A list of the critical stress intensity factors fracture toughness for common materials. For the case of a penny shaped crack situated in an infinite isotropic medium with the crack faces subjected to arbitrary tractions, the integral equations are solved explicitly. Theterm fracture mechanicsreferstoavitalspecializationwithinsolidmechanicsinwhichthepresenceofacrack. The use of these formulae is illustrated by a consideration of the special. The effective stiffness of a solid containing soarrays of equal pennyshaped cracks was determined by nematnasser et al. It has been revealed that the dynamic stress concentration factors for a small circular hole and a small spherical cavity and the dynamic stress intensity factor for a penny shaped crack are almost the same as those at low. Stress intensity factors for a penny shaped crack in a.
The paper discusses stress intensity factors for two thermal shock problems in transversely isotropic cylinders which contain either an external annular crack or a pennyshaped crack. Stress intensity factor coplanar pennyshaped crack periodic array interacting cracks abstract the effect of crack interactions on stress intensity factors is examined for a periodic array of coplanar pennyshaped cracks. Rather than deal with giant stress concentrations, fracture mechanics uses a stress intensity factor, k. Fracture mechanics assessment of large diameter wind. Investigated are the effects of material property parameters and geometry criterion on the stress intensity factor. A mathematical formulation is presented for the dynamic stress intensity factor mode i of a permeable pennyshaped crack subjected to a timeharmonic propagating longitudinal wave in an infinite poroelastic solid.
Fatigue crack growth, fatigue, and stress corrosion crack growth. Pdf the stress intensity factors for a periodic array of. Stress intensity factor and effective stiffness of a solid contained aligned penny shaped cracks article in international journal of solids and structures 37. This represents the effective local stress at the crack tip. The critical stress intensity factors k c for some engineering materials are grouped in the following categories. Indentation of a pennyshaped crack by an oblate spheroidal. The effect of the elasticity of the materials in the vicinity of the layer on the stress intensity factor was examined by arin and erdogan 1971. The geometric model of a cracked body is a spatially periodic medium whose unit cell contains a number of arbitrarily placed aligned circular cracks. This is applicable to cracks under plane stress, plane strain, and antiplane shear.
The stress intensity factors for a periodic array of. An axisymmetric problem for a pennyshaped crack bridged by fibres is considered. The effect of crack interactions on stress intensity factors is examined for a periodic array of coplanar pennyshaped cracks. This paper presents a threedimensional viscoelastic model to study the interactions of a penny shaped interfacial crack and a center of dilatation in the infinite viscoelastic bimaterial, which can model the rock fracture subjected to stress and thermal dilatation during some engineering process. Effect of test frequency on fatigue strength of low carbon steel. Results and discussion the results for the tests conducted on base metal specimens are shown. Based on the mixed mode dugdale model and the accumulated plastic displacement criterion for crack growth, a fatigue crack growth equation with fourpower effective stress intensity factor dependence is developed for a penny shaped crack under conditions of mixed mode loading and smallscale yielding. An expression for the surface displacement of the crack is also given. The line load solution which is derived from this is different in form to those given by previous workers and is more. By the use of ansys 16, stress intensity factor was estimated under different crack width conditions. An expression is developed for the stress intensity factor of a pennyshaped crack in an infinite elastic solid subjected to nonaxisymmetric normal loading. The energy release rate is directly related to the stress intensity factor associated with a given twodimensional loading mode modei, modeii, or modeiii when the crack grows straight ahead. Stress intensity factors at any point on the crack front of penny and halfpenny shaped cracks subjected to stress gradients are presented. The stress intensity factors for a periodic array of interacting coplanar pennyshaped cracks huseyin lekesiza,1, noriko katsubea.
A method is proposed to treat numerical noise around the crack front kink and at crack front end. When the crack is expanding under a constant flow rate, the classical solution by sack is found to be approximately. 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. It is supposed that the pennyshaped crack is subjected to a pair of normal concentrated forcesp applied in opposite directions at the points. The distribution of normalized k i is shown in fig. For a penny shaped crack embedded within an infinite solid and loaded remotely perpendicular to the crack at a stress.
The stress intensity factor for an edge crack is given by. Online companion guide to the asme boiler and pressure vessel codes. In addition, normalized empirical expressions for stress intensity factors are proposed. In this work, it was found that with increase in crack width stress intensity factor increases. 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. In this section, we apply the approximate method of kachanov and laures 1989 to the analysis of interacting cracks to obtain the mode i sif of an array of periodic coplanar penny shaped cracks in an infinite medium subjected to a remote normal traction at infinity, figure 1 a. Formulation for the mode i stress intensity factor. Figures 24 illustrate the variation of the stress intensity factor at the crack tip due to variations in the localized elastic nonhomogeneity. Stress intensity factors determination for an inclined. The stress state and effective elastic moduli of an isotropic solid containing equally oriented penny shaped cracks are evaluated accurately. The structural integrity of large diameter wind turbine bearings have been investigated using the builtin contour integral tool in abaqus finite element software package by modeling threedimensional penny shaped cracks and evaluating the stress intensity factors. Pdf measurement of modei stress intensity factor for a.
