A near optimal crack tip mesh

The near optimal crack tip mesh obtained by the authors in a previous paper is tested for a set of problems. The accuracy is maintained within the desired values. The direct displacement extrapolation method for SIF estimation is compared to the virtual crack extension. The methodology for crack tip mesh design discussed previously is validated.     

A quadrature rule for conforming quadratic crack tip elements

A simple quadrature rule that precisely integrates products of singular √r and quadratic shape function gradients for a two-dimensional six node triangle and a three-dimensional fifteen node prism is derived.     

Time dependent crack tip enrichment for dynamic crack propagation

We study several enrichment strategies for dynamic crack propagation in the context of the extended finite element method and the effect of different directional criteria on the crack path. A new enrichment method with a time dependent enrichment function is proposed. In contrast to previous approaches, it entails only one crack tip enrichment function. Results for stress intensity factors and crack paths for different enrichments and direction criteria are given.     

A mixed mode crack tip finite element

A special finite element for plane analysis of elastic structures with through the thickness cracks is presented. Generalized displacements are used in developing the element, and it contains the proper singularities. The opening (K _I), in plane shearing (K _II), and combined (K _I+K _II) modes of deformation are present. The stiffness matrix is given explicitly and its eigenvalues are shown. Numerical results are presented and compared with other solutions.

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Résumé On présente un système spécial d'éléments finis pour l'analyse en état plan de structures élastiques comportant des fissures traversant l'épaisseur du produit. Les déplacements généralisés sont utilisés pour le développement de ces éléments, ceux-ci comportant leurs propres singularités. On présente l'ouverture (K _I) en cisaillement plan (K _II) et en modes combinés de déformation (K _I+K _II). La matrice de rigidité est donnée explicitement et on montre qu'elle correspond à eigenvalues. Les résultats numériques sont présentés et comparés avec d'autres solutions existantes.

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This work was sponsored by Martin-Marietta's Independent Research and Development Program.     

A special bending crack tip finite element

The general expression of the Williams expansion around a bending crack tip is presented. Based on this a special circular bending crack tip finite element of an arbitrary high order is developed, and the element stiffness matrix is explicitly given, which is especially convenient for engineering analyses. Numerical examples are presented and compared with previous results to demonstrate the efficiency and accuracy of the special element.     

A methodology for cellular manufacturing design

A two-phase methodology is presented as an aid to organizing job shop production in a cellular manufacturing system. The first phase (selection/assignment phase) selects the machines to be kept on the shop floor and assigns parts to the machines retained. The second phase (partition/reassignment phase) establishes a partition of the set of parts and corresponding cells of machines and reassigns some of the operations with a view to eliminating some intercell material movements. This phase is repeated until a partition meeting the operator's requirements is obtained. The results obtained with this method on several examples found in the literature are consistently equivalent to or even better than those hitherto proposed, in terms of intercell moves.     

Semi-empirical crack tip analysis

Experimentally observed crack opening displacements are employed as the solution of the multiple crack interaction problem. Then the near and far fields are reconstructed analytically by means of the double layer potential technique. Evaluation of the effective stress intensity factor fesulting from the interaction of the main crack and its surrounding crazes in addition to the remotely applied load is presented as an illustrative example. It is shown that crazing (as well as microcracking) may constitute an alternative mechanism to Dugdale-Barenblatt models responsible for the cancellation of the singularity at the crack tip.

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Résumé Pour solutionner le problème d'interactions multiples des fissures, on utilise les COD observées expérimentalement. On reconstitue ensuite analytiquement les champs proche et lointain à l'aide de la technique du potentiel en deux couches. Comme exemple illustratif, on présente une évaluation du facteur effectif d'intensité de contraintes résultant de l'interaction d'une fissure principale avec les brisures qui l'entourent, ainsi que de la charge appliquée à distance. On montre que le phénomène de brisures-comme celui de microfissuration-constitue une alternative aux modèles de Dugdale-Barenblatt auxquels on doit la suppression de la singularité à l'extrémité de la fissure.

