A half plane and a strip with an arbitrarily located crack

The paper introduces a technique to deal with the problem of an elastic domain containing an arbitrarily oriented internal crack. The problem is formulated as a system of integral equations for a fictitious layer of body forces imbedded in the plane along a closed smooth curve encircling the original domain. The problems of a half plane with a crack in the neighborhood of its free boundary and of an infinite strip containing a symmetrically located internal crack with an arbitrary orientation are considered as examples. In each case the stress intensity factors are computed and are given as functions of the crack angle.     

Temperature distribution within a moving strip heat source

The temperature within a strip heat source moving at different speeds has been investigated. The results of the experiments are compared with the results of the theoretical analyses of other authors.     

The plastic zone and limit load of centre-cracked plate by the weighted residual method and elasto-viscoplastic theory

A combination of the weighted residual method and elasto-viscoplastic theory is used to study the plastic zone and the limit load of centre-cracked plate. A new set of displacement functions has been assumed, and a series of governing equations for elasto-plastic analysis are derived. Numerical examples show that this method offers good accuracy but requires very little computer time.     

On the response of a timoshenko beam under initial stress to a moving load

When an axial compressive force is present, the wavelength of the propagating free waves in a beam rapidly decreases. The conventional Euler-Bernoulli beam equations are often not adequate for determining dynamic behavior of the moving load on a beam supported on an elastic foundation when initial axial stress is present. Equations derived by Sun for the Timoshenko beam with initial axial stress (based on Trefftz's theory), form the basis of this investigation. Analytical solutions are presented for deformations of the beam both with and without damping. Expressions of the critical velocity as a function of initial axial stress and foundation modulus parameters, are obtained for the Timoshenko beam. Critical velocities of the Timoshenko beam, with and without axial stress, are compared with that obtained using Euler-Bernoulli beam formulation. Some significant agreements and disagreements in the behaviors of the two systems are described.     

Development of plastic strains in the vicinity of fissurelike defects under the influence of residual stresses

Strength of Materials -     

Theoretical and experimental determination of residual stresses in plane joints

We have developed a mathematical model for determining residual stresses and stress concentration in the neighborhood of a plane joint of dissimilar materials and formulated variational statements of direct and inverse problems. The parameters of the stress–strain state of the object under study measured by nondestructive methods serve as input data for the inverse problem. We carry out a numerical analysis of solutions of the direct and inverse problems of determining stress concentration in the neighborhood of a joint of materials with different moduli. Finally, we discuss the applicability of the developed approach to the monitoring of the stress–strain state of joints in the course of their operation and to the evaluation of their residual life.     

Steady thermal contact of a half strip and a strip

The steady temperature field of a strip and a half strip connected at one end but with different thermophysical properties is determined for mixed conditions in the contact region.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 53, No. 2, pp. 302–307, August, 1987.     

Boundary element analysis of actual residual stresses in elastic plastic bodies under cyclic loading

The BEM was applied to the evaluation of an actual residual stress field in an elastic — perfectly plastic body subjected to any given cyclic loading. A new mechanical model describing this problem was used.

A corresponding discrete model based on both the direct and indirect versions of the BEM was proposed. The BEM approximation of stresses applied was similar to that one used in the elasto-plastic analysis in so called modified tractions and modified body forces algorithm. Some numerical tests have been carried out where BE solutions were compared with those obtained by means of the FE and FD methods. These comparisons show that the discrete model based on the BEM is efficient in the residual stress analysis.     

The dynamical problem of a rectangular stamp moving on an elastic half plane

Summary In this work, the stresses under a rectangular rigid stamp moving on an elastic half plane are calculated. The boundary value problem has been formulated in the form of a singular integral equation whose unknown function is the stress distribution under the stamp. The solutions of the equation have been compared for the cases of absence or presence of friction and for the cases of motion or rest. The work is an extension of Muskhelishvili's results and differs numerically from these ones only when the speed of the stamp is comparable with the shear wave speed.     

Crack propagating in a functionally graded strip under the plane loading

In the present paper, a finite crack with constant length (Yoffe type crack) propagating in the functionally graded strip under the plane loading is investigated by means of the Schmidt method. By using the Fourier transform and defining the jumps of displacement components across the crack surface as the unknown functions, two pairs of dual integral equations are derived. To solve the dual integral equations, the jumps of the displacement components across the crack surface are expanded in a series of Jacobi polynomial. Numerical examples are provided to show the effects of the material properties, the thickness of the functionally graded strip, and speed of the crack propagating upon the dynamic fracture behavior.     

