Saeidi googarchin mechanical properties research laboratory mprl, department of mechanical engineering, k. Alan arnold griffiths energybased analysis of cracks in 1920 is considered to be the birth of the field of fracture mechanics 1. In service fatigue cracks are detected in a disk and blade dovetail type attachment. Calculation of stress intensity factors and crack opening. Stress intensity factors for near surface cracks by boundary collocation shawqi mohammad suleiman. The boundary element method is applied to calculate the stress intensity factors of a surface crack in the rotating inner raceway of a highspeed roller bearing. Determine the stress intensity modification factor k ik 0 for the actual geometry that you have. Multiply k 0 by k ik 0 to get k i, the actual stress intensity.
This page provides stress intensity factor solutions for common cases. The previous methods allow the calculation of the sif k in a many simple cases. On the base of this attachment dimensions and with taking into account the biaxial loading conditions of rotating compressor disk the two geometries of imitation model of gas. Stress intensity factors for near surface cracks by boundary collocation 1986. The elastic and plastic stress intensity factors used for the representation of the experimental results are computed by using fullsize 3d finite element analysis of the imitation models with surface quarter elliptical and throughthickness cracks. A procedure has been developed to calculate the stress intensity factors from the displacements along any arbitrary crack tip radial line on a quarterpoint singular finite element boundary. The crack initiation period is followed by the fatigue crack growth period, recall figure 2. Stress intensity factors for a wide range of nearly semielliptical surface cracks in pipes and rods are presented. The surface cracks were oriented on a plane normal to the axis of pipes or rods. Proceedings of the asme 2015 pressure vessels and piping conference. Minimize crack size a and maximize radius of curvature r t if crack is. Approximate determination of stress intensity factor for. The k factor values were calculated only at one point of the crack front, where the crack tip contacts the free surface, because the crack length during experimental investigations was measured just in this direction. Comparison of the stress intensity factor influence.
Stress intensity factors for mixedmode crack growth in. Comparison of the stress intensity factor influence coefficients for axial id surface cracks in cylinders of rsem and api 5791. The threedimensional model consists of an axially stressed surface cracked plate subjected to a moving hertzian contact loading. Note that the stress concentration factor is a function of the geometry of a crack, and not of its size. The stress intensity factor k i equations in asme section xi, appendix a are based on nondimensional coefficients g i that allow for the calculation of stress intensity factors for a cubic varying stress field for a surface crack, and linear varying stress field for a sub surface crack. Abstract this paper numerically discusses stress in tensity factor sie calculations for surface cracks in round bars subjected to single and combined loadings.
Energybalance approach griffith, 1921 actual fracture strength in most materials are significantly lower than expected from bond strengths. It uses methods of analytical solid mechanics to calculate the driving force on a crack and those of experimental solid mechanics to characterize the materials resistance to fracture in modern materials science, fracture mechanics is an important tool used to improve the. Improved formula for the stress intensity factor of semi. The stress intensity is given as stress kiy sqrtc where c is flaw depth and y 1. Stress intensity factors sifs can be calculated in the nuclear electrics r6 code software1 and other computer programs. The stress intensity, k i, represents the level of stress at the tip of the crack and the fracture toughness, k ic, is the highest value of stress intensity that a material under very specific planestrain conditions that a material can withstand without fracture. 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. Stress intensity factor of semielliptical surface crack in. However, due to the complexities of the nature of the surface crack problem, closed form solutions are not possible, and a numerical or an experimental approach must be used to determine the stress intensity factors for surface cracks. As the stress intensity factor reaches the k ic value, unstable fracture. Stress intensity factors calculation for surface crack in cylinders under longitudinal gradient pressure using general point load weight function h.
Fracture accidents of porcelain post insulator at lower stress level indicates that critical stress is not good enough to estimate the mechanical strength. Calculation of sifs for semielliptical surface cracks in. The opening mode stress intensity factor can always be expressed as ki. Raju 2 summary stress intenslty factor equations are presented for an embedded elliptical crack, a semielllptlcal surface crack, a quarterelllptlcal corner crack. Semielliptical surface cracks in welded joints under. Engineers are interested in the maximum stress near the crack tip and whether it exceeds the fracture toughness. Stress intensity factors for near surface cracks by. Normalized modei stress intensity factors sifs are presented for a wide practical range of tangential surface cracks contained in rotating hollow disks. Residual stress stress intensity factor surface crack nodal point residual stress field. 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. For edge cracks, a is the whole length of the crack. Stress intensity factor calculation of surface crack on porcelain post.
An accurate value for the threshold stress intensity factor range. The y term allows the effects of finite width, crack shape, position along crack front, bulging, stress concentration factors, local stress concentration due to. In order to determine the stress intensity factors for different crack sizes, ten diverse flaws in the blade were defined. Stress intensity factors for surface cracks in round bar. The stress intensity factor is generally expressed in the form k y. Abstract stress intensity factors for circumferential surface cracks in pipes have been derived using the finite element method.