     

A general treatment of crack tip contour integrals

Given a general balance statement we derive an expression for the associated crack tip flux integral. The conditions under which the integral is physically meaningful and yields a non-trivial result are outlined. To illustrate the approach a number of well known integrals in use in fracture mechanics are derived. It is demonstrated that complementary analogues to these integrals can be derived in a similar fashion and a result indicating the equality of dual integrals under quite general conditions is presented. We discuss the domain integral method as an alternative means of representing crack tip integrals and we show that the method may be interpreted as a particular form of Signorini's theorem of stress means. A discussion of some associated integral identities is presented.

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Résumé Une expression pour l'intégrale de flux á l'extrémité d'une fissure est obtenue sur base d'un état général d'équilibre. On souligne les conditions pour lesquelles l'intégrale a un sens physique et ne mène pas á des résultats triviaux. L'approche adoptée est illustrée par 1'établissement d'une série d'intégrales bien connues, utilisées en mécanique de rupture. On démontre que l'on peut tirer d'une manière similaire des contreparties compl'ementaires à ces intégrales et on présente un résultat indiquant que les intégrales doubles ainsi établies sont égales dans des conditions très générales. On discute de la méthode d'intégration sur un domaine comme variante de représentation des intégrales à l'extrémité d'une fissure et on montre que cette méthode peut être interprêtée comme une forme particulière du théorème de Signorini des contraintes médianes. On présente enfin une discussion sur diverses formes d'intégrales associées.

     

A diffusion-based approach for modelling crack tip behaviour under fatigue-oxidation conditions

Modelling of crack tip behaviour was carried out for a nickel-based superalloy subjected to high temperature fatigue in a vacuum and air. In a vacuum, crack growth was entirely due to mechanical deformation and thus it was sufficient to use accumulated plastic strain as a criterion. To study the strong effect of oxidation in air, a diffusion-based approach was applied to investigate the full interaction between fatigue and oxygen penetration at a crack tip. Penetration of oxygen into the crack tip induced a local compressive stress due to dilatation effect. An increase in stress intensity factor range or dwell times imposed at peak loads resulted in enhanced accumulation of oxygen at the crack tip. A crack growth criterion based on accumulated levels of oxygen and plastic strain at the crack tip was subsequently developed to predict the crack growth rate under fatigue-oxidation conditions. The predicted crack-growth behaviour compared well with experimental results.     

A simple methodology to visualize crack propagation for ceramic materials

Analysis of the crack growth behavior is critical for fracture and thermal shock assessment. The current work presents a simple methodology to visualize cracks in ceramic materials. The procedure is exemplified for refractory materials on the basis of images obtained during mechanical loading using a wedge splitting test. Complementary in situ crack growth observation verify that for one of the materials growth and opening displacement of the main crack is accompanied by pronounced micro-cracking, branching, and bridging processes. Apparent fracture resistance and thermal shock resistance parameters are discussed.     

A design methodology for fractal layout organization

Venkatadri el a.(HE Transactions, 29, 911-924, 1997) have proposed a new methodology for shop floor layout that involves the use of fractal cells and have compared the performance of their new layout with those obtained using the function, group and holographic layouts. A few inconsistencies are present in their results, expressed as flow scores. This note points out these inconsistencies through the use of appropriate examples.     

A design methodology for fractal layout organization

This paper proposes a methodology for designing job shops under the fractal layout organization that has been introduced as an alternative to the more traditional function and product organizations. We first begin with an illustration of how a fractal job shop is constituted from individual fractal cells. We then consider joint assignment of products and their processing requirements to fractal cells, the layout of workstation replicates in a fractal cell and the layout of cells with respect to each other. The main challenge in assigning flow to workstation replicates is that flow assignment is in itself a layout dependent decision problem. We confront this dilemma by proposing an iterative algorithm that updates layouts depending on flow assignments, and flow assignments based on layout. The proposed heuristic is computationally feasible as evidenced by our experience with test problems taken from the literature. We conclude by showing how the methodologies developed in this paper have helped us evaluate fractal job shop designs through specification of fractal cells, assignment of processing requirements to workstation replicates, and development of processor level layouts. This step has had the far-reaching consequence of demonstrating the viability and the validity of the fractal layout organization.     

