On the Validity of a Perturbation Theory for a Crack in an Elastically Graded Material
(2000) Meso-Mechanical Aspects of Material Behavior p.89-100- Abstract
- The stress intensity factor is investigated for a long plane crack with one tip interacting with a strip of graded elastic material. In the strip the material may have a non uniform modulus of elasticity whereas variation of Poisson’s ratio is ignored. The crack length and the body dimensions are assumed to be large compared to the linear extent of the graded region. The crack tip including the graded region is assumed to be embedded in a remote square root singular stress field. A finite element method is used to obtain the near tip stress intensity factor. The analytical solution to the problem for small deviations from a constant modulus of elasticity is communicated in brief. The analytical solution is shown to have a surprisingly wide... (More)
- The stress intensity factor is investigated for a long plane crack with one tip interacting with a strip of graded elastic material. In the strip the material may have a non uniform modulus of elasticity whereas variation of Poisson’s ratio is ignored. The crack length and the body dimensions are assumed to be large compared to the linear extent of the graded region. The crack tip including the graded region is assumed to be embedded in a remote square root singular stress field. A finite element method is used to obtain the near tip stress intensity factor. The analytical solution to the problem for small deviations from a constant modulus of elasticity is communicated in brief. The analytical solution is shown to have a surprisingly wide range of validity. If an error of 5% is tolerated, the modulus of elasticity may decrease in the graded region with around 40% and increase with around 60%. (Less)
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https://lup.lub.lu.se/record/3d5d5a40-d5b7-4e48-8d59-3c7540332855
- author
- Ståhle, Per LU and Jivkov, Andrey P. LU
- publishing date
- 2000
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- host publication
- Meso-Mechanical Aspects of Material Behavior : Symposium to Honor Professor Aoki’s 60th Birthday - Symposium to Honor Professor Aoki’s 60th Birthday
- pages
- 12 pages
- conference name
- Meso-Mechanical Aspects of Material Behavior
- conference location
- Yufuin, Oita, Japan
- conference dates
- 2000-08-21 - 2000-08-23
- language
- English
- LU publication?
- no
- id
- 3d5d5a40-d5b7-4e48-8d59-3c7540332855
- date added to LUP
- 2019-06-25 19:18:59
- date last changed
- 2020-03-25 16:22:49
@inproceedings{3d5d5a40-d5b7-4e48-8d59-3c7540332855, abstract = {{The stress intensity factor is investigated for a long plane crack with one tip interacting with a strip of graded elastic material. In the strip the material may have a non uniform modulus of elasticity whereas variation of Poisson’s ratio is ignored. The crack length and the body dimensions are assumed to be large compared to the linear extent of the graded region. The crack tip including the graded region is assumed to be embedded in a remote square root singular stress field. A finite element method is used to obtain the near tip stress intensity factor. The analytical solution to the problem for small deviations from a constant modulus of elasticity is communicated in brief. The analytical solution is shown to have a surprisingly wide range of validity. If an error of 5% is tolerated, the modulus of elasticity may decrease in the graded region with around 40% and increase with around 60%.}}, author = {{Ståhle, Per and Jivkov, Andrey P.}}, booktitle = {{Meso-Mechanical Aspects of Material Behavior : Symposium to Honor Professor Aoki’s 60th Birthday}}, language = {{eng}}, pages = {{89--100}}, title = {{On the Validity of a Perturbation Theory for a Crack in an Elastically Graded Material}}, year = {{2000}}, }