The development of an accurate model for the fatigue assessment of doubly curved cracks in tubular joints

Fatigue tests on tubular joints have shown that as a crack propagates through the chord wall, it curves under the weld toe. This produces, at the brace-chord intersection, a doubly curved semi-elliptical crack emanating from the weld toe. A doubly curved crack in a tubular joint is a very complex geometry which has proved to be difficult to model. In consequence, previous work on the evaluation of stress intensity factors in tubular joints adopted a simplified approach, ignoring the crack curvature under the weld toe. However, in the absence of benchmark solutions, the effects of any modelling approximation on accuracy are impossible to quantify. To address this problem and as part of the research on fatigue assessment methodologies, a technique which is able to accurately model doubly curved cracks in tubularT-joints has been developed at University of Wales, Swansea. This paper describes a detailed account of the generation of the finite element model and the procedure for evaluating the stress intensity factor solutions. The validation results are also presented to demonstrate the reliability of the model developed.     

Stress intensity factors for three‐dimensional weld toe cracks using weld toe magnification factors

In welded components, particularly those with complex geometrical shapes, evaluating stress intensity factors is a difficult task. To effectively calculate the stress intensity factors, a weld toe magnification factor is introduced that can be derived from data obtained in a parametric study performed by finite element method (FEM). Although solutions for the weld toe magnification factor have been presented, these are applicable only to non‐load‐carrying cruciform or T‐butt joints, due possibly to the requirement of very complicated calculations. In the majority of cases for various welded joints, the currently used weld toe magnification factors do not adequately describe the behaviour of weld toe cracks. In this study, the weld toe magnification factor solutions for the three types of welded joints such as cruciform, cover plate and longitudinal stiffener joints were provided through a parametric study using three‐dimensional finite elements. The solutions were formed with exponents and fractions that have polynomial functions in terms of a/c and a/t – that is, crack depths normalised by corresponding half crack lengths and specimen thickness. The proposed weld toe magnification factors were applied to evaluate the fatigue crack propagation life considering the propagation mechanisms of multiple‐surface cracks for all welded joints. It showed good agreement within a deviation factor of two between the experimental and calculated results for the fatigue crack propagation life.     

基于失效评定图(FAD)研究含疲劳裂纹T型圆钢管节点的安全性

失效评定曲线(FAD)常用来评价焊接结构在出现裂纹后的安全性,为了验证这种曲线在评价焊接管结构在节点部位出现疲劳裂纹后安全性的适用性,采用实验测试和有限元分析的方法研究了3个含疲劳裂纹的T型管节点试件在静力作用下的极限承载能力及破坏过程。3个T型管节点试件首先进行疲劳实验在焊趾处产生表面裂纹,然后通过在支管端部施加轴向拉力作用检测节点的破坏过程。基于自行开发的含表面裂纹T型管节点的有限元网格自动产生程序以及ABAQUS分析软件,研究了在管节点破坏过程中表面裂纹最深点的应力强度因子大小,并通过实验的荷载-位移曲线确定了T节点试件的塑性极限承载力。在这些结果的基础上,验证了FAD在评价含疲劳裂纹的焊接管节点安全性方面的适用性。研究结果标明:FAD在评价含疲劳裂纹管节点的安全性方面是安全可靠的,但偏于保守。     

Fatigue life prediction of offshore tubular joints using fracture mechanics

ABSTRACT Fatigue crack growth calculations were performed on offshore tubular joints using the Paris crack growth law. The stress intensity factors required for such calculations were obtained from T‐butt solutions previously proposed by the authors. The applicability of the solutions to tubular joints was first demonstrated by comparing the fatigue life of a base case with that obtained from a mean S–N curve, and the influence on fatigue life of various factors including load shedding, the size of initial defects, weld geometry, etc. was investigated. The solutions were then used to predict the lives of tubular T‐joints from an experimental database. The results show that the solutions underestimate the fatigue life; this underestimation was shown to be primarily due to ignoring the combined effects of load shedding and the intersection stress distribution. In general, however, the trends in the predicted fatigue lives with joint geometry and other details were seen to be superior to predictions from the S–N approach, with the solutions significantly reducing the dependency on loading mode exhibited by the test data.     

