Citeseerx the pennyshaped interface crack with heat flow. The boundary conditions of the problem have three different parts. Jan 01, 20 the effect of crack interactions on stress intensity factors is examined for a periodic array of coplanar pennyshaped cracks. Stress intensity factors for external and pennyshaped. This integral equation is solved numerically by using gaussian quadrature formulae.
The elastostatic problem which deals with a penny shaped crack was extended to cover effects such as anisotropy, nonhomogeneity, localized loading, effects of localized plastic flow, and dynamic loading. 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. 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 load prcos0 was applied in this case instead of just r cos 6 to avoid producing negative stress intensity factors. Citeseerx document details isaac councill, lee giles, pradeep teregowda. Introduction the classical problem related to the pennyshaped crack embedded in a homogeneous isotropic elastic medium was. Four examples are presented here for verification purposes. Panb adepartment of civil engineering, the university of hong kong, pokfulam road, hong kong, pr china bdepartment of civil engineering, university of akron, akron, oh 443253905, usa. The stress intensity factors, maximum stress intensity, and strain energy release rate for the epicycloid crack subject to shear load are presented graphically. Interaction of a pennyshaped crack and an external. 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 interaction of a pennyshaped crack and an external circular crack in a transversely isotropic composite is investigated using the techniques of hankel transform and multiplying factors. Stress intensity factors of two skewparallel pennyshaped. Assuming that the stress intensity factors for the semi ellipse and the semicircular crack are related in the same way as the embedded elliptical and penny shaped crack, he was able to empirically.
Stress intensity factors of square crack inclined to interface of transversely isotropic bimaterial z. Introduction the classical problem related to the penny shaped crack embedded in a homogeneous isotropic elastic medium was. The maximum stress intensity factors with respect to a time variable are approximated by a function of biots number and crack length. In the latter paper the solution is derived only in the case in which the stress field is due to the application of constant pressure to the faces of the crack. Mechanical engineering journal stress intensity factor of a pennyshaped crack with smalldisturbed crack front line masayuki arai abstract in this paper, the stress intensity factor for the crack front line. Download scientific diagram stress intensity factors ki, kii and kiii for a penny shaped 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. The convergence of the developed numerical method is checked, and the interaction of a pennyshaped interfacial crack and a center of dilatation are calculated and discussed. A solution is given for the thermal stresses due to a penny shaped crack at the interface between dissimilar materials loaded in tension for the case where the heat flux is into the material with higher distortivity. Stress intensity factors for external and pennyshaped cracks. Stress intensity factor wikipedia republished wiki 2.
The stress intensity factor, is used in fracture mechanics to predict the stress state stress intensity near the tip of a crack caused by a remote load or residual stresses. Stress intensity factors for external and penny shaped cracks in transversely isotropic cylinders subjected to thermal shock springerlink. This paper presents an analytical investigation of a nonclassical fracture mechanics axisymmetrical problem for a nearsurface pennyshaped crack at the interface of physical and mechanical properties of a material. The problem of determining the distribution of stress in the neighbourhood of a pennyshaped crack defined in terms of cylindrical coordinates. In particular, the effect of the waveinduced fluid flow on the dynamic stress intensity factor is analyzed. Stress intensity factors numerical calculations for two. The electric and magnetic ps model for pennyshaped cracks in 3d magnetoelectroelastic media was investigated by zhao et al, the.
Stress intensity factors numerical calculations for two penny. The stress state and effective elastic moduli of an isotropic solid containing equally oriented penny shaped cracks are evaluated accurately. 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. Electric and magnetic polarization saturations for a. Regions of separation and perfect thermal contact are developed at the crack faces. In their work, arin and erdogan considered a pennyshaped crack located in a layer sandwiched between two dissimilar halfspaces. Stress intensity factor for a centrally located penny shaped. The elastostatic problem which deals with a pennyshaped crack was extended to cover effects such as anisotropy, nonhomogeneity, localized loading, effects of localized plastic flow, and dynamic loading. The proposed model and the obtained numerical results are in good agreement when compared to gao 40. Stress intensity factors 251 2 circular crack embedded in a halfspace, linearly varying load figure 6 gives the stress intensity factor as a function of position on the crack border for this case. 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.
