WEIGHT FUNCTIONS AND STRESS INTENSITY FACTORS FOR SEMI-ELLIPTICAL CRACKS IN T-PLATE WELDED JOINTS

Weight functions were derived for the deepest point and surface point of a semi-elliptical surface crack in T-plate joints with weld angles between 0 and 45°. These weight functions were derived from reference stress intensity factor solutions obtained from three-dimensional finite element calculations, and verified using stress intensity factors for different non-linear stress fields and for far-field tension and bending cases. The differences between the weight function predictions and the finite element data were less than 10%. They are suitable for semi-elliptical surface cracks with aspect ratios in the range 0.05 ≤ a/c ≤ 1, together with relative depths 0 ≤ a/t ≤ 0.6 and weld angles 0 ≤ φ ≤ 45°.     

STRESS INTENSITY FACTORS FOR SURFACE CRACKS AT A HOLE BY A THREE-DIMENSIONAL WEIGHT FUNCTION METHOD WITH STRESSES FROM THE FINITE ELEMENT METHOD

Stress intensity factors for semielliptical surface cracks emanating from a circular hole are reported in this paper. The three-dimensional weight function method with three-dimensional finite element solutions for the uncracked stress distribution is used for the analysis. Two different loading conditions, i.e. remote tension and wedge loading, are considered for a wide range of geometrical parameters. Both single and double surface cracks are studied and compared with other solutions available in the literature. Typical crack opening displacements are also provided.     

裂纹面荷载作用下多裂纹应力强度因子计算

该文基于比例边界有限元法计算了裂纹面荷载作用下平面多裂纹应力强度因子.比例边界有限元法可以给出裂纹尖端位移场和应力场的解析表达式,该特点可以使应力强度因子根据定义直接计算,同时不需要对裂纹尖端进行特殊处理.联合子结构技术可以计算多裂纹问题的应力强度因子.数值算例表明该文方法是有效且高精确的,进而推广了比例边界有限元法的...     

STRESS INTENSITY FACTOR SOLUTIONS FOR SEMI-ELLIPTICAL WELD-TOE CRACKS IN T-BUTT GEOMETRIES

Abstract— Weld toe magnification factors are widely used in the evaluation of stress intensity factors for cracks in welded structures. Traditionally, the weld magnification factor has been determined from 2-D plane strain models containing edge cracks. However, it has long been recognised that a semi-elliptical weld toe crack cannot be accurately represented by a 2-D approximation due to the 3-D nature of the geometry. As a consequence, some recent research has been carried out using 3-D numerical modelling, which highlights the limitations of the 2-D approach. Nevertheless, 3-D solutions are still scarce and are of limited validity due to the difficulties associated with creating the numerical models. This paper reports the most extensive 3-D numerical investigation of semi-elliptical cracks in T-butt geometries to date. Based on the numerical results, new and accurate equations for weld magnification factors were derived, which quantify the 3-D effects present and emphasise the importance of the attachment. The results obtained from these equations are then used in an assessment of existing solutions.     

STRESS INTENSITY FACTORS FOR CORNER CRACKS AT A HOLE BY A 3-D WEIGHT FUNCTION METHOD WITH STRESSES FROM THE FINITE ELEMENT METHOD

Abstract— Stress intensity factors for quarter-elliptical corner cracks emanating from a circular hole are determined using a 3-D weight function method combined with a 3-D finite element method. The 3-D finite element method is used to analyze uncracked configurations and provide stress distributions in the region where a crack is likely to occur. Using this stress distribution as input, the 3-D weight function method is used to determine stress intensity factors. Three different loading conditions, i.e. remote tension, remote bending and wedge loading, are considered for a wide range of geometrical parameters. The significance of using 3-D uncracked stress distributions is studied. Comparisons are made with solutions available in the literature.     

J-ESTIMATION FOR SEMI-ELLIPTICAL SURFACE CRACKS IN WIDE PLATES UNDER DIRECT TENSION

Large marine structures can be subjected to extensive localized damage, with strains reaching 10  times the yield strain. Small defects might propagate, and accurate defect assessment is required for safe operation. To simulate this problem, J -integrals have been computed for semielliptical cracks in wide steel plates under tension. Three-dimensional (3D) elastic–plastic finite element analysis was used to model shallow crack geometries with 0.2 ≤ a / c ≤ 0.57 and 0.05 ≤ a / t ≤ 0.15. The material responses were linear elastic followed either by power hardening, or perfect plasticity and power hardening. It was found that, in contrast to previous studies on single edge notch geometries, the material law does not have a major influence on the J –strain behaviour. Results obtained from the 3D analyses form the basis for the development of a J -based estimation scheme.     

