It follows from 8 that the presence of the free surface leads to a nontrivial stress intensity factork ii. N2 this paper considers the large time asymptotic behavior of a nearsurface hydraulic fracture, that. Electric and magnetic polarization saturations for a. The effect of the elasticity of the materials in the vicinity of the layer on the stress intensity factor was examined by arin and erdogan 1971. An analytical solution for the axisymmetric problem of a. Multiple surface cracks in pressure vessels 549 optblok, the reduction of the stiffness matrix is done only once although the reduction of load vector and back substitution may be repeated for any number of iterations, with only a small additional computational time. Stress intensity factors at any point on the crack front of penny and halfpenny shaped cracks subjected to stress gradients are presented. Unlike the case involving the direct loading of the surfaces of the pennyshaped crack by surface tractions, the action of the surface boussinesq force can in. Additionally, crack size has important and slightly different effects on the crack extension forces for the zfc and fc cases. In their work, arin and erdogan considered a penny shaped crack located in a layer sandwiched between two dissimilar halfspaces. 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. The effects of various ratios of crack depth to plate thickness will also be examined. The pennyshaped crack at a bonded plane with localized. 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 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. Stress intensity factor determination for threedimensional crack. The rock mass is infinitely extended, homogeneous, and isotropic. Pdf stress intensity factor for a centrally located penny. Citeseerx document details isaac councill, lee giles, pradeep teregowda.
Dynamic stress intensity factor mode i of a permeable. Stress intensity factors for external and pennyshaped cracks in transversely isotropic cylinders subjected to thermal shock. Stress intensity factors for the pennyshaped crack under. Surface crack subject to mixed mode loading harvard john a.
Stress intensity factor of a pennyshaped crack with small. The penny shaped crack in an infinite solid and subjected to an internal pressure described by a fourier series. Stress intensity factors for surface cracks in round bar. The geometric model of a cracked body is a spatially periodic medium whose unit cell contains a number of arbitrarily placed aligned circular cracks. Crack opening displacements and stress intensity factors are also obtained for a throughthickness, center cracked bar with variable thickness. The problem is solved by the method of boundary integral equations using an iterative algorithm. 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. This paper presents an analytical investigation of a nonclassical fracture mechanics axisymmetrical problem for a nearsurface pennyshaped crack at the interface of physical and mechanical properties of a material. Stress intensity factors for a penny shaped crack in a. With a limitless increase in the distanceh from the crack to the free boundary, we obtain the case of a crack in an infinite material in general formulation we obtain the case of a pennyshaped crack at the interface of two halfspaces. An expression is developed for the stress intensity factor of a pennyshaped crack in an infinite elastic solid subjected to nonaxisymmetric normal loading. Kachanovs approximate method for crack interactions int.
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 proposed procedure is robust for sif calculation and crack propagation purposes. The stressintensity factor for a pennyshaped crack between two dissimilar materials. Stress intensity factors 243 where is a function determined by the stress distribution on the crack surface. Crack face interactions 1 introdnetion mechanical power transmission is successfully con ducted by the application of the cylindricalshaped bar. 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. A transient stress analysis for the problem of a torque applied suddenly to the surface of a pennyshaped crack in an infinite elastic body is carried out. 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. Stress intensity factors for penny and halfpenny shaped.
This expression is derived from existing results for a point load on an embedded pennyshaped crack and a concentrated ring load. A1, the stress intensity factor k ia for an edge crack with length a a is k ia 1. An asymmetric problem concerned with a pennyshaped crack in a long circular cylinder subjected to such stress has been considered by the present author in recent years 6. 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. Without loss of generality, bueckners fundamental field strength may be. We also propose the approach based on the determination of the effective stress field formed in the vicinity of a fixed crack by neighboring cracks interacting with this crack and with boundary surface. In this paper, the stress intensity factor k for the crack front line.
Accurate and fast evaluation of the stress intensity factor for planar cracks shows the. Read stress intensity factors for pennyshaped cracks perpendicular to graded interfacial zone of bonded bimaterials, engineering fracture mechanics on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. In our derivation, a twostep superposition scheme is utilized to obtain the stress field over the imaginary crack site. Fracture occurs when the stress at the atomic level cohesive strength of material. 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. 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. Stress intensity factors for complete circumferential. Stress intensity factor for a centrally located penny shaped crack.
