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.     

Cracks emanating from a circular hole under biaxial load

The principle of linear superposition has been employed in studying cracks emanating from a circular hole in a finite sheet under biaxial loading. The series type analytical solution around the crack tip has been combined with numerical analysis for the purpose of this investigation. The method presented here makes it possible to demonstrate both analytically and numerically, the effects of applied load biaxiality on the stress intensity factor. The ratio of the hole-radius-to-crack-length (R/c) is shown to determine the effect of the applied load biaxiality on the crack emanating from a circular hole in a finite sheet.     

An integral equation approach for simultaneous solution of rectangular hole and rectangular block problems

The elastostatic rectangular hole problem has been solved in the past. However, the corners of the hole have been rounded-off and the stresses at these corners have been found to be finite. It is known that the stresses at the corners of a rectangular hole are infinite. This paper considers the sharp-cornered rectangular hole problem and obtains solution such that the stresses have the correct singularity at the corners. Geometry of the rectangular hole is obtained by means of four perpendicular cracks. When these cracks intersect, the region outside the cracks corresponds to the infinite plane with a rectangular hole whereas the region surrounded by the cracks corresponds to a free rectangular block. Formulation of the problem reduces to four singular integral equations. Numerical solution of these equations yields results for the hole and the block problems. Stress intensity factors at the corners of the hole and stress distributions are presented in graphical form.     

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.     

Stresses in a thick plate with a circular hole under axisymmetric loading

An exact theoretical solution is given for the stresses and displacements in an infinite plate of finite thickness having a circular hole and subjected to axisymmetric normal leading. The solution is given in the form of Fourier-Bessel series and integral. Numerical results are given for stresses in plates having different thickness to hole diameter ratios and loadings. The results are compared with the available approximate theoretical and experimental results.     

Numerical analysis of plastic deformation of a circular sheet metal subjected to transverse impact loading

Based on the concept of Tensor Code a numerical method is presented for analysis of the plastic deformation process of circular sheet metals subjected to transverse impact loading. In the solution process, the equation of motion is solved explicitly with finite difference method in a series of small time steps over a Lagrangian mesh of zones. Using this method, a code has been developed and utilized for investigation of the deformation behavior of an explosively loaded circular sheet metal under various conditions. Deformation characteristics of a sheet under rectangular and triangular pressure distributions are discussed. It is shown that when these simple distributions are combined with each other, their individual effects on the deformation behavior are also combined in the deformation process. Effects of shape and duration of pressure pulse as well as boundary conditions have been explored. Moreover, results of the numerical simulation have been compared with those of theoretical solution and experiments reported by other researchers. Good agreements between them show the validity of the developed code.     

A combination of the finite element and singular-integral equation methods for the solution of the generally cracked body

A method which combines the finite element technique and the singular-integral equation method is presented. The association of the two methods is obtained with the help of Schwarz's alternating method (SAM). The method was applied with satisfactory results to the solution of a series of problems of a circular arc crack lying inside a finite thin plate for various lengths of the circular arc and for various dimensions of the rectangular cracked sheet.     

A new method for measurement of three dimensional residual stresses in a multi-pass butt welded joint

In this paper, a new method for the measurement of three dimensional residual stresses in a multi-pass butt welded joint is presented. The method involves the measurement of strain changes at a through hole surface as a coupon of material with the hole is separated from the body of interest and split. The finite element calculations are used to relate the strain changes at the measurenent points to the initial residual stresses at the hole location. The accuracy of the method is demonstrated by using it to measure a known stress field in a bent beam. The method has been used to measure the through thickness distribution of three dimensional residual stresses in a multi-pass butt welded joint. It could also be applied to the measurement of residual stresses in other welded joints.     

