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.     

Identifying the residual stress field developed by hole cold expansion using finite element analysis

The split sleeve cold expansion process is a cost effective method of enhancing the fatigue performance of aircraft fastener holes. However, the 3‐D nature of the induced residual stress fields is not fully understood. For this research, 2‐D and 3‐D models with uniform hole expansion and 3‐D models with expansion produced by contact with a rigid mandrel were developed. The models’ relative capabilities of capturing the residual stress fields were then evaluated. The residual stress profiles varied significantly through the thickness of the workpiece and were also strongly influenced by the direction of mandrel motion. Therefore the uniform expansion models were inadequate. The 3‐D contact models indicate that the mandrel entry face is the critical fatigue location, reporting the lowest circumferential compressive stresses adjacent to the hole. The effect of varying the frictional coefficient and plastic hardening laws were also investigated using the 3‐D contact models.     

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.     

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.     

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.     

Numerical predictions and experimental measurements of residual stresses in fatigue crack growth specimens

Controlling macro residual stress fields in a material while preserving a desired microstructure is often a challenging proposition. Processing techniques which induce or reduce residual stresses often also alter microstructural characteristics of the material through thermo-mechanical processes. A novel mechanical technique able to generate controlled residual stresses was developed. The method is based on a pin compression approach, and was used to produce well-controlled magnitudes and distributions of residual stresses in rectangular coupons and compact tension specimens typically used in fatigue crack growth testing. Residual stresses created through this method were first computationally modeled with finite element analysis, and then experimentally reproduced with various levels of pin compression. The magnitudes and distributions of residual stresses in experimental specimens were independently assessed with fracture mechanics methods and good correspondence was found between residual stresses produced using the pin compression and processing techniques. Fatigue crack growth data generated from specimens with low residual stresses, high residual stresses resulting from processing, and high residual stresses introduced through the new pin compression technique were compared and validated. The developed method is proposed to facilitate the acquisition and analysis of fatigue crack growth data generated in residual stresses, validate residual stress corrective models, and verify fatigue crack growth simulations and life predictions in the presence of residual stresses.     

A Strip Yield Analysis of Fatigue Crack Growth in the Residual Stress Field

An advanced procedure has been developed to analyse the fatigue crack growth in the residual stress field. The method is based on an extension of the strip yield crack closure model for part-through crack problems. In this method, the residual stress relaxation due to both the fatigue loading and the crack growth is considered. It has been shown that the effect of the residual stress can be reasonably analysed according to fracture mechanics methods so long as the residual stress field and its redistribution can be correctly evaluated and the elastic-plastic crack closure analyses are performed. Several examples are provided for the constant and variable amplitude loading conditions. This revised version was published online in July 2006 with corrections to the Cover Date.     

Characterizing the effect of residual stresses on high cycle fatigue (HCF) with induction heating treated stainless steel specimens

A new method for introducing a predetermined amount of residual stresses in stainless steel thick-walled hollow fatigue test specimens was developed by the authors [1] using high frequency induction heating. The advantage of the proposed method over more traditional approaches is to avoid any change in other important fatigue parameters, i.e. surface roughness, geometry, and microstructure, while introducing the residual stresses. The last point only holds if the material under study does not undergo any phase transformation within the range of temperatures and time exposures reached during the heat treatment. In this paper, the effect of residual stresses on high cycle fatigue (HCF) life of annealed AISI 304L stainless steel is investigated by introducing a residual stress field in thick-walled hollow fatigue specimens and by comparing the fatigue life obtained with the reference S–N curve. For the particular case studied, a surprising observation is made. Introducing tensile residual stresses beneath the surface of hollow fatigue specimens using the method proposed by Paquet et al. [1] leads to improved HCF lives. Validity of this result is confirmed by a statistical analysis. Residual stresses were analyzed by the X-ray diffraction (XRD) technique to rationalize this experimental result. The increase in fatigue life is explained by residual stresses evolution within the specimen cross section during the fatigue test, leading to a build up of compressive residual stresses beneath its surface. This is a clear demonstration that assimilating residual stresses resulting from fabrication processes to superimposed static mean stresses can lead to considerable errors in fatigue life predictions.     

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.     

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.     

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.     

Fatigue crack growth in residual stress fields

A fatigue crack growth (FCG) model for specimens with well-characterized residual stress fields has been studied using experimental analysis and finite element (FE) modeling. The residual stress field was obtained using four point bending tests performed on 7050-T7451 aluminum alloy rectangular specimens and consecutively modeled using the FE method. The experimentally obtained residual stress fields were characterized using a digital image correlation technique and a slitting method, and a good agreement between the experimental residual stress fields and the stress field in the FE model was obtained. The FE FCG models were developed using a linear elastic model, a linear elastic model with crack closure and an elastic–plastic model with crack closure. The crack growth in the FE FCG model was predicted using Paris–Erdogan data obtained from the residual stress free samples, using the Harter T-method for interpolating between different baseline crack growth curves, and using the effective stress intensity factor range and stress ratio. The elastic–plastic model with crack closure effects provides results close to the experimental data for the FCG with positive applied stress ratios reproducing the FCG deceleration in the compressive zone of the residual stress field. However, in the case of a negative stress ratio all models with crack closure effects strongly underestimate the FCG rates, in which case a linear elastic model provides the best fit with the experimental data. The results demonstrate that the negative part of the stress cycle with a fully closed crack contributes to the driving force for the FCG and thus should be accounted for in the fatigue life estimates.     

