A model for graded materials with application to cracks
(2003) In International Journal of Fracture 124(1-2). p.93-105- Abstract
- Stress intensity factors are calculated for long plane cracks with one tip interacting with a region of graded material characteristics. The material outside the region is considered to be homogeneous. The analysis is based on assumed small differences in stiffness in the entire body. The linear extent of the body is assumed to be large compared with that of the graded region. The crack tip, including the graded region, is assumed embedded in a square-root singular stress field. The stress intensity factor is given by a singular integral. Solutions are presented for rectangular regions with elastic gradient parallel to the crack plane. The limiting case of infinite strip is solved analytically, leading to a very simple expression. Further,... (More)
- Stress intensity factors are calculated for long plane cracks with one tip interacting with a region of graded material characteristics. The material outside the region is considered to be homogeneous. The analysis is based on assumed small differences in stiffness in the entire body. The linear extent of the body is assumed to be large compared with that of the graded region. The crack tip, including the graded region, is assumed embedded in a square-root singular stress field. The stress intensity factor is given by a singular integral. Solutions are presented for rectangular regions with elastic gradient parallel to the crack plane. The limiting case of infinite strip is solved analytically, leading to a very simple expression. Further, a fundamental case is considered, allowing the solution for arbitrary variation of the material properties to be represented by Fourier's series expansion. The solution is compared with numerical results for finite changes of modulus of elasticity and is shown to have a surprisingly large range of validity. If an error of 5% is tolerated, modulus of elasticity may drop by around 40% or increase with around 60%. (Less)
- Abstract (Swedish)
- Stress intensity factors are calculated for long plane cracks with one tip interacting with a region of graded material characteristics. The material outside the region is considered to be homogeneous. The analysis is based on assumed small differences in stiffness in the entire body. The linear extent of the body is assumed to be large compared with that of the graded region. The crack tip, including the graded region, is assumed embedded in a square-root singular stress field. The stress intensity factor is given by a singular integral. Solutions are presented for rectangular regions with elastic gradient parallel to the crack plane. The limiting case of infinite strip is solved analytically, leading to a very simple expression. Further,... (More)
- Stress intensity factors are calculated for long plane cracks with one tip interacting with a region of graded material characteristics. The material outside the region is considered to be homogeneous. The analysis is based on assumed small differences in stiffness in the entire body. The linear extent of the body is assumed to be large compared with that of the graded region. The crack tip, including the graded region, is assumed embedded in a square-root singular stress field. The stress intensity factor is given by a singular integral. Solutions are presented for rectangular regions with elastic gradient parallel to the crack plane. The limiting case of infinite strip is solved analytically, leading to a very simple expression. Further, a fundamental case is considered, allowing the solution for arbitrary variation of the material properties to be represented by Fourier's series expansion. The solution is compared with numerical results for finite changes of modulus of elasticity and is shown to have a surprisingly large range of validity. If an error of 5% is tolerated, modulus of elasticity may drop by around 40% or increase with around 60%. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/c175147d-6fa1-40bc-b7a4-fd6ed493404a
- author
- Jivkov, A. P. LU and Ståhle, P. LU
- publishing date
- 2003
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Asymptotic analysis, Elastic material, Fracture toughness, Inhomogeneous material, Stress intensity factor
- in
- International Journal of Fracture
- volume
- 124
- issue
- 1-2
- pages
- 13 pages
- publisher
- Springer
- external identifiers
-
- wos:000188097500007
- scopus:0742267680
- ISSN
- 0376-9429
- DOI
- 10.1023/B:FRAC.0000009309.01041.00
- language
- English
- LU publication?
- no
- id
- c175147d-6fa1-40bc-b7a4-fd6ed493404a
- date added to LUP
- 2019-06-25 18:06:53
- date last changed
- 2022-04-26 02:28:00
@article{c175147d-6fa1-40bc-b7a4-fd6ed493404a,
abstract = {{Stress intensity factors are calculated for long plane cracks with one tip interacting with a region of graded material characteristics. The material outside the region is considered to be homogeneous. The analysis is based on assumed small differences in stiffness in the entire body. The linear extent of the body is assumed to be large compared with that of the graded region. The crack tip, including the graded region, is assumed embedded in a square-root singular stress field. The stress intensity factor is given by a singular integral. Solutions are presented for rectangular regions with elastic gradient parallel to the crack plane. The limiting case of infinite strip is solved analytically, leading to a very simple expression. Further, a fundamental case is considered, allowing the solution for arbitrary variation of the material properties to be represented by Fourier's series expansion. The solution is compared with numerical results for finite changes of modulus of elasticity and is shown to have a surprisingly large range of validity. If an error of 5% is tolerated, modulus of elasticity may drop by around 40% or increase with around 60%.}},
author = {{Jivkov, A. P. and Ståhle, P.}},
issn = {{0376-9429}},
keywords = {{Asymptotic analysis; Elastic material; Fracture toughness; Inhomogeneous material; Stress intensity factor}},
language = {{eng}},
number = {{1-2}},
pages = {{93--105}},
publisher = {{Springer}},
series = {{International Journal of Fracture}},
title = {{A model for graded materials with application to cracks}},
url = {{http://dx.doi.org/10.1023/B:FRAC.0000009309.01041.00}},
doi = {{10.1023/B:FRAC.0000009309.01041.00}},
volume = {{124}},
year = {{2003}},
}