Analysis of thermal stress intensity factors for cracked cylinders using weight function method

In this paper a general weight function was derived to evaluate the thermal stress intensity factors of a circumferential crack in cylinders. The weight function derived is valid for a wide range of thin- to thick-walled cylinders and relative crack depth. Closed-form stress intensity factor based on the weight function method was derived as a function of the Biot number and relative depth and various inner-to-outer radius ratios of cylinders. The accuracy of the analysis has been examined using the finite element method results and were compared to existing solutions for uniform loading in the literature for special geometries, indicating an excellent agreement.     

An investigation of the stress intensity factor for a finite internally cracked plate by using variational method

The eigenfunction expansion variational method (EEVM) is proposed to determine the stress intensity factors for two-dimensional cracked bodies. In the new method, the undetermined coefficients in the truncated eigenfunction expansion form are determined by using the variational method. It is expected that the uncertainty initiated in boundary collocation scheme can be avoided. Several numerical examples are given, which can prove the efficiency of the EEVM method.     

The stress intensity factor for a double edge cracked plate by boundary collocation method

A set of complex functions for the double edge cracked plate is proposed. The boundary collocation method is used for estimating the stress intensity factors and the results obtained by this method compare very favorably with existing solutions for many cases.

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Résumé On propose un jeu de fonctions complexes pour représenter une plaque fissurée sur ses deux bords. On utilise la méthode de collocation des limites pour estimer les facteurs d'intensité de contraintes. Dans de nombreux cas, les résultats obtenus par cette méthode supportent très favorablement la comparaison avec les solutions existantes.

     

Calculation of mode III stress intensity factor by BEM for cracked axisymmetric bodies

This paper is concerned with the numerical calculation of Mode III stress intensity factor by BEM for cracked axisymmetric bodies, under torsion. Mode III stress intensity factors K _III are obtained using the asymptotic displacement field in the vicinity of the crack border. The asymptotic field is derived by integration along the boundary of the meridian of the cylinder. For traction free cracks no discretization of the crack surface was found necessary. Numerical results proving the efficiency of the proposed method are presented and compared with results given in the literature and with those obtained by FEM.     

Two-dimensional stress intensity factor computations using the boundary element method

A multidomain boundary element formulation for the analysis of general two-dimensional plane strain/stress crack problems is presented. The numerical results were accurate and efficient. The analyses were performed using traction singular quater-point boundary elements on each side of the crack tip(s) with and without transition elements. Traction singular quarter-point boundary elements contain the correct √r displacement and 1/√r traction variations at the crack tip. Transition elements are appended to the traction singular elements to model the √r displacement variation. The 1/√r traction singularity is not represented with these elements. Current research studies for the crack propagation analysis of quasi-static and fatigue fracture problems are discussed.     

The calculation of stress intensity factors using the finite element method with cracked elements

The calculation of stress intensity factors for complicated crack configurations in finite plates usually presents substantial difficulty. A version of the finite element method solves such problems approximately by means of special cracked elements. A general procedure for evaluating the stiffness matrix of a cracked element is developed, and numerical results obtained by the simplest elements are compared with those provided by other methods.

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Zusammenfassung Die Berechnung von Spannungsintensitätsfaktoren für komplizierte Rißgefüge in endlichen Platten bereitet gewöhnlich erhebliche Schwierigkeiten. Fine Variante finite element method löst annähernd solche Probleme mit Hilfe von spezieller gerissenen Elementarteilen.Es wird ein allgemeines Verfahren zur Ermittlung der Steifheits-Matrix eines gerissenes Elementarteilchens aufgestellt. Die numerischen Ergebnisse welche mit den einfachsten Elementarteilen bestimmt wurden, werden mit den nach anderen Verfahren erzielten Ergebnissen verglichen.

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Résumé Pour une plaque finie et une configuration de fissures compliquée, le calcul des coefficients d'intensité de contraintes s'avère normalement difficile, voire pratiquement impossible.Toutefois, une variante de la méthode des éléments finis permet de résoudre ce genre de problèmes de façon approximative moyennant l'adoption d'un élément fissure.Dans cet article l'auteur développe une méthode générale permettant d'évaluer la matrice de raideur d'un élément fissuré.Ensuite il procède pour des éléments simples à une comparaison des résultats numériques obtenus respectivement par d'autres méthodes et par la sienne.