Dynamic stress intensity factors of a penny shaped crack subjected to an annular impact. The effect of crack interactions on stress intensity factors is examined for a periodic array of coplanar pennyshaped cracks. In particular, the effect of the waveinduced fluid flow. The stress intensity factor for a pennyshaped crack in an elastic. Indentation of a precompressed pennyshaped crack nasaads. The stress intensity factor, k \\displaystyle k, is used in fracture mechanics to predict the stress state stress intensity near the tip of a crack caused by a remote load or residual stresses. The mode i, ii and iii stress intensity factors sifs are calculated to investigate the possible propagation of the preexisting pennyshaped interfacial crack.
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. Results are presented for uniform tension and linearly. Pdf stress intensity factor for a centrally located penny. In their work, arin and erdogan considered a penny shaped crack located in a layer sandwiched between two dissimilar halfspaces. Stress intensity factors at any point on the crack front of penny and half penny shaped cracks subjected to stress gradients are presented.
I am now following abaqus example problems manual 6. Calculate the stress intensity factors by using abaqus. Stress intensity factors for penny and halfpenny shaped. Normalized stress intensity factors along crack front for penny shaped crack as a function ofthe angle from the symmetry plane e 0 towards the other symmetry plane e 90 and normalized stress intensity factors assuming. Elastic modulus of the graded interfacial zone is assumed to be an exponential function of the depth. Dynamic stress intensity factors of a pennyshaped crack. Hypersingular integral equations for the solution of penny. Stress intensity factors now that the stresses on the surface of crack a have been obtained, we are to determine the stress intensity factors on the boundary of crack a. In the former paper the analysis given applies to an axisymmetric distribution of pressure p.
The first is a linear elastic, plane strain, doubleedged notch specimen under mode i loading, for which bowie 1964 has provided a series solution for the stress intensity factor, k i. The interaction of a penny shaped crack and an external circular crack in a transversely isotropic composite is investigated using the techniques of hankel transform and multiplying factors. 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. 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. Stress intensity factors for a penny shaped crack in a half.
The case of a penny shaped crack with arbitrary normal displacements prescribed at its faces inclusion problem was solved exactly and in closed form by. Stress intensity factors ki, kii and kiii for a pennyshaped crack. Stress intensity factors are presented for a circular crack approaching the surface of a semiinfinite solid. Stress intensity factors for the pennyshaped crack under. The solutions to the resulting integral equations permit only the determination of stress intensity factors and energy release rate, and do not directly provide crack opening and sliding displacements. An analytical solution for the axisymmetric problem of a.
Stress intensity factor for a centrally located penny shaped crack surrounding a spherical cavity in a cylinder subjected to axial load. The stable growth of a crack created by the hydraulic pressurizing of a penny shaped crack in a dry rock mass is investigated. The rock mass is infinitely extended, homogeneous, and isotropic. The paper concerns the contact interaction of the opposite faces of a penny shaped crack under harmonic wave at oblique incidence. N2 this paper considers the large time asymptotic behavior of a nearsurface hydraulic fracture, that is, when the radius r is much larger than the depth h. The problem is formulated by using integral transform technique under uniform load and reduced to a singular integral equation. Weight functions and stress intensity factors for ring. Stress intensity factor solutions for the ringshaped crack in an infinite body loaded by constant stress normal to the crack plane fig. Based on the theory of elasticity, previous analytical solutions concerning a penny shaped interface crack employ the derivative of the crack surface opening displacements as the primary unknowns, thus leading to singular integral equations with cauchytype singularity. Jan 01, 2005 this paper examines the stress intensity factors that are associated with a penny shaped crack perpendicular to the interface of a bimaterial bonded with a graded interfacial zone.
The paper concerns the contact interaction of the opposite faces of a pennyshaped crack under harmonic wave at oblique incidence. Stress intensity factors for cracks in anisotropic. Stress intensity factors are given for various penny. Please help me how can i start and please provide me any tutorialexampleguidance if you have. Hypersingular integral equations for the solution of pennyshaped interface crack problems. Pdf stress intensity factor for a centrally located. In the zeroviscosity limit, we derive two terms of a large rh asymptotic solution. 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. Stress intensity factors for a penny shaped crack in a half space. The stress state and effective elastic moduli of an isotropic solid containing equally oriented pennyshaped cracks are evaluated accurately. The stress intensity factors are studied for different values of the wave frequency. A mathematical formulation is presented for the dynamic stress intensity factor mode i of a permeable penny shaped crack subjected to a timeharmonic propagating longitudinal wave in an infinite poroelastic solid. Dynamic stress intensity factor mode i of a permeable penny.