Elastic-Plastic Analysis Under Proportional and Non-Proportional Loading Paths Using Deformation Plasticity Theory

Abstract

An estimation of elastic-plastic stresses and strains is presented for mechanical components, using pseudo elastic analysis based on the deformation theory of plasticity. Analysis of two applications, one under proportional loading and other under non-proportional loading paths using pseudo elastic finite element method, is presented. A rectangular plate with a hole under tension loading and a rectangular plate fixed at one end under bending-tension non-proportional loading are considered for analysis. Pseudo Elastic finite element analysis for proportional loading uses elastic solutions and varies material properties for elements in plastic zone to estimate elastic-plastic solution. A finite element code is developed based on pseudo elastic analysis method. An attempt is made to extend pseudo elastic analysis to analyze bending-tension non-proportional loading problem. Both applications in consideration are assumed to be of Von Mises material and follow isotropic hardening rule with elastic-linear hardening material model. Non-linear analysis of the plate with a hole under proportional tensile loading and that of rectangular plate under bending-tension non-proportional loading are performed in ANSYS and results are compared for validation and are observed to be in good agreement with present analysis.     

Residual stresses of thin,short rectangular plates

The analysis of the residual stresses in thin, short rectangular plates is presented. The analysis is used in conjunction with a shadow Moiré interferometry technique by which residual stresses are obtained over a large spatial area from a strain measurement. The technique and analysis are applied to a residual stress measurement of polycrystalline silicon sheet grown by the edge-defined film growth technique.     

矩形钢管K型节点复合型应力强度因子计算方法研究

相比圆形钢管桁架,矩形钢管桁架在施工方面具有一定的技术经济优势,并已广泛应用于桥梁工程中,鉴于断裂力学法评估该类结构疲劳性能的需要,该文探讨矩形钢管K型节点在支管拉压平衡荷载作用下的应力强度因子计算方法。提出带表面裂纹矩形钢管K型节点有限元建模方法,并与试验进行验证;通过参数分析,研究节点和裂纹几何参数对节点几何修正系数Y的影响;多元回归分析拟合得到矩形钢管K型节点应力强度因子计算公式及其修正后的设计计算公式,并通过算例分析给出基于断裂力学的钢管节点剩余疲劳寿命评估方法。结果表明：有限元结果与试验结果比值均值为1.012,变异系数为0.034,两者最大差值仅为5.5%,表明有限元计算结果可靠;节点几何参数2γ、τ与Y呈正相关,θ与Y呈负相关,其原因主要在于节点相贯线处刚度和受拉荷载变化,改变了裂纹尖端应力场,从而影响了裂纹扩展速率,裂纹几何参数c/a与Y呈正相关,但影响不明显,a/t₀与Y呈负相关;提出的应力强度因子计算公式与有限元计算结果吻合良好,且修正后用于设计的计算公式具有95%的可靠度;圆形钢管节点应力强度因子高于矩形钢管节点,平均提高24.9%,说明在相...     

Fatigue growth of multiple-cracks near a row of fastener-holes in a fuselage lap-joint

The fatigue growth of multiple cracks, of arbitrary lengths, emanating from a row of fastener holes in a bonded, riveted, lap joint in a pressurized aircraft fuselage is studied. The effects of residual stresses due to a rivet misfit, and of plastic deformation near the hole, are included. A Schwartz-Neumann alternating method which uses the analytical solution for a row of multiple colinear cracks in an infinite sheet (the crack-faces being subject to arbitrary tractions), is developed to analyze this MSD problem on a personal computer. It is found that for a range of crack lengths, a phenomena wherein the shorter cracks may grow faster than longer cracks may exist.     

Experimental determination of residual stresses in composite laminates [02/θ2]s

The present work aims to determine the residual stresses in carbon fiber/epoxy composite laminates, by means of the incremental hole-drilling method. Based on mechanical theories of composite laminates and an elastic plate with a circular hole, the relationship between the relaxed strains on the surface of laminates and the residual stresses in laminates was established. This newly deduced theoretical formula was adapted into the incremental hole-drilling method and allowed us to further study the residual stresses in the through-thickness direction for various composite laminates. Related numerical modeling of composite laminate with a hole was built to calibrate the coefficients within the formula. Experiments were conducted and the residual stresses in composite laminates [0₂/θ₂]_s are presented. The proposed approach was validated with the consistence between our results for cross-ply laminates and those in literature.     

