On the expansion of a pennyshaped crack by a rigid circular. 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. This study describes the evolution of the stress intensity factor k i for fissures in brittle elastic materials subjected to transient thermal actions. On the expansion of a pennyshaped crack by a rigid. Pennyshaped crack in an infinite solid the alternating method uses an elasticity solution for an embedded circular crack in an infinite solid to represent the singular stress field near the flaw front. It illustrates the manner in which the stress intensity factor can be in. Kassir department of civil engineering, the city college. This chapter applies the formulation presented in the first two chapters to a range of piezoelectric problems containing pennyshaped cracks. T1 stress intensity factor and effective stiffness of a solid containing aligned penny shaped cracks. Stress intensity factors for penny and halfpenny shaped. If the crack is not located centrally along the width, i. The thermal stress field is analyzed by means of the potential function method for transversely isotropic solids. 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.
The stress intensity factor for a through crack of length, at right angles, in an infinite plane, to a uniform stress field is 3. An axisymmetric problem for a penny shaped crack bridged by fibres is considered. The contact interaction of the opposite faces of a pennyshaped crack under oblique incidence of a harmonic tensioncompression wave is considered. Complex stress functions that satisfy the equilibrium equations and compatibility conditions in the cracked plate as well as the stress condition on crack surfaces are presented. It includes a penny shaped crack in an infinite piezoelectric plate, a piezoelectric strip, a fiber embedded in a matrix, a piezoelectric cylinder with elastic coating, and the fundamental solution for. Elastodynamic problem for a layered composite with penny.
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. The effect of crack interactions on stress intensity factors is examined for a periodic array of coplanar pennyshaped cracks. Citeseerx document details isaac councill, lee giles, pradeep teregowda. The study is reduced to the analysis of a hypersingular integral equation with respect to the relative crackface separation over a circular domain occupied by crack. Seghi mode i stress intensity factor estimate for a halfpenny shaped crack in a.
Stress intensity factors for cracked finite plates with. 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. Stress intensity factors for external and pennyshaped cracks. Semianalytical expressions for both the crack opening displacements and the stress intensity factor distribution of a penny shaped crack under a circular line load and a surface load on a circular region, arbitrarily located in the crack area, are given.
The influence of layer thickness on the stress intensity. The pennyshaped crack at a bonded plane with localized. Pdf stress intensity factor for a centrally located. Photoelastic determination of stress intensity factors for. In this paper, the stress intensity factor k for the crack front line. N2 the stable growth of a crack created by the hydraulic pressurizing of a pennyshaped crack in a dry rock mass is investigated.
Stress intensity factors for a penny shaped crack in a. 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. Dynamic stress intensity factor mode i of a permeable penny. It includes a pennyshaped crack in an infinite piezoelectric plate, a piezoelectric strip, a fiber embedded in a matrix, a piezoelectric cylinder with elastic coating, and the fundamental solution for. The stress intensity factor at the tip of a pennyshaped crack of radiusthe stress intensity factor at the tip of a pennyshaped crack of radius a in an infinite domain under uniaxial tension sigma view the full answer.
Mode i stress intensity factor estimate for a halfpenny. For piezoelectric materials subjected to tensile stress and electric field parallel to the poled direction, the stress intensity factor and electrical displacement intensity factor are independent of the applied electric field, while the electric field intensity inside the crack is a function of the applied stress and electric field. 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. The cracks are located symmetrically and in parallel to one another in the isotropic cylinder. Pdf measurement of modei stress intensity factor for a. Multiple pennyshaped cracks interaction in a finite body. Numerical results are obtained to examine the effects of the layer thickness and boundary conditions of the layer surfaces on normal stress and displacement. 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. The case studied is a penny shaped crack located in a rock mass and through which runs a fluid whose temperature falls in time. The stress intensity factor sif at the crack s tip is often used to predict the failure load and, therefore, has the theoretical as well as practical interest. 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. Hypersingular integral equations for the solution of pennyshaped interface crack problems.
A2, the stress intensity factor for a pennyshaped crack with diameter 2a b d2. Previous question next question transcribed image text from this question. Stress intensity factor and effective stiffness of a solid. Stress intensity factors at any point on the crack front of penny and halfpenny shaped cracks subjected to stress gradients are presented. The stressintensity factor for a pennyshaped crack between two dissimilar materials. Fracture analysis of a pennyshaped magnetically dielectric. In this paper we consider a pennyshaped crack embedded in the central layer of a composite viscoelastic material. Hypersingular integral equations for the solution of penny. As a typicalexample, a closedform solution is first obtained for a penny shaped crack subjected to a pair ofconcentrated forces acting in opposite directions and a pair of point charges on crack surfaces. An expression is developed for the stress intensity factor of a pennyshaped crack in an infinite elastic solid subjected to nonaxisymmetric normal loading. The penny shaped crack in an infinite solid and subjected to an internal pressure described by a fourier series. The torsion of a penny shaped crack in a functionally graded strip is considered. The pennyshaped interface crack with heat flow citeseerx.
