Stress intensity factor for a semielliptical rail head. Pdf weight function method to determine stress intensity. In theory the stress at the crack tip where the radius is nearly zero, would tend to infinity. However, the cracked pressure vessel problems that have been solved so far require that the stress field around the semielliptical crack varies only throughthethickness of the vessel, but is constant along the axial. Improved formula for the stress intensity factor of semi elliptical surface cracks in welded joints under bending stress by yang peng, chao wu, yifu zheng and. Approximate determination of stress intensity factor for. Pdf variation of stress intensity factor and crack.
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. Expression 3 is valid for a wide plate with a central crack. Stress intensity factor solutions for nozzle corner cracks 315 finite element procedure was used by raju and newman for the solution of semi elliptical surface flaws in thin plates. 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. The stressintensity factor sif of the semielliptical surface crack in the finite body under extensional stress is sclculated by using the fem software ansys release 5. Further, a number of methods are now available for evaluating stress intensity factors 2 to 8 and limit loads9 to 15 of structures containing flaws.
Effect of crack inclination and residual stress on the. The stress intensity factor for the circumferential semielliptical surface cracks in a hollow cylinders cross section under torsion is calculated using a finiteelement technique. The problem is solved for a semi circular crack front and various crack inclination angles. General stress intensity factor expressions for cracks in mode i the stress intensity factor is defined as. Stress intensity factors for semielliptical surface. An empirical stress intensity factor equation for a surface crack. Evaluation of the formula of stress intensity factor k i for. For a plate where the crack size and width have the same order there is an additional coefficient f for equation 3. For plates with semi elliptical surface crack, newman, raju and kou have reported the stress intensity factor. Stress intensity factors for elliptical and semielliptical cracks. Surface cracks in finite thickness and width plates. Materials 2017, 10, 166 3 of 19 determination of the sif under bending stress 35. Stress intensity factor for elliptical cracks physics forums. Stress intensity factors sifs can be calculated in the nuclear electrics r6 code software1 and other computer programs.
A magnification factor is commonly used to multiply the sif of semielliptical surface cracks to account for the stress concentration effect in welded connections. Stress intensity factors for elliptical and semielliptical cracks subjected to an arbitrary mode i loading. As a result of the symmetry, only oneeighth of the cylinder is considered in the modeling. Fracture mechanics of throughcracked cylindrical pressure. 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.
For a semi circular surface crack in a semi infinite solid and a semi elliptical surface crack in a plate of finite thickness, smith, emery, and kobayashi 6, and kobayashi 7, respectively, used the alternating method to obtain stress intensity factors along the crack front. Stress intensity factor for a semielliptical crack subjected to an arbitrary mode i. Nov 05, 2011 hi, i just wanted some clarification with respect to a few equations relating stress intensity factor to semi elliptical and quarter elliptical cracks in solids. In the present study the problem of calculation of stress intensity factors of semielliptical and quarter elliptical crack located in stress concentrated areas of. Effect of crack inclination and residual stress on the stress intensity factor of semi elliptical crack in a pressure vessel springerlink. Evaluation of the formula of stress intensity factor k i. Stress intensity factor sif of the crack is evaluated for. These unknown parameters can be determined from reference stress intensity factor and t. Weight functions and stress intensity factors for semi. Stress intensity factors for elliptical and semi elliptical cracks subjected to an arbitrary mode i loading. Crack tip stress dependence on the stress intensity factor k s y x w xy v yy v xx m u y r a s s s 3 yy 2 k x v s 2 yy 2 k x v s k 1 stress components, v ij, at the crack tip depend on the stress intensity factors k i which is influenced by.
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. Stress intensity factors for semielliptical surface cracks in. Variation of stress intensity factor and crack opening displacement of semi elliptical surface crack. The magnitudes of these stresses at a given point are entirely dependent on k. The analytical formula proposed by lukas and klesnil4 which was deduced from the numerical. A higher sif means larger stress pattern at the line of crack continuation axis x. Pdf stress intensity factor for a semielliptical crack subjected to. Weight functions and stress intensity magnification factors for elliptical and semi.
