J integral solution for semi-elliptical surface crack in high density poly-ethylene pipe under bending

The goal of this work is to analyse the severity of semi-elliptical crack defects and to study the degree of damage in the poly-ethylene pipe in bending during the crack propagation. The semi-elliptical cracks are considered in this work located in different position in the wall of the pipe. The three finite element method based on the computation of the J integral was used to analyse the fracture behaviour of these structures. The effect of the position, shape and size of the crack on the J integral values was highlighted. The effects of strain rate and the temperature on the J integral values were also examined. The obtained results show that the strain rates have a strong influence on the J integral values especially for circumferential crack at higher bending moment. However, the energy for circumferential crack is more important compared to axial crack. The effect of the depth of the crack becomes important when the ratio (a/t) reaches a critical value of 0.6 (a/t = 0.6), especially when the ratio a/c is weak (semi-elliptical crack, a/c = 0.2) where the J integral values becomes independently of the crack depth, this conclusion is opposite to the above for the poly-ethylene pipe subjected to internal pressure. We recall finally, that the temperature effect on circumferential cracks behaviour is more important compared to the axial cracks at critical crack size (a/c = 0.2 and a/t = 0.6). It is also shown that in the wall of pipe, the internal cracks are more dangerous than the external cracks.     

Oblique semi-elliptical surface crack in semi-infinite solid subjected to tension

This note is concerned with a semi-elliptical surface crack arbitrarily inclined to the free surface of a semi-infinite solid subjected to tension. The analysis is performed by the body force method, and the stress intensity factor at the maximum depth point on the crack front are given for various shapes and inclination angles of the crack. The numerical results are fitted to a reliable polynomial for convenience in engineering applications.     

Stress intensity factors of semi-elliptical surface cracks in pressure vessels by global-local finite element methodology

In the present study the problem of calculation of the stress intensity factors (SIF) of semi-elliptical cracks located in the stress concentration areas of a pressure vessel is numerically solved by advanced global-local finite element (FE) analysis. The common characteristic of the cases solved is that the stress field at the crack area varies along the axial, the circumferential, as well as, the through-the-thickness directions. SIF solutions for such problems are not available, neither analytically, nor numerically, as the currently existing solutions in the literature (numerical results, Newman-Raju empirical equations, weight function solutions, etc.) are only valid for uniform stress distribution along the axial and circumferential directions of the pressure vessel and allow variation only through-the-thickness. The crack locations considered are the intersection of the cylinder to a nozzle and the connection of the cylinder with its hemi-spherical ends. The stress intensity factors are presented in a suitable table format for various geometrical configurations of both the pressure vessel and the semi-elliptical crack, thus providing a useful tool for the fracture mechanics design of cracked pressure vessels. The modeling details of the sub-structuring methodology, employed in the analysis, are extensively discussed and the numerical approach is proven to be very efficient for the SIF calculation of pressure vessel semi-elliptical cracks.     

A finite element analysis of ship sections subjected to underwater explosion

This paper presents numerical simulations of dynamic responses of a ship section to non-contact underwater explosion using ABAQUS. The finite element model of the ship section including the size of fluid mesh, initial and boundary conditions etc. has been built up. Comparisons of the acceleration and velocity response between the experimental and numerical results have been investigated. The numerical results agree well with the measured results. Furthermore, the effect of the mass proportional damping factor on the velocity response have been investigated numerically. The dynamic response modes of the ship section subjected to a side-on non-contact underwater explosion are discussed.     

A finite element analysis of quasistatic crack growth in a pressure sensitive constrained ductile layer

Polymeric adhesive layers are employed for bonding two components in a wide variety of technological applications. It has been observed that, unlike in metals, the yield behavior of polymers is affected by the state of hydrostatic stress. In this work, the effect of pressure sensitivity of yielding and layer thickness on quasistatic interfacial crack growth in a ductile adhesive layer is investigated. To this end, finite deformation, finite element analyses of a cracked sandwiched layer are carried out under plane strain, small-scale yielding conditions for a wide range of mode mixities. The Drucker–Prager constitutive equations are employed to represent the behavior of the layer. Crack propagation is simulated through a cohesive zone model, in which the interface is assumed to follow a prescribed traction–separation law. The results show that for a given mode mixity, the steady state fracture toughness |K|_ss is enhanced as the degree of pressure sensitivity increases. Further, for a given level of pressure sensitivity, |K|_ss increases steeply as mode II loading is approached.     

