Finite Element Analysis of Singular Inplane Stress Field around an Inclusion’s Corner Tip

Abstract

Many engineering applications involve a junction of multiple materials to enhance the mechanical performance of engineering materials. However, according to linear elasticity, the stresses at the bonded interface are often unbonded and present high stress singularities, which provides a source of crack initiation. In order to study the fracture starting at the inclusion corner tip by the method of fracture mechanics, the singular stress field has to be taken into account. It is well known that singular stresses are often assumed to have the asymptotic form: σij = Kr λ f ij (θ), in which (r, θ) are the polar coordinates originated at the singular stress point, λ is the singularity order, f ij(θ) gives the angular variation and K is the generalized stress intensity factors. There are a lot of studies on the singular order and the singular stress fields, as far as the inclusion problems, the work of Chen [1] based on complex function method is representative. It should be noted that analytical technique can be only applied to some typical problems of simple geometrical discontinuity and/or particular combination of materials, therefore, numerical methods are powerful alternative. in this paper, based on the principle of a novel hybrid finite element technique introduced in [2], a kind of corner-tip element (see Figure) is established to study singular stress fields around the inclusion corner tip. As applications, the influences of the ratio of lengh and width and the distance of two inclusions on the generalized stress intensity factors are investigated.