Irwin arrived at the definition of \k\ as a nearcracktip approximation to westergaards complete solution for the stress field surrounding a crack 2. Stress intensity factor for a corner crack at the edge of. 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. Finite element method analysis of stress intensity factor. Stress intensity factors for an inclined edge crack in a. K is not to be confused with the elastic stress concentration factor k t. As b approaches zero, the situation approaches that of a very fine crack. In this paper, based on a huge amount of numerical analysis, an empirical formula of stress intensity factors sifs for cracks initiated from the interface edge with various directions and crack length has been proposed. All three modes of crack surface displacements are considered, as well as specialized results applicable to plate and shell bending, results for various media e,g, anisotropic, viscoelastic or nonhomogeneous are contrasted. Stress intensity factor, holeedge cracks, finite element, franc software.
The magnitudes of these stresses at a given point are entirely dependent on k. The y term allows the effects of finite width, crack shape, position along crack front, bulging, stress concentration factors, local stress concentration. Introduction to fracture mechanics david roylance department of materials science and engineering massachusetts institute of technology. Some of these solutions are based on the use of thinshell theory18, which does not take into account the three dimensional nature. Apr 17, 2017 2d ct specimen stress intensity factor analysis. The correction factor which relates the stress intensity factor for this problem to that for an isolated crack in an infinite body is evaluated for a range of orthotropic material properties. As the stress intensity factor reaches the k ic value, unstable fracture. Single edgecrack stress intensity factor solutions. The stress intensity, k i, represents the level of stress at the tip of the crack and the fracture toughness, k ic, is the highest value of stress intensity that a material under very specific planestrain conditions that a material can withstand without fracture.
The correction factors for various geometrical conditions under a given load. The plane strain fracture toughness for the material kis 26 ksiyin and yield strength is 75 ks. Stressintensity factors by boundary collocation for. Jun 09, 2016 stress intensity factor of edge crack.
Stress intensity factor for small edge crack in interfacial. Empirical formula for stress intensity factor of crack. Relationship between crack propagation and the stress. Paper open access stress intensity factors of double edge. Each of the terms accounts for a specific aspect of the crack geometry or loading. The stress intensity factor weight function for a single edge crack originating from the tplate weld toe was derived from a general weight function form and two reference stress intensity factors. For problems of purely mode i crack behavior, bowie and freese present the weight function expression as 1 k 1 1 k 1 2 h 2. In order to determine the stress intensity factor, various numerical methods were utilized. Failure occurs once the stress intensity factor exceeds the materials fracture toughness. The stress intensity factor for two cracks of unequal length at the edge of an elliptical hole increases with the crack length and the majortominor axis ratio of the elliptical hole.
The crack growth rate accelerates as the maximum stress intensity factor approaches the fracture toughness of the material. It is a theoretical construct usually applied to a homogeneous, linear elastic material and is useful for providing a failure criterion for brittle materials. Stress intensity factor solution for edge interface crack. Single edgecrack stress intensity factor solutions sciencedirect. Stressintensity factors for singleedgenotch specimens in. This section will present a catalog of stress intensity factor solutions for some typical crack geometries. Numerical evaluation of stress intensity factors ki j.
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. Stress intensity factor for a corner crack at the edge of a. Analysis of stress intensity factors for an edge cracked tsection in tension by. This threshold value of k is called the fracture toughness or critical stress intensity factor, k. Stress intensity factor for a thinwalled cylinder containing an edge circumferential crack under bending p. Stressintensity factors for singleedgenotch specimens. Analysis of stress intensity factors for an edge cracked t section in tension.
