Assembly stress for the reduction of stress concentration

A systematic study utilizing the experimental method of reflected photoelasticity was undertaken to determine the effects of assembly stress on the stresses around circular holes under uniaxial tension. The assembly stresses are the result of the contact and bearing stresses between the bolts and the member. It has been concluded that assembly stress contributes to reducing the stresses around the hole.     

高炉炉壳开孔位置对应力集中的影响

考虑到冶金行业中高炉炉壳开孔的实际情况，本文应用有限元分析的方法研究受远场均匀拉伸载荷，二维有限区域内菱形分布的圆孔中间不同开孔位置下的应力分布，得到最大应力集中系数随孔位置变化的三维变化曲面。此外，孔沿座标轴及沿原孔边缘位置变化对应力集中系数的影响被详细研究，从而为合理设计炉壳开孔提供了理论依据。     

含两个圆孔的正交异性板孔口补强应力分析

应用数学弹性力学和Ｆａｂｅｒ级数展开的方法，对于含有两个圆孔，且孔周各补强一弹性加强环的正交异性板，给出了其在无限远处均布的外力作用下，环及板内的应力场解；其特例与前人结果一致。     

Reinforcement of a plate with a circular hole by an eccentric circular patch

We study the reinforcement of an infinite elastic plate with a circular hole by a larger eccentric circular patch completely covering the hole and rigidly adjusted to the plate along the entire boundary of itself. We assume that the plate and the patch are in a generalized plane stress state generated by the action of some given loads applied to the plate at infinity and on the boundary of the hole. We use the power series method combined with the conformal mapping method to find the Muskhelishvili complex potentials and study the stress state on the hole boundary and on the adhesion line. We consider several examples, study how the stresses depend on the geometric and elastic parameters, and compare the problem under study with the case of a plate with a circular hole without a patch. In scientific literature, numerous methods for reinforcing plates with holes, in particular, with circular holes, have been studied. In the monographs [1, 2], the problem of reinforcing the hole edges by stiffening ribs is solved. Methods for reinforcing a circular hole by using two-dimensional patches pasted to the entire plate surface are studied in [3, 4]. The case of a plate with a circular cut reinforced by a concentric circular patch adjusted to the plate along the boundary of itself or along some other circle was studied in [5, 6]. The reinforcement of an elliptic hole by a confocal elliptic patch was considered in [7].     

Photoelastic analysis of stresses around oblique holes

A three-dimensional photoelastic analysis was conducted to determine the magnitude and distribution of stresses around oblique holes in a uniaxially loaded plate. The holes were circular and inclined at angles of 45 deg and 60 deg with the faces of the plate. The plate-thickness-to-hole-diameter ratiot/D was 2.40. One end of each hole was blended to the face of the plate through a break radius equal to the radius of the hole. The plate dimensions were sufficiently large to simulate conditions of an infinite plate. The plates were loaded perpendicular to the plane of skewness. Stress distributions were obtained on sections perpendicular to the direction of loading. Results point to two critical areas of stress concentration: one at the acute-angle intersection of the hole and the surface of the plate and the other in the break-radius area. The stress concentrations in the latter area reach values of 4.6 and 6.7 compared to 3.6 and 4.5 at the acute-angle intersection, for the inclination angles of 45 deg and 60 deg, respectively. A simplified analysis used for the break-radius area gave results in agreement with the experiment. Thus, it was shown that break radii in oblique penetrations may have deleterious rather than beneficial effects. Comparison of results for the acute-angle intersection with existing theoretical and experimental values shows a definite and pronounced dependence of the stress-concentration factor on thickness-to-diameter ratio.     

集中力作用下含尖孔无限域的反平面剪切问题

论文采用了一种新的方法求解含孔元发域的反平面剪切问题，以闭合形式导出了在集中力作用下，孔口尖点的应力强度因子表达式。同时，给出了对称翼状尖孔、内摆线状尖孔、震状尖孔及圆孔径向边裂纹的应力强度因子，其结果在理论上和应用中都具有重要的意义。     

Experimental and numerical study of residual stresses caused by cold expansion of adjacent holes

Cold expansion is a useful process for imposing compressive residual stresses around the holes in riveted and bolted connections. These stresses increase the fatigue life of holed parts. Distribution and amount of exerted residual stress dependent on various parameters as material, distance of adjacent holes, hole diameter, cold expansion ratio and plate thickness. In this study, experimental and numerical results for two different aluminum alloys and various holes distances are investigated and compared. Effects of mentioned parameters on the residual stress are studied.     