Stressintensity factors for semielliptical surface cracks under. Rajuan empirical stressintensity factor equation for the. In addition, a recent threedimensional fe study on the sif of a tshaped welded joint was reported in reference. Generally occurring surface crack is of semi elliptical shape. Weight functions for the surface and the deepest point of an internal longitudinal semi elliptical crack in a thickwall cylinder r i t 1 were derived from a general weight function and two reference stress intensity factors. In addition, the crack orientation was also changed, and the stress intensity factor was determined both analytically and numerically. This paper attempts to propose a weight function method to. The results reveal that the compressive loading cannot eliminate the branching process. Stress intensity factor calculations for semi elliptical surface cracks in round bars subjected to bending and torsion using a threedimensional finite element model are presented. Stress intensity factor, approximate method, semi elliptical cracks, multiple site damage 1. It is a theoretical construct usually applied to a homogeneous, linear elastic material and is useful for providing a failure criterion for brittle materials, and is a critical technique in the discipline of.
The aim of this article is to calculate stress intensity factors ki, kii and kiii along the semi elliptical crack front using the ansys code. Solution the application of the lefm to fatigue crack growth, through the range of stress intensity factor, varies from simple substitution into the relevant equations see the theory card, to rather complex. Improved formula for the stress intensity factor of semielliptical surface cracks in welded joints under bending stress. Stress intensity factor sif of the crack is evaluated for friction and traction force by varying the speed of the train. However, for plates with partly throughwall cracks, namely an semi elliptical crack with an imaginary crack depth a which is greater than the thickness t of the plate, the stress intensity factor was not reported.
Thus a complete stress intensity factor formula for the hoop wrapped cylinder can be written as 7 to verify above equation, a specific case is calculated for the hoop wrapped cylinder with an axial crack. The formula can be divided into the following two parts. By definition the stress concentration factor, k t, is the ratio of the maximum stress at the hole to the nominal stress at the same point. Department of transportation federal aviation administration. Stress intensity factor k stresses in the vicinity of the crack tip are dependent on r, and k. The effect of the weld toes in welded joints is considered using a weld toe magnification factor m k, and the scf equations are. K is called a stress field parameter, or stress intensity factor. The correction factor decreases with the larger ratio ab and the lower value of 2cb. Pdf stress intensity factor for a semielliptical rail. Stress intensity factors for semielliptical surface cracks in pressurised cylinders using the boundary integral equation method.
The complex loading conditions in rails induce stress and deformations in the material which keep on accumulating and evolve to rolling contact fatigue rcf cracks as soon as ductility exhaust. The stress intensity factor of a semi elliptical crack in a tshaped welded joint. Improved formula for the stress intensity factor of semi. Stressintensity factors for semielliptical surface cracks under tension or bending.
Rather than deal with giant stress concentrations, fracture mechanics uses a stress intensity factor, k. Calculating stress intensity factors for a semielliptical surface crack. In this report, we emplo the domain integy ral method to obtain the mode i stress intensity factor distributions for elliptical and straight cracks emanating from a centrall located countersunk y rivet hole in a square plate subjected to remote tension. Lets say we have within a structural member an elliptical hole of major axis 2a with radius of curvat.
Stress intensity factor equations for partelliptical cracks and their. This represents the effective local stress at the crack tip. The sif results in reference were used to further validate the accuracy of the modified formula. The exact analytical sif solutions for an elliptical crack were obtained only for some particular cases of polynomial applied stress fields. The stress intensity factor is generally expressed in the form k y. Weight function method to determine stress intensity factor for semi elliptical crack with high aspect ratio in cylindrical vessels. Stress intensity factors for a semielliptical surface. The problem is, from a diagram i have, it seems the first one is the quarter elliptical corner crack and the latter is the edge. How can i calculate the stress intensity factor of semi. Here, we consider a semi elliptical crack located in such a way that its major axis is perpendicular to the rail axis and minor axis is in the depth direction. K is not to be confused with the elastic stress concentration factor k t. For several linear and nonlinear crack face stress, fields, the weight functions were validated against finite element data.
