Proper Defect Density Parameters ForAnisotropic Solids With Cracks And EllipticalHoles (original) (raw)
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Elliptical cracks arbitrarily oriented in 3D-anisotropic elastic media
International Journal of Engineering Science, 2009
An elliptical crack in an infinite anisotropic elastic medium is considered. For a polynomial external stress field, an efficient numerical algorithm of the solution of the problem is developed. The discontinuity of the displacement field on the crack surface (the crack opening vector) is presented in the form of 2D-regular integrals that can be evaluated numerically for any crack orientation with respect to the principal axes of the anisotropy of the medium. The integrand functions in these integrals are expressed via the Fourier transform of the Green function of the medium. The cases of constant and linear external stress fields are considered in detail. Simplifications for particular crack orientations in the cases of orthotropic and transversely isotropic media are indicated. The stress intensity factors are obtained in the form of regular integrals that depend only on the Fourier transform of the Green function of the medium. An equation for the tensor of effective elastic constants of an anisotropic media containing a random set of elliptical cracks is presented.
On the anisotropy of cracked solids
International Journal of Engineering Science, 2018
We consider the effective elastic properties of cracked solids, and verify the hypothesis that the effect of crack interactions on the overall anisotropy-its type and orientation-is negligible (even though the effect on the overall elastic constants may be strong), provided crack centers are located randomly. This hypothesis is confirmed by computational studies on large number of 2-D crack arrays of high crack density (up to 0.8) that are realizations of several orientation distributions. Therefore, the anisotropy can be accurately determined analytically in the non-interaction approximation (NIA). Since the effective elastic properties possess the orthotropic symmetry in the NIA (for any orientation distribution of cracks, including cases when, geometrically , the crack orientation pattern does not have this symmetry), the orthotropy of cracked solids is not affected by interactions.
International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 1991
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International Journal of Solids and Structures, 2002
Pores and defects in real materials often have very irregular shapes. Thus, micromechanical modeling based on the analytical solutions of elasticity becomes inapplicable. The objective of this paper is to present a computational procedure to calculate the contribution of the irregularly shaped defects into the effective moduli of two-dimensional elastic solids. In this procedure, the cavity compliance tensor is constructed
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Recent Advances in Fracture Mechanics, 1998
The problem of a kinked crack is analysed for the most general case of elastic anisotropy. The kinked crack is modelled by means of continuous distributions of dislocations which are assumed to be singular both at the crack tips and at the kink vertex. The resulting system of singular integral equations is solved numerically using Chebyshev polynomials and the reciprocal theorem. The stress intensity factors for modes I, II and III and the generalised stress intensity factor at the vertex are obtained directly from the dislocation densities.
Mechanics of Solids
The method earlier developed by one of the authors for identifying ellipsoidal defects is numerically tested for the applicability to the problem of identification of a degenerate ellipsoidal defect, i.e., an elliptic crack. The method is based on the reciprocity functional and the assumption that the displacements are measured in a uniaxial tension test of an isotropic linearly elastic body. Calculations show that the earlier developed method is also efficient for identification of an elliptic crack and its parameters (the center coordinates, the normal to the crack plane, and the directions and lengths of the semiaxes) can be determined with high accuracy. Some examples where the crack has a non-elliptic shape are also considered. It is discovered that, in many cases, the ellipsoids that were constructed by formulas reconstructing the ellipsoidal crack from the data on the external boundary of the body that correspond to a nonelliptic crack, approximate the actual defect with sufficient accuracy. The method stability was investigated with respect to noise in the initial data.
Crack tip stress fields for anisotropic materials with cubic symmetry
Fracture mechanics of linear elastic materials is generally based on the K field which has been derived for isotropic materials. Many applications require the use of advanced materials, which are often anisotropic and thus the isotropic elastic K-field is not applicable. In this work, a sharp crack lying in a homogenous, anisotropic material with cubic symmetry is studied and crack tip stress fields are presented. It is shown that the crack tip fields depend on material properties through the anisotropy factor, ρ. The stress fields are applicable for both plane stress and plane strain conditions, though the definition of ρ is different in each case. The theoretical K field obtained has been compared to results from finite element studies and excellent agreement has been obtained.
Eshelby tensor for a crack in an orthotropic elastic medium
Comptes Rendus Mécanique, 2005
In the present Note, we provide new analytical expressions of the components of Hill tensor P (or equivalently the Eshelby tensor S) associated to an arbitrarily oriented crack in orthotropic elastic medium. The crack is modelled as an infinite cylinder along a symmetry axis of the matrix, with low aspect ratio. The three dimensional results obtained show explicitly the interaction between the primary (structural) anisotropy and the crack-induced anisotropy. They are validated by comparison with existing results in the case where the crack is in a symmetry plane. To cite this article: C. Gruescu et al., C. R. Mecanique 333 (2005). 2005 Académie des sciences. Published by Elsevier SAS. All rights reserved.
Elastic solids with many cracks: A simple method of analysis
International Journal of Solids and Structures, 1987
A simple method of stress analysis in elastic solids with many cracks is proposed. It is based on the superposition technique and the ideas of selLconsistency applied to the average tractions on individual cracks. The method is applicable lo both two-and threedimensional crack arrays of arbitrary geometry. It yields approximate analytical solutions for the stress intensity factors (SIFs) accurate up to quite close distances between cracks. It is also suggested how a full stress field can be approximately constructed. Applications lo a configuration "crack-microcrack array" and lo a problem ol effective elastic properties of a solid with cracks are considered.