Situation may well arise where the aspect ratio of cracks is larger than one. Stress intensity factor for cracks emanating from a shaft. External surface cracks can occur in cylindrical vessels due to damage and propagate in the manufacturing process and during service life. Initially, the mathematical model representing tapered rotating disc is solved and the equations for radial stress are obtained.
Dynamic stress intensity factors for a longitudinal semi. For a slender crack c a 1 the stress intensity factor reaches its largest values at the deepest points 2. Fatigue cracks nucleate at the surface of the shaft operating under cyclic load. Stress intensity factors for an elliptical crack approaching the surface of a semielliptical solid. Hence, there is a great need to determine the stress intensity factor in cracked shafts by using finite element method. It is shown that the stress intensity factors oscillate around the steady state solution.
Stress intensity factors sifs are generally used to predict the remaining life of cracked tubular kjoints used in the offshore structures. Stress intensity factor, surface crack, crack propagation, fatigue, fracture. This page provides stress intensity factor solutions for common cases. The configurations were subjected to either remote. Semielliptical surface cracks are one of the most frequent cracks found in many structures in service, such as offshore structures and aircraft components. However, for plates with partly throughwall cracks, namely an semielliptical crack with an imaginary crack depth a which is greater than the thickness t of the plate, the stress intensity factor was not reported. Stressintensity factors for semielliptical surface. An external longitudinal surface crack is assumed to. Stress intensity factors for semielliptical surface. For this reason, results for finite geometry stress intensity factors are usually reported in terms of. A stress intensity factor sif which includes this effect increases the accuracy of fatigue lives prediction.
The stress analysis of cracks handbook, third edition. The most effective method of evaluating the stress intensity factor induced by an applied stress field is by using the weight function for a given cracked body. The weight function method was applied and appropriate weight functions have been derived using the petroskiachenbach crack opening displacement expression. Pdf weight function and stress intensity factors for. The purpose of this paper is to present stressintensity factors for a wide range of nearly semielliptical surface cracks in pipes and rods. Figure 11 shows the results for a surface stressintensity factors of semielliptical surface cracks in finitethickness plates 825 2,0 1. Early theoretical solutionsfor surface flaw problems usually involved the discussion of semicircular or semielliptical cracks in semiinfinite solids refs. This high stress concentration reduces fatigue lives of welded structures.
The objective of this study is to determine the stress intensity factor for cracks emanating from a shaft by using finite element method and also to verify the finite element results with those obtained semianalytically. Stress intensity factors for a semielliptical surface. Consider a cylinder with a finite elliptical axial surface crack, subject to the. Stress intensity factors for semielliptical surface cracks in. Stress intensity factors for axial semielliptical surface cracks and embedded elliptical cracks at longitudinal butt welded joints of steellined pressure tunnels and shafts considering weld shape. Finite element investigation of stress intensity factors. First, the weight function method for the calculation of tstress previously developed for twodimensional crack problems was extended for the tstress calculation for threedimensional crack problems.
In the present study the problem of calculation of the sif of semielliptical crack sec located in the stress concentration areas of ej installed between the lower barrel and the upper barrel of a rr pressure vessel is numerically solved by advanced globallocal finite element fe analysis. Weight functions for tstress for semielliptical surface. Stress intensity factors for an elliptical crack approaching the surface of a semi elliptical solid. Read stress intensity factor of semielliptical surface crack in a cylinder with hoop wrapped composite layer, international journal of pressure vessels and piping on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. The stress intensity factor solution given by isida et al. In order to validate the submodeling technique, several numerical examples are. Finally, dynamic stress intensity factors are calculated at the deepest and the surface points of an internal axial semielliptical surface crack in a thickwalled cylinder. The only exact analytical weight function for a planar crack was obtained for a circular one. The effect of the weld toes in welded joints is considered using a weld toe magnification factor m k, and the scf equations are taken into account for misalignment.
New displacementcontrolled surface crack in center of a plate sc33. The purpose of this paper is to present the effect of finite boundary on the stress intensity factor of an internal semi. A magnification factor is commonly used to multiply the sif of semielliptical surface cracks to account for the stress concentration effect in welded connections. Analysis of stress intensity factor along semielliptical. Determination of weight functions for semielliptical surface cracks by direct adjustment to reference stress intensity factor solutions. An empirical stressintensity factor equation for the. The purpose of this research is to compare both british standard bs 7910 20 and american standard api 579asme ffs1 2016 stress intensity factor sif solutions by considering a series of semielliptical surface cracks located in the external surface of a pressurized hollow cylinder in the axial direction. Stressintensity factors for an internal semielliptical. On the calculation of stress intensity factors and j.
Abstract this paper presents an empirical stressintensity factor equation for a surface cracks as a function of parametric angle, crack depth, crack length, plate thickness and plate width for tension and bending loads. For plates with semielliptical surface crack, newman, raju and kou have reported the stress intensity factor. Assuming an isotropic material with linear elastic behavior, the stress field on any linear elastic body that holds a crack can be determined, according to irwin 1, as follows. The stress intensity factor, is used in fracture mechanics to predict the stress state stress intensity near the tip of a crack or notch caused by a remote load or residual stresses. Raju proposed an empirical stress intensity factor equation for a semielliptical surface crack in a finite plate under tensile stress 22 in the following form. Stress intensity factors for elliptical cracks dtic. The formula can be divided into the following two parts. Stress intensity factors for axial semielliptical surface. The most e ective method of evaluating the stress intensity factor induced by an applied stress eld is by using the weight function for a given cracked body.