Solution of the problem of a crack in a finite plane region using an indirect boundary-integral method

In a previous paper [1], an indirect boundary-integral approach was developed for the treatment of a finite, plane, linear-elastic region weakened by a hole of arbitary shape. It was suggested there that this method would yield excellent results on and near the hole boundary.

In this presentation, the method is applied to the problem of a finite, plane, linear-elastic region containing a sharp crack. Numerical results are obtained for a simple geometry and the crack-opening-displacement and crack tip stresses are compared to the known solution. It is shown that the boundary-integral solution is quite accurate.     

T-stress Solutions for Cracks Emanating from a Circular Hole in a Finite Plate

The boundary element method is employed to obtain T-stress solutions for cracks emanating from a circular hole in finite rectangular plates. Numerical values of the T-stress are obtained using the M-contour integral approach. A range of crack lengths are analyzed for two hole sizes, and the cases of a single crack and double-cracks emanating from the hole in the plate under both uniform remote tension and simple bending are considered. For completeness, stress intensity factor solutions are also presented. These results will be useful for failure assessments using two-parameter linear elastic fracture mechanics.     

On the elasto-plastic stress concentration at a circular hole in an anisotropic sheet

Summary The classical problem of determining the stress concentration factor at a circular hole embedded in an infinite sheet subjected to remote uniform tension is investigated. A finite strain elasto-plastic deformation theory based on Hill's new anisotropic flow theory [7] is used. It is shown that the governing field equations can be reduced to a single first order differential equation from which the stress concentration factor is obtained by a standard numerical method. The solution covers the entire elasto-plastic range and is valid for any strain hardening function. Comparison with experimental results, for a few materials, shows good agreement.With a pure power hardening law and within the framework of small strain plasticity, our results agree with those obtained from a more general solution discovered by Budiansky [8].With 3 Figures     

Linear and elastic–plastic fracture mechanics revisited by use of Fourier transforms – theory and application

This paper investigates whether and how discrete Fourier transforms (DFT) can be used to compute the local stress/strain distribution around holes in externally loaded two-dimensional representative volume elements (RVEs). To this end, the properties of DFT are first reviewed and then applied to the solution of linear elastic and time-dependent elastic plastic material response. The equivalent inclusion method is used to derive a functional equation which allows for the numerical computation of stresses and strains within an RVE with heterogeneities of arbitrary shape and stiffness. This functional equation is then specialized to the case of circular and elliptical holes of different minor axes which eventually degenerate into Griffith cracks. The numerically predicted stresses and strains are compared to the corresponding analytical solutions for a single circular as well as an elliptical hole in an infinitely large plate under tension as well as to finite element calculations (for time-independent elastic/plastic material response).     

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.     

Influence of Bauschinger effect on springback and residual stresses in plane strain pure bending

A finite deformation elastic plastic analysis of plane strain pure bending of a wide sheet is presented. The general closed-form solution is proposed for a kinematic hardening law assuming that the material is incompressible. The stage of unloading is included in the analysis to investigate the influence of the Bauschinger effect, elastic properties of the material and process parameters on the distribution of residual stresses and springback. A simple example is provided to illustrate the procedure for finding the solution and some quantitative features of the process.     

Effect of stacking sequence and thickness on the interlaminar stresses for quasi-isotropic laminated plates with a hole

This paper discusses the evaluation of interlaminar stresses, in the presence of in-plane stress gradients, for composite laminates by using three-dimensional equilibrium equations. The stress gradients are calculated by means of an improved finite difference scheme. A quasi-isotropic laminated plate with a circular hole subjected to a uniform tension stress is considered. The effects of stacking sequence and the thickness of the laminate on the interlaminar stresses have been studied.