STRESS INTENSITY FACTORS FOR CIRCUMFERENTIAL SURFACE CRACKS IN PIPES

Abstract Stress intensity factors for circumferential surface cracks in pipes have been derived using the finite element method. Both cracks located at the in- and outside of the pipes have been analysed. The derived solutions cover a wide range of geometry and load configurations and are presented in a tabular form that defines influence functions for the stress intensity factor along the whole crack front. The solutions show good agreements in comparisons to other published solutions.     

MODE I STRESS INTENSITY FACTOR EQUATIONS FOR CRACKS AT NOTCHES AND CAVITIES

Abstract— In this paper, the notch-crack problem is treated in two different ways: if the non-dimensional crack length l /ρ ( l = crack length; ρ= notch root radius) is smaller than the transition crack length l _T/ρ, it is treated as an edge crack lying within the local stress field around the notch tip; if l/ ρ is larger than l _T/ρ, the notch-crack is considered as a simple flat crack problem subjected to remote loading, the flat crack size being the sum of notch depth and the real crack length. Based on currently available numerical data, expressions for the transition crack length, l _T, and for the geometric factor F = K _I/(1.1215K_tσ√π l ) are developed for various notch problems for the crack length range l ≦ l _T. It is found that the stress (σ_yy) normalized by the peak stress (σ_peak), σ_yy/σ_peak, for the pre-cracked component is very similar to the geometric factor for short cracks.     

ON DETERMINING STRESS INTENSITY FACTORS FOR MIXED MODE CRACKS FROM THERMOELASTIC DATA

Abstract— An alternative methodology is presented for determining stress intensity factors for cracks subject to mixed-mode displacements. The methodology involves thermoelastic data generated from a SPATE (Stress Pattern Analysis by Thermal Emission) system and has been adapted from one used successfully in photoelasticity. The thermoelastic data is collected throughout the elastic stress field dominated by the crack tip singularity. The stress field is described using a Fourier series within Muskhelishvili's approach. This method allows different applied stress fields to be described which may include transient or non-uniform stress fields. The results obtained using the new methodology are at least as good as those obtained previously for pure mode I cases, and generally better for mixed mode displacement conditions.     

表面裂纹应力强度因子计算的边界元法

本文用8节点二次等参元边界元法计算了半椭圆形表面裂纹的应力强度因子。在裂纹尖端附近使用了8节点奇异元,而在除裂尖附近以外的边界使用了4～8节点的变节点单元,以便于网格的疏密过渡。文中采用的等精度积分等处理方法都在一定程度上提高了解法的有效性。通过将本文解与高自由度的Newman有限元解比较表明:本文解的精度是较高的,也说明了用边界元法解这类问题只需很少的自由度就能得到令人满意的结果。     

STRESS INTENSITY FACTORS FOR CRACKS IN NOTCHED FINITE PLATES SUBJECTED TO BIAXIAL LOADING

Stress intensity factors were calculated, based on Bueckner's principle for cracks in both infinite and finite plates with notches subjected to biaxial loading. Approximate Green's functions have been obtained by modifying two existing Green's functions, originally for unnotched plates. Values of stress intensity factors calculated using Bueckner's principle with the approximate Green's functions are in good agreement with published stress intensity factors for cracks in both infinite and finite plates containing a circular notch or an elliptical notch, previously found by the method of boundary collocation.     

拉伸环向周期裂纹管的应力强度因子

利用裂纹非自发扩展的能量释放率,即G^*-积分理论分析求解了拉伸周期裂纹管应力强度因子问题,给出了周期裂纹管应力强度因子的系列解答.该解亦可作为开裂曲板应力强度因子的近似解.     

CRACK-LINE AND EDGE GREEN'S FUNCTIONS FOR STRESS INTENSITY FACTORS OF INCLINED EDGE CRACKS

Abstract— Fretting loads on the surfaces of structural components can cause accelerated growth of short cracks. The rate of growth will depend on the combined stress intensity factor resulting from both remote and local loading. Many stress intensity factor solutions are available for remote loading, but solutions for arbitrary fretting loads are not readily accessible. In this paper accurate crack-line Green's functions are obtained from a boundary element analysis and then used to develop the Green's functions for loads on the edge of a half-plane containing a slant crack at various angles to the edge. These latter Green's functions can be used to obtain stress intensity factors for arbitrary stresses (normal or shear) on the edge of the half-plane without further stress analysis; simple integration procedures are all that is required.     