First consider a conventional strength of materials approach. However, the cracked pressure vessel problems that have been solved so far require that the stress field around the semielliptical crack varies only throughthethickness of the vessel, but is constant along the axial and circumferential coordinates of the cylindrical shell. And in the limit, it applies to an ellipse flattened to form a crack. Stress intensity factors for surface semielliptical crack in. Stress intensity factors for surface semielliptical crack. Shin cs, cai cq 2004 experimental and finite element analyses an stress intensity factors of an elliptical surface crack. It is found that when the embedded depth is 4 times larger than the minor semi axis of the ellipse, the weld surface effects on the crack can be neglected and the numerical solutions for the stress intensity factors well agree with the analytical ones. Weight function method to determine stress intensity factor. Fracture analysis is widely used to predict component failure caused by preexisting small cracks, allowing one to take precautions to prevent further crack growth or to determine the remaining life of the structure. 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. A stress intensity factor sif which includes this effect increases the accuracy of fatigue lives prediction. This paper considers mode i stress intensity factors for a tshaped geometry, representative of one flange and part of the web of a steel 1section, which contains a flat semi elliptical surface crack in the flange. Fonte md, ereitas md 1499 stress intensity factor for semi elliptical sdce cracks in round has under bending and torsion. Apr 11, 2016 stress intensity factor pge 334 reservoir geomechanics.
Considering the stress intensity factor of cracks that emanate normal to the loading direction, so far no closedform solution is available. The stress intensity factors are presented for the deepest and surface points for semi elliptic cracks with aspect ratios of 005 and 01, and values of 02, 05, and 08. Several researchers, however, have provided numerical results. In present study stress intensity factors for semi elliptical surface cracks is based on 3d finite element analysis, taking into account the two critical angular. The stress intensity factor for cracks emanating from a notchtip, fig. Today, it is the critical stress intensity factor k ic, found in the plane strain condition, which is accepted as the defining property in linear elastic fracture mechanics. The weight function method is an efficient technique to calculate the stress intensity factors using uncracked stress field. For small semi elliptical cracks the maximum value of stress intensity is in point a and the correction factor is approximately equal to 1. Pdf stress intensity factors for circumferential semi. The examples in this section aim to illustrate this variety.
Therefore there is no need to derive ready made stress intensity factor for each load system and resulting internal stress distribution. I want to model a 2d crack in material and calculate stress intensity factor in abaqus software. Modified stress intensity factor equations for semielliptical surface. This high stress concentration reduces fatigue lives of welded structures. 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. Comparison of stress intensity solutions for a crack at an edge notch in a semi infinite plate a ab 12, b ab 1 and c ab 2.
Sep 01, 20 read weight function method to determine stress intensity factor for semi elliptical crack with high aspect ratio in cylindrical vessels, engineering fracture mechanics on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. Stress intensity factor for a semielliptical crack subjected to an. The objective is to calculate the stress intensity factor sif of a longitudinal semi elliptical crack on the wall of an aluminum cylinder with fgm. Oct 01, 20 read stress intensity factor of semi elliptical 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. Stress intensity factor of semielliptical surface crack in. Pdf stress intensity factors and weight functions for. Computation of the stress intensity factor ki for external. Calculation of the stress intensity factors for elliptical.
