Three-dimensional stress concentrations at elliptic holes in elastic isotropic plates subjected to tensile stress

The through-thickness variations of stress concentration factors along the wall of elliptic holes in finite thickness plates of isotropic materials subjected to remote tensile stress have been systematically analyzed using the finite element method. The three-dimensional stress concentration factor Kt is found to be a function of the thickness to root radius ratio B/ρ and the aspect ratio t (short to long axial length) of the elliptic hole under tensile loading. It is found that the maximum stress concentration factor through the thickness, (Kt)max, is 24–123% higher than the value on the free surface (Kt)surf when t changes from 1 to 0.01, and the ratio of the surface value (Kt)surf to the corresponding planar solution (Kt)p−σ at the root is only 0.82–0.48 when t ranges from 1 to 0.01 if B/ρ is large enough. When B/ρ is smaller than 1, both of the ratios will approach 1. Simple and efficient empirical formulae for the relationships between the three values were obtained by fitting the numerical results with good engineering accuracy for large range of B/ρ (from 1 to 100,000) and t (from 0.01 to 1). Combining with the plentiful known two-dimensional stress concentration factors in handbooks, the proposed formulae can be used to solve the maximum three-dimensional stress concentration factors of holes, notches and be useful for strength and fatigue designs of engineering structures with similar defects.