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.     

The stress distribution around holes in thermal barrier coatings

The residual stress distribution in the thermally grown oxide (TGO) around holes in thermal barrier coatings has been measured using luminescence piezospectroscopy. Far removed from the holes the residual stress field in the oxide is equi-biaxial and independent of position but in the vicinity of the holes, the mean stress decreases monotonically towards the edge of the hole. The characteristic distance over which the stresses vary is of the order of the half the hole radius, typically 10–100 times the thickness of the TGO, consistent with a shear-lag model for stress redistribution. The measurements also indicate that the stress distribution in the TGO is unaffected by the presence of an as-deposited thermal barrier coating.     

Edge distance effects on residual stress distribution around a cold expanded hole in Al 2024 alloy

Cold expansion process is a well-known technique for improving the fatigue life of aerospace structures by introducing a compressive residual stress around the fastener holes. However, there are concerns about the residual stress distribution around those holes which are located near the free edges of structure. The purpose of this study is to investigate the influence of edge distance ratio (e/D) on the residual stress distribution around a cold expanded hole in Al 2024 alloy. A two-dimensional finite element simulation was carried out with various degrees of cold expansion and various values of e/D. It was found that for edge distance ratios less than e/D = 3, there are considerable effects on the residual stress profile. Also, the dependency of residual stress distribution on the degree of expansion was reduced significantly for small e/Ds. The results revealed that the bulging of the plate free edge increases with reduction of e/D but in worse cases the maximum bulging at the plate free edge was lower than 3% of the hole radius. The weight function method was then used for determining stress intensity factors for a crack emanating from a cold expanded hole.     

Stress distribution around holes in wedges

This paper deals with the study of stress distribution around holes in wedges. Ling and Hsu have reported a theoretical analysis for an infinite wedge of uniform thickness and variable depth (with a circular hole), using stress functions. In the present investigation, a large number of electrical resistance strain gauges of small gauge length (3 mm) were used for obtaining the distribution of stresses in a cantilevered wedge of uniform thickness and variable depth, with a circular hole subjected to end loading. The wedge was made of perspex. The results obtained indicate a maximum stress concentration factor of 1.7 using Timoshenko's method of calculating the nominal stress in the wedge at the hole boundary (using his theory of calculating stresses in a wedge without a hole). The experiments on the cantilevered wedge indicate a lower stress-concentration factor compared with the results obtained theoretically by Ling and Hsu for an infinite wedge. In addition to vertical loading, stress distribution with a load inclined to the vertical was also obtained.     

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.     

Residual stress magnitudes and related properties in quenched aluminium alloys

Abstract

The surface and through thickness residual stress magnitudes present in heat treated high strength aluminium alloy components are frequently reported to exceed the uniaxial yield stress of small specimens of the same alloy measured immediately after quenching. In thick section plate and forgings, it is proposed that these high residual stress magnitudes are a consequence of hardening precipitation that occurs during quenching which allows a greater elastic stress to be supported. To investigate this theory, a Jominy end quench technique is used to determine the hardness of aluminium alloys 7010, 7175 and 5083 as a function of distance from the quenched end. Cooling curves have been measured for Jominy end quench specimens using deeply buried thermocouples and are compared with finite element model predictions. Tensile properties are also determined for small specimens quenched into cold and boiling water. Vickers hardness and X-ray diffraction residual stress measurements are undertaken on specimens of varying size acting as a comparison with the Jominy results. These results in combination with optical and electron microscopy data do suggest that low temperature rather than high temperature precipitation during the quench leads to increased as quenched mechanical strengths, with the consequence that less quench sensitive alloys will support higher residual stress magnitudes as section thicknesses increase.     

A boundary element method for determining the effect of holes on the stress distribution around a crack

A boundary integral procedure is obtained for examining the effect of a finite number of holes on the crack tip stress intensity factors for a plane crack in a homogeneous anisotropic elastic material. Numerical results for specific examples involving a transversely isotropic material are given.     

Plane thermal stresses around holes under steady distribution of temperature

Summary A method for determining the plane thermal stress distribution in a multiply connected region under steady distribution of temperature is presented. The analysis is based on the complex variable approach and permits, if the thermal field is known, the simple determination of theKolosoff functions. The method is illustrated using two examples.

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Zusammenfassung Es wird eine Methode zur Bestimmung des ebenen Wärmespannungszustandes in einem mehrfach zusammenhängenden Bereich unter stationärer Temperaturverteilung angegeben. Die Analyse benützt die komplexe Darstellung und erlaubt die einfache Bestimmung derKolosoff-Funktionen, wenn das Temperaturfeld bekannt ist. Die Methode wird anhand von zwei Beispielen illustriert.

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Notation c constant which take valuesc=E/(1–) for plane strain and - c E for plane stress - Re{} real part of - u, v components of displacement vector - T temperature - z complex variable (x+i y) - coefficient of thermal expansion - complex variable in a mapped plane - boundary value ofz or - Kolosoffs constant which takes values =3–4 for plane strain and =(3–)/(1+) for plane stress - shear modulus of elasticity - Poissons ratio - _xx,_yy,_xy components of stress tensor - () mapping function     

Fatigue damage accumulation of cold expanded hole in aluminum alloys subjected to block loading

Fatigue damage accumulation of cold expanded hole in aluminum alloys used in land transportation components was investigated. Tests were carried out using pre-cracked SENT specimens and inserting an expanded hole at the crack tip. The degree of the cold expansion was chosen equal to 4.3%. Tests were performed in two and four block loading under constant amplitude. Two sequences were compared.The increasing and the decreasing magnitude were compared. The experimental results were compared to the damage calculated by the Miner's rule and a new simple fatigue damage indicator. This comparison shows that the ‘model of the damage stress’, which take into account of the loading history, yields a good estimation of the experimental results. Moreover, the error is minimized in comparison to the Miner's model.     