Improved quarter-point crack tip element

We present a modification to the quarter-point crack tip element and employ this element in two-dimensional boundary integral fracture analysis. The standard singular element is adjusted so that the near-tip crack opening displacement satisfies a known constraint: the coefficient of the term which is linear in the distance to the tip must vanish. Stress intensity factors calculated with the displacement correlation technique are shown to be highly accurate, and significantly more accurate than with the standard element. The improvements are especially dramatic for mixed-mode problems involving curved and interacting cracks.     

A tensile crack in creeping solids with large damage near the crack tip

An asymptotic analysis of stationary mode I crack in creeping solids with large damage near crack tip is conducted. To consider the damage effect, Kachanov damage evolution law is utilized and incorporated into the power-law creep constitutive equation. With the compatibility equation, a nonlinear eigenvalue problem which can be solved by numerical approaches is established. From this result, the distribution of stress and strain rate are obtained with the coupling effect of damage and creep under plane stress condition. Also the influence of material parameters on the stress is examined. According to the result, it is shown that the creep exponent n and damage parameter (=/(1+k)) have a significant effect on determining the eigenvalue s and angular distribution of stress and strain rate near the crack tip. The creep exponent n plays the role to soften and damage parameter plays the role to harden the material near the crack tip. The stress and strain rate show quite different behavior from those of HRR problem.     

A generalization of Elliott's model of a crack tip

Elliott's model of a crack tip is generalized to encompass a wider range of force laws. The associated crack extension criterion is shown to be equivalent to that obtained using the classic Griffith equation, and the relation between the generalized Elliott model and the cohesive zone model is also discussed. The original Elliott model, which is based on the stress and displacement distribution in the vicinity of a sharp crack tip, appears as a special case.     

Various limit processes for evaluating stresses at crack tip and notch crown tip

The stress at a crack tip point can be obtained in several ways. In the first way, after letting an elliptic notch become a crack, a moving point approaches the crack tip. In the second way, after letting a moving point approach the crown point of notch, the elliptic notch becomes a crack. It is found that for some particular stresses in question the finally obtained results by using two ways are different. The mentioned result is caused by change of the order of limitation for evaluating the stress. Assumed that there are two processes, one is by letting the moving point approach the crown point of elliptic notch, and other is by letting the ellipse become a crack. In the third way, the two processes are completed simultaneously. It is found that, for example, in case that a remote shear is applied to a elliptic notch of infinite plate, the shear stress at the crown point can reach an arbitrary value, provided an appropriate limit process is assumed in the third way. Similar result is found in the normal remote loading of an elliptic notch. In addition to the detail analysis, the obtained results are summarized in the form of theorem.     

Effect of crack closure on non-linear crack tip parameters

Crack closure concept has been widely used to explain different issues of fatigue crack propagation. However, some authors have questioned the relevance of crack closure and have proposed alternative concepts. The main objective here is to check the effectiveness of crack closure concept by linking the contact of crack flanks with non-linear crack tip parameters. Accordingly, 3D-FE numerical models with and without contact were developed for a wide range of loading scenarios and the crack tip parameters usually linked to fatigue crack growth, namely range of cyclic plastic strain, crack tip opening displacement, size of reversed plastic zone and total plastic dissipation per cycle were investigated. It was demonstrated that: (i) LEFM concepts are applicable to the problem under study; (ii) the crack closure phenomenon has a great influence on crack tip parameters decreasing their values; (iii) the ΔK_eff concept is able to explain the variations of crack tip parameters produced by the contact of crack flanks; and (iv) the analysis of remote compliance is the best numerical parameter to quantify the crack opening level. Therefore the crack closure concept seems to be valid. Additionally, the curves of crack tip parameters against stress intensity factor range obtained without contact may be seen as master curves.