Closed-form functions for elastic stress concentration factors in notched bars

Abstract

The closed-form equations given are based on the results of finite element analyses of double-edge-notched plates subject to tension or in-plane bending. The notch dimensions were varied in a parametric survey from shallow, part-circular forms to deep, sharp, slits with semi-circular ends, giving stress concentration factors varying from 1.2 to 13 (net stress basis). The concept of a configuration factor for notches, similar to that used to calculate crack-tip stress field intensity factors, is introduced. It is shown in the first instance that the analogous crack configuration factor can be used directly to modify the elastic stress concentration factor for an elliptical hole, giving closed-form functions that do not involve empirical fitting constants and have acceptable practical accuracy. Reasons for the effectiveness of this form are given, together with an analysis of the points where the notch stress concentration factors diverge from the simple closed form. Further refinements that improve accuracy are given and comparisons are also made with stress concentration factors for hyperbolic edge notches.