An FE analysis for assessing the effect of short-term exposure to elevated temperature on residual stresses around cold expanded fastener holes in aluminum alloy 7075-T6

A previous experimental study revealed fatigue life reduction in Al 7075-T6 cold expanded fastener holes exposed to 120 °C for 1 h. The obtained experimental evidence indicated a residual stress reduction associated with material softening at elevated temperatures, termed as thermo-mechanical stress relaxation. In order to identify and characterize the potential features of this phenomenon, FE analysis is carried out in this study and a detailed body of evidence is provided for occurrence of a time-independent thermo-mechanical residual stress relaxation around cold expanded fastener holes due to exposure to elevated temperature. The results of FE simulation demonstrate a good agreement with experimental results obtained earlier.     

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.     

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.     

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 experimental investigation on the effect of short time exposure to elevated temperature on fatigue life of cold expanded fastener holes

An experimental study has been carried out to investigate the effect of short time exposure to elevated temperature on fatigue life of cold expanded fastener holes. When cold expanded holes are subjected to temperature variations their fatigue life changes remarkably. However the exact governing mechanism has not been clearly addressed before. In this study, another stress relaxation mechanism rather than creep has been introduced which happens at a short time due to temperature rise. Results of fatigue tests on Al 7075-T6 show that the effect of this mechanism can be beneficial or detrimental. This research has sought to clarify this issue.     

Investigation of carburising treatment of injector flange in diesel engine

The applicability of carburising treatment of injector flange in a diesel engine was investigated. Initially, a carburized case structure made of low-carbon (0.23%) steel was approximately modelled by five sub-regions. Then, finite element stress analyses were performed using Abaqus CAE^® software to determine performances of several models, which the thickness of five sub-regions were changed. Examining performances of case thicknesses with respect to load bearing capacity, minimum case thickness value was approximately determined to be 1 mm. After determining this superior case thickness configuration, for real service loading and boundary conditions, FE analyses were repeated to determine the cyclic stress components for a fatigue analysis. Based on the FE results, carburising treatment was applied and superior strength was determined for a case, in which the maximum hardness is 570 ± 20 Hv on surface and 290 ± 25 Hv at depth 1.05 mm from the surface with the condition that heat treatments before and after cold forming were properly applied. Experiments and FE analyses give almost similar results. The result showed that carburising treatment of injector flange provides 8% increase in static load bearing capability with 1 mm case thickness. Additionally, it is realized that the case hardened flange had a reasonable fatigue safety factor. In the real service test with 200 carburized flanges on 50 diesel engines, no failure was observed during 3000 engine operation hours (approximately 2 years).     

Thermal relaxation of residual stresses in shot peened surface layer of (TiB + TiC)/Ti-6Al-4V composite at elevated temperatures

As an effective and important surface treatment method, shot peening can introduce high residual compressive stress and microstructure variation at near surface deformation layers. In this work, residual stresses relaxation behaviors of the shot peened layer of (TiB + TiC)/Ti-6Al-4V composite were investigated during thermal exposure, and the microstrain was calculated according to the integral breadth after isothermal annealing. The microstrain decreased fast and reached the minimum at 500 °C, which resulted from the thermal recovery and dynamic recrystallization. At elevated temperatures, the residual compressive stresses were relaxed in the whole deformation layers, which were caused by the thermally activated gliding of dislocations. The processes of relaxation can be described using a Zener-Wert-Avrami function and the activation energy of the residual stresses relaxation was higher than that of titanium self diffusion, which was ascribed to the hindrance effects of reinforcements as sink sources of dislocations during annealing.     

Fatigue life predictions using fracture mechanics methods

In the present work, a simple engineering approach which is based on a relatively solid background and which is checked against fatigue test data for various test conditions was developed: it may provide a practical and reliable basis for the analysis of structures under in-service loading conditions, in the presence of previous corrosion attack, or in the presence of a residual stress field, by using widespread fracture mechanics software. In particular, the approach was checked against an experimental program which consists of the following fatigue tests: base and friction stir welded (FSW) material under constant amplitude loading at different loading ratios (R = 0.1, 0.5, −1); pre-corroded base and FSW material under constant amplitude loading at load ratio R = 0.1; centre hole FSW specimens under the standardised variable amplitude loading spectrum FALSTAFF. Moreover, from the literature fatigue experiments under FALSTAFF of cold expanded as well as not cold expended holes were also used to validate the approach. The predictions were performed with the last version of AFGROW and NASGRO 3.0 software.     

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.     

