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.     

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.     

Initial cyclic deformation of material in the zone of a hole with contact interaction based on data of the holographic interferometry method

This article presents dependences of maximum local deformations at the periphery of a hole in a strip on nominal stresses at the initial stage of cyclic sign-variable aasymmetric tensile- compressive loading over a short-time fatigue range. An open hole, and holes stopped by means of washers with initial clearance and interference, which model the working of an element of a joint, are analyzed. This data was obtained for the first time by measuring the components of surface displacements using the method of holographic interferometry. A series of factors that facilitate the enhancement of operating life of elements of joints with radial interference are established and their quantitative characteristics determined.Translated from Problemy Prochnosti, No. 7, pp. 90–95, July, 1993.     

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.     

FATIGUE OF THICK-SECTION COLD-EXPANDED HOLES WITH AND WITHOUT CRACKS

Abstract— Fatigue tests under spectrum loading were conducted to evaluate hole cold-expansion in thick-section open-hole aluminium alloy specimens, some of which contained residual fatigue cracks before cold expansion. Cold expansion resulted in an increase in life by a factor of about 7. Small residual fatigue cracks did not inhibit the effectiveness of the cold-expansion process, indicating that it may not be essential to remove such cracks prior to hole cold-expansion. The increase in life is primarily associated with a reduced crack propagation rate compared with that for cracks from non-cold-expanded holes. Cold-expanded hole fractures displayed a marked disparity in crack depths adjacent to the two faces of the specimens. Considerable differences were evident in crack depths and fatigue crack areas at failure between cold-expanded and non-cold-expanded hole specimens. These findings have ramifications in the damage tolerance assessment of aircraft structures.     

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.     

Correlation of residual stresses and fatigue limit with torsion under conditions of stress concentration Report 1. Substantiation of strength and longevity criteria

Results are given for a calculation and experimental study of the effect of residual stresses on fatigue limit with torsion for specimens with circular notches of semicircular and rectangular shape made of steels 40, 30KhGSA, EI961, and aluminum alloy V95. The possibility is demonstrated of a criterion for mean integral residual stresses through the thickness of a surface layer equal in depth to a nonpropagating fatigue crack in order to estimate the influence of residual compressive stresses on fatigue limit in the case of torsion with stress concentration.Translated from Probleray Prochnosti, No. 5, pp. 43–46, May, 1991.     

Stability of residual stresses in surface layers of pump rods during use

Summary A combined method of surface strengthening has been devised for pump shafts, which involves producing compressive residual stresses in the surface by means of shot-blast working with the subsequent deposition of metallization and polymer coatings.When a pump rod has operated for three years in a borehole, the compressive residual stresses provided by the combined treatment are substantially redistributed and change sign. In such cases, there is a reduction in the resistance to corrosive fatigue failure. To improve the working life of pump shafts working in boreholes, repeat hardening is required periodically.Translated from Fiziko-Khimicheskaya Mekhanika Marerialov, Vol. 26, No. 3, pp. 120–122, May–June, 1990.     

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.     

Investigation of the fatigue life of pre- and post-drilling hole in dog-bone specimen subjected to laser shot peening

The influence of processing sequence of laser shot peening (LSP) on the fatigue properties of fastener hole was investigated with finite element method and experiments. The results show that different processing sequences lead to different residual stress distributions and different fatigue lives. The compressive residual stresses (CRS) are squeezed into two-sided surface layers of fastener hole by two sided laser shot peening, and the ellipse CRS fields are found on both sided surfaces of sample. However, when the pre-drilling hole in dog-bone specimen is subjected to LSP, the tensile stresses appear at its mid-thickness region, while the CRS distribute in the entire thickness region of the post-drilling hole after LSP. The fatigue crack initiation of specimens treated by LSP stems from the subsurface layer of hole edge. The fatigue striation spacing of specimen with post-drilling hole after LSP is narrower in comparison with that of case with pre-drilling hole before LSP. The fatigue life of post-drilling hole is longer than that of the pre-drilling hole.     

Raising the fatigue strength of a construction by local laser heating

A method is proposed for raising the fatigue strength of a construction by inducing residual stresses by local heating with a high-power pulsed laser. Fatigue failure can be slowed or eliminated, as can the formation of fatigue defects, if a pattern of compressive residual stresses is produced in the most readily damaged zones. Experiments have been done on how laser heating affects the fatigue strengths of planar specimens and fatigue crack growth. Finite-element calculations have been used to examine the effects of the heating parameters on the residual stresses.Translated from Problemy Prochnosti, No. 4, pp. 10–17, April, 1995.     

芯棒锥面结构对孔冷挤压强化残余应力场的影响

为了在紧固孔周引入均匀的残余压应力,以延长紧固孔构件的疲劳寿命、提高其抗应力腐蚀性能,利用ANSYS有限元软件,建立了轴对称弹塑性有限元模型,对直接芯棒冷挤压强化过程进行了仿真,特别是对芯棒的前锥段曲线结构形式进行了设计与分析,研究了前锥段曲线形式对残余应力场分布的影响.结果表明:孔壁表面的周向残余应力分布复杂且不均匀,比较而言,外凸型正弦曲线型芯棒所产生的残余压应力沿孔壁深度方向分布更加均匀;几种曲线形式的芯棒在上表面近孔边区域均产生了径向残余拉应力,在孔的挤入段产生了轴向残余拉应力,但外凸型正弦曲线型芯棒在上述区域所产生的残余拉应力较小,且分布区域也较小.     

