Evaluation of stress singularity coefficient from the solution of the notch problem

Abstract

In this paper, the notch problem for an infinite plate containing an elliptic rigid inclusion is considered. Three loading conditions: (1) σ ∞ xx = q, (2) σ ∞ yy= p and (3) a concentrated force X 0 in the x-direction applied on the rigid inclusion, are assumed. The stress concentration singularity coefficients (SCSC) are defined as C x= π lim ρ→0 σ xx,A ρ , C y= π lim ρ→0 σ yy,A ρ , where σ xx, A and σ yy, A are the stress component at the crown point A of the elliptic contour, p is the radius at the crown point A of notch. The problem for an infinite place containing a rigid line is also considered. The stress singularity coefficients (SSC) are defined as S 1x= 2π lim s→0 σ xx,0 s , S 1y= 2π lim s→0 σ yy,0 s , where σ xx,0 and σ yy,0 are the stress components at a point which is located ahead of rigid line tip with a distance s. In all three loading cases, the following relation is found C x (κ+1) = C y (3−κ) = S 1x (κ+3) = S 1y [−(κ−1)] , where K = 3− 4 v in plane strain condition, k = (3− v) (1 + v) in plane stress condition, and v is Poisson's ratio. The relation provides an approach to obtain the stress singularity coefficient from the solution of notch problems.