Application of the cyclic crack propagation law proposed byaradradonculver, namelyd2adn n where. A new potential of a simple layer is introduced to account for the effect of the electric field. If the crack is first loaded in tension and then subjected to a heat flux, it seems reasonable to anticipate that. Sep 05, 2012 comparison of penny shaped and throughthickness cracks on a 1 0 0 crack plane looking at figures 3 and 8 we observe many of the same type of events in the two types of simulations. Stress intensity factor for an embedded elliptical crack under arbitrary normal loading article pdf available in international journal of fatigue 31s 1112. 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. Chiu and lin 25 were considering the fracture mechanics parameters, including the strain energy release rate, the stress intensity factors and phase angles. Sometimes a crack line may form a closed loop for example, when modeling a full pennyshaped crack without invoking symmetry conditions. Dynamic stress intensity factor mode i of a permeable. These authors also observed that pennyshaped cracks evolve from initial flaws of irregular shape.
A surface finish correction is made to the fatigue limit of the material to obtain an estimate of the fatigue limit of the part in the condition it is actually being used. Defect size dependence on threshold stress intensity for high. The stress intensity factors for a periodic array of. K apparent fracture toughness for blunt crack k critical stressintensity factor for fracture n load cycles. 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. Table 1 comparison of fully plastic h 1 factors for penny shaped crack. The stress intensity factors along the front of the pennyshaped crack can be found in figure 19. It is a theoretical construct usually applied to a homogeneous, linear elastic material and is useful for providing a failure criterion for brittle materials. Regions of separation and perfect thermal contact are developed at the crack faces. The accuracy of the stress intensity factor calculation is satisfactorily examined for rectangular, penny shaped and elliptical planar cracks. The critical stress for extension of a fiberbridged crack has been analyzed using the stressintensity approach. The stress intensity factor for an edge crack is given by. This paper investigates the variations of mode i stress intensity factor ki for inner pennyshaped and circumferential cracks in functionally graded solid and hollow thick walled cylinders, respectively with the changes of crack geometry, material gradation and loading conditions.
Keff when the crack is small in length 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. Dynamic stress intensity factor mode i of a pennyshaped. 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. Interaction of a pennyshaped crack and an external circular. K change in stress intensity factor during cyclic loading. Thermomechanical characterization of glass and its effect on. The stress intensity factor for a penny shaped crack in an elastic body under the action of symmetric body forces the effect of two point forces symmetrically placed. Radio frequency identification applications in pavements. Linear elastic fracture mechanics lefm cracks three modes. 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 and induction field of a spheroidal inclusion or a pennyshaped crack in a transversely isotropic piezoelectric material. Kachanov m, laures j 1989 threedimensional problems of strongly interacting arbitrarily located pennyshaped cracks. Subcritical propagation of an oilfilled pennyshaped. A2, the stress intensity factor for a pennyshaped crack with diameter 2ab d2.
The pennyshaped interface crack with heat flow core. 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. It includes a pennyshaped crack in an infinite piezoelectric plate. Atomistic modeling of pennyshaped and throughthickness. This paper considers the transient stress intensity factor mode i of a penny shaped crack in an infinite poroelastic solid. 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. Analysis of stress intensity factors for an edge cracked t. Stress intensity factors for external and pennyshaped. Over most of the range of fractional bonded area, the stress intensity calculated is constant at 0. The first approach is based on the conventional finite element method, which typically requires you to conform the mesh to the cracked geometry, to explicitly define the crack front, and to specify the virtual crack extension direction. Investigation of stress intensity factor for internal. Stress intensity factor of a pennyshaped crack with small. Because the stress field near the crack tip is asymptotic dominant or singular, it is characterized by the stress intensity factor. 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.
Formulation for the mode i stress intensity factor. Stress intensity factor determination plays a central role in linearly elastic fracture mechanics problems. Inversion formulae for integral transform pairs of general kinds properties of the mellin transform, y. Fatigue crack propagation behaviour derived from sn data in. A generation of special triangular boundary element shape. Stress intensity factors at any point on the crack front of penny and half penny shaped cracks subjected to stress gradients are presented. These authors also observed that penny shaped cracks evolve from initial flaws of irregular shape.
Comparison of pennyshaped and throughthickness cracks on a 1 0 0 crack plane looking at figures 3 and 8 we observe many of the same type of events in the two types of simulations. The stress intensity factor is a measure of the driving force for crack propagation. The stress intensity factor at the crack tips a and b of internal cracks is approximated by those for a penny. The line load solution which is derived from this is different in form to those given by previous workers and is more. The thermal stress field is analyzed by means of the potential function method for transversely isotropic solids. The pennyshaped interface crack with heat flow, part 1. In the 0 1 01 0 1 system we get formation of fcc followed by twinning in both cases, and in the 0 1 00 0 1 system we only get some fcc formation. Theoretical crack growth analysis indicated that when initiating an engineering size. A closed form fundamental solution is then obtained for a penny shaped crack subjected to pointforces and point charges symmetrically applied on its upper and lower surfaces. Use of the stressintensity factor for a pennyshaped internal.
When evaluating the formulas, the angles and must lie in the ranges, respectively. Interaction of a pennyshaped crack and an external. Thiscritical stress intensity factor isthenameasureof materialtoughness. Dynamic pennyshaped crack in a transversely isotropic. Defect size dependence on threshold stress intensity for. The stress intensity factor for a griffith crack in an elastic body in which body forces are acting. International journal of solids and structures 3319, 27192737 1996. 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.
