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%.     

Calculation of stress intensity factors for a longitudinal semi-elliptical crack in a finite-length thick-walled cylinder

The purpose of this paper is to present the effect of finite boundary on the stress intensity factor of an internal semi-elliptical crack in a pressurized finite-length thick-walled cylinder  ( R _i/ t = 4)  . The three-dimensional finite element method, in conjunction with the weight function method, is used for computing the stress intensity factor at the deepest and surface points of an axial semi-elliptical crack in a cylinder. The transition aspect ratios, the aspect ratios in which the maximum stress intensity factor translates from the deepest to the surface points of the crack, are calculated for different relative depths and cylinder lengths. The results show that the stress intensity factor increases as the cylinder length decreases, especially at the corner point of the crack compared with the deepest point. The major advantage of this paper is that a closed-form expression is extracted for the stress intensity factor at the surface point of a semi-elliptical crack, which experiences higher changes due to the effect of the finite boundary of the cylinder.     

Stress intensity factors for long axial surface cracks at the outer wall of a pipe loaded by stress gradients

By means of the finite element method crack opening displacements were calculated for long axial surface cracks at the outer wall of a pipe. The wall thickness to inner radius ratio of the pipe was 1 to 10. Following a procedure introduced be Mattheck et al. weight functions were evaluated by means of the finite element results. Using these weight functions it is possible to calculate stress intensity factors for arbitrary radially varying stress distributions. In this paper stress intensity factors were evaluated for a constant hoop stress loading as well as for stress distributions with a linear and a quadratic dependence on the radius.     

Thermal Shock loading of a surface crack in a hollow sphere

Temperature and stress distributions in a hollow sphere are calculated, caused by a sudden cooling (thermal shock) of the inner surface of a hollow sphere. The thermal stresses are acting as load of surface cracks of approximate semi-elliptic shape. By means of the weight functions method stress intensity factors are estimated at the deepest point of the cracks using the well-known Newman-Raju solution for semi-elliptical surface cracks in a plate as reference solution.     

A new weight function for one‐dimensional subsurface cracks under general loading

In the present study, weight functions (WFs) of a subsurface crack were derived by proposing a new general form for approximate one‐dimensional WF. The WFs coefficients were considered as a function of crack length to depth ratio and were obtained using reference stress intensity factors (SIFs) of 16 cracks under uniform, linear, and parabolic normal and shearing loadings. The verification was performed by comparison of the straight and coupled SIFs calculated by WF and finite element modelling under some complicated loadings. In conclusion, the WFs can be simply and effectively employed for evaluating the cracks under any complex stress distributions.     

Calculation of Stress Intensity Factors for axial semi-elliptical surface cracks in a pipe with cladding loaded thermally

By means of the weight functions method stress intensity factors were calculated for axial semi-elliptical surface cracks in a pipe with cladding. The component is loaded by a thermoshock. Starting from a stress-free state the inner surface of the cladding is suddenly cooled down. The time-dependent temperature and hoop stress distributions of the uncracked component were calculated for the loading case considered. Numerical values of the stress intensity factors at the deepest point and at the surface points of the crack were evaluated at different time steps for a wide range of crack depths and crack lengths.     

Spannungsintensitätsfaktoren für halbelliptische Umfangsoberflächenrisse in einem Rohr bei Innendruck- und Biegebelastung

Stress Intensity Factors for Semi-Elliptical Circumferential Surface Cracks in a Pipe Loaded by Internal Pressure and Bending Pipes are often loaded by superposed tensile and bending stresses. Flaws in circumferential direction, for example at welded joints, may be caused by these stresses to grow. In this paper, semi-elliptical circumferential surface cracks in a pipe are studied. By means of the weight function method stress intensity factors at the deepest point and at the surface points of the cracks are evaluated in dependence on crack length and crack depth. The application of the weight function method in the form used here requires that the half crack length measured by the angle of circumference is not greater than 15 degrees. Longer cracks should be studied by the finite element method.     

Stress Intensity Factors of a circumferential surface crack at the outside of a thermally loaded pipe

Stress intensity factors were calculated for partly circumferential surface cracks at the outside of a pipe. The pipe is loaded by internal pressure and by thermal stresses. The weight functions method is used to calculate averaged weighted stress intensity factors at the deepest point and at the surface points of the crack. The evaluation of temperatures and stresses in the pipe and the application of the weight functions method are described. Numerical results are given for an application to steam generator tubes.     

Stress intensity factors for circumferential semielliptical surface cracks in a pipe under thermal loading

Stress intensity factors are calculated at the deepest point and at the surface points of circumferential semielliptical surface cracks in a thermally shocked pipe. The method of calculation is based on weight functions following a proposal by Munz et al. Numerical values of the stress intensity factors are given for a wide range of crack depths and crack lengths considering a pipe with a wall thickness to inner radius ratio of $\text{1}\text{10}$.     

Weight function calculation for surface cracks using the line-spring model

A numerical method for calculating weight functions for surface cracks in plates and shells is proposed. Thick-shell finite elements are used to create the discrete model of a body with a through-wall flaw. Line-spring elements transform the through-wall flaw into a surface crack. A quadratic line-spring element is presented. Weight functions for some semielliptical surface cracks in a plate have been calculated. The weight functions obtained may be used for computing stress intensity factors related to two-dimensional stress fields at the crack surface.     

