An Exact Solution on the Stress Analysis of Fillet Welds

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The exact solution of stress distribution in fillet welds

I.Intr0ducti0nInanearlierpaper['],theexactsolutionofstressdistributioninweldsundertheactionofconcentratedforcePwasobtained.Thedesignmethoduptonowaretheutilizationofaveragestressactingontherelatingthroatsectionofweldsandthestressdistribution0btainedbythisa…     

Study of residual stresses in linearly varying biaxial-stress fields

A theory has been developed for the calculation of relaxation strains effected by drilling a hole in a plate with a linearly varying stress field. With this theory, a technique was developed for the measurement of residual stress at the toe of tee-fillet welds. The above technique was employed for the measurement of residual stresses at the toe of tee-fillet welds in 11/2-in. HY-80 steel with the fillet in the as-welded, ground, shot peened, ground and shot peened, and mechanically peened condition. It was found that experimental data conform to the assumed theory, and that residual stresses in aswelded tee-fillet welds in both the transverse and longitudinal directions approach the yield strength of the steel. It was also found that residual stresses are reduced approximately 25 percent by grinding, 50 percent by shot peening and 50 percent by grinding and shot peening. Mechanical peening drastically affected residual stresses by converting high tension at the toe of the fillet weld to high compression of approximately the same magnitude.     

Structural failures precipitated by weld discontinuities

A literature review was conducted to assess the effects of weld defects upon the failure of welded structures. This effort was focussed on storage tank failures with emphasis on those fabricated for cryogenic liquid containment in order to assess the significance of past storage tank failures relative to the 9% nickel steel storage tanks currently in service. Consideration of past failures can be instructive for insuring the integrity of these vessels.Along with other documented failures, three cryogenic storage tank failures are documented herein. One of these was a liquefied natural gas (LNG) tank, the other two were designed to store liquid ethylene. Although details of design differed slightly, the overall design was the ‘tank within a tank’ concept. In each of the three failures detailed in this review, a breach of the outer tank integrity resulted when cryogenic liquid came in contact with the outer tank wall. This can be attributed to the fact that the outer steel wall was brittle at service temperatures.In addition to the above failures, this review has revealed a pattern of failures in pressure vessels resulting from faulty welds (usually fillet welds) associated with nozzle attachments and branch connections. These are undoubtedly areas of concern in cryogenic storage tanks along with the ones delineated more fully in this review.     

Optimization of geometry of elastic bodies in the vicinity of singular points on the example of an adhesive lap joint

The stress state in adhesive lap joints with various geometric shapes of spew fillet is studied. It is noted that the applied design models of the considered problem include singular points at which infinite stress values are possible if one uses the linear elasticity theory to calculate the stress state. Based on the conclusions of the solution of the geometry optimization problem in the vicinity of the singular points of elastic bodies, variants of the geometry of spew fillet, which provide the most significant decrease in the concentration of stresses in adhesive lap joints, are proposed.     

A general failure criterion for spot welds under combined loading conditions

The circumferential failure mode of spot welds is investigated under combined loading conditions. Failure mechanisms of spot welds under different loading conditions are first examined by the experimental observations and a plane stress finite element analysis. An approximate limit load analysis for spot welds is then conducted to understand the failure loads of spot welds under combinations of resultant forces and resultant moments with consideration of the global equilibrium conditions only. The approximate limit load solution for circumferential failure is expressed in terms of sheet thickness, nugget diameter and combinations of loads. Failure contours are generated for spot welds under opening and shear loading conditions. The results indicate that failure contours become smaller when the ratio of the sheet thickness to the nugget diameter increases. Based on the approximate limit load solution, a general quadratic failure criterion for spot welds under combined three resultant forces and three resultant moments is proposed with correction factors determined by fitting to the experimental results of spot welds under combined loading conditions. The failure criterion can be used to characterize the failure loads of spot welds with consideration of the effects of sheet thickness, nugget diameter and combinations of loads. Experimental spot weld failure loads under combined opening and shear loading conditions and those under combined shear and twisting loading conditions are shown to be characterized well by the proposed failure criterion. Finally, a simplified general failure criterion for spot welds under three resultant forces and three resultant moments is proposed by neglecting the coupling terms of the resultant forces and moments for convenient use of the failure criterion for engineering applications.     

