Analysis of a crack in and near an elastically graded material

The behaviour of the stress intensity factor is investigated for a long plane crack with one tip interacting with a strip of graded elastic properties. The material outside the strip is postulated to be homogeneous linear elastic and the material in the graded region is assumed to have continuous change of modulus of elasticity. Changes of the Poisson’s ratio are ignored. The body is assumed to be large in comparison to the crack length, and the crack length itself to be large compared to the linear extent of the graded region. The study is performed using finite element method and the results are extrapolated to infinitesimal variations of the graded region’s modulus of elasticity from the one of the surrounding body. The crack tip, including the graded region, is considered embedded in a square root singular stress field governed by the stress intensity factor for a body without a strip. Hence, the numerical solutions are obtained for remote boundary conditions in a form of prescribed displacements supplied by that stress intensity factor. The analytical solution to the problem for an infinitesimally small variation of the region’s modulus of elasticity, obtained recently by the authors, is communicated in brief. A particular function describing the modulus of elasticity change is treated so that a comparison between the finite element solutions and the analytical results is facilitated. The analytical solution is shown to have a surprisingly large range of validity. If an error of 5% is tolerated, modulus of elasticity may decrease with around 40% or increase with around 60%.