Elastodynamic problem for a layered composite with penny. The stressintensity factor for a pennyshaped crack between two. The stress intensity factor for a pennyshaped crack in an elastic. 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.
N2 the stable growth of a crack created by the hydraulic pressurizing of a pennyshaped crack in a dry rock mass is investigated. 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 determination for threedimensional crack. Both the elastic moduli and sif are strongly dependent on the density and the geometrical arrangement of cracks. 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. In this paper we consider a pennyshaped crack embedded in the central layer of a composite viscoelastic material. Numerical examples concern the effects of the dimensionless wave number, the material mismatch, and the crack.
Multiple pennyshaped cracks interaction in a finite body. Formulation for the mode i stress intensity factor. The singular state associated with the embedded crack with finite, nonaxisymmetric normal loading is that of. Kachanovs approximate method for crack interactions kachanov, m. The mixed boundary problems for finite plates with one crack or two collinear cracks are studied. 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 pennyshaped interface crack with heat flow citeseerx. Stress intensity factor for a pennyshaped crack in a halfspace. 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.
Fracture analysis of a pennyshaped magnetically dielectric. Interaction of a center of dilatation and a pennyshaped. Pdf elastic tstress solution for pennyshaped cracks under. Kachanovs approximate method for crack interactions int. Pdf stress intensity factor for a centrally located penny. Stress intensity factor and effective stiffness of a solid. Stress intensity factors for penny and halfpenny shaped. If the crack is located centrally in a finite plate of width and height, an approximate relation for the stress intensity factor is 3. Four models, that is, a square plate with one crack or with two collinear cracks and an airfoilshaped plate. Measurement of modei stress intensity factor for a penny shaped crack in a beam under pure bending using scatteredlight photoelasticity. In this paper, the stress intensity factor k for the crack front line. 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. Dynamic stress intensity factor mode i of a pennyshaped.
It illustrates the manner in which the stress intensity factor can be in. 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. 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. 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. The influence of layer thickness on the stress intensity factor of a penny shaped crack in a sandwiched viscoelastic bimaterial.
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. Stress intensity factor for a crack within a strip under arbitrary loading. Interaction of a pennyshaped crack and an external. 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. This file is licensed under the creative commons attributionshare alike 3. Hankel transform is used to reduce the problem to solving a fredholm integral equation. 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 distribution of the stress intensity factor opening mode is studied for di. Iii dynamic stress intensity factor in the crack vicinity. 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. Seghi mode i stress intensity factor estimate for a halfpenny shaped crack in a.
The stress intensity factors for a periodic array of interacting coplanar pennyshaped cracks huseyin lekesiza,1, noriko katsubea. The torsion of a pennyshaped crack in a functionally graded strip is considered. Stress intensity factors for a penny shaped crack in a half. An elastic layer with a pennyshaped crack subjected to. 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. Dynamic stress intensity factor mode i of a permeable penny. The stress intensity factor for a penny shaped crack between two dissimilar materials m. 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. Investigated are the effects of material property parameters and geometry criterion on the stress intensity factor. 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.
The accuracy of the stress intensity factor calculation is satisfactorily examined for rectangular, pennyshaped and elliptical planar cracks. An expression is developed for the stress intensity factor of a pennyshaped crack in an infinite elastic solid subjected to nonaxisymmetric normal loading. Kassir department of civil engineering, the city college of the city university of new york, new york, n. 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. Stress intensity factors for external and pennyshaped cracks in transversely isotropic cylinders subjected to thermal shock. Pdf stress intensity factor for a centrally located. The crack tip stress field is obtained by considering the asymptotic behavior of bessel function. Contact interaction of faces of the pennyshaped crack. Stress intensity factors for external and pennyshaped.
In particular, the effect of the waveinduced fluid flow on the dynamic stress intensity factor is analyzed. Stress intensity factor for a centrally located penny shaped crack surrounding a spherical cavity in a cylinder subjected to axial load. A finite element alternating method for evaluation of. Local stress field for torsion of a pennyshaped crack in a. Four examples are presented here for verification purposes. Photoelastic determination of stress intensity factors for. The load prcos0 was applied in this case instead of just r cos 6 to avoid producing negative stress intensity factors.
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 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. Stress intensity factors are presented for a circular crack approaching the surface of a semiinfinite solid. Stress intensity factor piezoelectric material piezoelectric layer versus versus versus.
The stable growth of a crack created by the hydraulic pressurizing of a penny. Based on the results of these numerical calculations, several conclusions can be made, as follows. 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 general method to determine the stress intensity factor of multiple collinear cracks. Numerical results for the stress intensity factors are obtained for the square configuration shown in figure 1 b. 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. Numerical determination of the stress intensity factor ki in. 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 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. T1 stress intensity factor and effective stiffness of a solid containing aligned pennyshaped cracks.
