Dugdale model solutions for a single edge cracked plate

International Journal of Fracture - A technique for improving the convergence rate of the Gauss-Seidel iterative procedure for finite element analysis is discussed. It is noted that this technique...     

Bilby,Cottrell and Swinden model solutions for centre and edge cracked plates subject to arbitrary mode I loading

Solutions to the Bilby, Cottrell and Swinden model are presented for centre and edge cracks in plates subject to arbitrary mode I loading. They are in good agreement with known plane strain solutions. The recent determination of centre and edge crack compliance functions for crack length to plate width ratios of up to 1 enable solutions to be obtained up to general yield. The solutions for a crack in an infinite body and in a half-plane are compared with the finite width results and their region of applicability discussed.

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Résumé On présente des solutions aux modèles de Bilby, Cottrell et Swinden dans le cas de fissures centrales et latérales disposées dans des tôles soumises à un mode de charge I arbitraire. Ces solutions sont en bon accord avec la solution connue en état plan de déformation.La détermination récente des facteurs de compliance relatifs à des fissures centrales et latérales et pour des rapports de largeur de fissures à largeur de tôles allant jusqu'à 1, permet d'obtenir des solutions valables jusqu'à la limite d'écoulement généralisé. Dans les cas d'une fissure située dans un corps infini, et de la fissure située dans un demi-plan, les solutions sont comparées avec les résultats relatifs à des largeurs finies, et leurs limites d'application en sont discutées.

     

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.     

Fully plastic J-integral solutions for surface cracked plates under biaxial loading

In this paper, surface cracked plates under biaxial tension are studied. Three-dimensional elastic-plastic finite element analyses have been carried out to calculate the J-integral for surface cracked plate for a wide range of geometry, biaxiality and material properties. Fully plastic J-integral solutions along the front of the surface cracks are presented for Ramberg-Osgood power law hardening material of n = 3, 5, 10 and 15. Geometries considered are a/c = 0.2, 1.0 and a/t = 0.2, 0.4, 0.6 and 0.8 and the biaxial ratios of 0, 0.5 and 1. Based on these results, the J-integral along the crack front for general elastic-plastic loading conditions can be estimated using the EPRI scheme. These solutions are suitable for fracture analyses for surface cracked plates under biaxial loading.     

Validity limits of the Dugdale model for thin cracked plates under biaxial loading

Experimental results show that there are significant biaxial effects on the fracture behaviour of thin cracked plates. In this paper we examine the possibility of extending the Dugdale model in the presence of biaxial loads. This investigation is mainly concerned with the validity limits of the model in respect of the plastic flow rules. Through a careful analysis of the correspondence between applied and local stresses, it is shown that the Dugdale model fails when the applied stress parallel to the crack plane is higher than the applied stress normal to it. In this case the flow rules are significantly violated.     

A hybrid-displacement finite element model for the bending analysis of thin cracked plates

Based on Kirchhoff's hypothesis and relevant variational principles, this work presents an assumed hybrid-dis-placement finite element model to solve the bending problems of thin cracked plates subjected to static and dynamic loadings. To provide a potential method of non-destructive testing in evaluating the integrity of structure, natural vibrations of the thin cracked plate are also studied. Since the integrand of the associated functional contains the second-order derivatives of the lateral displacement of the plate, the compatibility requirements for the lateral displacement and its normal slope at inter-element boundaries are enforced in an integral sense through the use of a Lagrangian multiplier technique. The proper singular behaviours for the bending stresses and strains are incorporated in the singular elements around the crack-tips. The static and dynamic symmetric and anti-symmetric bending stress intensity factors can be directly computed. To avoid underestimation of dynamic bending stress intensity factors, the important role of the singular elements is also demonstrated. Good correlations between the computed results and available solutions in the literature show the accuracy and efficiency of the present work. Some new solutions for the bending thin cracked plates are then drawn.

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Résumé En se basant sur I'hypothèse de Kirchoff et sur des principes adéquats d'adaptation, on présente dans ce travail un modèle par éléments finis à déplacements hydrides qui est supposé résoudre les problèmes de flexion de tôle mince soumise à des charges statiques et dynamiques. On a également étudié les vibrations naturelles de la tôle mince fissurée en vue d'établir une méthode potentielle d'essai non destructif pour évaluer l'intégrité de la structure. Comme l'intégrant de la fonction associée comporte des dérivées du second ordre du déplacement latéral de la tôle, les exigences de compatibilité pour le déplacement latéral et pour la pente normale à la liaison entre les éléments sont contenues dans un sens intégral en utilisant la technique des multiplicateurs de Lagrange. Les comportements singuliers relatifs aux contraintes et aux déformations de flexion sont incorporés dans les éléments singuliers au voisinage des pointes de la fissure. Il est possible de calculer directement les facteurs d'intensité de contraintes symétriques et antisymétriques, qu'ils soient statiques ou dynamiques. En vue d'éviter une sous-estimation des facteurs d'intensité de contrainte en flexion dynamique, on démontre également le rôle important des éléments singuliers. La précision et l'utilité de ce travail sont démontré par les bonnes corrélations obtenues entre les résultats calculés et les solutions disponibles dans la littérature. Quelques solutions nouvelles relatives à la flexion de tôle mince fissurée sont ensuite présentées.

     

A wide range weight function for a single edge cracked geometry with clamped ends

A single edge cracked geometry with clamped ends is well suited for fracture toughness and fatigue crack growth testing of composites and thin materials. Stress intensity factors may be determined by the weight function method. A weight function for the single edge cracked geometry with clamped ends is developed and verified in this paper. It is based on analytical forms for the reference stress intensity factor and crack mouth opening displacement. The analytical forms are shown to be valid, by comparison with finite element results, over a wide range of crack depths and plate aspect ratios. Use of the analytical form enables the weight function to be calculated for any plate aspect ratio without the need for preliminary finite element analysis. Stress intensity factors and crack mouth opening displacements, predicted using this weight function, correlated well with finite element results for non-uniform crack surface stress distributions. This revised version was published online in August 2006 with corrections to the Cover Date.     