     

Determination of stress intensity factors in cracked plates by the finite element method

Stress fields near crack tips in an elastic body can be specified by the stress intensity factors which are closely related to the stress singularities arising from the crack tips. These singularities, however, cannot be represented exactly by conventional finite element models. A new method for the analysis of stresses around cracks is proposed in this paper on the basis of the superposition of analytical and finite element solutions. This method is applied to several two-dimensional problems whose solutions are obtained analytically, and it is shown that their numerical results are in excellent agreement with analytical ones. Sufficiently accurate results can be obtained by the conventional finite element analysis with rather coarse mesh subdivision. Computational efforts are then considerably reduced compared with other methods.     

Stress intensity solutions for cracked plates by the dual boundary method

We describe the application of the dual boundary element method for the determination of stress intensity factors in plate bending problems. The loadings considered include internal pressure, and also combined bending and tension. Mixed mode stress intensity factors are evaluated by a crack surface displacement extrapolation technique and the J-integral technique. The boundary element results for the case studies considered in the paper have been compared with either analytical or finite element results and in all cases good agreement has been achieved. __________ Translated from Problemy Prochnosti, No. 5, pp. 81–93, September–October, 2007.     

Two-dimensional finite element method for stress intensity factor using adaptive mesh strategy

Finite element analysis (FEA) combined with the concepts of Linear Elastic fracture mechanics (LEFM) provides a practical and convenient means to study the fracture and crack growth of materials. A numerical analysis (FEM) of cracks was developed to derive the SIF for two different geometries, i.e., a rectangular plate with half circle-hole and central edge crack plate in tension loading conditions. The onset criterion of crack propagation is based on the stress intensity factor, which is the most important parameter that must be accurately estimated and facilitated by the singular element. Displacement extrapolation technique (DET) is employed, to obtain the stress intensity factors (SIFs) at crack tip. The fracture is modeled by the splitting node approach and the trajectory follows the successive linear extensions of each crack increment. These comprehensive tests are evaluated and compared with other relevant numerical and analytical results obtained by other researchers.     

Analysis of stress intensity factors for three-dimensional finite cracked bodies by a variational alternating method

A variational alternating method which is suitable for analyzing finite three dimensional cracked solid is presented. The stress analysis of the unracked solid is performed by the functional variable displacement solution and the variational method. The stress intensity factor solution for an embedded elliptical crack and a surface flaw in a finite plate for the case of mode-I loading are obtained by the variational alternating method. The results are compared with that of reference.     

Computation of the weight function from a stress intensity factor

A simple representation for the crack-face displacement is employed to compute a weight function solely from stress intensity factors for a reference loading configuration. Crack face displacements given by the representation are shown to be in good agreement with analytical results for cracked tensile strips, and stress intensity factors computed from the weight function agree well with those for edge cracks in half planes, radial cracks from circular holes, and radially cracked rings. The technique involves only simple quadrature and its efficacy is demonstrated by the example computations.     

The calculation of stress intensity factors ssing the finite element method with cracked elements

The calculation of stress intensity factors for complicated crack configurations in finite plates usually presents substantial difficulty. A version of the finite element method solves such problems approximately by means of special cracked elements. A general procedure for evaluating the stiffness matrix of a cracked element is developed, and numerical results obtained by the simplest elements are compared with those provided by other methods.

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Zusammenfassung Die Berechnung von Spannungsintensitätsfaktoren für komplizierte Rißgefüge in endlichen Platten bereitet gewöhnlich erhebliche Schwierigkeiten. Eine Variante finite element method löst annähernd solche Probleme mit Hilfe von spezieller gerissenen Elementarteilen.Es wird ein allgemeines Verfahren zur Ermittlung der Steifheits-Matrix eines gerissenes Elementarteilchens aufgestellt. Die numerischen Ergebnisse welche mit den einfachsten Elementarteilen bestimmt wurden, werden mit den nach anderen Verfahren erzielten Ergebnissen verglichen.

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Résumé Pour une plaque finie et une configuration de fissures compliquée, le calcul des coefficients d'intensité de contraintes s'avère normalement difficile, voire pratiquement impossible.Toutefois, une variante de la méthode des éléments finis permet de résoudre ce genre de problèmes de façon approximative moyennant l'adoption d'un élément fissuré.Dans cet article l'auteur développe une méthode générale permettant d'évaluer la matrice de raideur d'un élément fissuré.Ensuite il procède pour des éléments simples à une comparaison des résultats numériques obtenus respectivement par d'autres méthodes et par la sienne.

