Subcritical propagation of an oilfilled pennyshaped crack. A distinct issue associated with the present work is the incorporation of viscoelastic behavior. The shapes of cracks opened by tension or bending are approximated by conic sections and the conic section coefficients related to plate geometry by very simple empirical equations. Stress intensity factors for surface cracks in round bar. The maximum stress intensity factors with respect to a time variable are approximated by a function of biots number and crack length. Shear stress intensity factors for a planar crack with.
Does anyone know how to calculate the stress intensity. Dynamic stress intensity factor mode i of a permeable. Interaction of a pennyshaped crack and an external. Figs 4 and 5 show the effect of threshold stress intensity factor k ith of the source rock on the crack propagation distance and excess oil pressure. 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. The load prcos0 was applied in this case instead of just r cos 6 to avoid producing negative stress intensity factors. Fonte md, ereitas md 1499 stress intensity factor for semielliptical sdce cracks in round has under bending and torsion. The effect of crack interactions on stress intensity factors is examined for a periodic array of coplanar penny shaped cracks. Investigated are the effects of material property parameters and geometry criterion on the stress intensity factor. An expression is developed for the stress intensity factor of a pennyshaped crack in an infinite elastic solid subjected to nonaxisymmetric normal loading. An analytical solution for the axisymmetric problem of a. In contrast, we treat a permeable crack filled with an incompressible fluid.
It illustrates the manner in which the stress intensity factor can be in. Closedform solutions for modei and ii stress intensity factors are obtained. The boundary conditions of the problem have three different parts. Kachanovs approximate method for crack interactions kachanov, m. The stress state and effective elastic moduli of an isotropic solid containing equally oriented penny shaped cracks are evaluated accurately. Calculation of stress intensity factors for interfacial.
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. Dynamic fracture analysis for a penny shaped crack in an fgm interlayer between dissimilar half spaces show all authors. The stress intensity factor for a pennyshaped crack in an. Therefore, the weight functions for the point a and b have been derived analogously to. Fracture occurs when the stress at the atomic level cohesive strength. Modelling petroleum migration through microcrack propagation. For the same reason, if we consider an inner or interfacial small and sharp penny crack of radius c crack front and the crack will grow in a soft manner, i. Clearly during the pressure buildup process, stress intensity factor increases with the increasing excess pressure. Weight functions and stress intensity factors for ring. A simple stress intensity factor expression is given for a deep edge crack in a plate in tension. 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. Dynamic stress intensity factors studied by boundary.
Pennyshaped crack in a long circular cylinder subjected. Local stress field for torsion of a pennyshaped crack in a. 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 pennyshaped cracks in an infinite medium subjected to a remote normal traction at infinity, figure 1 a. Boundary integral equations are presented, by using the integral transform method, for a pennyshaped crack under normal and shear stresses. The stressintensity factor for a pennyshaped crack between. Thiscritical stress intensity factor isthenameasureof. Stress intensity factors for toe cracks or root faces in welded joints are only rarely.
According to his results, a simpletensile load would lead to the singularities both in stress and electric displacement at the crack tipas well as both intensity factors. The singular state associated with the embedded crack with finite, nonaxisymmetric normal loading is that of plane strain. 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. Previous question next question transcribed image text from this question. Considering an elliptical crack, the stress intensity factor along the crack front varies reaching a maximum at the minor axis of the ellipse and a minimum at the major axis. Elasticity, fracture mechanics, penny shaped crack, stress intensity factor, mixed boundary value. The mixed boundary problems for finite plates with one crack or two collinear cracks are studied. Stress intensity factors at any point on the crack front of penny and half penny shaped cracks subjected to stress gradients are presented. Subcritical propagation of an oilfilled pennyshaped. Stress intensity factors numerical calculations for two. Primary migration of oil through selfpropagating fractures. Dynamic stress intensity factor mode i of a permeable penny.
Using the extended displacement discontinuity boundary element method, penny shaped cracks in transversely isotropic plane of threedimensional piezoelectric semiconductors are studied, and the stress, electric displacement, and electric current intensity factors under uniform mechanicalelectriccurrent loads applied on the penny shaped crack. The shear modulus is allowed to vary in an arbitrarily continuous manner along its thickness direction. Jan 01, 20 the effect of crack interactions on stress intensity factors is examined for a periodic array of coplanar pennyshaped cracks. Crack tip stress dependence on the stress intensity factor k s y x w xy v yy v xx m u y r a s s s 3 yy 2 k x v s 2 yy 2 k x v s k 1 stress components, v ij, at the crack tip depend on the stress intensity factors k i which is influenced by. Stress intensity factor wikipedia republished wiki 2. Stress intensity factor and effective stiffness of a solid. Stress intensity factors determination for an inclined. The assumptions of dugdale are applied to estimate the effects of plasticity around the edge of the crack. Citeseerx document details isaac councill, lee giles, pradeep teregowda. Thiscritical stress intensity factor isthenameasureof materialtoughness. The stress intensity factor describes the stress state at a crack tip, is related to the rate of crack growth, and is used to establish failure criteria due to fracture. Local stress field for torsion of a pennyshaped crack in.