The y term allows the effects of finite width, crack shape, position along crack front, bulging, stress concentration factors, local stress concentration. If the crack is located centrally in a finite plate of width and height, an approximate relation for the stress intensity factor is. Stress intensity factor sif is a measure of stress intensity in the crack tip. Pdf stress intensity factor calculation for semielliptical cracks on. Semi elliptical cracks at notches the fatigue cracks emanating from notches are most often semi elliptical. In the present work the exact analytical sif solution has been obtained for an elliptical crack embedded in an infinite elastic body and subjected to an arbitrary applied normal stress field mode i.
The weight function method is an efficient technique to calculate the stress intensity factors using uncracked stress. Improved formula for the stress intensity factor of semielliptical. Stress intensity factor of semielliptical surface crack in a. Evaluation of stress intensity factor for semi elliptical and quarter. If the weight function is known for a given cracked body, the stress intensity factor due to any load system applied to the body can be determined by using the same weight function. Hi, i just wanted some clarification with respect to a few equations relating stress intensity factor to semi elliptical and quarter elliptical cracks in solids. Weight functions and stress intensity factors for semielliptical cracks in tplate welded joints. Calculation of sifs for semielliptical surface cracks in. Paper open access stress intensity factor for a semi. Modified stress intensity factor equations for semielliptical. Weight functions for the determination of stress intensity.
The stress intensity factor is calculated for a given geometry and load, and compared with a threshold value of k above which cracks will propagate in the given material. This method is used to derive the weight functions for both k and t for semi. Therefore, the weight functions for the point a and b have been derived analogously to. In order to calculate the fatigue life of cylinders subjected to internal pressure using the fracture mechanics approach, the stress intensity factors sifs for internal semi elliptical cracks are needed. Calculation of stress intensity factors and crack opening a. Stress intensity factors for elliptical and semielliptical. Stress intensity factors for surface cracks in round bar. There are various stress intensity factor solutions, particularly for flat plates and pressure vessels with various cracked geometries. This result can be used to distinguish a shallow embedded crack from a deep embedded crack. Stress intensity factors along threedimensional elliptical crack fronts may 1998 final report this document is available to the u.
The relation between m f and the semielliptical shape ac, the relative crack depth ab, the variation of angle. Stress intensity factor of a wide range of semielliptical. Pdf weight functions and stress intensity factors for semi. If the crack is not located centrally along the width, i. Mixedmode stress intensity factors at the surface and deepest points of quarter elliptical corner cracks in mechanical joints such as bolted or riveted joints are analyzed by weight function method. Dotfaaar95111 stressintensity factors for elliptical. This page provides stress intensity factor solutions for common cases. A uniform stress and a linear stress distribution were used as the two references to determine the weight functions. View semi elliptical corner crack at the interface of the. The correction factor m f of sif at different point along the front of the crack is determined. Calculation of sifs for semielliptical surface cracks in u.
That is, since the nominal stresses and the peak stress at the edge of the hole, are all uniaxial. Stress intensity factor equations for internal semi. The stress intensity factor sif of the semi elliptical surface crack in the finite body under extensional stress is sclculated by using the fem software ansys release 5. The defect studied in this survey has a form of a longitudinal semi elliptic crack, located on. Weight functions and stress intensity magnification. K is not to be confused with the elastic stress concentration factor. Stress intensity factors for semielliptical surface cracks ac 0. A magnification factor is commonly used to multiply the sif of semi elliptical surface cracks to account for the stress concentration effect in welded connections. The configuration of the semi ellipse follows the equation b 2 s.
However, in most practical cases the deepest point a fig. Modified stress intensity factor equations for semi. The generalpurpose finite element code abaqus is used in this study to obtain the stress fields of the hoopwrapped composite cylinder and the stress intensity factor along the semi elliptical crack front. Stress intensity factor analysis of elliptical corner. In this investigation, the weight function method was employed to calculate stress intensity factors for semielliptical surface crack in a hollow cylinder. Stress intensity factor of symmetric cracks emanating from the elliptical hole. 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 relation between m f and the semi elliptical shape ac, the relative crack depth ab, the variation of angle. Introduction three dimensional cracks such as a surface or.
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