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. Crack opening displacements and stress intensity factors are also obtained for a throughthickness, center cracked bar with variable. Stress intensity factor for a semielliptical crack. Here, we consider a semielliptical crack located in such a way that its major axis is perpendicular to the rail axis and minor axis is in the depth direction. Domarkas stanford university stanford, california 94305 abstract the reflection coefficient of a rayleigh wave at a surface crack is measured in both the long wave. The stress intensity factors k 1 calculated by extrapolation from stresses and displacements and by the energy release rate agree well within a tolerance of about 10%. The real stress concentration at the weld toe is characterized by the notch stress concentration factor, k s, and it is defined as 11 k s. Stress intensity factor for semielliptical sdce cracks in round has under bending and torsion. Stress intensity factors for toe cracks or root faces in welded joints are only rarely. Hence, there is a great need to determine the stress intensity factor in cracked shafts by using finite element method.
A detailed description of the hybridrdisplacement finite element procedure for 3d crack analysis can be found in references 6, 7. Read general point load weight function for semielliptical crack in finite thickness plates, engineering fracture mechanics on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. General point load weight function for semielliptical crack. The paper includes an initial parametric study and discussion of k ivalues calculated for a number of semielliptical, surfacecrack geometries in. Stress intensity factors for elliptical and semielliptical. Using the obtained displacement field, normal stresses and the stress intensity factor variation along the crack periphery are calculated for different crack depth to bar thicknessratios.
The stress intensity factor of a semielliptical crack in a tshaped welded joint. Stress intensity factor for a semielliptical crack subjected to an. Improved formula for the stress intensity factor of semi. 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. 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. However, in most practical cases the deepest point a fig.
Therefore, the weight functions for the point a and b have been derived analogously to. Crack opening displacement for an embedded elliptical crack. To compute the stress intensity factor, i added the stress from elementary beam theory evaluated at the crack plane to the seewald stress correction term eq. For semielliptical surface cracks, the stress intensity factor solutions should be.
Stress intensity factors for elliptical and semielliptical cracks subjected to an arbitrary mode i loading. Stress intensity and crack displacement for small aedge cracks. Formulation of a problem of a surface semielliptical crack in a semiinfinite body 3. Paper open access stress intensity factor for a semi.
Fracture mechanics analysis of a pressure vessel with a semi. In solving the integral equations, the unknown functions of body force densities are approximated by the product of a polynomial and a fundamental density function. Variation of stress intensity factor and crack opening displacement of. Stress intensity factor for semielliptical surface cracks. Computation of the stress intensity factor ki for external. Fracture mechanics analysis of a pressure vessel with a. Then i computed the crack mouth displacement by substituting the stress intensity factor and the weight function into equation 5.
Sep 01, 20 read general point load weight function for semi elliptical crack in finite thickness plates, engineering fracture mechanics on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. Variation of stress intensity factor and crack opening displacement of semielliptical surface crack article pdf available in international journal of fracture 751. Stress intensity factor sif of the crack is evaluated for. Calculation of stress intensity factors for a crack subjected to a complex stress. To be able to apply the method of petroski ana achenbach8, we replace the semi elliptical crack by an edge crack which, for the reference load, has the reference stress intensity factor of the semi elliptical crack at its deepest point. The stress field induced by a body force doublet in an infinite body is used for a fundamental solution. Stress intensity factor for semielliptical surface cracks loaded by. The aim of this article is to calculate stress intensity factors ki, kii and kiii along the semielliptical crack front using the ansys code. Aem 535 hw10 jcontour for lefm stress intensity factors. 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. Calculation of stress intensity factors and crack opening. Stress intensity factors for axial semielliptical surface cracks and. Pdf a method for calculating stress intensity factors for edge and surface cracks.
In solving the integral equations, the unknown functions. Generally occurring surface crack is of semi elliptical shape. Figures 11 and 12 shows stress intensity factors obtained by several investigators for a semi elliptical surface crack in a finitethickness plate. Acknowledgements the authors gratefully acknowledge the financial support from the natural sciences and engineering research council of canada nserc. New displacementcontrolled surface crack in center of a plate sc33. This paper presents the application of the weight function method for the calculation of elastic t stress for semi elliptical surface cracks. Shin cs, cai cq 2004 experimental and finite element analyses an stress intensity factors of an elliptical surface crack in a circular shaft under tension and bending. Stress intensity factor for a semielliptical crack subjected. Stress intensity factor, approximate method, semi elliptical cracks, multiple site damage 1. In the present analysis, a planar triangular element is used to cover the total crack face. The variations of the stress intensity factor k of the jintegral and of the crack tip opening displacement ctod along the crack front are presented and discussed. Weight functions and stress intensity factors for internal surface semi.