Normal stress distribution adjacent to optimum holes in composite plates

An approximate solution in the form of a polynomial is presented for the normal stress distribution adjacent to a class of optimum holes in symmetrically laminated infinite composite plates under uniaxial loading. Comparison of the present approximate solution with that of the finite element method shows good agreement. The approximate solution is useful in assessing the strength of the laminated composite plates with holes. The present simple solution will be of immense use to design engineers who are interested in obtaining quick and reliable solutions for circular and optimized holes in symmetrically laminated composite plates.     

Modelling flow stress behaviour of aluminium alloys during hot rolling

Abstract

A mathematical model is proposed to predict the flow stress behaviour of aluminium alloys under hot rolling conditions. To do so, a dislocation model for evaluating flow stress during deformation is coupled with a finite element analysis to access metal behaviour under non-isothermal and variable strain rate conditions. Then, with the aid of the proposed model, a hot strip rolling process was simulated. In order to verify modelling results, flow stress behaviour of an aluminium alloy is studied employing hot compression tests in various temperatures and strain rates and the model was examined on this material. Non-isothermal hot rolling experiments were carried out and good agreement was found between predictions and experiments.     

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.     

Design procedure for reducing the stress concentration around circular holes in laminated composites

The stress concentration around a hole in a laminated composite may be decreased by increasing the thickness (bonding of two-dimensional panels) in this area. The problem may be described as an infinite orthotropic membrane with a finite circular orthotropic inclusion (ring) and a circular hole in the middle of the ring under arbitrary in-plane loading. A method for calculation of the stress concentration at the edge of the hole is presented. The method is based on the analytical solution for the case of an infinite inclusion. The finite dimensions of the inclusion are taken into account by means of a correction coefficient which is established empirically by processing a large amount of finite element results.     

螺栓连接层合板孔边挤压应力三维分布

孔边应力是复合材料连接设计中强度校核的重要依据,装配间隙对其有明显的影响。针对准各向同性铺层层合板单搭接连接结构,首先采用弹性基剪切梁模型推导了螺杆挠度的解析解,给出挤压载荷沿着层合板厚度方向的分布。在此基础上,将能计及装配间隙的二维情况下孔边挤压应力分布的Persson模型推广到三维情况,得到了孔边挤压应力分布及应力集中系数。理论结果通过三维细节有限元方法进行了验证。最后采用理论方法分析了装配间隙、层合板厚度及钉载对应力集中系数的影响。     

Fatigue behaviour of fastener holes in high‐strength aluminium plates repaired by cold spray deposition

This work examines the fatigue behaviour of additive cold spray (CS) repairs of AA7075 and AA2024 fastener holes. Structural ring repairs around fastener holes were made by machining blend‐outs ranging from 1/8 to 1/2 the thickness of the plate, then refilling the section of removed material with CS deposition. The repairs were then tested in a lap shear geometry with the repair on both the free (outside) and the mating (inside) surfaces, as well as in remote uniaxial tension. CS repairs for the inside lap shear AA7075 repair configuration and the outside lap shear AA2024 repair configuration were found to have significantly increased fatigue lives even exceeding the number of cycles to failure of the undamaged, unrepaired control plates. Further, none of the CS repairs caused any detrimental impact on fatigue life, and microhardness results indicate that no thermal damage to the substrate occurred. Some interface cracking was seen in the CS repairs; however, no separation of the repair from the substrate was observed.     

The mechanics and mechanisms of fracture in stress corrosion cracking of aluminium alloys

A fracture mechanics approach to stress corrosion cracking is highlighted. The mechanisms of stress corrosion cracking is presented. Experiments on 2024 and 7075 aluminium alloys are carried out to determine their mechanical properties, microstructure and plane strain fracture toughness (K_IC). Stress corrosion cracking tests, namely, cantilever beam tests as well as wedge opening loading tests using sea water as a corrosive medium, are conducted to establish the critical stress intensity factor for stress corrosion cracking (K_ISCC) for each aluminium alloy. It is found that the K_ISCC is in the range of (1/5) to (1/6) of the plane strain fracture toughness, K_IC, depending on the alloy. The scanning electron microscopy of fracture surfaces reveals a great dependence of the cracking and/or pit severity on the applied stress intensity factor. A brief discussion on the dislocation's role in stress corrosion cracking is given.     

Change of the ultrasonic characteristics with stress in some steels and aluminium alloys

Under application of tensile stress to specimens of several steels and aluminium alloys up to a stress close to their yielding stress, a continuous ultrasonic wave of approximately 5 MHz was propagated through the specimens in directions parallel and perpendicular to the tensile axis. The change of ultrasonic resonance frequency with applied stress was measured. The results of the measurement of the ultrasonic resonance frequency showed that the frequency ratio varied with the magnitude of applied stress, the material of the specimen, and ultrasonic wave propagating direction with respect to the direction of the stress. They also showed that the ultrasonic wave resonance frequency measuring method is useful in finding the ultrasonic characteristics of materials under applied stress.List of symbols density - , Lame's constants - l, m Murnaghan's constants - stress - wavelength - n order number of resonance frequency - f _n resonance frequency ofnth order - elastic strain - v Poisson's ratio - C ultrasonic velocity - L length of specimen