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.

     

Two-dimensional problems of the theory of elasticity for reinforced cracked plates

By using the method of singular integral equations, we develop a general approach to the solution of static problems of the two-dimensional theory of elasticity for thin-walled structural elements with curvilinear cracks reinforced by elastic patches. We analyze two basic types of fastening patches to plates, namely, continuous fastening (via the adhesive layer) and discrete fastening (riveting). It is assumed that both the cracked plate and reinforcing patches are characterized by the generalized two-dimensional stressed state. We constructed integral equations for an infinite plate with curvilinear crack reinforced by linear or two-dimensional elastic patches. We also present a brief survey of the literature devoted to the solution of problems of the indicated type.Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 31, No. 3, pp. 68–82, May–June, 1995.     

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 factor solutions for a cracked bolt loaded by a nut

This paper presents the calculation of stress intensity factor (K) solutions for surface cracks in the thread ground of bolts subjected to axial loading directly applied by the nut. The stress-strain computations have been done by means of the finite element method with quarter-point singular isoparametric elements along the crack front. The stress intensity factor is calculated through the stiffness derivative method, by using a virtual crack extension technique to compute the energy release rate. Two modifications are made to improve the accuracy of the results: the displacement not only of the main node, but also of the quarter-point nodes located in the normal plane and the adjacent nodes in the crack line, avoiding both the change of the singularity and the crack curving. The results show that direct loading on the thread flank by a nut increases the stress intensity factor. This effect decreases with the crack length. For the deepest circular cracks, however, nut loading relaxes the K-value, mainly at the crack surface.     

A finite element alternating approach for the bending analysis of thin cracked plates

Based on the classical plate theory, the analytical solution for an infinte thin plate containing a crack subjected to arbitrary symmetric bending moments on the crack surfaces is first derived. Using this solution, an efficient and accurate finite element alternating procedure is then devised to deal with symmetric plate bending problems with single or multiple cracks. The interaction effect among cracks and the influence of the geometric boundaries on the calculation of bending stress intensity factors are also presented in detail. Several numerical examples are solved to demonstrate the validity of the approach.     

应用Otsu改进广义模糊算子的边缘检测新方法

提出了改进的广义模糊算子(GFO)边缘检测新方法。该方法把 Otsu 理论应用到 GFO 参数确定中,从而实现了 GFO 中关键参数的自适应获取,使参数确定困难的问题得以解决。经该方法处理后的图像具有失真度小、细节分明等优点,优于目前现有的边缘检测方法。另外,为使得该方法在复杂图像边缘检测中取得良好效果,采用了先分割后处理的方案,即将复杂图像分割成若干子图像,然后根据各个子图像的灰度性质应用本文所提方法进行处理,再合成,从而为此方法在图像边缘检测中广泛应用提供了切实可行的解决方案。     

A BEM formulation for linear bending analysis of plates reinforced by beams considering different materials

In this work, a boundary element method (BEM) formulation to perform linear bending analysis of building floor structures where slabs and beams can be defined with different materials is presented. The proposed formulation is based on Kirchhoff's hypothesis, the building floor being modelled by a zoned plate, where the beams are treated as thin sub-regions with larger rigidities. This composed structure is treated as a single body, the equilibrium and compatibility conditions being automatically taken into account. In the final integral equation, the tractions are eliminated along the interfaces, therefore reducing the number of degrees of freedom. The displacements are approximated along the beam cross-section, leading to a model where the values remain defined on the beam skeleton line instead of their boundaries. The accuracy of the proposed model is shown by comparing the numerical results with a well-known finite element code.     

Converged stress solutions in thin plates by the extended field method

This paper presents numerical results calculated by the extended field method for the problem of the forced harmonic vibration of two plates—one rectangular and one triangular. The numerical results demonstrate that the extended field method, which is a deflection-based series solution method, is capable of producing converged stress solutions suitable for being bases of comparison for other approximate methods of analysis.     

The centrally cracked Brazilian disc: closed solutions for stresses and displacements for cracks under opening mode

Closed-form solutions for the stress and displacement fields in a centrally cracked Brazilian disc are obtained. The disc is subjected to uniformly distributed radial pressure along two finite symmetric arcs on its perimeter. The solution is based on the complex potentials method introduced by Kolosov and Muskhelisvili, and advantage is taken of a recently introduced closed-form solution for the intact Brazilian disc. Special attention is paid to the displacements of the crack lips, since they dictate whether the lips are in an opening or closing mode. The solutions obtained are valid for configurations for which the crack lips are in an opening loading mode, where there are no contact forces along the crack flanks. As well as stresses and displacements, the stress intensity factors are also determined in closed form and are found to be in good agreement with the respective values obtained from existing approximate solutions. Preliminary experimental data obtained using the digital image correlation technique support the analytically deduced conclusions for the deformation and rotation of the crack flanks.     

A model for calculating geometry factors for a mixed-mode I–II single edge notched tension specimen

In the present study, a novel approach is presented to obtain closed-form solutions for the geometry factors, which are used to determine the stress intensity factors for various configurations. A single edge notched tension specimen with an angled-crack is used as an example to demonstrate the applicability, simplicity and flexibility of the new approach. Several values for crack inclination angles, plate widths and crack lengths, including micro-cracks, are considered in the analysis. The new approach is validated through comparison with existing analytical and numerical solutions as well as experimental results.