Two parallel elliptical cracks in an infinite solid subjected to tension

Isida, Makoto; Hirota, Koichi; Noguchi, Hiroshi; Yoshida, Tadatsugu

doi:10.1007/bf00017211

Cited by 45 publications

(16 citation statements)

References 11 publications

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“…This configuration is considered here as a test; our results are compared with the ones of [13]. The smallest spacing between two circular parallel cracks (in the normal direction) considered in [13] was 0.5 of the crack diameter; the ratios K~/IQ~ calculated for the "offsets" of …”

Section: Normal Loading Of "Offset" Stacked Cracksmentioning

confidence: 99%

“…The smallest spacing between two circular parallel cracks (in the normal direction) considered in [13] was 0.5 of the crack diameter; the ratios K~/IQ~ calculated for the "offsets" of …”

Section: Normal Loading Of "Offset" Stacked Cracksmentioning

confidence: 99%

“…Moderate interactions were considered in [13] where a numerical study of two parallel elliptical cracks was done (with the smallest spacing between cracks of 1/4 of the minor axis of the ellipse) and in [30] where the problem of two stacked circular cracks of equal size under normal loading was reduced to dual integral equations (the smallest spacing for which numerical results were given was 1/4 of the crack diameter).…”

Section: Introductionmentioning

confidence: 99%

“…He derived, based on his earlier results for a single circular crack [17], a new form of integral equations for the problem of coplanar cracks; it has the advantage that the equations are non-singular and can be solved by rapidly converging iterations (for two coplanar cracks of equal size, the procedure converged up to spacings as small as 0.000 25 and 0.005 of the crack diameter for the normal and shear loadings, respectively). The results of [16,28] for strong coplanar interactions and the ones of [30] and [13] for moderate stacked interactions are used as tests for our method. (The available results for the cases of weak interactions do not constitute challenging tests since the method is asymptotically exact in these cases).…”

Section: Introductionmentioning

confidence: 99%

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Three-dimensional problems of strongly interacting arbitrarily located penny-shaped cracks

1989

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Three-dimensional elastic interactions of arbitrarily located and oriented penny-shaped cracks are considered, and solutions for the stress intensity factors (SIFs) are obtained for several crack geometries. The work is based on the method of analysis of many cracks problems developed by Kachanov [1 ]. Unlike most of the results available in literature, the obtained solutions remain accurate for closely spaced, strongly interacting cracks. The effects of stress "shielding" and "amplification" and the influence of various geometrical factors are examined. The simplest crack-microcrack interactions in three dimensions are considered. The approximations of "weak interactions" and of "widely spaced cracks" are discussed. The interactions that are weak in their impact on the effective elastic constants may be strong in their impact on SIFs; this indicates that no simple relation between the deterioration of elastic stiffness of a microcracking solid and its progression towards failure seems to exist.

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Section: Normal Loading Of "Offset" Stacked Cracksmentioning

confidence: 99%

“…The smallest spacing between two circular parallel cracks (in the normal direction) considered in [13] was 0.5 of the crack diameter; the ratios K~/IQ~ calculated for the "offsets" of …”

Section: Normal Loading Of "Offset" Stacked Cracksmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Three-dimensional problems of strongly interacting arbitrarily located penny-shaped cracks

1989

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“…This is mainly due to the neglect of multiple scattering in the present approach, but maybe also because the stochastic distribution tends to loose it meaning when the crack density becomes large. It has been shown by Isida et al (1985) that the static interac- But as shown by (Sotiropoulos and Achenbach, 1988, Eq. (46)) the neglect of multiple scattering is valid for surprisingly large crack densities at low frequencies.…”

mentioning

confidence: 98%

Effective spring boundary conditions for a damaged interface between dissimilar media in three-dimensional case

Golub

Doroshenko

Boström

2016

International Journal of Solids and Structures

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International Journal of Solids and Structures (ISSN: 0020-7683)Citation for the published paper: Golub, M. ; Doroshenko, O. ; Boström, A. (2016) AbstractElastic waves in the presence of a damaged interface between two dissimilar elastic media is investigated in the three-dimensional case. The damaged is modelled as a stochastic distribution of equally sized circular cracks which is transformed into a spring boundary condition. First the scattering by a single circular interface crack between two dissimilar half-spaces is investigated and solved explicitly for normally incident waves in the low frequency limit. The transmission by a distribution of cracks is then determined and is transformed into a spring boundary condition, where effective spring stiffnesses are expressed in terms of elastic moduli and damage parameters. A comparison with previous results for a periodic distribution of cracks shows good agreement.

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Interaction of a penny-shaped crack with an elliptic crack

Roy

Saha

1995

Int J Fract

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Three-dimensional problem of crack-microcrack interaction is solved. Both the crack and microcrack are embedded in an infinite isotropic elastic medium which is subjected to constant normal tension at infinity. One of the cracks is circular while the other is elliptic and they are coplanar and are positioned in such a way that the axis of the elliptic crack passes through the centre of the circular crack. A recently developed integral equation method has been used to solve the corresponding two dimensional simultaneous dual integral equation involving the displacement discontinuity across the crack faces that arises in such an interaction problem. A series of transformations first reduce them to a quadruplet infinite system of equations. A series solution is finally obtained in terms of crack separation parameter fl which depends on the separation of the crack microcrack centre. Analytical expression for the stress intensity factors have been obtained up to the order fit. Numerical values of the interaction effect have been computed for and results show that interaction effects fluctuate from shielding to amplification depending on the location of each crack with respect to the other and crack tip spacing as well as the aspect ratio of the elliptic crack. The short range interaction can play a dominant role in the prediction of crack microcrack propagation.

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Two parallel elliptical cracks in an infinite solid subjected to tension

Cited by 45 publications

References 11 publications

Three-dimensional problems of strongly interacting arbitrarily located penny-shaped cracks

Three-dimensional problems of strongly interacting arbitrarily located penny-shaped cracks

Effective spring boundary conditions for a damaged interface between dissimilar media in three-dimensional case

Interaction of a penny-shaped crack with an elliptic crack

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