Determination of stress intensity factor for embedded elliptical crack in turbine rotor

The stress intensity factor (SIF) for an embedded elliptical crack in a turbine rotor and the thermal shock stress intensity factor for a semi-elliptical surface crack in a finite plate are determined by means of Vainshtok's weight function method. The solution for the semi-elliptical surface crack is in good agreement with the previous one. The value of the SIF for the embedded elliptical crack in the turbine rotor under centrifugal and thermal loading is larger at the crack contour near the inner radius surface and almost constant at the opposite crack contour. The SIF decreases by increasing the crack ratio, and the distance between the inner radius surface and the crack center.     

Computation of stress intensity factor in cracked plates under bending in static and fatigue by a hybrid method

A hybrid weight-function technique is presented. It consists of dividing an elliptical crack into two zones, then using the appropriate weight function in the area where it is more efficient. The proportion between zones is determined by optimizing two crack parameters (axis ratio and curvature radius). Stress intensity factors for plates containing elliptical and semi-elliptical cracks are hence computed by a self developed computer code. Static and fatigue loadings of bending are considered. The results found by the present approach are in good correlation with the analytical solutions (when available) as well as with those of other researchers.     

Stress intensity factors for corner cracks in single‐edge notch bend specimen by a three‐dimensional weight function method

A three‐dimensional (3D) weight function method is employed to calculate stress intensity factors of quarter‐elliptical corner cracks at a semi‐circular notch in the newly developed single‐edge notch bend specimen. Corner cracks covering a wide range of geometrical parameters under pin‐loading and remote tension conditions are analysed. Stress intensity factors from the 3D weight function analysis agree well with ABAQUS‐Franc3D finite element results. An engineering similitude approach previously developed for the half‐elliptical surface crack in single‐edge notch bend specimen is also applied to the present corner crack configuration. The results compare well with those from the present weight function analysis.     

Point weight function method application for semi-elliptical mode I cracks

The method of the approximate weight function construction for a semi-elliptical crack was suggested. The weight function sought was written as the sum of asymptotic (weight function for an elliptical crack in an infinite body) and correction components. To take into account the influence of a body free surface on the asymptotic component behavior, fictitious forces symmetric with respect to the body free surface were introduced.As an example of the efficiency of the proposed method semi-elliptical axial cracks in pressure vessels were considered. The results of the stress intensity factor prediction are in good agreement with the corresponding results obtained by Raju and Newman. The only exception are the results for the points located near the major ellipse axis. This may be explained by the shortcomings of the employed empirical weight function expression for an elliptical crack in an infinite body.     

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.     

Interacting dissimilar semi-elliptical surface flaws under tension and bending

Stress intensity factors for two dissimilar interacting semi-elliptical coplanar surface flaws (cracks) in a semi-infinite elastic body are obtained under overall tension and bending. First the basic equations for a general planar crack normal to the free surface are established, using the method of equivalent eigen- or transformation strains (the body force method). Then the results are specialized for application to elliptical cracks. Numerical values are obtained for various configurations and crack shapes. Results are compared with those of two-dimensional collinear cracks. Finally, an approximate procedure for estimating the stress intensity factors for a general three-dimensional crack is suggested.     

Stress intensity factors for an elliptical crack approaching the surface of a semi-infinite solid

Stress intensity factors for an embedded elliptical crack approaching the free surface of the semi-infinite solid that is subjected to uniform tension perpendicular to the plane of crack are presented in a nondimensional form for various crack aspect ratios and crack distances from the free surface. Stress intensity factors are determined numerically using an alternating technique with two solutions. The first solution involves an elliptical crack in a solid and subjected to normal loading expressible in a polynomial of x and y. The second solution involves stresses in the half space due to prescribed normal and shear stresses on the surface. Effect of the Poisson's ratio on these stress intensity factors is also investigated. Stress intensity factors for a semi-elliptical surface crack in a tinite thickness plate are then estimated in a nondimensional form for various crack aspect ratios and crack depth to plate thickness ratios.Specialist Engineer, Aerospace Group, The Boeing Company, Seattle, Washington.Professor, Department of Mechanical Engineering, University of Washington, Seattle, Washington, and also Aerospace Group, The Boeing Company, Seattle.     

Stress intensity factor at the surface and at the deepest point of a semi-elliptical surface crack in plates under stress gradients

The weight function method is used to calculate stress intensity factors for a semi-elliptical surface crack in a plate exposed to stress gradients. Starting from a reference load and stress intensity factor an approximate reference displacement field is calculated analytically. The present method allows to calculate stress intensity factors with minimal numerical effort at the deepest point and at the surface. Comparisons with FEM-results from the literature are presented to show satisfying agreement.     

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.     

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).     

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.     

Stress intensity factor calculation of steel-lined hoop-wrapped cylinders with internal semi-elliptical circumferential crack

The purpose of this paper is to present mode I stress intensity factor for a circumferential semi-elliptical crack on the inner surface of a hoop-wrapped steel-lined CNG cylinder. The stress intensity factors along the crack front are directly computed by 3D finite element method for a wide range of variations of the crack geometry. Also influence of many parameters such as cylinder internal pressure, composite layer thickness, composite material properties and undertaking Auto-Frettage pressure are studied on the stress intensity factor of the crack and some conclusive results are drawn. For the sake of validation of the results and because of lack of the results for a circumferential semi-elliptical crack in the literature, a semi-elliptical axial crack in a composite hoop-wrapped cylinder has been modeled and the results have been compared with those in the literature showing a good agreement.     