Fracture analysis for a pennyshaped crack problem of a. Effect of heat conduction of pennyshaped crack interior. Abaqusstandard offers two different ways to evaluate the contour integral. The stress state and effective elastic moduli of an isotropic solid containing equally oriented pennyshaped cracks are evaluated accurately. Evolution and interaction of surface cracks under thermal. The paper concerns the contact interaction of the opposite faces of a penny shaped crack under harmonic wave at oblique incidence.
In other words, the crack is understood as a conducting medium, not a completely insulated medium since air of the crack interior has nonvanishing thermal conductivity, although it is low enough. By comparing the viewpoint of stress intensity factors for an edge crack and a penny shaped crack, we can understand the higher probability of fatigue fracture from surface defects. Prior to the presentation of thermal stress distribution induced by a penny shaped crack, let us first evaluate heat flux inside the crack. Stress intensity factors for external and pennyshaped. Numerical examples concern an asymmetric problem for interacting pennyshaped plane cracks in the unlimited and limited bodies. Stress intensity factor and effective stiffness of a solid. The stress intensity factors are studied for different values of the wave frequency. A threedimensional elastic stress analysis is performed on an infinite solid to study the interaction between a pennyshaped crack and a spherical inclusion.
The crack is located in a nearsurface layer parallel to the surface of a halfspace, which is subjected. The reported results show a considerable potential for using this method in calculating stress intensity factors for commonly encountered surface crack geometries in finite solids. The central difficulty in designing against fracture in highstrength materials is that the. Exact expressions for stress and electric displacement intensity factors are also presented. 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. Stress intensity factors for a penny shaped crack in a half space. It has been known that, for cracked ductile metals, plasticity results in an easing of stress intensity at. The stress intensity factors for a periodic array of. It illustrates the manner in which the stress intensity factor can be in. A formula is derived for the stress intensity factor at the rim of a pennyshaped crack in. 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 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. E shear modulus shear stress specimens stress intensity factors subjected to bending surface crack table.
Semianalytical expressions for both the crackopening displacements and the stress intensity factor distribution of a pennyshaped crack under a circular line load and a surface load on a circular region, arbitrarily located in the crack area, are given. An approximate expression is developed for the stressintensity factor due to concentrated point loads applied to the surfaces of a complete circumferential interior surface crack in a hollow circular cylinder. An axisymmetric problem for a penny shaped crack bridged by fibres is considered. Based on the theory of elasticity, previous analytical solutions concerning a pennyshaped interface crack employ the derivative of the crack surface opening displacements as the primary unknowns, thus leading to singular integral equations with cauchytype singularity. The accuracy of the stress intensity factor calculation is satisfactorily examined for rectangular, penny shaped and elliptical planar cracks. Stress intensity factor variation of a pennyshaped crack.
In their work, arin and erdogan considered a pennyshaped crack located in a layer sandwiched between two dissimilar halfspaces. Well known opening mode stress intensity factor variations for a penny shaped crack situated close and orthogonaly to the surface e. A threedimensional stress analysis of a pennyshaped. A mathematical formulation is presented for the dynamic stress intensity factor mode i of a permeable pennyshaped crack subjected to a timeharmonic propagating. The stress intensity factor, k \displaystyle k k, is used in fracture mechanics to predict the. T1 asymptotic solution for a pennyshaped nearsurface hydraulic fracture. 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. The singular solution is equivalent to that of the sudden appearance of a crack in a body under torsion. The accuracy of the stress intensity factor calculation is satisfactorily examined for rectangular, pennyshaped and elliptical planar cracks. Furthermore, the experimental observation that one single halfpenny crack rather than the two kidney cracks forms at higher indentation loads is explained by the model.
As a typicalexample, a closedform solution is first obtained for a pennyshaped crack subjected to a pair ofconcentrated forces acting in opposite directions and a pair of point charges on crack surfaces. 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. The effect of crack interactions on stress intensity factors is examined for a periodic array of coplanar pennyshaped cracks. N2 the stable growth of a crack created by the hydraulic pressurizing of a pennyshaped crack in a dry rock mass is investigated. Interaction of a pennyshaped crack and an external. Results are presented for uniform tension and linearly. 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. 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. Mode ii is a sliding inplane shear mode where the crack surfaces slide over one another in a direction perpendicular to the leading edge of the crack. Stress in a half space due to normal pressure and shear on. The stress intensity factor for a pennyshaped crack in an elastic. Pennyshaped crack in a long circular cylinder subjected. Hypersingular integral equations for the solution of penny.