The stressintensity factor concept, crackclosure mechanics, and the observation that fatigue is crack propagation in many engineering materials has led to a merger of fatigue and. Pdf the stress intensity factor of hole edge cracks in a. Stress intensity factors for cracklineloaded edgecrack. Analysis of stress intensity factors for an edge cracked t. The problem of an edge crack in a semiinfinite plane of linear elastic orthotropic material is studied. An edge crack of length a is introduced in the plate. Stressintensity factors by boundary collocation for single. The stress intensity factor solutions for edge cracks in a. A major achievement in the theoretical foundation of lefm was the introduction of the stress intensity factor k the demand as a parameter for the intensity of stresses close to the crack tip and related to the energy release rate bazant and planas 1998. Stress intensity factor at the holeedge crack tips in a. Dtdhandbook summary of stress intensity factor information.
The stress intensity factor is calculated for a given geometry and load, and compared with a threshold value of k above which cracks will propagate in the given material. At this point the crack will grow in a rapid and unstable manner until fracture. Single edge crack stress intensity factor solutions. Stress intensity factors for cracklineloaded edgecrack specimens by john e. Strength evaluation of butt joint by stress intensity factor. For the love of physics walter lewin may 16, 2011 duration. The stress intensity factor for edge crack in finite plate can be achieved by the formula 3 when 1 h b. A general survey of the results of elastic stress analyses of cracked bodies is the basic objective of this work, the stress intensity factor method of representing results is stressed and compared with other similar methods. It is characterized by the stress intensity factor. Stress intensity factor k stresses in the vicinity of the crack tip are dependent on r, and k.
The theoretical stress concentration at the edge of the hole is. Abaqus tutorials for beginnerscrack analysis in abaqus for 2d. The results are presented in terms of the dimensionless quantity y kibh32pa, where b and h are the. Williams stress function to determine values of the stress intensity factor ki for single edge cracks in plate specimens subject to splitting forces applied close to the crack and acting transversely to it. The geometry of the cracked body imposes an effect on the new crack tip stress field, thus modifying the value of the stress intensity factor. Thiscritical stress intensity factor isthenameasureof. Pdf the stress intensity factor solutions for edge cracks in a.
The stress intensity factor is generally expressed in the form k y. The small edge crack is strongly dominated by the singular stress field near the interface edge. A boundaryvaluecollocation procedure was used in conjunction with the williams stress function to determine values of the stress intensity factor k for single edge cracks of various depths in specimens subjected to pure bending. Thus, a small edge crack having the size a a a b 3 has an equivalent stress intensity factor with a large pennyshaped crack. Results for the remote tension loading are compared with those obtained by the boundaryintegral equation bie method and threedimensional finiteelement technique based on singular elements. Stress intensity factors and weight functions for special crack problems. At high stress intensities, crack growth rates are extremely high and little fatigue life is involved. Topics include stress intensity factors, fracture toughness, linear elastic.
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. This threshold value of k is called the fracture toughness or. Pdf the stress intensity factor solutions for edge. However, this evaluation method is inconvenient for engineering application due to its complicity. This represents the effective local stress at the crack tip. Many of these solutions are found in computer programs and handbooks. Pdf the stress intensity factor solutions for edge cracks. The stress intensity factor k at a crack is given by k c sigma squareroot pi a where sigma is the farfield stress, a is the crack length, and c is a parameter that depends on the geometry of the specimen and crack. Calculation of stress intensity factor k i using digital image correlation assuming three.
This section will present a catalog of stressintensity factor solutions for some typical crack geometries. Edgecrack specimens by john e, srawzey and bernard gross. 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. The results are of use in connection with ksub ic fracture toughness tests, which utilize rectangularsection cracknotch beam specimens loaded in fourpoint. Stress intensity factor, hole edge cracks, finite element, franc software.
Problem 2 the stress intensity factor for a tensile member plate with a single edge crack is given by the figure below. Stress intensity factors for edge cracks in round bars. Approximate determination of stress intensity factor for. The size and orientation of the crack with respect to the applied stresses play a very large role. Fracture mechanics materials technology eindhoven university. Stress intensity factor results for the case of circular corner crack obtained by the macroelement technique is presented in this paper. I saw the example of single crack, and i didnt end up understanding why the prescribed displacement is made. Region iii is characterized by rapid, unstable crack growth. Edge crack, bimaterial systems edge crack, composite materials edge crack, isotropic material interaction problem between a hole and a crack orthotropic rectangular plate with a rigid ribbonlike. A special situation that is often of practical interest is a. The stress intensity factor method of representing results is stressed and compared with other similar methods. Stressintensity factor results for the case of circular corner crack obtained by the macroelement technique is presented in this paper. For the case of the edge crack shown in the figure, c is given by.
