Limiting equilibrium of a spherical elastoplastic shell with two colinear cracks

The problem of the stress-strain state of an elastoplastic spherical shell with two colinear cracks is reduced to a system of singular integral equations with unknown integration limits and discontinuous right-hand sides. The system obtained is solved simultaneously for conditions of stress finiteness and plasticity. The algorithm of the numerical solution of such a system, which is based on the method of mechanical quadratures, is constructed. The dependence of the opening of the crack tips on the applied load and the distance between the crack centers is analyzed numerically.Translated from Problemy Prochnosti, No. 8, pp. 24–28, August, 1994.     

A finite line crack in a pressurized spherical shell

The deformation of a thin sheet having initial spherical curvature is shown to be associated with that of an initially flat plate resting upon an elastic foundation. Using an integral formulation the coupled Reissner equations for a shell with a crack of length 2c are solved for the in-plane and Kirchhoff bending stresses, and, among other things, it is found that the explicit nature of the stresses near the crack point depends upon the inverse half power of the non-dimensional distance from the point e. The character of the combined extension-bending stress field near the crack tip is investigated in detail for the special case of a radial crack in a spherical cap which is subjected to a uniform internal pressure q_o and is clamped at the boundary \(\overline {\text{R}} = \overline {\text{R}} _{\text{o}}\). Pending a complete study of the solution, approximate results for the combined surface stresses near the crack tip normal and along the line of crack prolongation are respectively of the form

$$\sigma _y (\varepsilon ,0)|_{\nu = {1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-\nulldelimiterspace} 3}} \approx 0.45\sqrt {{1 \mathord{\left/ {\vphantom {1 \varepsilon }} \right. \kern-\nulldelimiterspace} \varepsilon }} \tfrac{{q_O R}}{h} + ...$$     

Limiting equilibrium of a body with elliptic crack under complex loading

We deduce theoretical relations demonstrating that the forces acting in the direction parallel to the plane of an elliptic crack affect the stress intensity factor K _I. This enables us to find the characteristic of crack resistance K _Ic according to the known limiting forces under the conditions of complex loading.     

Stress-strain state of an open spherical shell of a medium thickness

We study the stress-strain state of a medium thickness spherical shell with a hole in the vicinity of the pole in a geometrically nonlinear statement using the classical Kirchhoff-Love model and refined Timoshenko-type model that takes into account the transverse shear strains. The study is based on the construction of an orthogonal curvilinear system of coordinates of a median surface that presents a doubly-connected domain and also on the reduction of the original nonlinear boundary problem to a sequence of linear two-dimensional problems and these latter to one-dimensional ones whose integration is performed by a robust numerical method. Using an open spherical shell as an example, the influence of the transverse shear strain on its stress-strain state is investigated under the action of uniform and nonuniform loads. As compared to the classical model, the use of the Timoshenko-type model is shown to result in a considerable refinement of displacements near the hole. __________ Translated from Problemy Prochnosti, No. 5, pp. 68–78, September–October, 2006.     

Limiting equilibrium and fracture in an orthotropic body containing a thin rigid inclusion

The limiting equilibrium and type of fracture of an orthotropic body containing a linear rigid inclusion in tension at infinity along the axis of the inclusion is studied under the conditions of plane problem. Localized process zones (of weakened contact) develop along the boundary of the inclusion from its ends to the central part. The analytic solution is obtained with the help of complex potentials by reducing the analyzed problem to the problem of conjugation. The influence of loading and the orthotropy of the matrix on the development of the process zones, the distributions of contact stresses and axial forces in the inclusion, and the character of fracture of the composition are investigated. We determine the ultimate loads of possible separation or rupture of the inclusion and compute these quantities for some special cases. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 42, No. 2, pp. 69–79, March–April, 2006.     

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.

