A model for graded materials with application to cracks

Abstract

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%.

On the fracture behavior of inhomogeneous materials––A case study for elastically inhomogeneous bimaterials

“…An extensive literature review is given in Simha et al (2003) and shall not be repeated here. Very recent studies have been presented, e.g., by Jivkov and Ståhle (2003), Weichen (2003), Bahr et al (2003), Kim and Paulino (2003), Rao and Rahman (2003), Wang et al (2003), and Abendroth et al (2002). Apart from the latter one, these recent papers deal with cracks in functionally graded materials.…”