Cylindrical interface crack between nonhomogeneous elastic materials under axially symmetric longitudinal shear

Conditions are discussed for which the contact zone at the tip of a two-dimensional interface crack between anisotropic elastic materials is small. For such “small scale contact” conditions combined with small scale yielding conditions, a stress concentration vector uniquely characterizes the near tip field, and may be used as a crack growth parameter. Representative calculations for an interface crack on a representative Cu grain boundary show small contact conditions to prevail, except possibly under large shearing loads.

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Penny-shaped Interface Crack in a Non-homogeneous Multilayered Medium under Axially Symmetric Torsion

ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik ◽

10.1002/1521-4001(200103)81:3<205::aid-zamm205>3.0.co;2-4 ◽

2001 ◽

Vol 81 (3) ◽

pp. 205-211 ◽

Cited By ~ 2

Author(s):

H.K. Hemed ◽

R.S. Dhaliwal

Keyword(s):

Interface Crack ◽

Axially Symmetric ◽

Multilayered Medium

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Determination of the Stress Intensity Factors for Axisymmetric Cylindrical Interface Crack by an Eigenvalue Method

Volume 6: Materials and Fabrication, Parts A and B ◽

10.1115/pvp2009-78014 ◽

2009 ◽

Author(s):

Lin Weng ◽

Zengliang Gao ◽

Xiaogui Wang

Keyword(s):

Finite Element ◽

Stress Intensity ◽

Interface Crack ◽

Stress Intensity Factors ◽

Stress Singularity ◽

Intensity Factors ◽

Singular Stress ◽

Cylindrical Interface ◽

Eigenvalue Method ◽

Fiber Matrix

An eigenvalue method was proposed to study the stress intensity factors associated with the oscillating stress singularity for the axisymmetric cylindrical interface crack of the fiber/matrix composites. The fiber is a transversely isotropic material and the matrix is isotropic. Based on the fundamental equations of the spacial axisymmetric problem and the assumption of first-order approximation of the singular stress field, the discrete characteristic equation was derived using the displacement functions in the form of separated variables and the technique of meshless method. The eigenvalue is relative to the order of stress singularity, and the associated eigenvector is with respect to the displacement angular variations. The stress angular variations were derived by introducing the displacement angular variations into the constitutive relations. A finite element fiber/matrix model was used to verify the validation of the proposed eigenvalue method. The numerical results of the order of stress singularity and normalized stress angular variations are in good agreement with those obtained by the eigenvalue method. Based on the order of stress singularity and stress angular variations obtained by the eigenvalue method, as well as the numerical singular stress fields obtained by the finite element method (FEM), the stress intensity factors were determined successfully with the linear extropolation method.

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Heat Concentration around a Cylindrical Interface Crack in a Composite Tube

Advances in Mathematical Physics ◽

10.1155/2020/5849690 ◽

2020 ◽

Vol 2020 ◽

pp. 1-13

Author(s):

J. W. Fu ◽

L. F. Qian

Keyword(s):

Heat Flux ◽

Intensity Factor ◽

Interface Crack ◽

Composite Structures ◽

Superposition Method ◽

Liner Material ◽

Composite Tube ◽

Cylindrical Interface ◽

Flux Intensity ◽

Heat Flux Intensity

Cracks always form at the interface of discrepant materials in composite structures, which influence thermal performances of the structures under transient thermal loadings remarkably. The heat concentration around a cylindrical interface crack in a bilayered composite tube has not been resolved in literature and thus is investigated in this paper based on the singular integral equation method. The time variable in the two-dimensional temperature governing equation, derived from the non-Fourier theory, is eliminated using the Laplace transformation technique and then solved exactly in the Laplacian domain by the employment of a superposition method. The heat concentration degree caused by the interface crack is judged quantitatively with the employment of heat flux intensity factor. After restoring the results in the time domain using a numerical Laplace inversion technique, the effects of thermal resistance of crack, liner material, and crack length on the results are analyzed with a numerical case study. It is found that heat flux intensity factor is material-dependent, and steel is the best liner material among the three potential materials used for sustaining transiently high temperature loadings.

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Study Of Three Dimensional Propagation Of Waves In Hollow Poroelastic Circular Cylinders

International Journal of Applied Mechanics and Engineering ◽

10.1515/ijame-2015-0037 ◽

2015 ◽

Vol 20 (3) ◽

pp. 565-587

Author(s):

S.A. Shah

Keyword(s):

Three Dimensional ◽

Elastic Solid ◽

Longitudinal Shear ◽

Frequency Equation ◽

Circular Cylinders ◽

Torsional Vibrations ◽

Saturated Porous Media ◽

Axially Symmetric ◽

General Frequency ◽

Propagation Of Waves

Abstract Employing Biot’s theory of wave propagation in liquid saturated porous media, waves propagating in a hollow poroelastic circular cylinder of infinite extent are investigated. General frequency equations for propagation of waves are obtained each for a pervious and an impervious surface. Degenerate cases of the general frequency equations of pervious and impervious surfaces, when the longitudinal wavenumber k and angular wavenumber n are zero, are considered. When k=0, the plane-strain vibrations and longitudinal shear vibrations are uncoupled and when k≠0 these are coupled. It is seen that the frequency equation of longitudinal shear vibrations is independent of the nature of the surface. When the angular (or circumferential) wavenumber is zero, i.e., n=0, axially symmetric vibrations and torsional vibrations are uncoupled. For n≠0 these vibrations are coupled. The frequency equation of torsional vibrations is independent of the nature of the surface. By ignoring liquid effects, the results of a purely elastic solid are obtained as a special case.

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