反应堆贯穿件J形焊缝残余应力研究1）

焊接残余应力是引起应力腐蚀开裂的主要原因,准确地掌握残余应力的分布是对结构完整性评定的关键.为了探明反应堆压力容器顶盖控制棒驱动机构（control rod drive mechanism,CRDM）贯穿件J形焊缝残余应力的分布,本研究加工两个CRDM贯穿件实验模拟件,采用盲孔法测试两个J形接头的焊接残余应力.通过实验探明了CRDM贯穿件焊缝残余应力的分布规律,为反应堆压力容器结构完整性的研究提供必要参考.     

Fatigue of fillet welded joints

The Albrecht method was used to compute stress intensity factors in non-load carrying fillet welds subjected to tension and cantilever bending for cracks growing from the tip of the weld toe through the plate thickness. The stresses were obtained using a two dimensional finite element programme with eight node isoparametric elements with two degrees of freedom in each node. A detailed study of the influence of weld and plate geometry on both the stress concentration and stress intensity factor values was carried out.The results in bending showed stress intensity values 20 to 30% lower than in tension. The weld affected the stress intensity and stress concentration results only for small crack length values less than 0.1 to 0.12 of the thickness of the main plate. The results also indicated that neither the lack of penetration nor the plate length affected the stress intensity values significantly. Weld angle and plate thickness were the main parameters influencing the stress intensity values. The results in tension were compared with similar results published in the literature and good agreement was found.     

Stresses in turbine-blade tenons subjected to bending

The photoelastic method was used to model large steam turbine tenon-shroud attachments under bending loads. Six models were used to investigate three basic tenon geometries: (a) single round tenon—here two different fillet radius-to-tenon diameter ratios were examined; (b) long narrow tenon—for this geometry the influence of shroud-seating clearance and shroud stiffness was investigated; (c) two separated round tenons. Stress-concentration factors for the tenon fillets were determined based on the nominal bending stress in the tenon using the moment of inertia of the tenon cross section. For the single round tenon, stress-concentration factors of 1.3 and 1.6 were found for fillet radius-to-tenon diameter ratios of 0.41 and 0.19. These compared very well with those values obtained by treating the geometry as a stepped round bar with a shoulder fillet subjected to bending. The long-narrow-tenon geometry showed a higher stress-concentration factor than the two separated round tenons—6.1 compared to 2.9. Increasing the shroud stiffness reduced the stress-concentration factor for the long-narrow-tenon design.     

Fatigue strength of welded joints based on local, semi-local and nominal approaches

Analysis based on the so-called “local approach” is made to estimate the fatigue strength of welded joints. Numerical analyses or strain gauges are employed for finding the stress and/or strain state in the vicinity of the weld toe. The notch stress intensity factor (NSIF) approach applied to fillet welded joints, as far as the opening angle between the weld and the main plate surface is constant (e.g. 135°, typical for many fillet welds), is able to rationalise the fatigue strength data both for different joint geometries and absolute dimensions. The NSIF approach has been previously developed as an extension of the Linear Elastic Fracture Mechanics (LEFM) to open V-notches and is based on the exponential local stress field around the V-notch tip. Several different “local approaches”, although simpler and more practical than the NSIF, are based on the stress (or strain) values determined beyond the exponential local one. To distinguish such approaches from the NSIF based one, we define the former as semi-local or nominal approaches while the latter is a local approach. The paper underlines that the local approaches, differently from the other ones, are able to unify in a single scatter band the fatigue strength data obtained from welded joints having different geometry and absolute dimensions.     

Loading-carrying welds joints analysis using boundary element method

The behavior of loading-carrying welds joints has been studied extensively using boundary element method. The symmetric boundary element method for multiple cracks problem is derived using Betti’s reciprocal theorem. The analysis can be performed effectively in single domain. High order element is proposed to solve the double integrals. The stress intensity factors are calculated for weld root and weld toe and the critical value for class F2 and W are obtained. Formulation for the critical value is obtained for the engineering design. The results are compared with those obtained by dual boundary element method and derived from the code of practice. Finally, the theoretical fatigue life of such joints is estimated.     