Relaxation of residual stress in shot peened Udimet 720Li under high temperature isothermal fatigue

The extent of residual stress relaxation in turbine disc material Udimet 720Li was measured using laboratory X-rays with the sin²ψ technique, for fatigue samples as a function of temperature and number of fatigue cycles for strain controlled loading to 1.2%. Results showed that extensive relaxation occurs upon the initial fatigue cycle. The maximum compressive residual stress (RS) parallel to the loading direction is found to decrease by 50% for all testing temperatures. The extent of relaxation upon further cycling increased with temperature. In the plastically deformed near surface region, the diffraction peak width decreased with increasing testing temperature and number of fatigue cycles (and exposure time), indicating that the relaxation of cold work is controlled by both thermal and mechanical processes.     

Characterization of residual stresses from cold expansion using spatial statistics

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

冷胀孔裂纹寿命增长效果估算模型

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

Investigation into effects of re-shot-peening on fretting fatigue behavior of Ti–6Al–4V

The effects of re-shot-peening treatment on fretting fatigue life/strength and the recovery of residual stress of the initially shot-peened Ti–6Al–4V were investigated at room and elevated temperatures. After subjecting to fretting fatigue up to about 40% of the total expected life of the initially shot-peened Ti–6Al–4V or to thermal exposure to 370 °C only, residual stress relaxed in the range of 20–50% of its value before fretting fatigue. The magnitude of stress relaxation depended upon the applied load level and test temperature. Re-shot-peening successfully recovered the relaxed residual stress up to the same level as obtained after the initial shot-peening. Further, fretting fatigue life after re-shot-peening, excluding pre-re-shot-peening fatigue life, was very close to that of the initially shot-peened specimen at a given stress level and test temperature. It thus appears that re-shot-peening nullified the effect of fretting fatigue damage after the initial shot-peening.     

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.     

Simulation of fatigue crack growth in components with random defects

The paper presents a probabilistic method for the simulation of fatigue crack growth from crack-like defects in the combined operating and residual stress fields of an arbitrary component. The component geometry and stress distribution are taken from a standard finite element stress analysis. Number, size and location of crack-like defects are ‘drawn’ from probability distributions. The presented fatigue assessment methodology has been implemented in a newly developed finite-element post-processor, P • FAT, and is useful for the reliability assessment of fatigue critical components. General features of the finite element post-processor have been presented. Important features, such as (i) the determination of the life-controlling defect, (ii) growth of short and long cracks, (iii) fatigue strength and fatigue life distribution and (iv) probability of component fatigue failure, have been treated and discussed. Short and long crack growth measurements have been presented and used for verification of the crack growth model presented.     

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.     

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.     

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.     

Fatigue of brittle materials—A critical appraisal

Recent demands for high performance ceramics and glass for various applications from bioceramics to cutting tools under fluctuating stress conditions has focussed attention of the scientific community towards fatigue behaviour of brittle solids. Attention to fatigue phenomena in alumina ceramics phenomenological to metals, having an endurance dependent on applied stress with a limit at around 50% of the single cycle fracture stress, was first drawn by the author in late sixties. Slip assisted fatigue process was not considered to be dominant in ceramic materials due to the absence of appreciable crack tip plasticity. With the background of this general survey of fatigue behaviour some fatigue studies based on mode of testing, theoretical and experimental analyses and fractographic evidence have been presented. Studies have shown that there is a dormant period between each successive crack advancement during which the residual stress and a plastic component is built up in a cumulative manner leading to eventual failure. During fatigue (plastic) and (residual stress) components are predominant for ductile metals and brittle glass/ceramics respectively. It is also apparent that dislocation assisted plastic component as a contributing factor in the failure of brittle materials under fatigue cannot be ruled out.     

Effect of laser shock processing on fatigue crack growth of duplex stainless steel

Duplex stainless steels have wide application in different fields like the ship, petrochemical and chemical industries that is due to their high strength and excellent toughness properties as well as their high corrosion resistance. In this work an investigation is performed to evaluate the effect of laser shock processing on some mechanical properties of 2205 duplex stainless steel. Laser shock processing (LSP) or laser shock peening is a new technique for strengthening metals. This process induces a compressive residual stress field which increases fatigue crack initiation life and reduces fatigue crack growth rate. A convergent lens is used to deliver 2.5 J, 8 ns laser pulses by a Q-switched Nd:YAG laser, operating at 10 Hz with infrared (1064 nm) radiation. The pulses are focused to a diameter of 1.5 mm. Effect of pulse density in the residual stress field is evaluated. Residual stress distribution as a function of depth is determined by the contour method. It is observed that the higher the pulse density the greater the compressive residual stress. Pulse densities of 900, 1600 and 2500 pul/cm² are used. Pre-cracked compact tension specimens were subjected to LSP process and then tested under cyclic loading with R = 0.1. Fatigue crack growth rate is determined and the effect of LSP process parameters is evaluated. In addition fracture toughness is determined in specimens with and without LSP treatment. It is observed that LSP reduces fatigue crack growth and increases fracture toughness if this steel.