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.     

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.

     

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.     

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.

     

The application of a displacement controlled weight function for a single edge cracked plate to thermal fatigue damage assessment

A weight function based on displacement boundary conditions for the single edge cracked plate is extended and tested against finite element analysis results for the stress intensity factor under a linear end displacement. The stress intensity factor fluctuation, caused by sinusoidal thermal striping on the surface of the plate, is predicted as a function of crack depth and plate aspect ratio by the frequency response model with the new weight function and by the finite element method. Good agreement is found. Sample calculations are presented for the threshold surface temperature fluctuation for propagation of existing surface defects.     

A model for selecting appropriate technology for incubator-university collaboration by considering the technology transfer mechanism

A technology incubator provides an important support for a technology transfer mechanism. A technology incubator bridges the incubatees to the technology provider. In our research, we propose a technology selection model for the incubatees. Incubator managers, as decision-makers, attempt to evaluate new technology for the incubatees by comparing its profit with that of the old or established technology. The technology is proposed by a technology provider, which in this case is a university. In the technology selection activity, the distance between the technology level of incubatees and transferred technology should be considered. Unfortunately, there has been no effort to formulate a technology selection model in the technology incubator that considers the technology distance and is linked to the incubatees’ profit as financial performance. We examine the impact of the technological-level and technology assimilation rate in the technology selection process in the technology incubator. We analyse the external factor of customer acceptance of new technology with a probabilistic value and technology obsolescence. Furthermore, we introduce a profit-sharing scheme to share the profit of the incubatees with the university as a technology provider. Utilising a profit-sharing scheme means sharing the risk between incubatees and the university.     

The methods of complex potentials, singular integral equations and integral transformations in a series of problems for the reinforcement of cracked plates

We study the initiation and propagation of a vertical crack in an elastic semi-infinite plate, reinforced on its boundary by an infinite discontinuous stringer within the limits of the theory of brittle failure. The plate is subjected to uniform distributed tensile forces at infinity, as well as to contact stresses due to application of forces to the stringer. We find the appropriate loading of the coherent stringer, and consequently we consider a problem where the stringer is cracked and a vertical crack has developed within the plate. We deduce the exact analytical solution for the principal singular integral equation for this case; hence the stringer is perfectly rigid and we calculate characteristic parameters of the problem. The results show that the crack tip has a logarithmic singularity, and the tangential contact stresses under the stringer at that end point are finite and generally differ from zero.     

A modified model for the penetration into moderately thick plates by a rigid,sharp-nosed projectile

The deep penetration model based on cavity expansion analysis (Int. J. Impact Eng. 27 (2002) 619) is modified to take account of the increase of the contact area between the projectile nose and the target medium before the projectile nose fully penetrates into the target. The modified penetration model is applicable to those penetration problems where the length of the projectile nose is comparable to the penetration depth. The predicted results are in good agreement with experimental results from Diskshit and Sundararajan (Int. J. Impact Eng. 12(3) (1992) 373) and Diskshit et al. (Int. J. Impact Eng. 16(2) (1995) 293).     

Higher order refined computational model with 12 degrees of freedom for the stress analysis of antisymmetric angle-ply plates – analytical solutions

Analytical formulations and solutions for the stress analysis of simply supported antisymmetric angle-ply composite and sandwich plates hitherto not reported in the literature based on a higher order refined computational model with twelve degrees of freedom already reported in the literature are presented. The theoretical model presented herein incorporates laminate deformations which account for the effects of transverse shear deformation, transverse normal strain/stress and a nonlinear variation of in-plane displacements with respect to the thickness coordinate thus modelling the warping of transverse cross sections more accurately and eliminating the need for shear correction coefficients. In addition, two higher order computational models, one with nine and the other with five degrees of freedom already available in the literature are also considered for comparison. The equations of equilibrium are obtained using Principle of Minimum Potential Energy (PMPE). Solutions are obtained in closed form using Navier’s technique by solving the boundary value problem. Accuracy of the theoretical formulations and the solution method is first ascertained by comparing the results with that already available in the literature. After establishing the accuracy of the solutions, numerical results with real properties using all the computational models are presented for the stress analysis of multilayer antisymmetric angle-ply composite and sandwich plates, which will serve as a benchmark for future investigations.     

The concept of a balance law for a cracked elastic body and the configurational force and moment at the crack tip

In this work, the derivation of the configurational equations for a cracked elastic body by postulating balance laws, is studied. To this end, a proper kinematics is proposed, according to which the evolution of the crack in the material configuration and the physical motion (deformation) are separated. A rigorous localization procedure provides the local equations in material space holding in the smooth part of the body, the corresponding jump conditions along the crack, as well as the configurational force and moment at the crack tip. The results are discussed in connection with the corresponding ones of fracture mechanics and some new interpretations are proposed.     

The method of fundamental solutions for acoustic wave scattering by a single and a periodic array of poroelastic scatterers

The method of fundamental solutions (MFS) is now a well-established technique that has proved to be reliable for a specific range of wave problems such as the scattering of acoustic and elastic waves by obstacles and inclusions of regular shapes. The goal of this study is to show that the technique can be extended to solve transmission problems whereby an incident acoustic pressure wave impinges on a poroelastic material of finite dimension. For homogeneous and isotropic materials, the wave equations for the fluid phase and solid phase displacements can be decoupled thanks to the Helmholtz decomposition. This allows for a simple and systematic way to construct fundamental solutions for describing the wave displacement field in the material. The efficiency of the technique relies on choosing an appropriate set of fundamental solutions as well as properly imposing the transmission conditions at the air–porous interface. In this paper, we address this issue showing results involving bidimensional scatterers of various shapes. In particular, it is shown that reliable error indicators can be used to assess the quality of the results. Comparisons with results computed using a mixed pressure–displacement finite element formulation illustrate the great advantages of the MFS both in terms of computational resources and mesh preparation. The extension of the method for dealing with the scattering by an infinite array of periodic scatterers is also presented.     

A microstructure based constitutive model for the mechanical behavior at high temperatures of nickel-base single crystal superalloys

A constitutive law is proposed for single crystal superalloys with a large volume fraction of the γ^′ phase in the high temperature regime. It relies on a mechanical model of the dislocation mechanisms in the matrix and the particles. The microstructure is taken as periodic. The homogenization problem is solved by Fourier series within the approximation of uniform plastic deformations in the three kinds of channels and in the precipitates. In particular, the internal stresses due to non-uniform deformations in the periodic cell and to the different lattice parameters in the matrix and the particles are estimated. Shearing of the precipitates by Superlattice Intrinsic Stacking Faults (SISF) and climbing of loops around the precipitates are taken into account. These mechanisms are responsible for the relaxation of the internal stresses (recovery) and the secondary creep.     

Stress intensity factors for a rectangular plate with a point-loaded edge crack by a boundary collocation procedure,and an investigation into the convergence of the solutions

The stress intensity factors K₁ for a rectangular plates with edge crack loaded on the crack surface has not been obtained so far. In this article, this calculation is done by a least square boundary collocation procedure. A criterion for the validity of the solution is given from the consideration of uniform approximation, which makes it possible to judge the validity of the solution by the method itself, independent to the analytical solution. The convergence of two different approximations usually used, i.e., interpolation approximation and average approximation, are discussed. It is found that the divergence of the former is caused by fluctuation of the approximating functions, known as “Runge phenomenon” in algebraic interpolation. For the latter, there will be no fluctuation in general, and the solutions are always convergent, but it may not converge to the exact solution of the problem. This shows the incompleteness of the Williams function.