N2 a threedimensional penny shaped crack under combined tensile and shear loadings is analyzed. Its size may be found from the condition that the crack must close smoothly at. The stress intensity factor can then be determined for pennyshaped cracks in infinite or finite solids subjected to symmetric loading about the plane containing the crack. 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 proposed methodology computes stress intensity factors along the crack front based on observed crack front shapes obtained from the experimental tests. Fracture mechanics of throughcracked cylindrical pressure. The stress intensity factor at the tip of a penny shaped crack of radiusthe stress intensity factor at the tip of a penny shaped crack of radius a in an infinite domain under uniaxial tension sigma view the full answer. Procedia materials science 3 2014 1279 1284 1283 the several k i distributions are normalized with f k i vsa 1 where v is the maximum remote stress due to bending loads and a is the crack length in the depth direction. T1 mixedmode fatigue crack propagation of pennyshaped cracks. Thiscritical stress intensity factor isthenameasureof materialtoughness. A torsional transient wave was assumed acting at infinity on the piezoelectric body with an embedded penny shaped crack. This paper considers the transient stress intensity factor mode i of a penny shaped crack in an infinite poroelastic solid. A method of successive approximation together with the fourier. The singular state associated with the embedded crack with finite, nonaxisymmetric normal loading is that of plane strain. A2, the stress intensity factor for a pennyshaped crack with diameter 2 a b d 2. Kachanovs approximate method for crack interactions kachanov, m. Stress intensity factors for external and pennyshaped.
There are various stress intensity factor solutions, particularly for flat plates and pressure vessels with various cracked geometries. The constants a, define the following stressstrain relationships in transversely isotropic bodies. Investigation of stress intensity factor of finite plate for. A distinct issue associated with the present work is the incorporation of viscoelastic. The stress intensity factor for a penny shaped crack between two dissimilar materials m. The stress intensity factor can then be determined for penny shaped cracks in infinite or finite solids subjected to symmetric loading about the plane containing the crack. Stress intensity factor and effective stiffness of a solid. The solution of some typical examples is given, and the significant effect of the stress intensity factor of the rock on the crack propagation is shown. This threepart mixed boundary value problem is solved using the techniques of triple integral equations. Citeseerx document details isaac councill, lee giles, pradeep teregowda. Stress intensity factors at any point on the crack front of penny and half penny shaped cracks subjected to stress gradients are presented.
The special case of a large crack subjected to mode. The lowest fracture toughness, k ic, for any steel under the most severe conditions is equal to about 25 ksi in the maximum applied stress was assumed to be equal to the tensile strength of the steel in the karea. The effects of the material anisotropy on the stress intensity factor and on the crack shape are investigated for a penny shaped crack in a transversely isotropic plate of finite thickness. Mixedmode thermal fracture of aisi 304 stainless steel with. The stress intensity factors were obtained using the j integral method. The thermal stress field is analyzed by means of the potential function method for transversely isotropic solids. In the former paper the analysis given applies to an axisymmetric distribution of pressure p. Local stress field for torsion of a pennyshaped crack in a. It is a theoretical construct usually applied to a homogeneous, linear elastic material and is useful for providing a failure criterion for brittle materials.
It is known that the fatigue strength of a cracked steel element depends on the stress intensity factor sif at the crack tip which is a function of the stress strain distribution of the. In particular integral formulae are obtained for the stresses on the plane of the crack beyond the crack tip, and hence for the stress intensity factors. Local stress field for torsion of a pennyshaped crack in. In practice, it is often replaced by a proxy such as the cmod.
A formula is derived for the stress intensity factor at the rim of a penny shaped crack in an infinite solid in which there is an axisymmetric distributing of body forces acting in a direction normal to the original crack surfaces. Previous question next question transcribed image text from this question. An analytical solution for the axisymmetric problem of a. 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. The study is reduced to the analysis of a hypersingular integral equation with respect to the relative crack face separation over a circular domain occupied by crack. Statement of problem and numerical analysis the numerical simulations were performed using franc3d wawrzynek et al. For a pennyshaped crack subjected to a normal loading, the shear tractions vanish in the plane zo, and eqn.
Unlike the energy release rates computed by the vcct, the stress intensity factors for interfacial cracks are convergent and not dependent on the virtual crack extension length mesh size a. The torsion of a penny shaped crack in a functionally graded strip is considered. 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. Fatigue crack growth rates were then plotted as a function of the stress intensity factor. Fracture mechanics assessment of large diameter wind turbine. The stress intensity factor is very difficult to measure. The pennyshaped crack at a bonded plane with localized. Radio frequency identification applications in pavements. The stress intensity factors k i and k ii for an inclined central crack on a plate subjected to uniform tensile loading were calculated for different crack orientations angles using finite element fe analysis, which was carried out in abaqus. Crack front shapes and stress intensity factors in plates. A method of successive approximation together with the fourier integral and the bessel series are.
