Jivkov's articles
A model for graded materials with application to cracks
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.
he 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%.