This paper presents the results of investigations conducted to analyze the singular stress field and the associated stress intensity factor sif for a centrally located penny shaped crack around. Stress intensity factors for a penny shaped crack in a half space. Hankel transform is used to reduce the problem to solving a fredholm integral equation. This stress intensity factor is evaluated in a series form in terms of a nondimensional parameter which involves the ratio of the radius of the rigid circular inclusion to the radius of the pennyshaped crack. The effects of the material anisotropy on the stress intensity factor and on the crack shape are investigated for a pennyshaped crack in a transversely isotropic plate of finite thickness. 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.
In particular, the effect of the waveinduced fluid flow on the dynamic stress intensity factor is analyzed. The stressintensity factor for a pennyshaped 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. Numerical determination of the stress intensity factor ki. Abstract in this paper we investigate the stress intensity factors sifs of multiple pennyshaped cracks in an elastic solid cylinder under mode i axial tension loading. The stress intensity factors for a periodic array of interacting coplanar pennyshaped cracks huseyin lekesiza,1, noriko katsubea. The singular state associated with the embedded crack with finite, nonaxisymmetric normal loading is that of plane strain. The crack tip stress field is obtained by considering the asymptotic behavior of bessel function. An analytical solution for the axisymmetric problem of a. The stressintensity factor for a pennyshaped crack between two. Stress intensity factor for a centrally located penny shaped crack surrounding a spherical cavity in a cylinder subjected to axial load. The load prcos0 was applied in this case instead of just r cos 6 to avoid producing negative stress intensity factors.
The stable growth of a crack created by the hydraulic pressurizing of a penny. Stress intensity factor piezoelectric material piezoelectric layer versus versus versus. 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 effects of various ratios of crack depth to plate thickness will also be examined. An elastic layer with a pennyshaped crack subjected to. The accuracy of the stress intensity factor calculation is satisfactorily examined for rectangular, pennyshaped and elliptical planar cracks. Stress intensity factors for cracks in anisotropic. The stress intensity factor for a penny shaped crack between two dissimilar materials m. It includes a pennyshaped crack in an infinite piezoelectric plate.
This paper considers the transient stress intensity factor mode i of a penny shaped crack in an infinite poroelastic solid. Stress intensity factor for a pennyshaped crack in a halfspace. 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 problem is solved by the method of boundary integral equations.
The solution to these singular integral equations permits the determination of not only the complex stress intensity factors but also the crack opening displacements. If the crack is located centrally in a finite plate of width and height, an approximate relation for the stress intensity factor is 3. 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. Pennyshaped crack in an infinite domain under uniaxial tension. Kachanovs approximate method for crack interactions int. The mode i, ii and iii stress intensity factors sifs are calculated to investigate the possible propagation of the preexisting penny shaped interfacial crack. In order to study the possibility of fracture within the central layer, we study the response of the crack, namely the stress intensity factor sif, to a remote applied mode. The stress intensity factor variation along a flaw border is most conveniently obtained by summing up the pertinent influence functions. Formulation for the mode i stress intensity factor.
The stress intensity factor for a pennyshaped crack in an elastic. The distribution of the stress intensity factor opening mode is studied for di. These quantities are defined by the collocation technique. Stress intensity factors for external and pennyshaped. Oct 01, 2003 read multiple penny shaped cracks interaction in a finite body and their effect on stress intensity factor, engineering fracture mechanics on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. The stress intensity factors for a periodic array of. N2 the stress state and effective elastic moduli of an isotropic solid containing equally oriented pennyshaped cracks are evaluated accurately. Interaction of a center of dilatation and a pennyshaped. The paper presents the integral equations governing the pennyshaped crack problem and the numerical results for the stress intensity factor at the tip of the crack. Dynamic stress intensity factor mode i of a permeable.
The singular state associated with the embedded crack with finite, nonaxisymmetric normal loading is that of. Contact interaction of faces of the pennyshaped crack. 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. Investigated are the effects of material property parameters and geometry criterion on the stress intensity factor. Kachanovs approximate method for crack interactions kachanov, m. The result can be expressed in terms of a fredholm integral equation of the second kind.