KK节点中表面裂纹应力强度因子的数值分析

海洋平台中的管节点在出现疲劳裂纹后,其残余寿命的估算依赖于对焊缝处表面裂纹应力强度因子的精确计算。首先介绍了包含表面裂纹的KK节点的有限元网格产生方法。采用了五种不同类型的单元,即六面体单元、四分之一结点的裂纹单元、棱柱单元、棱锥单元以及四面体单元来形成KK节点焊缝处表面裂纹的网格。然后通过交互J积分法计算出了KK节点表面裂纹的应力强度因子分布情况。     

Fatigue crack growth in a fillet welded joint

Existing theories for the growth of cracks at weld toes have proved difficult to verify because of a lack of experimental proof at short crack depths and slow growth rates. Arbitrary initial defect sizes have been employed in life calculations coupled with approximate two-dimensional stress analyses. In this study, the fatigue performance of a stress relieved fillet weld is determined by both theory and experiment. Crack growth results for shallow (less than 1 mm depth) elliptical cracks at weld toes are used to test an elastic expression for stress intensity using a correction factor from a three-dimensional stress analysis. No evidence of higher than expected growth rates, observed by others for very short cracks and cracks in notch plastic zones, is apparent. Integration of a growth law that includes the threshold stress intensity factor provides fatigue life predictions for various stress ratios and from experimentally measured defect depths. Needle peening the weld toe improves the fatigue life by retarding crack growth up to 1 mm below the weld toe.     

Fatigue analysis of non-load-carrying fillet welded cruciform joints

The goal of this investigation was to study the effect of local geometrical variations of the weld on the fatigue strength. Therefore the fatigue behaviour of non-load-carrying cruciform fillet welded joint under tensile loading has been studied parametrically. Several two-dimensional (2D) finite element models of the joint were analysed using plane strain linear elastic fracture mechanics (LEFM) calculations in order to get the magnification function M_k. A maximum tangential stress criterion was used to predict the crack growth direction under mixed mode K_I-K_II conditions. The derived M_k solution was then applied both for continuous weld toe cracks and also for semi-elliptical toe cracks at the deepest point of the crack front. An experimental crack aspect ratio development curve was used for propagating semi-elliptical cracks. The as-welded condition was assumed with the result that no crack initiation period was considered and stress ranges were fully effective. The Paris crack growth law was used to predict the growth rate. The effects of weld toe radius, flank angle and weld size on the fatigue strength were systematically studied. Finally, predicted fatigue strength values corresponding to different assumed crack sizes were compared with the available test results.     

A parametric fracture mechanics study of welded joints with toe cracks and lack of penetration

The existing design rules give quite general guidelines to the fatigue assessment of different types of welded joints. The goal of this investigation was to give designers some tools, which would allow more precise assessment of the effect of dimensional variations on the fatigue strength. Therefore the fatigue behaviour of 12 common types of welded joints has been studied parametrically. Two-dimensional (2D) finite element models of the joint were made and evaluated using plane strain linear elastic fracture mechanics (LEFM) calculations. The as-welded condition was assumed with the result that no crack initiation period was considered and stress ranges were fully effective. A maximum tangential stress criterion with the Paris’ crack growth law was used to predict the growth rate and direction of root and toe cracks under mixed mode K_I-K_II conditions. The effects of weld size and joint dimension ratios on the fatigue strength were systematically studied. In addition to tensile loading, bending and combined tension/bending moment loading in both directions are examined for positive and negative mean stress.     

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...     

