Kinking of a crack emanating from the free surface of a beam under pure bending

C. Levy; M. Perl

doi:10.1016/0020-7683(86)90060-0

Kinking of a crack emanating from the free surface of a beam under pure bending

C. Levy, M. Perl

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

A perturbation technique developed by Karihaloo et al. is employed to obtain the stress intensity factors at the tip of a kinking crack that emanates from the free surface of a beam under pure bending. Under the condition that the kink extends in the direction of vanishing K₁₁ the crack path is obtained as well as a path stability condition. From conditions on K₁ a material parameter r^* akin to that of Ramulu and Kobayashi's r_c is obtained. By analysis of the slope of the kinking crack a stability condition is obtained corroborating the stability condition from consideration of vanishing K₁₁. It is shown that for a beam in pure bending the nonsingular remote stress term T must be greater than some positive critical value for kinking to occur confirming the results of Sayir and Schindler.

Original language	English
Pages (from-to)	1525-1539
Number of pages	15
Journal	International Journal of Solids and Structures
Volume	22
Issue number	12
DOIs	https://doi.org/10.1016/0020-7683(86)90060-0
State	Published - 1 Jan 1986
Externally published	Yes

ASJC Scopus subject areas

Modeling and Simulation
General Materials Science
Condensed Matter Physics
Mechanics of Materials
Mechanical Engineering
Applied Mathematics

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10.1016/0020-7683(86)90060-0

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title = "Kinking of a crack emanating from the free surface of a beam under pure bending",

abstract = "A perturbation technique developed by Karihaloo et al. is employed to obtain the stress intensity factors at the tip of a kinking crack that emanates from the free surface of a beam under pure bending. Under the condition that the kink extends in the direction of vanishing K11 the crack path is obtained as well as a path stability condition. From conditions on K1 a material parameter r* akin to that of Ramulu and Kobayashi's rc is obtained. By analysis of the slope of the kinking crack a stability condition is obtained corroborating the stability condition from consideration of vanishing K11. It is shown that for a beam in pure bending the nonsingular remote stress term T must be greater than some positive critical value for kinking to occur confirming the results of Sayir and Schindler.",

author = "C. Levy and M. Perl",

note = "Funding Information: Acknowledgement-This work was supported by a Lady Davis Post-Doctoral Fellowship administered by the Technion-Israel Institute of Technology. The authors would like to thank Professor Sayir of ETH-Zentrum, Zurich, Switzerland, for helpful discussion of his work with Dr. Schindler. The authors would also like to thank Professor A. S. Kobayashi for providing them with several of his papers on the sUbject!l!' 12, 19).",

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T1 - Kinking of a crack emanating from the free surface of a beam under pure bending

AU - Levy, C.

AU - Perl, M.

N1 - Funding Information: Acknowledgement-This work was supported by a Lady Davis Post-Doctoral Fellowship administered by the Technion-Israel Institute of Technology. The authors would like to thank Professor Sayir of ETH-Zentrum, Zurich, Switzerland, for helpful discussion of his work with Dr. Schindler. The authors would also like to thank Professor A. S. Kobayashi for providing them with several of his papers on the sUbject!l!' 12, 19).

PY - 1986/1/1

Y1 - 1986/1/1

N2 - A perturbation technique developed by Karihaloo et al. is employed to obtain the stress intensity factors at the tip of a kinking crack that emanates from the free surface of a beam under pure bending. Under the condition that the kink extends in the direction of vanishing K11 the crack path is obtained as well as a path stability condition. From conditions on K1 a material parameter r* akin to that of Ramulu and Kobayashi's rc is obtained. By analysis of the slope of the kinking crack a stability condition is obtained corroborating the stability condition from consideration of vanishing K11. It is shown that for a beam in pure bending the nonsingular remote stress term T must be greater than some positive critical value for kinking to occur confirming the results of Sayir and Schindler.

AB - A perturbation technique developed by Karihaloo et al. is employed to obtain the stress intensity factors at the tip of a kinking crack that emanates from the free surface of a beam under pure bending. Under the condition that the kink extends in the direction of vanishing K11 the crack path is obtained as well as a path stability condition. From conditions on K1 a material parameter r* akin to that of Ramulu and Kobayashi's rc is obtained. By analysis of the slope of the kinking crack a stability condition is obtained corroborating the stability condition from consideration of vanishing K11. It is shown that for a beam in pure bending the nonsingular remote stress term T must be greater than some positive critical value for kinking to occur confirming the results of Sayir and Schindler.

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JF - International Journal of Solids and Structures

IS - 12

ER -

Kinking of a crack emanating from the free surface of a beam under pure bending

Abstract

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