Cold expansion of holes and resulting fatigue life enhancement and residual stresses in Al 2024 T3 alloy – An experimental study

This paper presents the experimental results of fatigue life enhancement and the residual stresses around the cold expanded holes in Al 2024, a widely used aerospace alloy. Two techniques for cold expansion of holes, namely split-sleeve with taper pin technique and split-sleeve with ball technique were considered for comparison, as the former involves surface contact and the latter has line contact during expansion. The techniques were compared based on the fatigue life enhancement in the expanded holes, the induced and the residual stresses due to expansion. The holes were expanded by 2%, 3%, 4%, 5%, and 6% using INSTRON machine in both the techniques. While both the techniques resulted in improvement in fatigue life of the expanded holes, the taper pin technique yielded 200% higher fatigue life improvement than that obtained by ball technique. The induced residual stresses were measured by mounting strain gages of 0.2 mm gage length. These are drawn as a function of induced strain. In both the techniques residual stresses increased with increase in percentage of expansion until 5% and then decreased for 6% expansion. The increase in fatigue life at 5% expansion was 1.88 times and 5.3 times higher than that of the non-expanded holes for ball and tapered method, respectively. The corresponding improvement in taper method was greater than the non-expanded holes. While, it was observed that the residual stresses decreased with respect to the distance from the hole in both the techniques, the ball technique resulted in lower residual stresses than that of taper pin technique.     

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.     

Machining residual stresses

As part of an extended investigation into the effects of pre-and post-processing on shot peening residual stresses, residual stresses due to a controlled turning process were investigated in the aircraft alloy 817M40. Cylindrical specimens were produced on a centre lathe with all machine parameters fixed except for feedrate. A variation in the feedrate was used to produce different surface roughnesses varying from 1·2 to 6·6 μm R_a. The residual stress field resulting from the varying feedrate was established by the well known centre hole drilling method, albeit with a modification which assisted in determining the variation of residual stresses with depth. The results indicated a definite variation in axial residual stress distribution with surface roughness, with a rough surface showing higher tensile residual stresses. This variation was however not duplicated for hoop or circumferential stresses. Maximum tensile residual stress varied from 90 MN m^?2 in the 6·6 μm R_a surface to 50 MN m^?2 in the 1·2 μm R_a surface. Although residual stresses are generally ignored in design, either because of a lack of experimental results or for ease of application, the results indicate that some consideration must be given to machining residual stresses as these can enhance or reduce the fatigue life of engineering components. The study also indicates that turning operations associated with large plastic deformations are encountered during the machining process.

MST/3230     

Analysis of the Residual Stress around a Cold-expanded Fastener Hole in a Finite Plate

Abstract:  In this paper, we present results of residual stresses around a cold-worked fastener hole in a thin, finite plate. An analytical model, with plane stress conditions, elastic nonlinear–plastic loading and unloading taken into account, is explicitly presented and has been developed from existing analytical models and methodologies. The solution also accounts for elastic deformation of the mandrel, and is applicable to different sizes of hole and mandrel. A parametric study of the strain-hardening exponent, plate size, Bauschinger parameter and expansion ratio was carried out in the context of the present solution. A sample study of a plate subjected to 4% hole-cold expansion was performed to compare this model with other analytical predictions, finite element simulation and X-ray diffraction experimental results. A brief review of related issues is given. This work is intended to present completely the closed-form equations able to generate residual stress profiles with ease around a cold-expanded hole in a thin, finite plate where boundary conditions are at issue.     

Influence of hydrovibration treatment of thin walled shells on the stressed and strained condition

The results of an experimental investigation of the hydrovibration method for reducing residual stresses are given. A mathematical model of the influence of the maximum and minimum cycle pressure in hydrovibration treatment on reduction of the component of tensile and compressive residual stresses is constructed. It was established that hydrovibration treatment makes it possible to reduce the original residual tensile stresses by 86%. This method makes it possible to significantly increase the fatigue strength and service life of welded parts such as thin-walled shells and tubes as the result of creation in them of the most favorable stressed condition, which is characterized by a quite high component of compressive and a low component of tensile residual stresses.Translated from Problemy Prochnosti, No. 6, pp. 98–101, June, 1990.     

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.     

Influence of cross sectional dimensions of surface strengthened specimens of D16T alloy on fatigue resistance under stress concentration conditions

The influence of cross sectional dimensions of solid and hollow strengthened cylindrical specimens of D16T alloy with stress raisers of semicircular profile on fatigue limit in loading by pure bending with rotation and transverse bending in a single plane is considered. For evaluation of the influence of strengthening on the fatigue limit of specimens with stress raisers a criterion of residual stresses taking into consideration the character of their distribution across the thickness of the surface layer and the scale factor is proposed. It is established that with a change in the diameter of the shot peened specimen from 10 to 40 mm the ratio of the increase in fatigue limit as the result of strengthening to the criterion of residual stresses changes within narrow limits and is an average of 0.36.Translated from Problemy Prochnosti, No. 4, pp. 75–79, April, 1990.     

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.