A simplified fatigue assessment method for high quality welded cruciform joints

The primary goal of this study was to develop an equation relating the geometric parameters to fatigue strength which can be used is routine design assessment. To attain this, the influence of local geometrical weld variations on the fatigue strength of non-load-carrying cruciform fillet welded joints were systematically studied using plane strain linear elastic fracture mechanics (LEFM). The effects of weld toe radius, flank angle and weld size were considered. Both continuous weld toe cracks and semi-elliptical toe cracks with alternate pre-existing defect depths were considered. A previously developed experimental crack aspect ratio development curve was used for assessing the growth of the semi-elliptical cracks using 2D FE models. A total of 152 experimental fatigue data points from six published studies of welded cruciform joints were evaluated. Details of the actual weld toe radius, flank angle and weld size were available for these joints. For the high quality welds evaluated, an assumed initial crack depth of 0.05 mm was found to correlate best with the experimental data. Of all the geometric parameters considered analytically, weld toe radius was found to have the most dramatic influence on fatigue life. A simple equation is proposed which relates welded joint fatigue strength to the ratio weld toe radius/plate thickness for high quality welds.     

THE EFFECT OF MISALIGNMENT ON THE FATIGUE STRENGTH OF WELDED CRUCIFORM JOINTS

Abstract— The effect of axial misalignment on the fatigue strength of load-carrying transverse cruciform welded joints was investigated using experimental and fracture mechanics methods. Where failure occurred by cracking from the weld toe, misalignment significantly reduced the fatigue strength. The reduction could be predicted using a nominal stress concentration factor (SCF). Misalignment had less effect where failure was due to cracking through the weld metal; an expression was deduced for the SCF in this case. For fracture mechanics assessments, an expression for an effective stress intensity factor using the SCF and stress intensity factors for aligned welds was shown to agree with the finite element (FE) results. Predictions of the effect of misalignment using the FE results agreed with experimental data. Misaligned transverse load-carrying cruciform joints should be assessed for fatigue failure from the toe using the same SCF as for a butt weld with the same misalignment. For failure through the throat, an alternative expression for the SCF is recommended. Fracture mechanics assessments of misaligned joints should be carried out using an effective stress intensity factor derived from the SCF and stress intensity factors for aligned joints. These recommendations are now incorporated in British Standard PD 6493:1991.     

A study of fatigue crack growth from artificial corrosion pits at welded joints under complex stress fields

The paper studies the effects of artificial corrosion pits and complex stress fields on the fatigue crack growth of full penetration load‐carrying fillet cruciform welded joints with 45° inclined angle. Parameters of fatigue crack growth rate of welded joints are obtained from S‐N curves under different levels of corrosion. A numerical method is used to simulate fatigue crack growth using different mixed mode fatigue crack growth criteria. Using polynomial regression, the crack shape correction factor of welded joints is fitted as a function of crack depth ratios. Because the maximum circumferential stress criterion is simple and easy to use in practice, fatigue crack growth rate is modified using this criterion. The relationship of effective stress intensity factor, crack growth angle and crack depth is studied under different corrosion levels. The simulated crack growth path obtained from the numerical method is compared with the actual crack growth path observed by fatigue tests. The results show that fatigue cracks do not initiate at the edge or bottom of pits but at the weld toes where the maximum stress occurs. The artificial corrosion pits have little effect on the effective stress intensity factor ranges and crack growth angle. The fatigue crack growth rates of welded joints with pits 1 and 2 are 1.15 times and 1.40 times larger than that of the welded joint with no pit, respectively. The simulated crack growth path agrees well with the actual one. The fatigue life prediction accuracy using the modified formulation is improved by about 18%. The crack shape correction factor obtained using the maximum circumferential stress criterion is recommended being used to calculate fatigue life.     