Stress intensity factor determination for threedimensional crack. The paper presents a solution for axisymmetric propagation of a pennyshaped crack driven by a thinning fluid. Reflection coefficient versus normalized crack depth for a halfpenny shaped surface crack using the two models is given in fig. A crack will not propagate under a static but insufficient stress intensity factor, but. Tsang et al 6 investigated the sif of parallel pennyshaped cracks under itype load. Accurate and fast evaluation of the stress intensity factor for planar cracks shows the.
The stress intensity factor for a pennyshaped crack in an elastic body under the action of symmetric body forces the effect of two point forces symmetrically placed. 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. The potential theory method has been generalized in this paper to analyze the piezoelectric crackproblem. 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. Pennyshaped crack in an infinite domain under uniaxial tension. The effect of crack interactions on stress intensity factors is examined for a periodic array of coplanar pennyshaped cracks. The stress intensity factor computed for two pennyshaped inplane cracks. Penny shaped crack in an infinite solid the figure shows a circular crack with radius a in an.
Citeseerx document details isaac councill, lee giles, pradeep teregowda. A closed form fundamental solution is then obtained for a pennyshaped crack subjected to pointforces and point charges symmetrically applied on its upper and lower surfaces. Stress intensity factor for an embedded elliptical crack. The functionally graded material of cylinders consists of epoxy and glass. Citeseerx the pennyshaped interface crack with heat flow. The paper presents a solution for axisymmetric propagation of a penny shaped crack driven by a thinning fluid. The magnitude of the normalized dynamic stress intensity is also calculated for the sample materials for a range of the frequency factor k as shown in fig. Sr 1 where sr is the nominal, uniform stress range at the detail and a is the crack depth.
The pennyshaped interface crack in a uniform tension field was treated by keer et al. As a common parameter to character the ability of crack propagation, the stress intensity factor sif is widely used in investigating the interactions among multicracks. Stress intensity factor piezoelectric material piezoelectric layer versus versus versus. Various energy balances can be constructed relating the energy released during fracture to the energy of the resulting. Penny shaped crack in 3d infinite domain subjected to. The boundary conditions of the problem have three different parts. The penny shaped interface crack in a uniform tension field was treated by keer et al.
Jan 01, 20 the effect of crack interactions on stress intensity factors is examined for a periodic array of coplanar pennyshaped cracks. In his study, the frequencydependent behavior of the dynamic stress intensity factor exhibits excellent agreement with that for the dry crack in an ordinary elastic medium chen and sih, 1977. Stress intensity factors at any point on the crack front of penny and halfpenny shaped cracks subjected to stress gradients are presented. A method of successive approximation together with the fourier integral and the bessel series are. Introduction to fracture mechanics david roylance department of materials science and engineering. A through thickness crack in 2d infinite plane subjected to remote tension 170 6. The singular state associated with the embedded crack with finite, nonaxisymmetric normal loading is that of plane strain. Evaluation of solidsolid bonds nondestructively using ultrasound. In order to test the accuracy, we also list the results in tables 3 5. Jul 19, 20 figure 11 shows the normalised stress intensity factor k i. A contact problem for a smooth rigid disc inclusion in a. The stresselectric intensity factors predicted by permeable and energetically consistent models are, respectively, independent of and dependent on the electric field for the pennyshaped crack and the two representative nonplanar cracks. Abaqusstandard offers two different ways to evaluate the contour integral.
Aug 25, 2005 stress concentration at a pennyshaped crack in a nonhomogeneous medium under torsion stress concentration at a pennyshaped crack in a nonhomogeneous medium under torsion huang, g wang, y yu, s. Thiscritical stress intensity factor isthenameasureof. Mathematically, the energy release rate is expressed as the decrease in total potential energy per increase in fracture surface area. C crack length n number of loading cycles a, n fracture properties of hma. This is applicable to cracks under plane stress, plane strain, and antiplane shear. Stress in a half space due to normal pressure and shear on. Matrix crack extension at a frictionally constrained fiber. Phurkhao 20 studied the dynamic stress intensity factor of an impermeable, tractionfree penny shaped crack in a poroelastic medium subjected to a timeharmonic longitudinal wave. The results indicated that the fracture mechanics stressintensityfactor range, ak, is the gov erning parameter for inducing fatigue crack initiation from a flaw. 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. 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. 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.
Results indicated that the range of calculated displacements and pore pressure were dependent upon the. The geometry can be found in figure 9, and three mesh models can also be found in figure 10a. Kachanovs approximate method for crack interactions kachanov, m. Reflection coefficient versus normalized crack depth for a half penny shaped surface crack using the two models is given in fig. The stress intensity factor computed for two pennyshaped inplane. Fatigue crack propagation behaviour derived from sn data. Discussion and conclusion the scattering of a plane longitudinal wave by a pennyshaped crack in a transversely isotropic material is investigated using the techniques of hankel transform. Subcritical propagation of an oilfilled pennyshaped crack. Kachanovs approximate method for crack interactions int. Equivalent stress intensity factor an overview sciencedirect topics.
The central difficulty in designing against fracture in highstrength materials is that the. The analysis uses a new shearlag formulation of the crackclosure traction applied by the bridging fibers based on the assumption of a constant sliding friction stress over the sliding length of the fibermatrix interface. In this example, an embedded pennyshaped crack under nonuniform loading is considered. Surface finish factor k sf fatigue limits are determined from small polished laboratory specimens. Xiao zm, lim mk, liew km 1995 stress intensity factors of two internal elliptical cracks in threedimensional solid. Thermomechanical characterization of glass and its effect. The energy release rate, is the rate at which energy is transformed as a material undergoes fracture and has units of energyperunitarea. 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.
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