A Cylindrical Interface Crack in a Nonhomogeneous Anisotropic Elastic Body

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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The Stroh Formalism

Anisotropic Elasticity ◽

10.1093/oso/9780195074475.003.0008 ◽

1996 ◽

Author(s):

T. T. C. Ting

Keyword(s):

General Solution ◽

Elastic Body ◽

Three Dimensional ◽

Anisotropic Elasticity ◽

Stroh Formalism ◽

Two Dimensional ◽

Stroh's Formalism ◽

Elasticity Problems ◽

Anisotropic Elastic ◽

Stroh’S Formalism

In this chapter we study Stroh's sextic formalism for two-dimensional deformations of an anisotropic elastic body. The Stroh formalism can be traced to the work of Eshelby, Read, and Shockley (1953). We therefore present the latter first. Not all results presented in this chapter are due to Stroh (1958, 1962). Nevertheless we name the sextic formalism after Stroh because he laid the foundations for researchers who followed him. The derivation of Stroh's formalism is rather simple and straightforward. The general solution resembles that obtained by the Lekhnitskii formalism. However, the resemblance between the two formalisms stops there. As we will see in the rest of the book, the Stroh formalism is indeed mathematically elegant and technically powerful in solving two-dimensional anisotropic elasticity problems. The possibility of extending the formalism to three-dimensional deformations is explored in Chapter 15.

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An inverse problem for a linear crack in an anisotropic elastic body and the enclosure method

Inverse Problems ◽

10.1088/0266-5611/24/2/025005 ◽

2008 ◽

Vol 24 (2) ◽

pp. 025005 ◽

Cited By ~ 6

Author(s):

Masaru Ikehata ◽

Hiromichi Itou

Keyword(s):

Inverse Problem ◽

Elastic Body ◽

Enclosure Method ◽

Anisotropic Elastic

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Theory of Elasticity of an Anisotropic Elastic Body

Physics Today ◽

10.1063/1.3051394 ◽

1964 ◽

Vol 17 (1) ◽

pp. 84-84 ◽

Cited By ~ 45

Author(s):

S. G. Lekhnitskii ◽

P. Fern ◽

Julius J. Brandstatter ◽

E. H. Dill

Keyword(s):

Elastic Body ◽

Theory Of Elasticity ◽

Anisotropic Elastic

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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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