A REVIEW OF FRACTURE MECHANICS MODELS OF TUBULAR JOINTS

Fracture mechanics methods are used to assess the significance of cracking in any structure, but a tubular joint is very complex to analyse. However the improvements in numerical methods, such as stress analysis using finite elements, and extensive full-scale laboratory testing (UKOSRP, ECSC, etc.) have allowed various workers to propose fracture mechanics models of tubular joints. This paper presents a critical review and comparison of these models. It concludes that simple plate models can provide upper and lower bound stress intensity factor solutions for cracked tubular joints. Stress intensity factors from three dimensional finite element analysis of a tubular joint are in reasonable agreement with semi-empirical data. However, in the absence of a validated database the paper concludes that any analytical assessment of a crack in a joint should be viewed as tentative.     

Numerical modelling and experimental investigation on welding residual stresses in large‐scale tubular K‐joints

This paper is devoted to the experimental and numerical assessment of residual stresses created by welding in the region surrounding the weld toe of tubular K‐shaped joints (i.e. region most sensitive to fatigue cracking). Neutron‐diffraction measurements were carried out on K‐joints cut from large‐scale truss beams previously subjected to high cycle fatigue. Tri‐axial residual stresses in the transverse, longitudinal and radial direction were obtained from the weld toe as a function of the depth in the thickness of the tube wall. In addition, thermomechanical analyses were performed in three‐dimensional using ABAQUS and MORFEO finite element codes. Experimental and numerical results show that, at and near the weld‐toe surface, the highest residual stresses are critically oriented perpendicularly to the weld direction, and combined with the highest externally applied stresses. Based on a systematic study on geometric parameters, analytical residual stress distribution equations with depth are proposed.     

Stress intensity factor solutions for estimation of fatigue lives of laser welds in lap-shear specimens

Fatigue behavior of laser welds in lap-shear specimens of high strength low alloy (HSLA) steel is investigated based on experimental observations and two fatigue life estimation models. Fatigue experiments of laser welded lap-shear specimens are first reviewed. Analytical stress intensity factor solutions for laser welded lap-shear specimens based on the beam bending theory are derived and compared with the analytical solutions for two semi-infinite solids with connection. Finite element analyses of laser welded lap-shear specimens with different weld widths were also conducted to obtain the stress intensity factor solutions. Approximate closed-form stress intensity factor solutions based on the results of the finite element analyses in combination with the analytical solutions based on the beam bending theory and Westergaard stress function for a full range of the normalized weld widths are developed for future engineering applications. Next, finite element analyses for laser welded lap-shear specimens with three weld widths were conducted to obtain the local stress intensity factor solutions for kinked cracks as functions of the kink length. The computational results indicate that the kinked cracks are under dominant mode I loading conditions and the normalized local stress intensity factor solutions can be used in combination with the global stress intensity factor solutions to estimate fatigue lives of laser welds with the weld width as small as the sheet thickness. The global stress intensity factor solutions and the local stress intensity factor solutions for vanishing and finite kinked cracks are then adopted in a fatigue crack growth model to estimate the fatigue lives of the laser welds. Also, a structural stress model based on the beam bending theory is adopted to estimate the fatigue lives of the welds. The fatigue life estimations based on the kinked fatigue crack growth model agree well with the experimental results whereas the fatigue life estimations based on the structural stress model agree with the experimental results under larger load ranges but are higher than the experimental results under smaller load ranges.     

Fatigue failure transition analysis in load‐carrying cruciform welded joints based on strain energy density approach

This paper details a study of the application of notch stress intensity theory to the fatigue failure mode analysis of the transition in load‐carrying cruciform welded joints. The weldment fatigue crack initiation point is difficult to predict precisely because it usually occurs in the vicinity of the weld toe or weld root. To investigate the relationship between fatigue failure location and the geometry of the weldments, we analysed the weld toe and root asymptotic notch stress fields were analysed using the notch stress intensity factors on the basis of the Williams' solution in Linear Elastic Fracture Mechanics (LEFM). Numerous configurations of cruciform joints of various plate thicknesses, transverse plate thickness, weld sizes and incomplete penetration size were used to investigate the location of the fatigue failure. The strain energy density (SED) surrounding the notch tip was introduced to unify the scalar quantity and preclude the inconsistency of the dimensionality of the notch stress intensity factors for various notch opening angles. The results of the investigation showed that the SED approach can be used to determine the transition zone for a variety of joint geometries. The validity of the SED criteria was verified by comparing the experimental results of this study with the complied results for load‐carrying cruciform welded joints reported in literature.     