Stressintensity factors for a wide range of semielliptical. Dynamic stress intensity factors for a longitudinal semi. Variation of stress intensity factor and crack opening displacement of semi elliptical surface crack. The sifs for a surface crack in the misaligned butt weld are magnified by the presence of notch stress at the weld toe, especially for shallow cracks. If the crack is not located centrally along the width, i. In this study, an improved technique for the evaluation of stress intensity factor sif along the 3d planar crack front is proposed. On the calculation of crack opening displacement from the stress. This paper presents the application of the weight function method for the calculation of elastic tstress for semielliptical surface cracks. Evaluation of stress intensity factor for semi elliptical and quarter. Stress intensity factors for semielliptical surface. Stress intensity factor for cracks emanating from a shaft.
It was derived by the approximate solution valid for an embedded elliptical crack in infinite body, and a suitable corrective function to account for the free surface effect was obtained on the basis of several accurate stress intensity factor solutions found in literature. Weight function for a semielliptical surface crack in a finite thickness plate theor. Weight functions for tstress for semielliptical surface. Variation of stress intensity factor and crack opening displacement of semielliptical surface crack. Variation of stress intensity factor and crack opening. Calculation of stress intensity factors and crack opening displacements for cracks subjected to complex stress. In addition, a recent threedimensional fe study on the sif of a tshaped welded joint was reported in reference. Influence of flaw shapes on stress intensity factors for. The stress intensity factor of semielliptical axial cracks lying at the.
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. The calculation shows that the present method gives the smooth variation of stress intensity factors along the crack front and crack opening displacement along the crack surface for various aspect ratios and poissons ratio. Read calculation of stress intensity factors for semielliptical cracks in a thickwall cylinder, 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. Here, mi is defined as the multiple of the stress intensity factor of the elliptical crack. A three dimensional finite element technique for nonhomogeneous elastic solids is used to solve the problem and the displacement correlation technique is used to. Approximate determination of stress intensity factor for. Figure 11 shows the results for a surface stressintensity factors of semielliptical surface cracks in finitethickness plates 825 2,0 1. 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. For several linear and nonlinear crack face stress, fields, the weight functions were validated against finite element data. The stress intensity factors derived are suitable for the analysis of semielliptical surface cracks in flat plates with fixed displacement boundary conditions. Apr 01, 2017 stress intensity factor determination for double edge cracked plate with abaqus using j contour integral, comparison to accepted solution.
The crack opening displacement for the reference problem is calculated with a method proposed by petroski and achenbach. There are other combinations for example nominal stresscrack length that also give the same. 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 semi analytically. Munzstress intensity factor at the surface and at the deepest point of a semielliptical surface crack in plates under stress gradients. Stress intensity factor of a wide range of semielliptical. To be able to apply the method of petroski ana achenbach8, we replace the semielliptical crack by an edge crack which, for the reference load, has the reference stress intensity factor of the semi elliptical crack at its deepest point. Stressintensity factor an overview sciencedirect topics.
This weight function approach is applied to a semi elliptical crack at blade mounting locations by considering the stresses. On the calculation of crack opening displacement from the stress intensity factor engng fracture. A displacement correlation technique provides pointwise stressintensity values along semielliptical surface cracks in fgms for comparison with values derived from the proposed domain integral. The problem is solved for a semicircular crack front and various crack inclination angles. Stressintensity factors for surface cracks in functionally. For plates with semi elliptical surface crack, newman, raju and kou have reported the stress intensity factor. General point load weight function for semielliptical. Stressintensity factors of semielliptical surface cracks in finitethickness plates 819 this model idealizes one eight of the body. Shim calculated the stress intensity factor ki in mode i using the xfem for various types of plate and pipe cracks.