Stress Concentration Factor in Functionally Graded Plates with Circular Holes Subjected to Anti-plane Shear Loading

Stress concentration factors due to the presence of geometrical discontinuities (circular holes) in functionally graded plates are derived. The material property inhomogeneity is assumed to be in the radial direction originating at the center of the plate. Variable separable closed-form solutions are obtained for the stresses and displacements in functionally graded plates (without and with holes) subjected to anti-plane shear loading. The stresses in functionally graded plates without a hole are not homogeneous as it is in the case of homogeneous plates. Either a stress concentration (more than the applied stress) or dilution (less than the applied stress) occurs depending on whether the modulus increases (hardening graded material) or decreases (softening graded material) away from the center of the graded plate without a hole. A novel definition of the stress concentration factor due to the geometrical discontinuity in functionally graded plates is derived. The effect of the circular hole in functionally graded plates is to magnify (compared to homogeneous plates) the stress concentration when the modulus decreases away from the center of the hole (softening material). Beneficial reduction of the stress concentration factor is achieved in hardening functionally graded materials.     

The symmetry and loading-independency of multiple inclusions enclosing uniform stresses in an infinite elastic plane

The identification of multiple interacting inclusions with uniform internal stresses in an infinite elastic matrix subjected to a uniform remote loading is of fundamental importance in the mechanics and design of particulate composite materials. In anti-plane shear and plane deformations, certain sufficient conditions have been established in the literature which guarantee uniform internal stresses inside multiple interacting inclusions displaying various symmetries when the matrix is subjected to specific uniform remote loading. Correspondingly, sufficient conditions which allow for the design of multiple interacting inclusions independent of any specific form of (uniform) remote loading have also been established. In this paper, we demonstrate rigorously that, in all cases, these sufficient conditions are also necessary conditions and indeed allow for the identification of all possible collections of such inclusions.     

Determination of residual stresses by an optical correlative hole-drilling method

In conjunction with the incremental hole-drilling method, a new evaluation procedure is presented for determining the residual stress state in components. In contrast to the classical method, the whole displacement field around the drilled hole is measured using the electronic speckle pattern interferometry technique. The displacement patterns, measured without contact to the surface, are then correlated with those obtained by finite-element simulations using statistical methods. The simulated displacement patterns, used for calibration purposes, result from the application of properly defined basic loads. In this way, the values and the orientation of the residual stresses can be determined by superposition of these properly scaled and shifted basic loads. Even complex states of stress can be evaluated. The theoretical background and experimental results are presented.     

Numerical-experimental Method for the Analysis of Residual Stresses in Cold-expanded Holes

Hole cold expansion is a technique widely used to improve the fatigue life of components with holes, e.g. bolted or riveted joints. As it has been demonstrated in literature by analytical, numerical and experimental analyses carried out by several authors, the compressive residual stresses introduced by the hole cold expansion have a beneficial influence on both the static and the fatigue strength of the treated component, because they reduce significantly the typical stress peaks around the hole due to stress concentration. In the literature, various analyses of the residual stresses introduced by the hole cold expansion have been performed by using several methods such as X-ray diffraction, neutron diffraction and the modified Sachs method. Unfortunately, all these method are affected by some limitations: low measurement depth (X-ray method), complex measurement procedure (neutron diffraction method) and approximate formulation (Sachs method). In order to overcome such drawbacks, in this study a new mechanical method, based on an innovative extension of the “rectilinear groove method” associated with the classical “integral method” calculation procedure, is proposed. Experimental assessment of the proposed method has been performed by using aluminum 5083 H321 specimens with holes subjected to various levels of cold expansion.     

具有中心圆孔的[0°/90°]_s复合材料层合板的边界元法分析

本文在文[1]的基础上,采用子结构法建立了多层复合板的边界元方法,对具有中心园孔[0°/90°]_s的层合板的层间应力作了计算,同有限元法的结果进行了比较,结果表明,应用边界元法处理这类问题,单元划分少,节约了计算机时,而且有较高的计算精度。     

Stress Distribution in an Orthotropic Plate with Circular Holes under Impulsive Loading

The photoelastic method is used to analyze the stress–strain state induced by an impulsive load in an orthotropic plate with circular holes. The distribution of dynamic stress concentration factors along the periphery of the holes is studied, and stresses and strains in representative sections are determined     

应用干涉云纹测量工艺应力分布

本文就冷胀孔周残余应力分布的测量技术和干涉螺接孔周干涉应力分布的测量技术进行了实验研究。沿着径向将试件切割,以释放欲测的应力,同时用干涉云纹技术测量由于释放应力而引起的附加应变场。文中还就残余应力在循环载荷作用下的松弛问题进行了实验研究。提供了典型的实验结果,讨论了引起实验误差的主要原因。     

Hole-drilling strain-gage method of measuring residual stresses

The hole-drilling strain-gage method of measuring residual stresses in elastic materials can be termed semidestructive if holes of very small diameters are used. The method permits the magnitudes and principal directions of residual stresses at the hole location to be determined. This is accomplished by means of an emirpically determined relation between the magnitudes and directions of the principal stresses and the strain relaxation about the hole as the hole is drilled. This relation was obtained for a nondimensional model of the hole-gage assembly in order to make the results independent of hole size. A generalization was postulated to extend the use of this calibrated solution to the measurement of residual stresses in all elastic, isotropic materials.I. Vigness was HeadPaper was presented at 1966 SESA Spring Meeting held in Detroit, Mich. on May 4–6.     