Weight functions and Stress Intensity Magnification factors for elliptical and semi-elliptical cracks under variable normal stress – Part II

Surface cracks under peak stresses are investigated. The calculational procedure is based on the general form of the weight function for an elliptical crack embedded in an infinite solid. Two points on the contour of the ellipse are investigated. A new correction procedure for transfer from the embedded crack to surface crack configurations is presented, which is valid for all a/t-values. Weight functions for both points have been found with the crack aspect ratio a/c as parameter. For the point at the end of the minor axis all weight functions for embedded cracks are describable by one equation only (using Heuman's lambda function). For various a/c-ratios of the surface crack under different stress distributions the stress intensity magnification factors are given.     

Stress intensity factors of sickle-shaped cracks in cylindrical bars

The stress intensity factor at the deepest point of sickle-shaped cracks is calculated for a constant, a linear and a quadratic locally varying stress distribution by use of a weight function derived from finite element results.     

Weight functions and Stress Intensity Magnification factors for elliptical and semi-elliptical cracks under variable normal stress – part I

Surface cracks under peak stresses are investigated. The calculational procedure is based on the general form of the weight function for an elliptical crack embedded in an infinite solid. Two points on the contour of the ellipse are investigated. The superposition method is used for transfer from the embedded crack to surface crack configurations. Weight functions for both points have been found with the crack aspect ratio a/c as parameter. For the point at the end of the minor axis all weight functions are describable by one equation only (Heuman's lambda function). For various a/c ratios of the surface crack under different stress distributions the stress intensity magnification factors are given.     

Application of an orthotropy rescaling method to edge cracks and kinked cracks in orthotropic two-dimensional solids

Oblique edge cracks and kinked cracks in orthotropic materials with inclined principal material directions under inplane loadings are investigated. The Stroh formalism is modified by introducing new complex functions, which recovers a classical solution for a degenerate orthotropic material with multiple characteristic roots. An orthotropy rescaling technique is presented based on the modified Stroh formalism. Stress intensity factors for edge cracks as well as kinked cracks are obtained in terms of solutions for a material with cubic symmetry by applying the orthotropy rescaling method. Explicit expressions of the stress intensity factors for a degenerate orthotropic material are obtained in terms of solutions for an isotropic material. The effects of orthotropic parameter, material orientation, and crack angle on the stress intensity factors for the degenerate orthotropic material are discussed. The stress intensity factors for cubic symmetry materials are calculated from finite element analyses, which can be used to evaluate the stress intensity factors for orthotropic materials. The energy release rate for the kinked crack in an orthotropic material is also obtained.     

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.     

Approximate weight function method for elliptical arc through cracks in mechanical joints

Mechanical joints such as bolted, riveted or pinned joints are widely used to join the constituent parts of structural components. Reliable stress intensity factor analysis of arbitrary cracks in mechanical joints is required for the safety evaluation or fracture mechanics design. It has been reported that cracks in mechanical joints usually nucleate as the corner crack and grow as the elliptical arc through crack. The weight function method is a useful technique to calculate the stress intensity factor using the appropriate weight function for a cracked body and the stress field of an uncracked body. In this paper, the weight function method for the two surface points of elliptical arc through cracks in mechanical joints is developed to analyze the mixed-mode stress intensity factors. Unknown coefficients included in the weight function are determined using the reference stress intensity factors obtained from finite element analysis.     

Weight functions for the determination of stress intensity factor and T‐stress for semi‐elliptical cracks in finite thickness plate

This paper presents the application of weight function method for the calculation of stress intensity factors (K) and T‐stress for surface semi‐elliptical crack in finite thickness plates subjected to arbitrary two‐dimensional stress fields. New general mathematical forms of point load weight functions for K and T have been formulated by taking advantage of the knowledge of a few specific weight functions for two‐dimensional planar cracks available in the literature and certain properties of weight function in general. The existence of the generalised forms of the weight functions simplifies the determination of specific weight functions for specific crack configurations. The determination of a specific weight function is reduced to the determination of the parameters of the generalised weight function expression. These unknown parameters can be determined from reference stress intensity factor and T‐stress solutions. This method is used to derive the weight functions for both K and T for semi‐elliptical surface cracks in finite thickness plates, covering a wide range of crack aspect ratio (a/c) and relative depth (a/t) at any point along the crack front. The derived weight functions are then validated against stress intensity factor and T‐stress solutions for several linear and nonlinear two‐dimensional stress distributions. These derived weight functions are particularly useful for the development of two‐parameter fracture and fatigue models for surface cracks subjected to fluctuating nonlinear stress fields, such as these resulting from surface treatment (shot peening), stress concentration or welding (residual stress).     

Numerical and experimental evaluation of SIF for threaded connectors

This paper presents a methodology for fatigue crack growth analysis in tubular threaded connectors. A solution for stress intensity factor for semi-elliptical surface cracks emanating from a thread root in a screw connector is also discussed in the paper. The solution is based on a mixed approach incorporating weight function and finite element methods. The weight functions used are the universal functions for cracks in mode I and these are linked with a thread through-thickness stress distribution obtained from finite element analysis to produce a stress intensity factor for a crack at the critical tooth of a thread. The resulting crack growth data are then validated experimentally.     

A Simple Procedure for the Estimation of Local Stress Intensity Factors for Semi-Elliptical Surface Cracks

Stress intensity factor solutions are available for semi-elliptical surface cracks under different stress distributions. But in most cases, only the two values at the deepest point and at the surface points are reported. A simple method is proposed, which allows the stress intensity factor to be estimated at other points of the crack front as well. This revised version was published online in July 2006 with corrections to the Cover Date.