A model for graded materials with application to cracks
(2003) In International Journal of Fracture 124(12). p.93105 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 squareroot 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 squareroot 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 squareroot 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 squareroot 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/c175147d6fa140bcb7a4fd6ed493404a
 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
 12
 pages
 13 pages
 publisher
 Springer
 external identifiers

 wos:000188097500007
 scopus:0742267680
 ISSN
 03769429
 DOI
 10.1023/B:FRAC.0000009309.01041.00
 language
 English
 LU publication?
 no
 id
 c175147d6fa140bcb7a4fd6ed493404a
 date added to LUP
 20190625 18:06:53
 date last changed
 20220426 02:28:00
@article{c175147d6fa140bcb7a4fd6ed493404a, 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 squareroot 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 = {{03769429}}, keywords = {{Asymptotic analysis; Elastic material; Fracture toughness; Inhomogeneous material; Stress intensity factor}}, language = {{eng}}, number = {{12}}, pages = {{93105}}, 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}}, }