Experimental evaluation of the effect of residual stress field on crack growth behaviour in C(T) specimen

The effects of the residual stress field resulting from shot peening and the indentation technique were investigated in relation to fatigue crack closure and crack growth behaviour. Compact Specimens of 20NiCrMo2 were used in this investigation. The regions of residual stress field were located behind the fatigue crack tip. Crack closure behaviour was measured with back face strain and crack mouth opening displacement gauges. Crack length was monitored by the compliance and microscopic methods. Residual stress was measured by the incremental hole-drilling method. Subsequently the closure level, propagation rate and resulting crack growth retardation were studied. Crack closure and attendant growth retardation were shown to be dependent on the residual stress field. Residual stresses produced by shot peening and indentation were both compressive. The maximum value of residual stress for both operations were on the surface and at the same intensity. However, the residual stress induced by the indentation technique was deeper. The results showed that the closure effect was stronger in the case of indentation technique.     

腐蚀环境下飞机结构疲劳寿命的分析方法

依据海军现役飞机的腐蚀环境特点及结构件腐蚀损伤深度拟合规律，采用应力场强法和局部应力应变法分别对疲劳缺口系数Kf及疲劳寿命计算模型进行了分析，提出了一种腐蚀环境下飞机结构疲劳寿命的评定方法。该方法以室温大气环境下的寿命评定结论为依据，考虑了结构件腐蚀损伤后潮湿空气、盐雾、盐雾＋SO2等环境介质对疲劳寿命的影响，并结合国产某型飞机机翼前梁缘条腐蚀损伤部位的疲劳寿命及剩余寿命估算实例进行了分析。     

Effects of residual stresses on the fatigue behaviour of welded steel structures

Residual stresses due to the welding process in steel structures can significantly affect the fatigue behaviour. Usually, high tensile residual stresses up to the yield strength are conservatively assumed at the weld toes. This conservative assumption can result in misleading fatigue assessments. Areas with compressive residual stresses may be present in complex structures, where the details are less critical than predicted. This is shown in the paper by the example of fillet‐welded stiffener ends, where beneficial compressive residual stresses cause the initiation of fatigue cracks at other locations in less‐strained areas. Another example for the effects of residual stresses concerns the stress initiation and propagation at a structural detail under fully compressive load cycles. Fatigue cracks are possible here due to high tensile residual stress fields. The conclusion is that the welding‐induced residual stresses should be known in advance for a reliable fatigue assessment, which becomes possible to an increasing extent by numerical welding simulation.     

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.     

The fatigue of aircraft structures

Current procedures for fatigue design and for fatigue life estimation, substantiation and monitoring of aircraft structures are reviewed. Major gaps in the present state of knowledge are identified and further research directed towards filling these gaps is discussed.Brief reference is made to the major fields of basic or fundamental research connected with the fatigue of structures including, the application of fracture mechanics to the theory of crack propagation, elevated temperature behaviour of aircraft materials, atmospheric turbulence, reliability based design and aeroelastic behaviour.It is seen that with the present advances in aircraft design and utilisation the fatigue assessment of aircraft structures is an increasingly complex problem for which no general method of solution has yet been established. At present reliance is placed on extensive testing of design details and components, usually in conjunction with a full scale fatigue test, to validate the fatigue analysis and substantiate, or provide the essential data used for fatigue life monitoring. There is however a well developed trend for basic studies of the various aspects of fatigue behaviour, to find increasing application in the interpretation of experimental results for fatigue life assessment and improved methods of fatigue design.     

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.     

A STUDY OF RESIDUAL CAUSTICS GENERATED FROM FATIGUE CRACKS

Abstract— The method of caustics was used to determine the stress intensity factor of fatigue cracks in steel compact tension specimens. Under zero load a residual caustic was observed at the tip of a fatigue crack indicating the presence of a residual stress field. Caustics were generated at increasing static loads and the stress intensity factors were compared with those predicted by theory. It was found that the difference between each measured stress intensity factor and its corresponding theoretical value was a constant for the range of loads. This difference was shown statistically to be equal to the stress intensity factor determined from the residual caustic. The proposed mechanism for the formation of this residual caustic was probably due to crack tip plasticity effects and not due to crack closure. It was concluded that residual caustics can be measured to quantify crack tip behaviour in fatigue cracks and have been shown to be a useful tool in the measurement of residual stress fields.     

The effect of residual stresses arising from laser shock peening on fatigue crack growth

Residual stresses have in the past been introduced to manipulate growth rates and shapes of cracks under cyclic loads. Previously, the effectiveness of shot peening in retarding the rate of fatigue crack growth was experimentally studied. It was shown that the compressive residual stresses arising from the shot peening process can affect the rate of crack growth. Laser shock peening can produce a deeper compressive stress field near the surface than shot peening. This advantage makes this technique desirable for the manipulation of crack growth rates. This paper describes an experimental program that was carried out to establish this effect in which steel specimens were partially laser peened and subsequently subjected to cyclic loading to grow fatigue cracks. The residual stress fields generated by the laser shock peening process were measured using the neutron diffraction technique. A state of compressive stress was found near the surface and tensile stresses were measured in the mid-thickness of the specimens. Growth rates of the cracks were observed to be more affected by the tensile core than by the compressive surface stresses.