The crack is formed by the sudden annihilation of the tractions. This paper considers the transient stress intensity factor mode i of a penny shaped crack in an infinite poroelastic solid. 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. If possible, please recommend some references or classical books which. Stress intensity factor for steel hollow pipe with axial crack. Crack opening displacements and stress intensity factors are also obtained for a throughthickness, center cracked bar with variable thickness. For the blade crack in the source rock with a modulus of e 2 gpa, it takes about 6. Accurate critical stress intensity factor griffith crack.
Four models, that is, a square plate with one crack or with two collinear cracks and an airfoil shaped plate with one. Stress intensity factor sifbased fracture modeling has received. The elliptical hole becomes a crack by decreasing the minor axis b to zero. 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. The stress intensity factor for a penny shaped crack between two dissimilar materials.
In particular, the effect of the waveinduced fluid flow on the dynamic stress intensity factor. The stress intensity factors for a periodic array of. Axisymmetric problems of a pennyshaped crack at the interface of a. Formulation for the mode i stress intensity factor. Journal of electrochemical energy conversion and storage. Stress intensity factor for a thinwalled cylinder containing. When the crack is expanding under a constant flow rate, the classical solution by sack is found to be approximately. Hankel transform is used to reduce the problem to solving a fredholm integral equation. The stressintensity factor for a pennyshaped crack between two dissimilar materials. A2, the stress intensity factor for a penny shaped crack with diameter 2 a b d 2. The pennyshaped crack at a bonded plane with localized. The line load solution which is derived from this is different in form to those given by previous workers and is more. Irwin arrived at the definition of \k\ as a near crack tip approximation to westergaards complete solution for the stress field surrounding a crack 2. Normalized stress intensity factors for a pennyshaped crack at the edge of a graded interface.
The reported results show a considerable potential for using this. Stress intensity factors for external and pennyshaped. 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. Computation of mixedmode stress intensity factors for cracks in. 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. Jul 27, 2015 calculate the stress under point load with no crack use a book like roark for this. Mixedmode fatigue crack propagation of pennyshaped cracks. Critical stress intensity factor k ic has been an approximation for fracture toughness using only loadcell measurements. Does anyone know how to calculate the stress intensity factor of 3d penny shaped internal crack under uniaxial compression.
If stress intensity is less than critical stress intensity factor, kic. Stress intensity factor an overview sciencedirect topics. Dynamic fracture analysis for a pennyshaped crack in an. Pdf the stress intensity factors for a periodic array of. The stress intensity factors were obtained using the j integral method. Harmonic and impact load on the crack surface has been considered. 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. Stress intensity factor for a thinwalled cylinder containing an edge circumferential crack under bending p. Accurate and fast evaluation of the stress intensity factor for planar cracks shows the proposed procedure is robust for sif calculation and crack propagation purposes. 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. Thus, the stress intensity factor k is commonly expressed in terms of the applied stresses at and. Pennyshaped cracks in threedimensional piezoelectric. 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. 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.
For a penny shaped crack embedded within an infinite solid and loaded remotely perpendicular to the crack at a stress. By approximating the shear modulus with a series of linear functions of the thickness, the problem can be solved by employment of hankel integral transforms technique and transfer matrix method. However, in most practical cases the deepest point a fig. This is applicable to cracks under plane stress, plane strain, and antiplane shear. An axisymmetric problem for a pennyshaped crack bridged by fibres is considered. 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. However, artificial manmade cracks several orders of magnitude longer and wider than natural flaws have required a correction factor term y that can be up to about 3 times the recorded experimental value. Dynamic stress intensity factor mode i of a pennyshaped.
N2 a threedimensional penny shaped crack under combined tensile and shear loadings is analyzed. Threedimensional viscoelastic interactions of a center of. Stress intensity factor solutions for the ring shaped crack in an infinite body loaded by constant stress normal to the crack plane fig. When the stress intensity factor reaches the threshold value k ith, which is usually a fraction e. The hankel transform technique is applied to convert the problem to dual integral equations. Modeling of the photothermalph tripleresponsive hydrogels considering the coupled effect of photothermal. 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. Hypersingular integral equations for the solution of penny. This paper analyses the dynamic stress intensity factor of a fluidfilled pennyshaped crack in an infinite porous medium when a plane, harmonic in time, longitudinal wave propagates perpendicularly to the surface of the crack. The crack problem for bonded inhomogeneous materials. Numerical results for a pennyshaped interface crack in al2o3pmma. Quantification of fracture interaction using stress intensity factor.
