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. Fracture mechanics provides a theory background for material and structures containing cracks and faults, and stress intensity factor sif is a key parameter in crack analysis. The corresponding pressures for the pennyshaped crack are 2. International journal of solids and structures 3319, 27192737 1996. 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. Stress intensity factors for a penny shaped crack in a half space. For example, consider a pennyshaped crack in an infinite body. 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. Fischer institute of mechanics, university for mining and metallurgy, franz josef stra. For a penny shaped crack embedded within an infinite solid and loaded remotely perpendicular to the crack at a stress. The singular state associated with the embedded crack with finite, nonaxisymmetric normal loading is that of plane strain.
Stress intensity factors for penny and halfpenny shaped. Subcritical propagation of an oilfilled pennyshaped crack. Today, it is the critical stress intensity factor k ic, found in the plane strain condition, which is accepted as the defining property in linear elastic fracture mechanics. 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. 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. 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. Irwin found that the stresses around a crack could be expressed in terms of a scaling factor called the stress intensity factor. It is a theoretical construct usually applied to a homogeneous, linear elastic material and i. 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. Formulation for the mode i stress intensity factor.
Elasticity, fracture mechanics, penny shaped crack, stress intensity factor, mixed boundary value. Stress intensity factor determination for threedimensional. Fracture mechanics assessment of large diameter wind turbine. The accuracy of the stress intensity factor calculation is satisfactorily examined for rectangular, penny shaped and elliptical planar cracks. Growth rate of a pennyshaped crack in hydraulic fracturing.
An axisymmetric problem for a penny shaped crack bridged by fibres is considered. In the former paper the analysis given applies to an axisymmetric distribution of pressure p. 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 or notch caused by a remote load or residual stresses. 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. Harmonic and impact load on the crack surface has been considered. The torsion of a penny shaped crack in a functionally graded strip is considered. 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. 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 variation of a pennyshaped crack. The mode i, ii and iii stress intensity factors sifs are calculated to investigate the possible propagation of the preexisting penny shaped interfacial crack. Interaction of a center of dilatation and a pennyshaped. Stress intensity factors at any point on the crack front of penny and half penny shaped cracks subjected to stress gradients are 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. Fracture of a finite piezoelectric layer with a pennyshaped.
The mode i, ii and iii stress intensity factors sifs are calculated to investigate the possible propagation of the preexisting pennyshaped interfacial crack. Quantification of fracture interaction using stress intensity factor. In theory the stress at the crack tip where the radius is nearly zero, would tend to infinity. Stress intensity factor wikimili, the free encyclopedia. In this brief note, we provide the failure stress of a solid containing a penny shaped crack by means of finite fracture mechanics. 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. This paper considers the transient stress intensity factor mode i of a penny shaped crack in an infinite poroelastic solid. Stress intensity factors at any point on the crack front of penny and halfpenny shaped cracks subjected to stress gradients are presented. Stress intensity factor wikipedia republished wiki 2. The line load solution which is derived from this is different in form to those given by previous workers and is more. Local stress field for torsion of a pennyshaped crack in a. Stress intensity factors for embedded cracks within.
Stress intensity factor for a centrally located penny shaped. 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. 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. The stressintensity factor for a pennyshaped crack between two. Thus, all of the activation processes, the applied field and the diameter of the penny shaped crack have significant effects on the intensity analysis and design of superconducting materials. This critical stress intensity factor is then a measure of. Experimental study on pennyshaped fluiddriven cracks in an. The crack is driven by a point source located at the origin, which has a known pumping rate. Stress intensity factor determination for threedimensional crack. The stress intensity factor of a concentric pennyshaped 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. Pennyshaped cracks by finite fracture mechanics request pdf. Interaction of a pennyshaped crack and an external circular. 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. Threedimensional static and dynamic stress intensity factor.
Fracture mechanics assessment of large diameter wind. Keywords magnetically dielectric crack pennyshaped crack field intensity factor cod fracture criterion magnetoelectroelastic behavior magnetoelectroelastic materials hankel transform 1 introduction materials possessing magnetoelectroelastic coupling effects have found increasing applications in engineer. By dr s al laham, structural integrity branch issue 2 date. Dynamic fracture analysis for a penny shaped crack in an fgm interlayer between dissimilar half spaces chunyu li and g. 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.