Moiré techniques for measuring strains during welding

The present work measures dynamic strains near welds using a projected-grating moiré technique. Experimental procedures are described for producing the orthogonal submaster gratings and etched heat-resistant specimen gratings necessary for this work. A modification of the gridanalyzer method allows all strain information to be obtained from a single photograph. A mathematical procedure combines fringe patterns from small adjacent sections of a surface into a larger continuous pattern. Computerized regression techniques enable more rapid and accurate analysis of the data. Results from welds in an Al?Mg alloy show the feasibility of dynamic welding-strain analysis using this approach. Welding deformation is found to be almost entirely shear straining, which explains the nature and orientation of high-temperature cracks sometimes found near welds.     

纵向焊接铝合金梁承载力研究

大多数结构用铝合金通常要经过热处理或加工硬化以得到更高的力学性能.这种合金焊接后,焊接热会使焊缝附近局部区域(称为热影响区HAZ)强度降低.这一特点使得焊接铝合金梁构件极限承载力的研究与焊接钢梁构件相比变得更为复杂.由于我国目前还没有关于铝合金结构的设计规范,为此本文对两种典型的纵向焊接工字型截面铝合金梁构件进行了试验研究,并在参考国外规范的基础上,提出了适用于静力设计的纵向焊接铝合金梁设计公式的建议.通过对试验构件进行数值分析,验证了有限元分析焊接梁的可靠性.在此基础上进行了大量的数值分析,并将试验结果及有限元计算结果与公式计算结果进行了比较,可以看出建议公式计算结果富有较大安全度,从而验证了其适用性,为我国《铝合金结构设计规范》的编制提供了依据和参考.     

Geometric functions of stress intensity factor solutions for spot welds in lap-shear specimens

In this paper, the stress intensity factor solutions for spot welds in lap-shear specimens are investigated by finite element analyses. Three-dimensional finite element models are developed for lap-shear specimens to obtain accurate stress intensity factor solutions. In contrast to the existing investigations of the stress intensity factor solutions based on the finite element analyses, various ratios of the sheet thickness, the half specimen width, the overlap length, and the specimen length to the nugget radius are considered in this investigation. The computational results confirm the functional dependence on the nugget radius and sheet thickness of the stress intensity factor solutions of [Zhang, S., 1997. Stress intensities at spot welds. International Journal of Fracture 88, 167–185; Zhang, S., 1999. Approximate stress intensity factors and notch stresses for common spot-welded specimens. Welding Journal 78, 173s–179s]. The computational results provide some geometric functions in terms of the normalized specimen width, the normalized overlap length, and the normalized specimen length to the stress intensity factor solutions of [Zhang, S., 1997. Stress intensities at spot welds. International Journal of Fracture 88, 167–185; Zhang, S., 1999. Approximate stress intensity factors and notch stresses for common spot-welded specimens. Welding Journal 78, 173s–179s] for lap-shear specimens. The computational results also indicate that when the spacing between spot welds decreases, the mode I stress intensity factor solution at the critical locations increases and the mode mixture of the stress intensity factors changes consequently. Finally, based on the analytical and computational results, the dimensions of lap-shear specimens and the corresponding approximate stress intensity factor solutions are suggested.     

节流孔截面形状对静压干气密封稳态性能和压力波动特性影响

建立了不同形状节流孔出口截面静压干气密封的几何模型,采用湍流大涡模拟方法数值求解了小孔节流静压干气密封的瞬态流场和压力场,对比了节流孔出口开设圆角、倒角与经典小孔节流静压干气密封的开启力、泄漏率等稳态性能参数和节流孔出口附近的压力波动特性,以较大密封开启力和较小压力波动为目标,获得了节流孔出口倒角和圆角的优选值范围. 结果表明:相较于经典小孔节流静压干气密封,节流孔出口开设倒角或圆角能提高静压干气密封的开启力,显著降低节流孔出口压力波动,且当倒角为0.3~0.4 mm,圆角为0.1~0.3 mm时具有最佳效果.      