Transient thermal stress intensity factors for an internal longitudinal semi-elliptical crack in a thick-walled cylinder

In this paper, the stress intensity factors are derived for an internal semi-elliptical crack in a thick-walled cylinder subjected to transient thermal stresses. First, the problem of transient thermal stresses in a thick-walled cylinder is solved analytically. Thermal and mechanical boundary conditions are assumed to act on the inner and outer surfaces of the cylinder. The quasi-static solution of the thermoelasticity problem is derived analytically using the finite Hankel transform and then, the stress intensity factors are extracted for the deepest point and the surface points of the semi-elliptical crack using the weight function method. The results show to be in accordance with those cited in the literature in the special case of steady-state problem. Using the closed-form relations extracted for the transient thermal stress intensity factors, some conclusive results are drawn.     

Assessment of partly circumferential cracks in pipes

This paper presents a new method for predicting the stress intensity factors around a partly circumferential elliptical surface crack in a pipe. The solution is applicable to structures with both double and single curvature. The technique involves a conformal transform in conjunction with a semi-analytical approach that uses a finite element model to obtain the stress distribution in the undamaged structure. By using an indirect methodology, the model development is simplified and the analysis time is minimised. As such a coarse mesh can be used to obtain solutions for multiple crack geometries. Three examples are presented to verify this methodology. They include a partly circumferential elliptical crack under uniform tension, a pipe subject to a residual stress field, and a problem involving double curvature. For simple loading the solution compares with other published solutions to within 5% for an external crack, and to within 15% for an internal crack. For more complex loading conditions the majority of the solutions were within 5% of other published results at the deepest point, and most solutions at the surface agreed to within 15%. For the problem involving double curvature, the solutions agreed to within 4% for an internal crack, and 15% for an external crack.     

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.     

External surface cracks in shells under cyclic internal pressure

The stress analysis and fatigue crack growth behaviour of a part‐through‐cracked double‐curvature thin‐walled shell is examined. An external surface crack is assumed to lie in one of the principal curvature planes of the shell, and to present a semi‐elliptical shape. The stress intensity factors (SIFs) along the crack front for different elementary opening stresses acting on the crack faces are determined through a three‐dimensional finite element analysis. Then approximate values of SIF in the case of a cracked pressure vessel are computed by employing the above results together with the superposition principle and the power series expansion of the actual opening stress. Finally, a numerical simulation procedure is carried out to predict the crack growth under cyclic internal pressure. Some results are compared with those of other authors.     

Developments in the analysis of interacting cracks

This paper presents an overview of the finite element alternating technique for the analysis of interacting cracks. To illustrate the ease and accuracy of this method the technique is used to analyse several problems associated with both widespread fatigue and multi-site damage, a problem which is attracting worldwide attention. Whilst this paper presents an overview of the technique for both two- and three-dimensional problems attention is focused on three-dimensional problems. In particular, the interaction effects between two fully embedded elliptical flaws and between two semi-elliptical surface flaws, and the effects of crack proximity and crack aspect ratio on the stress intensity factors are presented. For semi-elliptical surface flaws these results indicate that as the cracks approach each other the position of the point on the crack front with the highest stress intensity factor shifts. This subsequently suggests that surface cracks will tend to grow preferentially towards each other. The same trend is evidenced for fully embedded cracks. However, in this case there is no shift in the position of the maximum stress intensity factor. A discussion of the results in terms of stress intensity magnification factors is also presented.     

A new method to calculate k1 for semi-elliptical surface cracks in finite plates

Irwin's solution of the stress intensity factor K_I for an embedded elliptical cracks was extended to solve for K_I for semi-elliptical surface cracks in finite plates. A double series was set up to express the displacement of the crack surface, and the unknown coefficients of the series were determined by the crack surface displacements of two dimensional edge cracks and center cracks. The maximum displacement was determined with an energy method. The results reflected the influence of both the relative crack depth a/t and the relative crack length c/W. The cases in which elliptical axis ratio a/c > 1 were also included.     

Stress intensity factors for a wide range of long-deep semi-elliptical surface cracks, partly through-wall cracks and fully through-wall cracks in tubular members

To calculate the rate of fatigue crack growth in tubular members, one approach is to make use of the fracture mechanics based Paris law. Stress intensity factors (SIF) of the cracked tubular members are prerequisite for such calculations. In this paper, stress intensity factors for circumferential deep semi-elliptical surface crack (a/t > 0.8), semi-elliptical partly through-wall crack and fully through-wall crack cracks in tubular members subjected to axial tension are presented. The work has produced a comprehensive set of equations for stress intensity factors as a function of a/T, c/πR and R/T for deep surface cracks. For the partly through-wall cracks and fully through-wall cracks, two sets of bounding stress intensity factor equations were produced based on which all stress intensity factors within the range of parameters can be obtained by interpolation.     

Stress intensity factors of an elliptical crack or a semi-elliptical crack subject to tension

This paper is concerned with the analysis of stress intensity factors of a semi-infinite body with an elliptical or a semi-elliptical crack subject to tension. Analysis is based on the body force method [1] which has been applied to the various plane stress problems. In this paper the method is extended to three-dimensional problems. The numerical calculations are performed for various shapes and configurations of ellipses and the results are in agreement with the two-dimensional cases by M. Isida asb/a→0. The stress intensity factor of a semi-elliptical crack in a plate of finite width is also discussed.