On an annular crack near an arbitrarily graded interface in FGMs

Abstract

<p>Annular cracks can be generated during the fabrication of materials and around the pre-existing defects. Previous works on the annular crack problems were most limited to homogenous materials. This paper extends the analysis and examines the axisymmetric problem of a flat mixed-mode annular crack near and parallel to an arbitrarily graded interface in functionally graded materials (FGMs). The crack is modelled as plane circular dislocation loop and an efficient solution for dislocation in <a href="https://www.sciencedirect.com/topics/engineering/functionally-graded-material" title="Learn more about FGMs from ScienceDirect's AI-generated Topic Pages">FGMs</a> is used to calculate the stress field at the crack plane. The three-parts mixed boundary value problem is solved by a series expansion method. Analytical solutions of the <a href="https://www.sciencedirect.com/topics/engineering/stress-intensity-factor" title="Learn more about stress intensity factors from ScienceDirect's AI-generated Topic Pages">stress intensity factors</a> are obtained. Compared with many other existing analytical treatments to the crack problems in FGMs with the assumption of special gradation, the present method can consider arbitrarily graded <a href="https://www.sciencedirect.com/topics/mathematics/shear-modulus" title="Learn more about shear modulus from ScienceDirect's AI-generated Topic Pages">shear modulus</a> and <a href="https://www.sciencedirect.com/topics/engineering/poisson-ratio" title="Learn more about Poisson's ratio from ScienceDirect's AI-generated Topic Pages">Poisson's ratio</a>. It is shown that the present solution can reduce to existing solutions in literatures for annular crack in homogenous materials. Numerical study is conducted to investigate the fracture mechanics of annular crack in FGMs. A practical example of an annular crack in a real Epoxy-Glass FGM with measured data of material properties is also considered.</p>