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 AND WEIGHT FUNCTIONS FOR SEMI-ELLIPTICAL SURFACE CRACKS IN FINITE-THICKNESS PLATES UNDER TWO-DIMENSIONAL STRESS DISTRIBUTION

Abstract— A Fourier series approach is proposed to calculate stress intensity factors using weight functions for semi-elliptical surface cracks in flat plates subjected to two-dimensional stress distributions. The weight functions were derived from reference stress intensity factors obtained by three-dimensional finite element analyses. The close form weight functions derived are suitable for the calculation of stress intensity factors for semi-elliptical surface cracks in flat plates under two-dimensional stress distributions with the crack aspect ratio in the range of 0.1 ≤ a/c ≤ 1 and relative depth in the range of 0 ≤ a/t ≤ 0.8. Solutions were verified using several two-dimensional non-linear stress distributions; the maximum difference being 6%.     

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.     

SINGULAR p-VERSION FINITE ELEMENTS FOR STRESS INTENSITY FACTOR COMPUTATIONS

The finite element analysis of linear elastic fracture mechanics problems is complicated by the presence of the singular and finite non-singular stress distributions in the crack tip region. The availability of a constant stress term in addition to the singular term in the standard h-version singular finite elements is insufficient to model the finite nonsingular stress zone. A p-version singular finite element capable of modelling the higher-order non-singular stress terms in addition to the singular term and the constant term is presented. The formulation for the displacement substitution technique for computing the stress intensity factors using singular p-version triangular finite elements is developed. Unlike the standard h-version formulation, the stress intensity factors computed using the p-version displacement substitution technique do not depend on the specific arrangement and length of the quarter point elements, and require simple mesh designs as well as fewer number of degrees of freedom. Numerical studies comparing the convergence of the stress intensity factors computed by the p-version method against other available alternatives such as the h-version method and the contour integral method are presented to demonstrate the effectiveness of the present developments. © 1997 by John Wiley & Sons, Ltd.     

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.     

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.     

方形截面管横向裂纹的应力强度因子KI

利用裂纹张开能量释放率建立了一个求解方形截面管横向裂纹应力强度因子的一个方法。给出了方形截面管裂纹张开能量释放率的 G*-积分表征,以及和应力强度因子的关系。同时也给出了 G*-积分与载荷、几何参量以及机械性能参数的关系,进而得到方形截面管横向裂纹的应力强度因子。给出的方法不仅适用于一般箱形结构件的裂纹问题,也适用于其它有限边界多边管状结构的三维裂纹问题,过程极为简单。     

求解双材料界面裂纹应力强度因子的扩展有限元法

基于双材料界面裂纹尖端的基本解,构造扩展有限元法(eXtended Finite Element Methods, XFEM)裂尖单元结点的改进函数。有限元网格剖分不遵从材料界面,考虑3种类型的结点改进函数：弱不连续改进函数、Heaviside改进函数和裂尖改进函数,建立XFEM的位移模式,给出计算双材料界面裂纹应力强度因子(Stress Intensity Factors, SIFs)的相互作用积分方法。数值结果表明：XFEM无需遵从材料界面剖分网格,该文的方法能够准确评价双材料界面裂纹尖端的SIFs。     

INFLUENCE FUNCTIONS FOR INCLINED EDGE CRACKS

A theoretical technique is developed for determining both KI and K_II from influence functions for angled edge cracks subjected to arbitrary distributions of normal and tangential contact stresses. Numerical results are presented which indicate the effect of crack length and crack angle on four influence functions, from which KI and K_II can be readily determined for specified distributions of tangential or normal contact stresses. In order to illustrate the use of the influence functions, a worked example is presented which shows the variation of KI and K_II with crack length and crack angle calculated for an assumed parabolic distribution of tangential stress under a fretting pad. Corresponding values of KI and K_II for other distributions of tangential and normal stresses may be determined by the same simple summation techniques used in this report.     

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.     