The accuracy of the stress intensity factor calculation is satisfactorily examined for rectangular, pennyshaped and elliptical planar cracks. 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. Pdf it is common practice to calculate stress intensity factors for surface cracks in pipeplatetubular joints using stress intensity factor. 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 damage tolerance. Threedimensional stress intensity factor analysis of a. The stress intensity factor describes the stress state at a crack tip, is related to the rate of crack growth, and is used to establish failure criteria due to fracture. The stress intensity factor distributions along the crack front for various surface cracks ac 0. Stress concentrations around notches were considered in chapter 3 with the stress concentration factor k t as an important parameter for characterizing the severity of the stress distribution around the notch. Technical basis for equations for stress intensity factor.
This paper presents stress intensity factor influence coefficients sifics for axially and circumferentially oriented finitelength semielliptical inner surface flaws with aspect ratios total. These factors can be found in typical engineering reference materials to predict the stresses that could otherwise not be analyzed using strength of materials approaches. This work presents stress intensity factors for a wide range of semielliptical surface cracks on the inside of pressurized cylinders. If shear lips are created at the surface of the material, see figure 2. Stress intensity factors for partthrough surface cracks. The derived solutions cover a wide range of geometry and load configurations and are presented in a tabular form that defines influence functions for the stress intensity factor along the. Thus, the stress intensity factor k is commonly expressed in terms of the applied stresses at and.
Rice the partthrough surface crack in an elastic plate. These keywords were added by machine and not by the authors. Stress intensity factors calculation for surface crack in. Introduction three dimensional cracks such as a surface or. Stress intensity factors calculation by program sifbbc 51 g. Fem is used to compute the stress intensity factors at. Abstract general point load weight function gplwf for a longitudinal semi. Stress intensity factor equations are presented for an embedded elliptical crack, a semielliptical surface crack, a quarter elliptical corner crack, a semielliptical surface crack along the bore. The stressintensity factors used to develop the equation were obtained from a previous threedimensional, finiteelement analysis of semielliptical surface cracks. The ratio of crack depth to crack length ranged from 0. If stress intensity is less than critical stress intensity factor, kic.
Governing parameters are aspect ratio, depth and radial coordinate of the crack and ratios of disk radii and thickness. Currently, the coefficients are in tabular format for the case of a surface crack in a flat plate geometry. Therefore there is no need to derive ready made stress intensity factor for each load system and resulting internal stress distribution. Back plot fringe data generation by program cmfr 54. When the cracks are three dimensional, such as corner or surface. Calculate the stress under point load with no crack use a book like roark for this. The crack initiation life is highly dependent on the k tvalue.
Analysis of stress intensity factors for surface cracks. Pdf stress intensity factors for internal surface cracks. Stress intensity factor k for 3d cracks through crack front crack surface crack corner crack the through cracks, with a well defined crack front, are usually treated as a twodimensional problem. Stress intensity factors calculation for surface crack in cylinders. In this study a procedure to stress intensity factors calculation for imitation models made of titanium alloy is described. Stress intensity factors for tangential surface cracks in. An empirical stressintensity factor equation for the surface crack. This equation derives from analysis of an infinite plate, but is used for all configurations. Stress intensity factors for circumferential surface.
The values obtained for pressure load are normalized according to the sif value of a surface crack contained in an. Irwin arrived at the definition of \k\ as a near crack tip approximation to westergaards complete solution for the stress field surrounding a crack 2. Nearthreshold fatigue crack propagation without oxide. Accurate and fast evaluation of the stress intensity factor for planar cracks shows the proposed procedure is robust for sif calculation and crack propagation purposes. Stress intensity factor evaluation from displacements along arbitrary crack tip radial lines for warped surface flaws. Pdf on the calculation of stress intensity factors for surface cracks. The solution technique for multiple cracks in an infinite body has recently been developed by. The calculation of stress intensity factors for surface cracks in tubular joints is very important in fatigue life prediction, fracture assessment, and stress corrosion cracking analysis of those components. This is not to be confused with stress intensity factor.
This process is experimental and the keywords may be updated as the learning algorithm improves. In this equation, s is the remote loading stress, a is the crack length, and. 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. Pdf stress intensity factors for circumferential surface. The configurations were subjected to either remote tension or bending loads. Stress intensity factor evaluation from displacements. In the parametric study, the effects of the ratio of the surface crack depth to length ranged from 0. He was motivated by ingliss linear elastic solution for stresses around an elliptical hole 2, which predicted that the stress level approached infinity as the ellipse flattened to form a crack. On the calculation of stress intensity factors for surface. K th, is a key parameter for studying crack like defects. Fracture mechanics is the field of mechanics concerned with the study of the propagation of cracks in materials. Stress intensity factor calculations for the compressor.
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