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Axisymmetric Torsion of an Elastic Layer Sandwiched between Two Elastic Half-Spaces with Two Interfaced Cracks

Madani Fateh, Kebli Belkacem

Studia Geotechnica et Mechanica

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2019

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Vol. 41, nr 2

57--66

EN

The present article examines the problem related to the axisymmetric torsion of an elastic layer by a circular rigid disc at the symmetry plane. The layer is sandwiched between two similar elastic half-spaces with two penny-shaped cracks symmetrically located at the interfaces between the two bonded dissimilar media. The mixed boundary-value problem is transformed, by means of the Hankel integral transformation, to dual integral equations, that are reduced, to a Fredholm integral equation of the second kind. The numerical methods are used to convert the resulting system to a system of infinite algebraic equations. Some physical quantities such as the stress intensity factor and the moment are calculated and presented numerically according to some relevant parameters. The numerical results show that the discontinuities around the crack and the inclusion cause a large increase in the stresses that decay with distance from the disc-loaded. Furthermore, the dependence of the stress intensity factor on the disc size, the distance between the crack and the disc, and the shear parameter is also observerd.

2

Axisymmetric torsion of an internally cracked elastic medium by two embedded rigid discs

Madani F., Kebli B.

Mechanics and Mechanical Engineering

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2017

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Vol. 21, nr 2

363--377

EN

The present work aims to investigate a penny-shaped crack problem in the interior of a homogeneous elastic material at the symmetry plane, under an axisymmetric torsion by two circular rigid discs symmetrically located in the elastic medium. The two discs rotate with the same angle in the different direction about the axis passing through their centers. The general solution of this problem is obtained by using the Hankel transforms method. The corresponding doubly mixed boundary value problem associated with the rigid disc and the penny-shaped is reduced to a system of dual integral equations, which are transformed, to a Fredholm integral equations of the second kind. Using the quadrature rule, the resulting system is converted to a system of infinite algebraic equations. The variation in the displacement, stress and stress intensity factor are presented for some particular cases of the problem.

3

Analysis of mode I conducting crack in piezo-electro-magneto-elastic layer

Rogowski B.

International Journal of Applied Mechanics and Engineering

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2013

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Vol. 18, no. 1

153--176

EN

Within the theory of linear magnetoelectroelasticity, the fracture analysis of a magneto - electrically dielectric crack embedded in a magnetoelectroelastic layer is investigated. The prescribed displacement, electric potential and magnetic potential boundary conditions on the layer surfaces are adopted. Applying the Hankel transform technique, the boundary - value problem is reduced to solving three coupling Fredholm integral equations of second kind. These equations are solved exactly. The corresponding semi - permeable crack - face magnetoelectric boundary conditions are adopted and the electric displacement and magnetic induction of crack interior are obtained explicitly. This field inside the crack is dependent on the material properties, applied loadings, the dielectric permittivity and magnetic permeability of crack interior, and the ratio of the crack length and the layer thickness. Field intensity factors are obtained as explicit expressions.

4

Fracture analysis of a mode I magneto-electrically conducting crack in piezo-electro-magneto-elastic medium

Rogowski B.

International Journal of Applied Mechanics and Engineering

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2012

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Vol. 17, no. 4

1267-1295

EN

Within the theory of linear magnetoelectroelasticity, the fracture analysis of a magneto electrically conducting crack embedded in a magneto electro elastic medium is investigated. The prescribed normal stress and two cases of electromagnetic boundary conditions applied at infinity are adopted. Applying the Hankel transform technique, the boundary value problem is reduced to solving three pairs of dual coupling integral equations. These equations are solved exactly. The corresponding semi permeable crack face magneto electric boundary conditions are adopted and the electric displacement and magnetic induction of the crack interior are obtained explicitly. This field inside the crack is dependent on the material properties, applied loadings and the dielectric permittivity and magnetic permeability of the crack interior. Field intensity factors are obtained as explicit expressions.

5

Tension of two bonded materials with an interface crack

Rogowski B.

Zeszyty Naukowe Politechniki Świętokrzyskiej. Mechanika

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2003

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Z. 78

411-425

EN

The problem of a penny-shaped crack located at the interface of two bonded half-spaces is considered. Both materials are transversely isotropic and dissimilar. The representation of displacements and stress in the form of Hankel integrals leads to a set of simulataneous dual integral equations for two unknown functions. These equations are reduced to a singular integral equation for a complex-valued function. In terms of real and imaginary part of this function it is possible to completely specify the stress and displacement fields and crack energy. The explicit formulae are obtained for the physical quantities in the case when the applied pressure on the crack surface is constant.

PL

Rozpatrzono zagadnienie szczeliny kołowej usytuowanej w płaszczyźnie połączenia dwóch półprzestrzeni wypełnionych różnymi materiałami poprzecznie izotropowymi. Zagadnienie rozwiązano za pomocą transformacji całkowych i sprowadzono do układu dualnych równań całkowych, które z kolei zastąpiono singularnym równaniem całkowym typu Cauchy'ego względem nieznanej funkcji zespolonej. Otrzymano wzory określające stan naprężenia i przemieszczenia oraz energię szczeliny za pomocą rzeczywistej i urojonej części funkcji zespolonej. Dla przypadku stałego wewnętrznego ciśnienia, rozwierającego szczelinę, otrzymano jawną postać funkcji określającej energię szczeliny.

6

Penny-shaped crack in a piezoceramic cylinder under Mode I loading

Narita F., Lin S., Shindo Y.

Archives of Mechanics

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2003

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Vol. 55, nr 3

275-304

EN

The electroelastic response of a penny-shaped crack in a piezoelectric cylinder of finite radius is investigated in this study. Fourier and Hankel transforms are used to reduce the problem to the solution of a pair of dual integral equations. They are then reduced to a Fredholm integral equation of the second kind. Numerical values of the stress intensity factor, energy release rate and energy density factor for piezoelectric ceramics are obtained to show the influence of applied electrical loads.