A model for graded materials with application to cracks

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A model for graded materials with application to cracks

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Publication Article, peer reviewed scientific
Title A model for graded materials with application to cracks
Author(s) Jivkov, Andrey ; Ståhle, Per
Date 2003
English 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%.
DOI http://dx.doi.org/10.1023/B:FRAC.0000009309.01041.00 (link to publisher's fulltext)
Host/Issue International Journal of Fracture;1-2
Volume 124
ISSN 0376-9429
Pages 93-105
Language eng (iso)
Subject(s) Asymptotic analysis
Stress intensity factor
Inhomogeneous material
Fracture toughness
Elastic material
Research Subject Categories::TECHNOLOGY
Handle http://hdl.handle.net/2043/522 (link to this page)

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