There are various stress intensity factor solutions, particularly for flat plates and pressure vessels with various cracked geometries. Stress intensity factor of the hoopwrapped cylinder. In these equations, the newman and raju equation for a semielliptical surface crack in a plain plate is chosen as the base stress intensity equation. Wang department of mechanical engineering, university of waterloo, ontario, canada, n2l 3g1. Stress intensity factor variations for pressurized and unpressurized semielliptical inner surface cracks in pressurized cylinders with crack aspect ratios of 0. This paper presents the application of the weight function method for the calculation of elastic tstress for semielliptical surface cracks. For a slender crack ca 1 the stress intensity factor reaches its largest values at the deepest points 2. Stress intensity factor sif, first introduced by irwin, is a physical quantity used as a control parameter to evaluate the critical state of a crack. Closedform calculation of stress intensity factor for an axial id surface flaw in cylinder subjected to weld residual stresses. Most of research focuses on stress intensity factors for surface cracks with low aspect ratios, i. The weight function represents the sif induced by a unit concentrated load. Analysis of stress intensity factor along semielliptical surface crack reinforced by composite patching article type. Calculation of stress intensity factors for a longitudinal. The aim of this paper then, is to derive a closed form weight function for the surface point of semielliptical surface crack in a plate of finite thickness t.
Stress intensity factor for an embedded elliptical crack approaching the free surface of a semiinfinite solid and subjected to a linearly varying pressure is presented in a nondimensional form as a function of position around the crack periphery. Additional details on the development and verification of the new stress intensity factor models as well as for the revisions presented below can be found in appendix c of the nasgro v9. Stressintensity factor equations are presented for an embedded elliptical crack, a semielliptical surface crack, a quarterelliptical corner crack, a semielliptical surface crack along the bore of a circular hole, and a quarterelliptical corner crack at the edge of a circular hole in finite plates. Stress intensity factors of a semielliptical crack in a hollow cylinder. The aspect ratio ac of the semielliptical surface precracks could then be easily measured using an eyepiece with a properly graduated reticle. Stress intensity factors for semielliptical surface cracks in pressurised cylinders using the boundary integral equation method.
Pdf stress intensity factor for a semielliptical crack subjected to. In the present paper, calculations of the stress intensity factor sif in the linearelastic range and the jintegral in the elastoplastic domain of cracked structural components are performed by using the shelltosolid submodeling technique to improve both the computational efficiency and accuracy. Pdf stress intensity factors for circumferential surface. Stress intensity factor of semielliptical surface crack in a cylinder. Rice the partthrough surface crack in an elastic plate. The stress intensity factor can be determined at any point on the crack tip contour by using the general weight function. Calculation of stress intensity factors for cracks in. Figures 11 and 12 shows stressintensity factors obtained by several investigators for a semielliptical surface crack in a finitethickness plate. A method for calculating stress intensity factors for edge and surface cracks in weldments has been presented. Improved formula for the stress intensity factor of semi. The paper presents numerical estimation of stress intensity factor sif of such cracks in circular solid shaft when subjected to bending and twisting loads in elastic conditions.
Modified stress intensity factor equations for semi. Stress intensity factors for elliptical and semielliptical cracks. Stress intensity factor of semielliptical surface crack in. The distribution of the stress intensity factor along the axial crack front is varied according to different crack profiles. The derived weight functions account for both the global weldment geometry and. Stress intensity factor solutions for semielliptical weld.
Stressintensity factors for semielliptical surface cracks under. The paper concludes with a parametric study that provides a set of stressintensity factors for semielliptical surface. Stress intensity factors of semielliptical surface cracks. The stress intensity factors are presented in a suitable table format for various geometrical configurations of both the pressure vessel and the semielliptical crack, thus providing a useful tool for the fracture mechanics design of cracked pressure vessels. Calculation of stress intensity factors and crack opening. The accuracy of sifs depends very much on accurate modelling of the surface crack. The method presented below is based on the generalized weight function technique enabling the stress intensity factors to be calculated for any mode i loading applied to a planar semielliptical surface crack. Read stress intensity factors of semielliptical surface cracks in pressure vessels by globallocal finite element methodology, engineering fracture mechanics on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. New shape function solutions for fracture mechanics. Multiple surface cracks in pressure vessels 549 optblok, the reduction of the stiffness matrix is done only once although the reduction of load vector and back substitution may be repeated for any number of iterations, with only a small additional computational time. Some of these solutions are based on the use of thinshell theory18, which does not take into account the three dimensional nature of the highly localised stresses in the vicinity of the crack front. These cracks then grow into semielliptical shapes while extending into the shaft. Modified stress intensity factor equations for semielliptical surface. Stress intensity factors for semielliptical surface cracks in a plate.
Stress intensity factor for a semielliptical crack subjected to an. Stress intensity factor of semielliptical surface crack in internally. User friendly assessment of stress intensity factor in. Most practical crack configurations are embedded and surface breaking planar cracks subjected to com plex twodimensional stress fields. The problem of a beam containing a semielliptical surface crack and subjected to tension or bending loading is investigated. Stress intensity factors for semielliptical surface cracks with flaw aspect ratio beyond the asme xi limit. Stress intensity factor of semielliptical surface crack. Figures 11 and 12 shows stress intensity factors obtained by several investigators for a semielliptical surface crack in a finitethickness plate. Figure 11 shows the results for a surface stress intensity factors of semielliptical surface cracks in finitethickness plates 825 2,0 1.
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