The analysis of stress intensity factor of small edge crack near the interface in bimaterial and butt joint plates is carried out by changing the length and the location of the crack and the region dominated by the interface edge is examined. A2, the stress intensity factor for a pennyshaped crack with diameter 2 a b d 2. 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. A boundaryvaluecollocation procedure was used in conjunction with the williams stress function to determine values of the stressintensity factor k for single edge cracks of various depths in specimens subjected to pure bending. Two cracks with the same stress intensity will have the same behavior. The solutions are categorized by the location of the crack, either embedded, in a plate surface or edge, or at a hole, in tables 11. The calculation of stress intensity factors for the single edgecracked geometry has received much attention due to its frequent use as a test specimen in linear. Williams stress function to determine values of the stressintensity factor ki for singleedge cracks in plate specimens subject to splitting forces applied close to the crack and acting transversely to it. K is called a stress field parameter, or stress intensity factor. Influence coefficients were defined in the crack reference frame thus highlighting the coupling. Stress intensity factors for cracklineloaded edgecrack specimens. Finite element method analysis of stress intensity factor in. Problem 2 the stress intensity factor for a tensil. Hi everyone, im working in fracture mechanics, trying to find out how to calculate the stress intensity factor in mode i.
Rice the partthrough surface crack in an elastic plate. For example, the stress intensity factor solution for a single edge cracked plate in. Gentilcore a thesis j presented to the graduate and research committee of lehigh university in candidacy for the degree of master of science in mechanical engineering and mechanics lehigh university may 21, 1993. Constant amplitude crack growth technical background. For a through edge crack in a uniform stress field m s. In fracture mechanics, a stress intensity factor is calculated as a function of applied stress, crack size, and part geometry. This page provides stress intensity factor solutions for common cases. By interpolating finite element results in the angular range 0. Pdf the stress intensity factor weight function for a single edge crack originating from the tplate weld toe was derived from a general weight. The methods were the boundary element method 8,9, the meshless method 10,11, the finite element method 5, 1220, and virtual crack extension 21,22. In theory the stress at the crack tip where the radius is nearly zero, would tend to infinity. This is the case for linear elastic fracture mechanics lefm.
The stressintensity factor is the cornerstone of the damagetolerance and durability design concepts used by the aerospace community around the world. The general form of the stress intensity solution for any crack can be described as. Stress intensity factors of double edge cracks in large groove plates under mode i tension a e ismail1, m a azlan 1, m l m tobi and m h ahmad2 1faculty of mechanical and manufacturing engineering, universiti tun hussein onn malaysia, batu pahat, johor, malaysia. Strength evaluation of butt joint by stress intensity.
It is found that the dimensionless stress intensity factor of small crack, normalized by the singular. Abaqus tutorials for beginners crack analysis in abaqus for 2d. There are various stress intensity factor solutions, particularly for flat plates and pressure vessels with various cracked geometries. The calculation of stress intensity factors for the single edge cracked geometry has received much attention due to its frequent use as a test specimen in linear fracture mechanics studies. In this paper, based on a huge amount of numerical analysis, an empirical formula of stress intensity factors sifs for cracks initiated from the interface edge with various directions and. Irwins stress intensity factora historical perspective. 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. The results are of use in connection with ksub ic fracture toughness tests, which utilize rectangular.
282 557 523 957 1239 1365 911 30 129 132 179 501 1120 118 1 1001 1044 1107 1578 687 577 454 626 1048 1390 1549 450 123 18 324 107 817 465 1264 812 371 1269 302 1346 544 1347