The evolution of caustics from holes to cracks

The method of caustics was used for the study of the evolution of stress concentration around a circular hole, which progressively changes in shape and becomes an elliptic hole, tending to an internal crack. The influence of the amount of ellipticity of the holes and their orientation relative to the axis of the applied external loads at infinity on the form of caustics created around the discontinuity was studied, as the elliptic holes tended to become internal cracks. A series of experiments with tension specimens containing small elliptic holes of any ellipticity and orientation was performed. Comparison of experimentally obtained caustics with theory yielded a good agreement of both results. Finally, the use of small elliptic holes drilled all over a biaxial stress field for the determination of the individual principal stresses and the principal directions at the area of the holes was outlined.     

含圆孔缺陷三点弯曲梁动态焦散实验

应用新型数字激光动态焦散线实验系统,采用含预制裂纹的有机玻璃板试件进行落锤冲击实验,研究了含圆孔缺陷三点弯曲梁的动态断裂行为。通过实验得到了含圆孔缺陷三点弯曲梁裂纹尖端动态应力强度因子的变化情况、裂纹扩展速度的变化情况以及裂纹贯穿空孔的扩展情况等。实验结果表明:三点弯曲梁中的空孔位置对裂纹的扩展轨迹具有明显的导向作用;空孔位置的改变会影响三点弯曲梁的断裂时间;空孔位置的变化对空孔下方裂纹的扩展时间、扩展轨迹影响较小;在空孔位置居中的情况下,空孔上方裂纹的最大扩展速度大于空孔位置偏移时的情况。     

3D numerical simulation of drilling residual stresses

Drilling can affect the integrity of the surface of a mechanical component and reduce its fatigue life. Thus, drilling parameters such as lubrication or drilling velocity must be optimized to ensure a satisfactory residual mechanical state of the hole surfaces. Unfortunately, experimental tests are time consuming and it is not easy to observe the cutting process because of the confinement of the drill zone. The literature does not exhibit any numerical simulation capable of simulating 3D thermomechanical phenomena in the drill zone for large depth holes. Therefore, residual stresses cannot be easily simulated by means of the sole drilling parameters. The aim of this article is to propose a new numerical approach to compute drilling residual stresses for large-depth holes. A first simulation is developed to simulate heat transfer by means of a 3D thermoviscoplastic simulation in a new Rigid-ALE framework allowing the use of large calculation time steps. Then, a time interpolation and a spatial projection are implemented to rebuild the Lagrangian thermal history of the machined component. Finally, a thermo-elastoplastic simulation is carried out to compute residual stresses in the final workpiece. In this paper, the method is applied to a 316L austenitic stainless steel in the case of an unlubricated hole. The computed residual stresses are compared to experimental measurements.     

Residual Stresses Induced by Cold Expansion of Adjacent and Cut-Out Holes

Fatigue life of fastener holes can be enhanced via a cold-expansion process to introduce a compressive residual stress field around the hole edge and to reduce crack growth propagation. Considering that aerospace components contain multiple rows of holes, the present investigation focuses on the evaluation of the three-dimensional residual stress distribution in adjacent cold-expanded (CE) holes. The redistribution of residual stresses caused by a cut introduced between two adjacent holes was also investigated. Finite element (FE) analysis and experimental technique were used to assess the residual stress distribution in a 6082-T6 aluminum plate with two adjacent holes expanded sequentially at 4 % nominal interference. The influence of center-to-center distance between holes was explored to assess the optimal level of separation between adjacent holes. Results suggested that residual stresses near second CE hole are markedly lower than those of first CE hole and that a cutting process does not affect the beneficial compressive residual stress around CE holes. These effects may delay fatigue crack propagation from CE holes or cut-out holes.     

Transient thermal stresses in a strip with an eccentric hole

A procedure is presented for dealing with the constraint associated with the direction of the thickness of a thin model and for obtaining transient thermal stresses under plane-stress conditions; the stresses are induced by severe thermal loads. Thermal-stress-concentration factor in an unrestrained strip with an eccentric circular hole placed near the thermally loaded edge is obtained. One straight edge of the strip is cooled and the others are insulated. Consequently, two cases for which the hole acts remarkably as a stress raiser are found.