The stress intensity factors are calculated numerically using a socalled generalized kelvin solution based. The stable growth of a crack created by the hydraulic pressurizing of a pennyshaped crack in a dry rock mass is investigated. Fracture mechanics assessment of large diameter wind. Stress intensity factors for cracks in anisotropic materials. An expression is developed for the stress intensity factor of a pennyshaped crack in an infinite elastic solid subjected to nonaxisymmetric normal loading. The problem is solved by the method of boundary integral equations using an iterative algorithm.
Stress intensity factor determination for threedimensional crack. 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. This paper examines the stress intensity factors that are associated with a penny shaped crack perpendicular to the interface of a bimaterial bonded with a graded interfacial zone. A solution is given for the thermal stresses due to a pennyshaped crack at the interface between dissimilar materials loaded in tension for the case where the heat flux is into the material with higher distortivity. The stress intensity factors are determined for a penny shaped crack loaded by concentrated normal impact forces and concentrated radial shear impact forces. It is a theoretical construct usually applied to a homogeneous, linear elastic material and is useful for providing a failure criterion for brittle materials. Sometimes a crack line may form a closed loop for example, when modeling a full pennyshaped crack. The fracture is analyzed as an elastically clamped circular plate and stress intensity factors are determined by matching the outer plate problem to the inner problem of a nearsurface semiinfinite crack. Interaction of a pennyshaped crack and an external circular. The case of a pennyshaped crack with arbitrary normal displacements prescribed at its faces inclusion problem was solved exactly and in closed form by. This paper examines the stress intensity factors that are associated with a pennyshaped crack perpendicular to the interface of a bimaterial bonded with a graded interfacial zone.
A method of successive approximation together with the fourier integral and the bessel series. Fracture analysis of a pennyshaped magnetically dielectric. Dynamic stressintensity factors for pennyshaped crack in. Interaction of a center of dilatation and a pennyshaped. Suppose that is a pennyshaped crack, with radius so that the crack occupies the region where and are polar coordinates, and now, let be a simply connected domain in the plane defined as whose boundary has the polar equation, where is bounded and piecewise continuous and is a small positive parameter. Kachanovs approximate method for crack interactions int. A method of successive approximation together with the fourier integral and the bessel series are. 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. The thermal stress field is analyzed by means of the potential function method for transversely isotropic solids. The pennyshaped crack at a bonded plane with localized.
The integral equations are solved by numerical methods, and the results are plotted showing how the dynamic stress intensity factors are influenced by the asymmetric loading. 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. Stress intensity factor and effective stiffness of a solid. It is verified on the basis of the equations of fluid dynamics that the fracturing fluid cannot penetrate the entire domain of a crack when the crack is. Pdf the stress intensity factors for a periodic array of. Stress intensity factors of square crack inclined to. T1 asymptotic solution for a penny shaped nearsurface hydraulic fracture. Stress intensity factors for a penny shaped crack in a. A transversely isotropic elastic solid with a pennyshaped or external crack. The geometric model of a cracked body is a spatially periodic medium whose unit cell contains a number of arbitrarily placed aligned circular cracks. The representations of the stress intensity factors near the crack edges are obtained. Fracture mechanics assessment of large diameter wind turbine. The stress intensity factors for a periodic array of.
Asymptotic solution for a pennyshaped nearsurface hydraulic. Stress intensity factors at any point on the crack front of penny and halfpenny shaped cracks subjected to stress gradients are presented. Dynamic stress intensity factors for penny shaped crack in twisted plate. The accuracy of the stress intensity factor calculation is satisfactorily examined for rectangular, pennyshaped and elliptical planar cracks.
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. Weight functions and stress intensity factors for ringshaped. The jintegral, stress intensity factors, and tstress are widely used in fracture mechanics. Stress and displacement fields due to a pennyshaped shear. The singular state associated with the embedded crack with finite, nonaxisymmetric normal loading is that of plane strain.
The line load solution which is derived from this is different in form to those given by previous workers and is more. The analysis allows the evaluation of the indenting stress necessary to initiate the flaw opening mode stress intensity factors at the crack tip. Dynamic stressintensity factors for pennyshaped crack in twisted plate. Following kassir and sih 1975, the stress intensity factors on the boundary of a penny shaped crack in a transversely isotropic solid are discussed below. Dynamic stress intensity factors of a pennyshaped crack subjected to an annular impact chen, baoxing. The crack is located in a nearsurface layer parallel to the surface of a halfspace, which is subjected.
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