Elastodynamic analysis of crack by finite element method using singular element

The finite element method using a singular element near the crack tip is extended to the elastodynamic problems of cracks where the displacement function of the singular element is taken from the solution of a propagating crack. The dynamic stress intensity factor for cracks of mode III or mode I deformations in a finite plate is determined.The results of computation for stationary cracks or propagating cracks under dynamic loadings are compared with the analytical solutions of other authors. It is shown that the present method satisfactorily describes the time variation of the stress intensity factor in dynamic crack problems.

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Résumé La méthode des éléments finis utilisant un élément singulier au voisinage de l'extrémité d'une fissure a été étendue aux problèmes élastodynamiques des fissures tels qu'ils se posent lorsque la fonction de déplacement d'un élément singulier est prise à partir de la solution d'une fissure en cours de propagation. Le facteur d'intensité des contraintes dynamiques correspondant à des fissures de mode III ou des déformations de mode I dans une plaque finie a été déterminé. Les résultats des calculs correspondant à des fissures stationnaires ou des fissures en cours de propagation sous des charges dynamiques sont comparées aux solutions analytiques obtenues par d'autres auteurs. On montre que la méthode présentée décrit de façon satisfaisante la variation en fonction du temps du facteur d'intensité des contraintes dans les problèmes de fissuration dynamique.

     

Fracture analysis of interfacial crack by global-local finite element

An eigenfunction expansion is used to formulate the global element on the crack tip. The global-local finite element method employs both conventional finite element and classical Rayleigh-Ritz kinematic approach. The hybrid Ritz method not only preserves the finite element modelling capability but adds the advantage of using prior information regarding the anticipate behaviour of the particular problem. Thus, it is able to achieve better accuracy with fewer elements in comparison with conventional finite element. Several examples relative to crack problems are presented to demonstrate the global-local finite element method.     

Variations of stress intensity factor of a semi-elliptical surface crack subjected to mixed mode loading

Maximum stress intensity factors of a surface crack usually appear at the deepest point of the crack, or a certain point along crack front near the free surface depending on the aspect ratio of the crack. However, generally it has been difficult to obtain smooth distributions of stress intensity factors along the crack front accurately due to the effect of corner point singularity. It is known that the stress singularity at a corner point where the front of 3 D cracks intersect free surface is depend on Poisson's ratio and different from the one of ordinary crack. In this paper, a singular integral equation method is applied to calculate the stress intensity factor along crack front of a 3-D semi-elliptical surface crack in a semi-infinite body under mixed mode loading. The body force method is used to formulate the problem as a system of singular integral equations with singularities of the form r ⁻³ using the stress field induced by a force doublet in a semi-infinite body as fundamental solution. In the numerical calculation, unknown body force densities are approximated by using fundamental density functions and polynomials. The results show that the present method yields smooth variations of mixed modes stress intensity factors along the crack front accurately. Distributions of stress intensity factors are indicated in tables and figures with varying the elliptical shape and Poisson's ratio.     

Prediction of fatigue crack growth rates using crack closure finite element analysis

A three-dimensional finite element fatigue crack closure model of a corner crack and of a through thickness crack has been developed to evaluate the range of effective stress intensity factor from the distribution of the range of stress ahead of the crack tip. The corresponding fatigue crack growth rate was evaluated from a Paris law fit to experimental data from high stress ratio tests. The point of origin for the range of stress distribution was adjusted in accordance with Irwin’s plastic zone correction. Encouraging comparisons of finite element predictions of fatigue crack growth rate incorporating closure effects with experimental measurements were obtained.     

Cracks emanating from a rhombus hole in infinite and finite plate subjected to internal pressure

This note deals with the stress intensity factors (SIFs) of cracks emanating from a rhombus hole in a rectangular plate subjected to internal pressure by means of the displacement discontinuity method with crack-tip elements (a boundary element method) proposed recently by the author. Moreover, an empirical formula of the SIFs of the crack problem is presented and examined. It is found that the empirical formula is very accurate for evaluating the SIFs of the crack problem.     

Three-dimensional finite element analysis for through-wall crack in thick plate

A superposition method, in which analytical and finite element solutions are combined through the variational principle, is presented for determining the three-dimensional stress intensity factors of the through-wall crack. Cumbersome volume integral due to the singular terms at the crack tip is carried on by applying the least squares methods to the results obtained by the Legendre-Gauss quadrature. Several numerical calculations are made based on the present method, showing that the three-dimensional effects cannot be neglected especially for the cases of larger Poisson's raito. The comparison of the present method with the other finite element methods proposed for determining the three-dimensional stress intensity factors indicates that the former has the obvious superiority to the latters in respect to the numbers of elements and nodal points necessary to obtain reasonable results.     

