Stress gradient calculations at notches

Abstract Calculations of the relative stress gradient ahead of notches are presented. Attention has been focused on finite width plates under tension weakened either by a central hole or by two semicircular lateral notches. In this paper stress field solutions given by Neuber as well as analytical solutions in the form of power series expansions, given by Howland (central hole) and Ling (semi-circular notches), have been employed in the derivation of the stress gradient. Comparisons have been made with gradient calculations derived from approximate stress field formulas developed by Xu et al. (Practical stress expressions for stress concentration regions. Fatigue Fract Eng Mater Struct 1995;18(7/8)885–95) and by Glinka and Newport (Universal features of elastic notch-tip stress fields. Int J Fatigue 1987;9(3):143–50). It is shown that the effect of the finite dimensions of the specimen on the stress gradient is correctly captured only if exact analytical solutions are employed. The results presented in this paper are useful for calculating the stress intensity factors for cracks growing in notches and to assess the fatigue strength of notched components.