities of the fields within the expanded sections and their global outer shapes. We particularly focused on the phenomena prevailing between sheets. The simulation showed that deformations at the interface were greatly reduced when the stack was stiffened axially. Moreover, high circumferential and axial residual stresses were generated in the sheets. Results were compared with a single hole expanded without axial stiffening.
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Optimization Of The Cold Expansion Process For Titanium Holes
2015Co-Authors: Victor Achard, Alain Daidié, Manuel Paredes, Clément ChirolAbstract:Cold Expansion of metallic holes is widely used in the aerospace industry as an efficient industrial process for improving fatigue performance of mechanical assemblies. To increase the efficiency of the process, it is worth considering the possibility of carrying out the Expansion twice in succession in the same hole. This paper discusses the consequences of such an operation on a single titanium hole through a numerical and experimental study. More precisely, dedicated finite element modelling of the Cold Expansion process has been developed in order to simulate cases where the Expansion is carried out twice: in the same direction and in opposite directions. The residual fields generated are analyzed and the results compared with experimental results. Furthermore, we propose in this study to assess a new methodology for measurement of the intensity of the compressive residual stresses generated at the hole edge. Specifically, we will use the incremental hole drilling technique to characterize the expanded holes, including or not a reaming operation of the Cold worked hole. Results show that double Expansion has a very positive impact on the homogeneity of the compressive fields generated as long as the direction of Expansion is properly selected to guarantee the efficiency of the process.
Zhufeng Yue - One of the best experts on this subject based on the ideXlab platform.
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Effect of Thinckness on Residual Stress Fields of Cold Expansion Hole
Advanced Materials Research, 2010Co-Authors: Yongshou Liu, Bing Wang Gou, X.j. Shao, Zhi Feng Jiang, Zhufeng YueAbstract:In this paper, four axisymmetrical finite element models have been established to study effect of thinckness on residual stress fields of Cold Expansion hole, experiments were carried out to measure the residual stress of Cold Expansion hole and verify simulation results. The experiment results also show that Cold Expansion processing can decrease surface roughness of holes and improve surface quality. The FEM results show, at the top(bottom) surface, the volue of the radial residual stress varies with the plate’s thickness, and the regularities of distribution of the radial residual stress are identical. The volue and the regularities of distribution of the circumferential residual stress vary with the plate’s thickness. At the mid-thickness surface, the volue and the regularities of distribution of radial residual stress vary with the plate’s thickness. The volue of the circumferential residual stress varies with the plate’s thickness, and the regularities of distribution of the radial residual stress are identical.
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Effect of Cold Expansion on Crack Opening Displacement and Stress Intensity Factor
Key Engineering Materials, 2009Co-Authors: Yongshou Liu, Bing Wang Gou, Zhufeng YueAbstract:Two-dimensional (2D) finite element analyses have been carried out to study the crack opening displacement and stress intensity factor of a cracked centre-hole plate. With the different interference levels (2%, 4%, 6% and 8%) and acted by residual stress caused by Cold Expansion, the crack opening displacement, the stress intensity factor and J-integral around the crack tip is presented. With the different interference levels and acted by different applied loads , the crack opening displacement, the stress intensity and J-integral around the crack tip is also presented. The results of the 2D FEM analysis show, 1) with the different interference levels and acted by residual stress caused by Cold Expansion, the crack mouth is throughout closed and the middle part is open, but the opening displacement is constant; 2) under some applied loads, with the interference levels up, the stress intensity factor on the crack tip and J-integral, become weak gradually, then they keep constant values; 3) with the interference increases, the stress intensity factor and J-integral decreases. When the interference increases a certain value, the stress intensity factor and J-integral do not decrease and keep constant values.
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Effect of Cold Expansion on fatigue performance of open holes
Materials Science and Engineering: A, 2008Co-Authors: Jianrui Liu, Xiao Jun Shao, Yongshou Liu, Zhufeng YueAbstract:In this paper, residual stress measurements were made on aluminium alloy 2A12T4 open holes after Cold Expansion. By contrast, a finite element method (FEM) was also used to analyze the residual stress distribution around Cold Expansion hole. Then a series of uniaxial fatigue tests were carried out using specimens containing non-Cold expanded holes and Cold expanded holes to assess the effect of direct Cold Expansion process on fatigue performance of open hole. At last the fracture morphology of the specimens after fatigue test was examined by scanning electron microscopy. The results reveal that direct Cold Expansion technique could elevate about six times fatigue life. After Cold Expansion, fatigue crack of open holes always initiates on entrance face.
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Experiment and FEM Simulation on Residual Stress of Cold Expansion Hole
Materials Science Forum, 2007Co-Authors: Xiao Jun Shao, Yongshou Liu, Jun Liu, Zhufeng YueAbstract:A 2D cylindrical plate model has been established to study the distribution of residual stress of Cold Expansion hole under different interference values. In addition, the effects of material models on residual stress fields are considered also. Experiments are carried out to measure the residual stress of Cold Expansion hole and verify simulation results. FEM results show, with interference values increasing, the higher residual radial and circumferential stresses are obtained. At same interference value, the residual stress of Hardening Material( HM ) model is much larger than that of Elastic Perfectly Plastic Material( EPPM ) model.
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FEM Simulation and Experimental Test on Residual Stress of Cold Expansion Hole of Rectangular Plate
Key Engineering Materials, 2007Co-Authors: Xiao Jun Shao, Yongshou Liu, Jun Liu, Zhufeng YueAbstract:A 2D rectangular plate model has 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. The FEM results show, with interference values developing, the maximum values of circumferential residual compressive/tensile stress increase and higher positive stress values are obtained at the boundary of the rectangular plate. However, higher positive stresses at the boundary of plate are harmful to the capacity of fatigue resistance, the determinations of best interference value to a certain wide plate were proposed. Finally, the effect of the plate width on the residual stress distribution was analyzed.