Stress intensity factor determination for threedimensional crack. 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. Measurement of modei stress intensity factor for a penny shaped crack in a beam under pure bending using scatteredlight photoelasticity. The convergence of the developed numerical method is checked, and the interaction of a penny shaped interfacial crack and a center of dilatation are calculated and discussed. Both the elastic moduli and sif are strongly dependent on the density and the geometrical arrangement of cracks. Results are presented for uniform tension and linearly. Exact expressions for stress and electric displacement intensity factors are also presented. Stress intensity factor for a crack within a strip under arbitrary loading.
Pdf elastic tstress solution for pennyshaped cracks under. A general method to determine the stress intensity factor of multiple collinear cracks. N2 the stable growth of a crack created by the hydraulic pressurizing of a penny shaped crack in a dry rock mass is investigated. Iii dynamic stress intensity factor in the crack vicinity. Emery journal of applied mechanics 1967 208 stress intensity factors for semicircular cracks. The stressintensity factor for a pennyshaped crack between. Numerical examples concern the effects of the dimensionless wave number, the material mismatch, and the crack. The stress intensity factor at the tip of a pennyshaped crack of radius a \displaystyle a in an infinite domain under uniaxial tension. Read mode i stress intensity factor estimate for a halfpenny shaped crack in a trilayer structure by reduction to a bilayer model, engineering fracture mechanics on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. A finite element alternating method for evaluation of.
The coefficients of the polynomial p x1, x2 are determined using the boundary conditions on the surfaces of the pennyshaped cracks where the stresses on the crack surfaces are zero. Local stress field for torsion of a pennyshaped crack in a. 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. Based on the results of these numerical calculations, several conclusions can be made, as follows. An expression for the stress intensity factor at the pennyshaped crack is evaluated in a simple form of a series which involves coefficients of the solutions of the simultaneous equations. Numerical results for the stress intensity factors are obtained for the square configuration shown in figure 1 b. The stress intensity factors at the inner and the outer crack tips are obtained in exact expressions as the products of a dimensional quantity and nondimensional functions. In the former paper the analysis given applies to an axisymmetric distribution of pressure p. Stress intensity factors are presented for a circular crack approaching the surface of a semiinfinite solid. The presence of a pennyshaped crack is shown to have a strong effect on the magnitude of the stress intensity of the external circular crack.
Kassir department of civil engineering, the city college of the city university of new york, new york, n. The stress intensity factor of a concentric penny shaped mode iii crack in a finite long cylinder of a finite radius is determined by using the basic theorem of the hankel transform and the fourier series. Local stress field for torsion of a pennyshaped crack in. Four models, that is, a square plate with one crack or with two collinear cracks and an airfoilshaped plate. 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. Four examples are presented here for verification purposes. Dynamic stress intensity factor mode i of a pennyshaped. General solutions of a pennyshaped crack in a piezoelectric. 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. Pdf stress intensity factor for a centrally located penny.
This chapter applies the formulation presented in the first two chapters to a range of piezoelectric problems containing penny shaped cracks. 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 interface penny shaped 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. Stress intensity factors for a penny shaped crack in a half. This stress intensity factor is evaluated in a series form in terms of a nondimensional parameter which involves the ratio of the radius of the rigid circular inclusion to the radius of the penny shaped crack. 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. 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. The stressintensity factor for a pennyshaped crack between two dissimilar materials m. This file is licensed under the creative commons attributionshare alike 3. T1 stress intensity factor and effective stiffness of a solid containing aligned pennyshaped cracks.
N2 the stress state and effective elastic moduli of an isotropic solid containing equally oriented penny shaped cracks are evaluated accurately. 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 factor wikipedia republished wiki 2. Interaction of a pennyshaped crack and an external. The torsion of a pennyshaped crack in a functionally graded strip is considered. Numerical determination of the stress intensity factor ki in. Stress intensity factors for external and pennyshaped cracks in transversely isotropic cylinders subjected to thermal shock. Stress intensity factor of a pennyshaped crack with small. The mixed boundary problems for finite plates with one crack or two collinear cracks are studied. If the crack is located centrally in a finite plate of width and height, an approximate relation for the stress intensity factor is. Stress in a half space due to normal pressure and shear on a rectangular portion of the half space boundary. The problem of a concentric pennyshaped crack of mode iii in. 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. Read multiple pennyshaped cracks interaction in a finite body and their effect on stress intensity factor, engineering fracture mechanics on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available.
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