An analysis of fatigue cracks in fillet welded joints

In most of the lower fatigue strength welded joints failure occurs by the propagation of a semi-elliptical surface crack which initiates at the weld toe. In order to analyse the progress of these cracks using fracture mechanics techniques, the solution for the stress intensity factor, K, is required. Fatigue cracks in most welded joints adopt shapes which give low a/2c values (up to approximately 0.3) while solutions in the literature are more applicable to a/2c values close to 0.5. Therefore, results in the literature were used to estimate the stress intensity factor for cracks with low a/2c values. Furthermore, the effect of the weld stress concentration factor was incorporated in the solution. The accuracy of the resulting solution was confirmed by using it to determine ΔK values of weld toe cracks for which crack propagation data were available. The results agreed with the expected da/dN vs. ΔK scatterband obtained from centre-notched specimens.     

Crack aspect development curves and fatigue life prediction for surface cracks at weld toes in the presence of residual stress

An engineering procedure is proposed for estimating the crack growth behaviour and fatigue lives of semi-elliptical surface cracks at weld toes, based on a database of stress intensity factors. Some examples of crack aspect development curves (CADC) are given for some typical cracked welded joints subjected to service loading and residual stress conditions. The significance for predicting fatigue life according to the natural crack growth path, namely along the CADC, is emphasized through examples.     

From a local stress approach to fracture mechanics: a comprehensive evaluation of the fatigue strength of welded joints

This paper investigates the possibility of unifying different criteria concerned with the fatigue strength of welded joints. In particular, it compares estimates based on local stress fields due to geometry (evaluated without any crack-like defect) and residual life predictions in the presence of a crack, according to LEFM. Fatigue strength results already reported in the literature for transverse non-load-carrying fillet welds are used as an experimental database. Nominal stress ranges were largely scattered, due to large variations of joint geometrical parameters. The scatter band greatly reduces as soon as a 0.3-mm virtual crack is introduced at the weld toe, and the behaviour of the joints is given in terms of Δ K _I versus total life fatigue. Such calculations, not different from residual life predictions, are easily performed by using the local stress distributions determined near the weld toes in the absence of crack-like defects. More precisely, the analytical expressions for K _I are based on a simple combination of the notch stress intensity factors K ₁^N and K ₂^N for opening and sliding modes. Then, fatigue strength predictions, as accurate as those based on fracture mechanics, are performed by the local stress analysis in a simpler way.     

Analysing the onset of multiple site damage at mechanical joints

A detailed analysis has been performed on the onset of multiple site damage at mechanical joints. The crack initiation is analysed based on non-linear stress analyses and the crack closure model. It has been found that the stress-strain response at the joint can have a stabilised linear relation under fatigue loading even if considerable plastic yield has occurred. This makes it possible to analyse the post yield multiple crack initiation based on fracture mechanics solutions for the crack growth in a residual stress field. Weight function method has been used to solve stress intensity factors and Green's functions for the crack growth analyses according to a strip yield crack closure solution. In this analysis, the small crack behaviour as well as the post yield effect have been accounted for. Intrinsic material parameters have been extensively used so that the method is not limited to the specified problems. Together with the crack growth analyses, a probabilistic model has been developed to account for uncertainties in initial flaw, stochastic crack propagation, geometrical inconsistency, as well as variation in the fatigue load. According to the probabilistic solution, important information about the onset of multiple site damage, e.g. the probability of crack occurrence, and the probability of crack break-through etc., are predicted as a function of the stress and the construction of joint. One example is provided to illustrate the procedure and to highlight problems in dealing with the onset of multiple site damages at mechanical joints.