Three-dimensional photoelastic study of stresses in rack gears

A three-dimensional photoelastic analysis using the stress-freezing and slicing techniques was employed in studying the stress distribution and concentration across the thickness of a thick rack-gear tooth. Full-size photoelastic models of about 25-mm thickness, having various teeth parameters were machined from PLM-4B plates. A special mounting fixture was designed to hold the models in the loading frame and a knife-edged line load was used in loading the models. In the analysis, the method of oblique incidence was adopted for the separation of the principal stresses. The intension was to determine the magnitude and location of the maximum stress at the tensile fillet and to establish the stress-concentration factors for various geometric tooth configurations.From this study, it was concluded that the fillet stresses depend largely upon the pressure angle, fillet radius and the position of the load. Maximum values of the tensile fillet stresses occur at the middle plane of the tooth thickness. Furthermore, the value of the stress-concentration factor increases with the increase of the tooth thickness. In general, this investigation gave values of stresses much higher than those values calculated by the simple-flexure theory.     

On the uncertainty quantification of the unsteady aerodynamics of 2D free falling plates

The aim of this paper is to conduct a statistical analysis of the effects of the fillet radii on the dynamics of the falling plate using the nonintrusive spectral projection (NISP) method. The free fall of two-dimensional cards immersed in a fluid was studied using a deterministic and stochastic numerical approach. The motion is characterized by the fluid-body interaction described by coupling the Navier–Stokes and rigid body dynamic equations. The model’s predictions have been validated using both experimental and numerical data available in the literature. In the stochastic simulations, the fillet radius of the plate was considered a random variable characterized by a uniform probability density function introducing, in this way, some uncertainties in the plate’s trajectory. To take into account the uncertainties, we employed the NISP method based on polynomial chaos expansion. The analysis was focused on finding the ensemble mean trajectory and error bar for a confidence interval of 95 % for both tumbling and fluttering regimes.     

Photoelastic and holographic analysis of a turbine-engine component

Isopachics obtained by holographic methods are combined with the isochromatics and isoclinics of a conventional photoelastic analysis to obtain a complete two-dimensional stress analysis of a highly critical region of a jet engine. The analysis of the disk/blade dovetail region of the third stage fan of a turbine engine shows a stress-concentration factor of 5.2 in the disk fillet and 4.8 in the blade fillet relative to the average stress in the neck section of the disk. The stress distribution along the edge of the blade fillet and on an interior line in the disk lug is also reported. Preliminary redesign of the disk fillet indicates that a 27-percent reduction in the fillet stress of existing third-stage disks is possible by remachining the relief area between the blade and disk lugs.     

A new ductile fracture theory and its applications

This investigation discusses further the extent to which a new damage theory recently proposed by the author can serve as a unified theory to characterize various ductile failure problems. A general damage integral and corresponding criterion for ductile fracture are presented. A new parameter for ductile fracture is emphasized, which is experimentally verified as a material constant independent of stress state, has clear physical meaning, and can easily be determined. The applicability of this theory to evaluation of the ductility of welds and engineering materials under various conditions is examined. Also, it is used to predict the effect of residual stress on failure of welds, to predict sheetforming limits, and to correlate the variability of elasto-plastic fracture toughness valuesJ _1c and δ _c with different specimen geometries. A new constraint correction method is proposed, and constraint corrected new toughness parameterJ _dc and δ _dc are recommended. Experiments have shown that the toughness variation with different specimen geometries can effectively be removed by use of the method. The general applicability of the theory to characterization of various ductile failures provides a new design tool for engineering components or structures.     

A semi-inverse shape optimization problem in linear anti-plane shear

The design of a semi-infinite fillet for efficient stress transmission is considered. The problem is treated within the context of anti-plane shear deformations of a homogeneous, isotropic, linearly elastic solid. Under a remote state of simple shear, it is desired to determine the shape of the traction-free lateral boundaries of a symmetric plane domain so that the shear stress distribution on the finite end is as uniform as possible. A semi-inverse approach for a particular class of semi-infinite profiles is used to examine this issue.