     

Elasto-plastic analysis for a finite thickness rectangular plate containing a through-thickness central crack

The objective of this work is to present a three-dimensional analysis of the elasto-plastic response of a center-cracked rectangular panel by using an alternate method, the method of lines (MOL). The problem of a finite thickness rectangular plate containing a through-thickness central crack under uniaxial tension is studied in detail. An incremental procedure is used to seek the 3-D elasto-plastic stress and strain distribution. The Prandtl-Reuss equations and the associated von Mises flow rule are employed. The material is assumed to be elastic-plastic with nonlinear work-hardening. Effective stress and effective strain concepts are used. The MOL is used to reduce the governing equations on displacements to a coupled set of ordinary differential equations (ODE) along x, y, z lines. These are integrated by Peano-Baker method. Since the ODE are of constant coefficient the coefficient matrix is diagonalized and the matrizon is easily evaluated. Numerical results on stresses, displacements, the growth of plastic zone and the crack surface opening displacements are reported and their variation along the thickness are presented in graphs. The variation of the stress intensity factor K ₁, along the thickness direction is given. It is found that the computation time needed for determining the distribution of stresses and strains is much less than what has been reported by using other methods. A comparison of results on SIF with those obtained by other methods is also given.

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Résumé L'objet du travail est de présenter une analyse tridimentionnelle de la réponse élastoplastique d'un panneau rectangulaire présentant une fissure centrale, et utilisant une méthode alternative, la méthode des lignes MOL. On étudie dans le détail le problème de la plaque rectangulaire d'épaisseur finie comportant une fissure centrale traversante et soumise à la contrainte uniaxiale. Une procédure incrémentale est utilisée en vue de rechercher la distribution des contraintes et des déformations élastoplastiques suivant les trois dimensions. On utilise les équations de Prandtl-Reuss et la règle d'écoulement de von Mises qui lui est associée. On suppose que le matériau est élastoplastique et qu'il présente un vieillissement non linéaire. On recourt au concept des contraintes effectives et des déformations effectives. Le MOL est utilisé en vue de ramener les équations gouvernant les déplacements à un ensemble d'équations différentielles ordinaires suivant les axes X, Y, Z; on fait appel à la méthode de Peano-Baker pour leur intégration. Comme les équations différentielles ont un coéfficient constant, la matrice de coéfficient peut être résolue par diagonales et le matriciel peut être aisément évalué. Les résultats numériques relatifs aux contraintes, aux déplacements, à la croissance de la zône plastique et aux déplacements d'ouverture de la surface de la fissure sont présentés, et leur variation sur l'épaisseur sont mises en graphiques. On fournit la variation du facteur d'intensité de contrainte K suivant la direction de l'épaisseur. On trouve que le temps de calcul nécessaire à la détermination de la distribution des contraintes et déformations est beaucoup moindre que celui nécessaire par l'utilisation d'autres méthodes. Une comparaison des résultats relatifs aux facteurs d'intensité de contraintes avec ceux obtenus par d'autres méthodes est également fournie.

     

Torsion of a semifinite nonuniform cylinder with a crack

Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 26, No. 4, pp. 75–80, July–August, 1990.     

Formation of a Griffith's crack in a nonuniform stress field

Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 26, No. 1, pp. 26–31, January–February, 1990.     

The crack tip opening angle associated with the growth of a crack in a nonuniform stress field

A general analysis gives the crack tip opening angle associated with the growth of a crack in an infinite solid that is subject to a nonuniform stress distribution. The results allow one to study the effect of nonuniform stresses e.g. residual stresses, on inert environment crack growth and also environmentally assisted crack growth.     

Limiting equilibrium of a welded joint of gas main

We study the dependence of the crack-tip opening displacement for a surface crack in a welded joint of gas main on the geometric and physicomechanical parameters of pipe. It is assumed that the strength characteristics of the material in the zone of thermal influence and the base material are different. We propose a simplified formula for the evaluation of the opening displacements of surface cracks. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 36, No. 2, pp. 113–117, March-April. 2000.