To describe the modes of a crack will require us to talk about the field around the. The stress intensity factor is computed using the standard procedure of the fredholm integral. Dynamic fracture analysis for a pennyshaped crack in an fgm interlayer between dissimilar half spaces chunyu li and g. The stress intensity factor for a penny shaped crack between two dissimilar materials. Stress intensity factor variation of a pennyshaped crack situated close to the free surface of a halfspace k. It is a theoretical construct usually applied to a homogeneous, linear elastic material and is useful for providing a failure criterion for brittle materials. The central difficulty in designing against fracture in highstrength materials is that the. Fracture analysis of a pennyshaped magnetically dielectric. The variation of shear mode stress intensity factors for a penny crack situated near to the free surface and the square corner is also reported for the first time, complementing the available results for tensile mode.
An expression is developed for the stress intensity factor of a pennyshaped crack in an infinite elastic solid subjected to nonaxisymmetric normal loading. The accuracy of the stress intensity factor calculation is satisfactorily examined for rectangular, pennyshaped and elliptical planar cracks. The problem of a concentric pennyshaped crack of mode iii in. Citeseerx document details isaac councill, lee giles, pradeep teregowda. Let us consider a 3d pennyshaped crack, defined in polar coordinates by the system r. The modes describe the local condition around a point on the front. Fracture mechanics of throughcracked cylindrical pressure. Considering a pennyshaped crack mode i, the stress intensity factor ki is related to the elastic pressure pr,t via 6,9. The stress intensity factors for a periodic array of. The stressintensity factor for a pennyshaped crack between.
Stress intensity factor sifbased fracture modeling has received. The result reduces to the closed form solution when the thickness of the piezoelectric layer becomes infinite. 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 stress intensity factor is a function of the applied load, the crack size and shape, and the geometry of the structure. Stress and induction field of a spheroidal inclusion or a pennyshaped crack in a transversely isotropic piezoelectric material. Elasticity, fracture mechanics, pennyshaped crack, stress intensity factor, mixed boundary value. The result can be expressed in terms of a fredholm integral equation of the second kind. Fracture analysis for a pennyshaped crack problem of a. 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. Dr r a ainsworth, group head, structural integrity branch dr m j h fox, team leader, structural. 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. 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 factors studied by boundary integro. The stress intensity factor for a pennyshaped crack in an elastic.
Thiscritical stress intensity factor isthenameasureof. Exact expressions for the stress and electric displacement at the crack border are given as a function of the stress intensity factor, which is determined by the applied thermal flux. The stress intensity factor, k \displaystyle k k, is used in fracture mechanics to predict the. This paper considers the transient stress intensity factor mode i of a pennyshaped crack in an infinite poroelastic solid. Fracture of a finite piezoelectric layer with a pennyshaped crack article in international journal of fracture 1721 november 2011 with 7 reads how we measure reads. In this section, we estimate the relative importance of toughnessrelated stress. The variation of shear mode stress intensity factors for a penny crack situated near to the free surface and the square corner is also reported for the. The torsion of a pennyshaped crack in a functionally graded strip is considered. 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 crack tip stress field is obtained by considering the asymptotic behavior of bessel function.
Additionally, crack size has important and slightly different effects on the crack extension forces for the zfc and fc cases. The stressintensity factor for a pennyshaped crack between two dissimilar materials. Engineering fracture mechanics volume 3, issue 3, october. The corresponding pressures for the penny shaped crack are 2. Dynamic fracture analysis for a pennyshaped crack in an fgm. Accurate and fast evaluation of the stress intensity factor for planar cracks shows. Sif plays a dominate role because it indicates the singular intensity of linear elastic crack field stress and strain. Stress intensity factor for a centrally located penny shaped crack. Hankel transform is used to reduce the problem to solving a fredholm integral equation. 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. Fracture propagation is controlled by the stress field near the crack tip. 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. 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.
An analytical solution for the axisymmetric problem of a. In this brief note, we provide the failure stress of a solid containing a pennyshaped crack by means of finite fracture mechanics. The boundary conditions of the problem have three different parts. Considering a pennyshaped crack mode i, the stress intensity factor k i is related to the elastic pressure pr,t via 6,9. On the expansion of a pennyshaped crack by a rigid circular. Thus, all of the activation processes, the applied field and the diameter of the pennyshaped crack have significant effects on the intensity analysis and design of superconducting materials.