A2, the stress intensity factor for a pennyshaped crack with diameter 2a b d2. Pennyshaped crack in an infinite domain under uniaxial tension. 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. The stressintensity factor for a pennyshaped crack. Stress intensity factor of a pennyshaped crack with small. Numerical determination of the stress intensity factor ki. The thermal stress field is analyzed by means of the potential function method for transversely isotropic solids. 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. Local stress field for torsion of a pennyshaped crack in. If the crack is located centrally in a finite plate of width and height, an approximate relation for the stress intensity factor is. The stressintensity factor for a pennyshaped crack between two dissimilar materials.
This paper considers the transient stress intensity factor mode i of a penny shaped crack in an infinite poroelastic solid. The problem is solved by the method of boundary integral equations. Dynamic stress intensity factor mode i of a permeable. Stress intensity factors for a penny shaped crack in a half space. The stressintensity factor for a pennyshaped crack between. The contact interaction of the opposite faces of a pennyshaped crack under oblique incidence of a harmonic tensioncompression wave is considered.
Mode i stress intensity factor estimate for a halfpenny. The penny shaped crack in an infinite solid and subjected to an internal pressure described by a fourier series. In the former paper the analysis given applies to an axisymmetric distribution of pressure p. Previous question next question transcribed image text from this question. The stressintensity factor for a pennyshaped crack between two dissimilar materials m. This study describes the evolution of the stress intensity factor k i for fissures in brittle elastic materials subjected to transient thermal actions. Effective spring stiffness for a periodic array of interacting coplanar pennyshaped cracks at an interface between two dissimilar isotropic materials international journal of solids and structures. On the expansion of a pennyshaped crack by a rigid. Numerical results are obtained to examine the effects of the layer thickness and boundary conditions of the layer surfaces on normal stress and displacement. 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.
The solution to these singular integral equations permits the determination of not only the complex stress intensity factors but also the crack opening displacements. The effects of various ratios of crack depth to plate thickness will also be examined. The stress intensity factor at the tip of a pennyshaped crack of radius a \displaystyle a in an infinite domain under uniaxial tension. The pennyshaped crack at a bonded plane with localized. Results are presented for uniform tension and linearly. Kassir department of civil engineering, the city college. 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. Stress intensity factors at any point on the crack front of penny and halfpenny shaped cracks subjected to stress gradients are presented. 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.
Stress intensity factors for a penny shaped crack in a. If the crack is not located centrally along the width, i. It includes a pennyshaped crack in an infinite piezoelectric plate. 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. 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.
The influence of layer thickness on the stress intensity. 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. The stress intensity factor variation along a flaw border is most conveniently obtained by summing up the pertinent influence functions. The effect of crack interactions on stress intensity factors is examined for a periodic array of coplanar pennyshaped cracks. The result can be expressed in terms of a fredholm integral equation of the second kind. Stress intensity factors for external and pennyshaped cracks. The rock mass is infinitely extended, homogeneous, and isotropic. 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. Stress intensity factors for cracks in anisotropic. 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. Pdf measurement of modei stress intensity factor for a. The case of a pennyshaped crack with arbitrary normal displacements prescribed at its faces inclusion problem was solved exactly and in closed form by. Citeseerx document details isaac councill, lee giles, pradeep teregowda.
The problem of a concentric pennyshaped crack of mode iii in. 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. 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. An axisymmetric problem for a penny shaped crack bridged by fibres is considered. 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 singular state associated with the embedded crack with finite, nonaxisymmetric normal loading is that of plane strain. The torsion of a penny shaped crack in a functionally graded strip is considered. 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. 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. 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. On the expansion of a pennyshaped crack by a rigid circular. This chapter applies the formulation presented in the first two chapters to a range of piezoelectric problems containing pennyshaped cracks.
Stress in a half space due to normal pressure and shear on a rectangular portion of the half space boundary. 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. General solutions of a pennyshaped crack in a piezoelectric. 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 stress intensity factors for a periodic array of. 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. 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.
Stress intensity factors for cracked finite plates with. The cracks are located symmetrically and in parallel to one another in the isotropic cylinder. 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. 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.
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 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. 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. Hypersingular integral equations for the solution of pennyshaped interface crack problems. The mode i, ii and iii stress intensity factors sifs are calculated to investigate the possible propagation of the preexisting penny shaped interfacial crack.
N2 the stress state and effective elastic moduli of an isotropic solid containing equally oriented penny shaped cracks are evaluated accurately. These quantities are defined by the collocation technique. N2 the stable growth of a crack created by the hydraulic pressurizing of a penny shaped crack in a dry rock mass is investigated. An analytical solution for the axisymmetric problem of a. Stress intensity factor wikipedia republished wiki 2. N2 the stress state and effective elastic moduli of an isotropic solid containing equally oriented pennyshaped cracks are evaluated accurately. Hypersingular integral equations for the solution of penny. This chapter applies the formulation presented in the first two chapters to a range of piezoelectric problems containing penny shaped cracks. T1 stress intensity factor and effective stiffness of a solid containing aligned penny shaped cracks.
The stress intensity factor for a through crack of length, at right angles, in an infinite plane, to a uniform stress field is 3. Emery journal of applied mechanics 1967 208 stress intensity factors for semicircular cracks. 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. 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.
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