A LOCAL GRID REFINEMENT METHOD FOR DETERMINING STRESS INTENSITY FACTORS FOR CRACKS AT NOTCHES

Abstract— Stress intensity calibrations have been determined for cracks at the root of a semi-circular edge notch loaded in tension using a localised grid refinement technique for finite element analysis. The technique is of particular value in situations where a fully connected mesh model is difficult to achieve or where enhanced accuracy is needed in a small sub-region of a model. Solutions were as accurate as those from a conventional refined mesh but with an approximately two fold reduction in run time. The resulting stress intensity factors are in good agreement with those estimated using a notch correction function and the equivalent un-notched crack solution.     

GROWTH OF SEMI-ELLIPTICAL SURFACE CRACKS IN FERRITIC STEEL PLATES UNDER CYCLIC THERMAL SHOCK LOADING

Abstract— Investigations of crack growth under thermal fatigue loading are presented. The experiments were performed with a ferritic reactor pressure vessel steel. A plate, containing a semi-elliptical surface crack is heated up to a homogeneous temperature and cyclically cooled down by a jet of cold water. On the basis of linear elastic fracture mechanics, stress-intensity factors are calculated with the weight function method. The prediction of crack growth under thermal fatigue loading using data from standard specimens is compared with the experimental result.     

STRESS INTENSITY FACTORS FOR CORNER CRACKS AT A SEMI-CIRCULAR NOTCH UNDER STRESS GRADIENTS

Abstract— A weight function method, recently developed by the authors, is applied to calculate stress intensity factors for corner cracks emanating from a semi-circular notch under crack face polynomial pressure loading. A wide range of configuration parameters are considered. These results, combined with superposition principle, allow determination of stress intensity factors under general loading conditions. The approach is demonstrated by obtaining stress intensity factors for the load cases of remote tension and shot-peening residual stresses at the notch.     

焊接接头应力强度因子计算公式的改进

针对焊接接头的半椭圆表面裂纹的应力强度因子SIF 的计算公式, 该文介绍了目前常用的Newman-Raju-Maddox 模型和Yamada-Hirt-Albert模型以及两种模型的异同性。经过分析, 发现Yamada-Hirt-Albert模型存在不足, 其SIF 公式难以合理地计算均匀受拉状态下的SIF 值。在对现有文献中研究数据的分析基础上, 改进了Yamada-Hirt-Albert 模型, 提出了新的SIF 计算公式。经与Benchmark 数据以及其他国外试验结果的比较, 验证了该文所提出的SIF 改进公式具有更好的可靠性。     

自增强厚壁圆筒轴向内表面裂纹的应力强度因子

本文研究用有限元通用程序计算具有残余应力的自增强厚壁圆筒内半椭圆形表面裂纹的应力强度因子的方法。所考虑的应力强度因子被分为相应于工作内压及残余应力两部分，分别用三维有限元通用程序算得的裂纹前沿单元节点的垂直位移直接计算，对后者又运用了＂叠加原理＂。结果表明，残余应力的存在能有效地降低内裂纹的应力强度因子值，自增强度高者这一作用亦显著，残余应力引起的应力强度因子对裂织数目不敏感。     

残余应力平板表面裂纹的线弹簧模型

建立了残余应力平板表面裂纹的线弹簧模型,利用边裂纹权函数得到了裂纹表面上沿厚度非线性分布残余应力向线性分布转化的公式;基于Reissner板理论和连续分布位错思想,通过积分变换方法,推导了问题的控制方程和应力强度因子表达式;利用Gauss-Chebyshev方法给出了数值计算结果,并与现有的有限元解进行了比较,结果表明:该模型简单有效,而且精度较高。     

EXPERIMENTAL DETERMINATION OF STRESS INTENSITY FACTORS FOR CRACKS IN TURBINE DISCS

Stage-II fatigue crack growth paths in firtree fixtures have been predicted using a photoelastic technique. Initiation was assumed to occur at the edge of contact on the load-bearing flanks and, subsequently, the cracks were extended in the direction of the maximum circumferential stress. After a short initial length, in which propagation was perpendicular to the contact surface, the direction of crack growth was, in a broad sense, equivalent to the hoop direction in the disc. Stress intensity factors were found for the majority of the crack path using data taken from the isochromatic fringe patterns. It was concluded that the most catastrophic failure was likely to occur from the innermost land of the firtree and that the width of the firtree had little influence on the stress intensity factors.