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On the Validity of a Perturbation Theory for a Crack in an Elastically Graded Material

Ståhle, Per LU and Jivkov, Andrey P. LU (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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publishing date
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},
}