     

A numerical mode I weight function for calculating stress intensity factors of three-dimensional cracked bodies

A numerical mode I weight function first presented by Parks and Kamenetzky [1] is extended for application to three-dimensional cracked bodies. This weight function makes use of the stiffness derivative method as part of finite element calculations. A virtual crack extension is employed. The major difficulty is proper interpretation of the shape function variation for implementation in three dimensions. Numerical examples in two and three dimensions are examined. Excellent results are obtained in comparison to solutions in the literature, as well as some further finite element studies which are carried out here.     

Time domain boundary element method for dynamic stress intensity factor computations

This paper presents a procedure for transient dynamic stress intensity factor computations using traction singular quarter-point boundary elements in combination with the direct time domain formulation of the Boundary Element Method. The stress intensity factors are computed directly from the traction nodal values at the crack tip. Several examples of finite cracks in finite domains under mode-I and mixed mode dynamic loading conditions are presented. The computed stress intensity factors are represented versus time and compared with those obtained by other authors using different methods. The agreement is very good. The results are reliable and little mesh dependent. These facts allow for the analysis of dynamic crack problems with simple boundary discretizations. The versatile procedure presented can be easily applied to problems with complex geometry which include one or several cracks.     

Three-dimensional stress intensity factor calibration for a stiffened cracked plate

Three-dimensional finite element analyses are used in this paper to calibrate the stress intensity factor in a cracked stiffened plate subjected to remote uniform traction. An accurate numerical determination of the stress field and stress intensity variation through the thickness of a central cracked plate was first carried out in order to evaluate three-dimensional effects. A stiffened cracked plate was then analysed, taking into account the results and the conclusions obtained in the previous study. Such a structure was chosen due to the growing interest for large integral metallic structures for aircraft applications, following the continuous need for low cost and the emergence of new technologies. The J-Integral technique was used to calculate the values of the stress intensity factor along the plate thickness. The plane strain behaviour near the crack front and the variation of the opening stress are discussed.     

Evaluation of the T-stress and stress intensity factor for a cracked plate in general case using eigenfunction expansion variational method

This paper investigates the T-stress and stress intensity factor for a cracked plate in general case. In the general case, the shape of boundary and the applied loading are arbitrary. The eigenfunction expansion variational method (EEVM) is developed to evaluate the T-stress and stress intensity factor. For the traction boundary value problem, the EEVM is equivalent to the theorem of least potential energy in elasticity. Therefore, the EEVM possesses a clear physical meaning and it does not depend on any boundary collocation scheme. Several numerical examples are presented, which include: (1) a line crack in circular plate and (2) a line crack in rectangular plate. Numerical examination for convergence in an example is carried out.     

Calculation of stress concentration in the manipulator element using a combined finite and boundary element method

Elastic stress concentration in a manipulator element is calculated within the framework of the two-dimensional stressed state model. The purpose here is to make recommendations for selecting the radius of joining of the beam parts of the element based on analysis of maximum stresses in the stress concentration zone. Combination of the finite element and boundary element methods is proposed for solving the problem. A coarse finite element subdivision is used for the initial calculation for the entire element. Then, the solution is refined by using boundary elements in the identified zone. Comparison of calculation results with solutions obtained by the finite element and boundary element methods points to the effectiveness of the proposed algorithm for stress concentration calculations.Translated from Problemy Prochnosti, No. 6, pp. 72–74, June, 1991.     

Compliance based assessment of stress intensity factor in cracked hollow cylinders with finite boundary restraint: Application to thermal shock part I

The evaluation of mode I stress intensity factor associated with the creep-free thermal shock (TS) of finite length elastically/thermo-elastically restrained cracked hollow cylinders is a problem of interest. Among existing evaluation methodologies, the mechanical weight function approach is often perceived to be an optimal compromise between simplicity and accuracy for and more generalised K_I evaluation. However, to confidently apply a mechanical weight function methodology in such circumstances requires the derivation of different weight functions for each potential boundary restraint configuration, i.e. free, flexible or rigid boundary conditions. In this article, the traditional mechanical weight function philosophy is complimented with an elastic compliance analysis, enabling the mechanical weight function and geometry factors for an equivalent semi-infinite cracked hollow cylinder to be used to evaluate associated with a wide range of finite length elastically/thermo-elastically restrained cracked hollow cylinders. The need for deriving different weight functions is therefore removed and the proposed Compliance Adjusted Weight Function (CAWF) approach becomes more ‘user-friendly’. The targeted cracked hollow cylinders are assumed to exhibit an exterior circumferential edge crack or an exterior circumferential semi-elliptical surface crack.