Stress intensity factor is maximum at the open ends while it is minimum at the center. Dynamic stress intensity factor mode i of a pennyshaped. The sifs which are exact for a penny shaped crack are based on the well known solution for a point load acting normally to such a crack. The assumptions of dugdale are applied to estimate the effects of plasticity around the edge of the crack. The structural integrity of large diameter wind turbine bearings have been investigated using the builtin contour integral tool in abaqus finite element software package by modeling threedimensional pennyshaped cracks and evaluating the stress intensity factors. The crack tip stress field is obtained by considering the asymptotic behavior of bessel function. Seghic a department of mechanical and aerospace engineering, the ohio state university, columbus, oh, usa bdepartment of materials science and engineering, the ohio state university, columbus, oh. Crack propagation behavior in type 304 stainless steel. A formula is derived for the stress intensity factor at the rim of a pennyshaped crack in an infinite solid in which there is an axisymmetric distributing of body forces acting in a direction normal to the original crack surfaces. The interface pennyshaped crack reconsidered 169 where 41 42 it can be shown that kw,g has the following property we note that in the present form the size of the contact region, l a, is not yet determined. Dynamic stress intensity factor mode i of a permeable. Stress intensity factors for penny and halfpenny shaped. Pdf stressintensity factor equations for cracks in. For a variety of loadings, fabrikant 1990 has derived new single crack solutions in elementary functions.
A steel plate welded joint 1 formed by buttwelding steel plates 2, 2 in which brittle crack arresting properties kca of at least a part of the area of a base metal are 4000 nmm1. Jul 19, 20 figure 11 shows the normalised stress intensity factor k i. Stress intensity factor for cracks emanating from a shaft. Hankel transform is used to reduce the problem to solving a fredholm integral equation. The stress intensity factor for a pennyshaped crack in an.
In his study, the frequencydependent behavior of the dynamic stress intensity factor exhibits excellent agreement with that for the dry crack in an ordinary elastic medium chen and sih. Threedimensional viscoelastic interactions of a center of. In his study, the frequencydependent behavior of the dynamic stress intensity factor exhibits excellent agreement with that for the dry crack in an ordinary elastic medium chen and sih, 1977. Appropriate governing equations and boundary conditions have been built within the threedimensional electroelasticity. An expression for the stress intensity factor has been found by cherepanov 1974, a result which was generalized for a nonhomogeneous body by sankar and fabrikant 1983 a. Request pdf on jan 23, 2017, yongjia song and others published dynamic stress intensity factor mode i of a permeable penny shaped crack in a fluidsaturated poroelastic solid.
Mixedmode fatigue crack propagation of pennyshaped cracks. The line load solution which is derived from this is different in form to those given by. Study of stress intensity factor of a cracked steel plate. Thus, a small edge crack having the size a a a b 3 has an equivalent stress intensity factor with a large pennyshaped crack. The stressintensity factor for a pennyshaped crack. In their work, arin and erdogan considered a pennyshaped crack located in a layer sandwiched between two dissimilar halfspaces. Defect size dependence on threshold stress intensity for high. In particular, the effect of the waveinduced fluid flow on the dynamic stress intensity factor is analyzed. The case of a pennyshaped crack with arbitrary normal displacements prescribed at its faces inclusion problem was solved exactly and in closed form by. The dynamic stress concentration factor and the stress intensity factor under the ultrasonic fatigue tests were calculated. The solutions are used to derive stress intensity factors for a circular crack near the surface of a beam in pure bending and an approximation of the thickness effect on the stress intensity factor for a deep surface flaw in a plate is presented. The stress distribution produced by the identation of a penny shaped crack by an oblate smooth spheroidal rigid inclusion in a transversely isotropic medium is investigated using the method of hankel transforms.
Phurkhao 20 studied the dynamic stress intensity factor of an impermeable, tractionfree pennyshaped crack in a poroelastic medium subjected to a timeharmonic longitudinal wave. Stress intensity factor of a pennyshaped crack with small. Stress intensity factor measurement of surface cracks in order to understand the principles of the measurement, consider first a sample with a flat elliptical shaped crack present in the interior. Dynamic analysis of a piezoelectric material with an. Reflection coefficient versus normalized crack depth for a half penny shaped surface crack using the two models is given in fig. Thiscritical stress intensity factor isthenameasureof. Stress intensity factors for a penny shaped crack on a half space, engineering fracture mechanics, pp. Calculation of stress intensity factors for interfacial. A1, the stress intensity factor kia for an edge crack with length a a is kia 1. Composite fiber patching techniques have been considered as alternatives to traditional methods of strengthening and fatigue crack repair in steel structures. This stress decays with distance from the crack tip as sqrt1r. By virtue of the integral transform methods, the poroelastodynamic mixed boundary value problems is formulated as a set of dual integral equations, which, in turn, are reduced to a. Mar 28, 2015 the ordinate shows the stress intensity factor ratio, k r, which is the ratio of the k value at the tip of a crack in the loaded structure, k app, to the fracture toughness of the material, k 1c or k j, shown in figure 2 as k mat, hence k r k app k mat. Roter steel a533 204214 pressurevessel steel hy 170 highstrength steel.
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