A NOTCH INTENSITY FACTOR APPROACH TO THE STRESS ANALYSIS OF WELDS

In the context of linear elastic stress gradients that are present in welded joints, a stress field approach based on notch stress intensity factors is presented with the aim of describing stress distributions in the neighbourhood of weld toes, since fatigue strength is dependent on such distributions. This paper summarizes the analytical fundamentals and gives an appropriate definition of the parameters for stress components under opening and sliding modes. Then, by comparing the expected results with those obtained by numerical analysis, the contributions of the symmetric and skew-symmetric loading modes are quantified for different geometries, and summarized into concise expressions which also take into account the influence of the main geometrical parameters of the welded joint. The range of validity and the application limits of this field approach in the presence of weld toe radii are discussed. Finally, a synthesis of experimental fatigue strength data based on the new field parameters is reported.     

平面裂纹应力强度因子的半解析有限元法

利用弹性平面扇形域哈密顿体系的方程,通过分离变量法及共轭辛本征函数向量展开法,推导了一个圆形奇异解析单元列式,该单元能准确地描述平面裂纹尖端场。将该解析元与有限元相结合,构成半解析的有限元法,可求解任意几何形状和载荷的平面裂纹应力强度因子及扩展问题。对典型算例的计算结果表明本文方法简单有效,具有令人满意的精度。     

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.     

各向异性平面内双边半无限裂纹问题的基本解

应用复变函数的方法，对于含双边半无限裂纹的各向异性平面，给出了其在任意集中力作用下的复应力函数基本解与应力强度因子基本解；结果表明：当外载作用在裂纹表面上时，其应力强度因子与相应各向同性的情形相同     

椭圆形截面管环向裂纹应力强度因子分析方法

应力强度因子是断裂力学中一个重要的参量。基于虚功原理和弯曲理论,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椭圆形截面管环向裂纹应力强度因子问题,给出了椭圆形截面管裂纹张开能量释放率的G*-积分表征,得出不同载荷作用下椭圆形截面管环向裂纹应力强度因子的具体表达式。通过将其结果与有限元分析所得结果的比较,表明该方法最大的特点是能够给出封闭解,且计算简单。     

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.     

修正的内部基扩充无网格法求解多裂纹应力强度因子

修正的内部基扩充无网格Galerkin法求解了多裂纹应力强度因子。采用特征距离对内部基扩充无网格法进行修正,应用变分原理推导了系统离散方程,给出相互作用能量积分计算混合型模式下的应力强度因子的公式。求解3个平面应力条件下的多裂纹问题,并与其他数值方法的计算结果进行比较。数值算例表明：修正的内部基扩充无网格Galerkin法可以方便、有效地求解多裂纹问题,在不增加附加节点和自由度的情况下便可以得到较高精度的计算结果。     

A NEW METHOD FOR THE MEASUREMENT OF MODE II FATIGUE THRESHOLD STRESS INTENSITY FACTOR RANGE ΔKτth

Abstract— In order to evaluate the threshold value Δ K _τth for mode II fatigue crack growth, a new measurement method of mode II fatigue crack growth has been developed. This method uses a conventional closed-loop tension—compression fatigue testing machine without additional loading attachments. Mode II fatigue tests for structural steel and rail steel have been carried out. This method has proved successful and has reproduced mode II fatigue fracture surfaces similar to those found in the spalling of industrial steel-making rolls. The crack length during testing was measured by an AC potential method. The relationships between d a /d N and Δ K _τ and AK _τth for several materials have been obtained.     

A STUDY OF RESIDUAL CAUSTICS GENERATED FROM FATIGUE CRACKS

Abstract— The method of caustics was used to determine the stress intensity factor of fatigue cracks in steel compact tension specimens. Under zero load a residual caustic was observed at the tip of a fatigue crack indicating the presence of a residual stress field. Caustics were generated at increasing static loads and the stress intensity factors were compared with those predicted by theory. It was found that the difference between each measured stress intensity factor and its corresponding theoretical value was a constant for the range of loads. This difference was shown statistically to be equal to the stress intensity factor determined from the residual caustic. The proposed mechanism for the formation of this residual caustic was probably due to crack tip plasticity effects and not due to crack closure. It was concluded that residual caustics can be measured to quantify crack tip behaviour in fatigue cracks and have been shown to be a useful tool in the measurement of residual stress fields.