For a pennyshaped crack subjected to a normal loading, the shear tractions vanish in the plane zo, and eqn. Its size may be found from the condition that the crack must close smoothly at r a, or. This study describes the evolution of the stress intensity factor k i for fissures in brittle elastic materials subjected to transient thermal actions. 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 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. This critical stress intensity factor is then a measure of. 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. Calculation of stress intensity factors and crack opening a. In this paper the elastodynamic response of a penny shaped crack located in a functionally. Dominant regimes are obtained by using a scaling analysis. Stress intensity factors for external and pennyshaped cracks in transversely isotropic cylinders subjected to thermal shock springerlink.
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. Aug 25, 2005 the problem of a penny shaped crack in a nonhomogeneous medium under torsion is investigated. The stressintensity factor for a pennyshaped crack. Conversion for stress intensity factors set both units and the input value on the left hand side. In the former paper the analysis given applies to an axisymmetric distribution of pressure p. Does anyone know how to calculate the stress intensity factor.
The torsion of a penny shaped crack in a functionally graded strip is considered. The stressintensity factor for a pennyshaped crack between two. Then, a conversion coefficient is proposed to convert the pixel coordinate into. Axisymmetric problems of a penny shaped crack 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. Stress intensity factors for penny and halfpenny shaped. Stress intensity factors for a penny shaped crack in a half. The crack propagation criterion of stress intensity factor is examined with the strain energy release rate. Recently, huang 1997 obtained explicit expressions ofstress and electric displacement intensity factors for a pennyshaped crack embedded in an infinitetransversely isotropic piezoelectric solid subjected to three loading conditions, respectively impermeable conditions on crack surfaces were employed. The constants a, define the following stressstrain relationships in transversely isotropic bodies. In this study, the stress intensity factor of a penny shaped crack hith smalldisturbed crack front line, hhich is subjected to a tensile load at the far field, is formulated on basis of rice formulation. 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. Dynamic stress intensity factor mode i of a permeable pennyshaped crack in a. 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 penny shaped crack at a bonded plane with localized. 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. Hence, blade cracks can more readily form interconnected fracture networks than pennyshaped cracks. Kachanovs approximate method for crack interactions int. The special case of a large crack subjected to modei loading is. The case studied is a penny shaped crack located in a rock mass and through which runs a fluid whose temperature falls in time. By using the hankel transform and the fourier series, the stress intensity factor of a concentric penny shaped crack in a finite long cylinder of a finite radius for mode iii is found. The stress intensity factor is evaluated directly based on displacement discontinuities dd using a threedimensional displacement discontinuity, boundary element method based on the equations of proposed in 1. Stress intensity factors for cracked finite plates with mixed. T1 mixedmode fatigue crack propagation of pennyshaped cracks. Numerical determination of the stress intensity factor ki. It is a theoretical construct usually applied to a homogeneous, linear elastic material and is useful for providing a failure criterion for brittle materials. 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. 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 stress intensity factors for a periodic array of interacting coplanar pennyshaped cracks huseyin lekesiza,1, noriko katsubea. Combined effect of pressure and shear stress on penny. The accuracy of the stress intensity factor calculation is satisfactorily examined for rectangular, penny shaped and elliptical planar cracks. Introduction the classical problem related to the penny shaped crack embedded in a homogeneous isotropic elastic medium was.
Crack shapes and stress intensity factors for edge cracked. The use of these formulae is illustrated by a consideration of the special case in which the. An expression for the surface displacement of the crack is also given. Shear stress intensity factors for a planar crack with slightly curved front recent work rice, 1985a has presented the calculations of the first order variation in an elastic displacement field associated with arbitrary incremental planar advance of the location of the front of a halfplane crack in a loaded elastic full space. 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, usa. The stress intensity is given as stress kiy sqrtc where c is flaw depth and y 1. The crack tip stress field is obtained by considering the asymptotic behavior of bessel function. Engineers are interested in the maximum stress near the crack tip and whether it exceeds the fracture toughness. 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. Subcritical propagation and coalescence of oilfilled cracks. Beam analysis 2d finite element analysis fea bolted joint analysis bolt pattern force distribution lug analysis column buckling fracture mechanics fatigue crack growth stress strain curve stress concentration mohrs circle unit conversion. 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 effect of crack interactions on stress intensity factors is examined for a periodic array of coplanar pennyshaped cracks.
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