Influence of crack closure on the stress intensity factor for plates subjected to bending—A 3-D finite element analysis

Plates with central through cracks subjected to bending is analysed taking into account the closure of the crack faces on the compression side. A three-dimensional finite element method employing three-dimensional degenerate solid element is used for the analysis. The crack faces have been modelled such that they come in contact over an area on the compression side and interfere with each other. The influence of the crack closure on the variation of the stress intensity factor across the plate thickness is obtained for finite and infinite plate geometries.     

Elasto-plastic finite element analysis of a crack in an infinite plate

The elastic support method was recently developed to simulate the effects of unbounded solids in the finite element analysis of stresses and displacements. The method eliminates all the computational disadvantages encountered in the use of `infinite' elements or coupled finite element boundary element methods while retaining all the computational advantages of the finite element method. In this paper, the method is extended to the elasto-plastic analysis of fracture in infinite solids by using the load increment approach and including the effects of strain hardening. Numerical tests and parametric study are conducted by analysing a straight crack in an infinite plate. Present results for J integrals and plastified zones are compared, respectively, with analytical solutions and available results obtained by using the body force method. The agreement between the results is found to be very good even if the truncation boundary of the finite element model is located very close to the crack tip or the plastified zone.     

Fatigue crack closure determination by means of finite element analysis

Plasticity-induced crack closure is an observed phenomenon during fatigue crack growth. However, accurate determination of fatigue crack closure has been a complex task for years. It has been approached by means of experimental and numerical methods. The finite element method (FEM) has been the principal numerical tool employed. In this paper the results of a broad study of fatigue crack closure in plane stress and plane strain by means of FEM are presented. The effect of three principal factors has been analysed in depth, the maximum load, the crack length and the stress ratio. It has been found that the results are independent of maximum load and the crack length, and there exists a direct influence of the stress ratio. This relation has been numerically correlated and compared with experimental results. Differences have also been established between opening and closure points and between the different criteria employed to compute crack closure.     

Tension and bending of finite thickness plates with a semi-elliptical surface crack

This paper deals with the tension and bending of finite thickness plates with a semi-elliptical surface crack. The analysis is performed by means of a modified body force method, in which the accuracy and the validity are greatly improved by using reasonable patterns of the body force densities and the resultant force boundary conditions. Numerical calculations are done for various combinations of the shape and the size of the crack, and practically exact values of the stress intensity factors are determined by extrapolating the numerical results for several mesh patterns. Empirical formulae in polynomial forms are also presented for convenience of practical use.

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Résumé L'étude traite de la mise sous traction et flexion d'une plaque d'épaisseur finie comportant une fissure de surface semi-elliptique. On recourt pour l'analyse à une méthode modifiée d'évaluation des champs de force, où la précision et la validité ont été améliorées en utilisant des configurations pondérées des densités des forces, et des conditions aux limites qui en résultent.Des calculs numériques sont effectués pour diverses combinaisons de forme et de taille d'une fissure, et l'on détermine des valeurs pratiquement exactes des facteurs d'intensité de contraintes en extrapolant les résultats numériques ä diverses configurations de maillage.Des formules empiriques sous forme polynominale sont également présentées en vue de rendre aisée leur utilisation pratique.

     

A mixed hybrid finite element for three-dimensional elastic crack analysis

A new three-dimensional crack tip element is proposed, which is based on a mixed hybrid stress/displacement model. A truncated series expansion of eigenfunctions for the straight semi-infinite crack is deduced and assumed for the internal stress and displacement fields in the element. The basic approach of constructing these hybrid elements is outlined. Their good capability, efficiency and accuracy for analyzing three-dimensional elastic crack problems are demonstrated by first numerical examples.

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Résumé On propose un nouveau type d'élément tridimensionnel pour l'extrémité d'une fissure, basé sur un modèle mixte contraintes hybrides/déplacements. On en tire un développement en séries tronquées des eigenfonctions relatives à une fissure droite semi-infinie, et on suppose qu'elle est représentative des champs de contraintes internes et de déplacements dans l'élément. L'approche de base utilisée pour construire ces éléments hybrides est soulignée. On démontre par de premiers exemples numériques qu'ils ont la capacité, l'efficacité et la précision nécessaires à l'analyse des problèmes élastiques et tridimensionnels de fissuration.