For plates with semielliptical surface crack, newman, raju and kou have reported the stress intensity factor. Finite element investigation of stress intensity factors. Various numbers of wedges were used to form the desired configuration. In table 9 the values of mi 0, 0 are tabulated for various aspect ratio and poissons ratio. Generally occurring surface crack is of semielliptical shape. In this paper, we use the weight function for an elliptical crack embedded in an infinite elastic media in conjunction with the alternating method to derive the exact analytical solution for the stress intensity factor for a semi elliptical surface crack subjected to an arbitrary mode i loading. Ac kn, as kn coefficients of expansion of crack opening displacement wr. The paper includes an initial parametric study and discussion of k ivalues calculated for a. Stress intensity factors for elliptical and semielliptical cracks.
Stress intensity factors for elliptical and semi elliptical cracks subjected to an arbitrary mode i loading. First, the weight function method for the calculation of t stress previously developed for twodimensional crack problems was extended for the t stress calculation for threedimensional crack problems. The results reveal that the compressive loading cannot eliminate the branching process. Stress intensity factors for surface semielliptical crack in. Finite element investigation of stress intensity factors of. Crack opening displacement for an embedded elliptical crack 5.
Department of transportation federal aviation administration. Figure 27 shows crack opening displacement of semielliptical surface crack on the free surface uz x, 0 in comparison with an elliptical crack. The sif results in reference were used to further validate the. Introduction three dimensional cracks such as a surface or. Shin cs, cai cq 2004 experimental and finite element analyses an stress intensity factors of an elliptical surface crack in a circular shaft under tension and. Weight functions for the surface and the deepest point of an internal longitudinal semielliptical crack in a thickwall cylinder r i t 1 were derived from a general weight function and two reference stress intensity factors. The sif results in reference were used to further validate the accuracy of the modified formula. Pdf stressintensity factors for semielliptical surface cracks in. Pdf variation of stress intensity factor and crack. Calculation of stress intensity factors for semielliptical. Stress intensity factors along threedimensional elliptical crack fronts may 1998 final report this document is available to the u. 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. Improvement of stress intensity factor analysis using overall.
To obtain a good representation of the cracktip quarterpoint. Crack opening displacements and stress intensity factors are also obtained for. Stress field induced by body force doublet in a semi infinite body is used as a fundamental solution. Stress intensity factors for surface semielliptical crack. Figures 11 and 12 shows stressintensity factors obtained by several investigators for a semielliptical surface crack in a finitethickness plate. Thus, at a given location on the crack front the crack propagation rate would be a function of the mode i stress intensity factor. The displacement extrapolation method is based on the nodal displacements around the crack tip. Dynamic stress intensity factors for a longitudinal semielliptical. Pdf variation of stress intensity factor and crack opening. In this paper, we use the weight function for an elliptical crack embedded in an infinite elastic media in conjunction with the alternating method to derive the exact analytical solution for the stress intensity factor for a semielliptical surface crack subjected to an arbitrary mode i loading. Figure 11 shows the results for a surface stress intensity factors of semi elliptical surface cracks in finitethickness plates 825 2,0 1. Weight functions and stress intensity factors for internal surface semielliptical crack. A three dimensional finite element technique for nonhomogeneous elastic solids is used to solve the problem and the displacement correlation technique is used to calculate the stress intensity factor. For several linear and nonlinear crack face stress, fields, the weight functions were validated against finite.
Calculation of stress intensity factors and crack opening a. The coefficients of these functions are determined assuming piece wise polynomial stress distribution along the crack. Stress intensity factor, approximate method, semielliptical cracks, multiple site damage 1. Then the problem is formulated as an integral equation with a singularity of the form of r 3. The stress intensity factor of a semi elliptical crack in a tshaped welded joint.
Pdf stress intensity factor for a semielliptical crack subjected to. Stress intensity factors for surface cracks in round bar. Application to thermal shock problems as an example for the application to stress gradients, a thermally shocked pipe is considered with a surface crack in the longitudinal direction. 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. Semielliptical surface cracks in finitethickness plates. An explicit weight function for semielliptical surface. Stress intensity factors for surface semi elliptical crack in cylindrical specimen under combined torsion and axial compression p. If the crack is located centrally in a finite plate of width and height, an approximate relation for the stress intensity factor is. 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.
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