Embedded beam under equivalent load induced from a surface moving load

Summary The paper is concerned with a specific problem in the study of an infinite beam embedded in a two-parameter elastic foundation (Vlazov-layer) under the equivalent load induced from a surface load moving normal to its length. Expressions for the deflection, flexural moment, and shear in the infinite beam are presented in an integral form. Numerical results are given for the deflection and flexural moment induced in the embedded beam due to the action of the moving load.With 5 Figures     

The plastic zone ahead of a mode II plane strain crack

The problem of a mode II plane strain crack in an elastic perfectly-plastic solid is analysed. It is shown that the elastic singular field for a crack cannot be matched with the near-tip field. Hence, the usual definition of small scale yielding is inappropriate. By matching the stress field in the plastic zone with the elastic dominant field for a blunt crack near the crack line at the elastic-plastic boundary, the elastic-plastic boundary ahead of the crack is determined.

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Résumé On analyse le problème d'une fissure de mode II en état de déformation plane dans un solide élastique parfaitement plastique. On montre que le champ singulier élastique relatif à une fissure ne peut être atteint par le champ régnant au voisinage de l'extrémité de la fissure considérée. Dès lors, la définition habituelle de l'écoulement platique à petite échelle n'est pas adéquate. On détermine la limite élastique-plastique en avant de la fissure en faisant se correspondre le champ de contraintes dans la zone plastique avec le champ principal élastique correspondant à une fissure arrondie située près de la ligne de la fissure.

     

A steadily moving load on an elastic strip resting on a rigid foundation

An infinite elastic strip resting on a flat rigid foundation is loaded by a downward directed concentrated force, which moves at constant speed. The resulting non-symmetric mixed boundary value problem is reduced on the basis of the plane strain theory of elasticity to singular integral equations over the regions of non-contact. With force magnitude and speed as parameters, the location of the non-contact regions, the lower boundary displacements, and foundation contact pressure are computed and illustrated graphically.     

Crack propagation in a strip of material under plane extension

The problem of a uniformly propagating finite crack in a strip of elastic material is solved using the dynamic equations of elasticity in two-dimensions. Two specific conditions of loading on the strip with finite width are discussed. In the first case, the rigidly clamped edges are pulled apart in the opposite directions. The second case considers equal and opposite tractions applied to the crack surface. By varying the strip width to the crack length ratio, the amplitude of the dynamic stresses ahead of the running crack is determined as a function of the crack velocity. The local dynamic stresses are found to be lower than the corresponding static values for the displacement loading condition and higher for the stress loading condition. This effect becomes increasingly more important as the crack length to strip width ratio is enlarged. Numerical results for the dynamic crack opening displacement are also presented.     

Kinetics of plastic strain zone formation near crack tip in fracture of construction materials under plane stress and plane strain

X-ray-diffraction analysis is used to determine the depth of the plastic deformation zones in steel. 15Kh2MFA and alloy D16 beneath the surface of fractures that are obtained under plane stress (PS) and plane deformation (PD) conditions. We propose a scheme illustrating the kinetics of the formation of two plastic deformation zones near the crack tip under one-time loading in conditions of the plane stress state: a strongly deformed microzone and a weakly deformed macrozone.Translated from Problemy Prochnosti, No. 4, pp. 57–63, April, 1993.     

Closed-form solution for the size of plastic zone in an edge-cracked strip

This paper is concerned with the problem of plastic zone at the tip of an edge crack in an isotropic elastoplastic strip under anti-plane deformations. By means of complex potential and Dugdale model, the stress intensity factor and the size of plastic zone are obtained in closed-form. Furthermore, the analytic solutions for an edge crack at the free boundary of a half-space and a semi-infinite crack heading towards a free surface are determined as the limiting cases of the strip geometries.     

Edge delamination in a laminated composite strip under generalized plane deformations

Edge delamination cracks in an elastic laminated composite strip are considered within the range of generalized plane deformations. By way of a simple regular finite element method, the method of mutual integral, wherein generalized plane strain solutions are employed as auxiliary fields, is applied to edge delamination cracks to obtain the complex stress intensities. The proposed numerical scheme is found to be very efficient and accurate. Moreover, the crack growth stability is examined for various loadings, including compression, bending and torsion, in terms of the energy release rate and mode mixity.