Concentration of Normal Stresses in Flat Plates and round Bars with Periodic Notches

Abstract

The stress concentrations produced by tensile loading of elastic solids with periodic notches are addressed. The criterion suggested by Neuber, which likens the periodic notch to a single notch of similar shape but smaller depth, is evaluated. According to Neuber, the depth reduction factor only depends on the ratio between the depth and pitch of the periodic notch, regardless of its particular shape. This work benchmarks the criterion against many axially loaded flat plates and round bars with periodic V-notches, which are analysed by means of the boundary element method. The investigation highlights a strong disparity between Neuber's predictions and numerical findings. However, upon slight adjustment of the depth reduction factor with respect to Neuber's proposal, a satisfactory agreement is achieved. The good correlation holds true both for shallow notches (notched semi-infinite plate) and for deep notches (notched plates or bars of finite width), which were not covered in Neuber's work. Excellent correspondence is also found for the stress concentration around an infinite row of equispaced circular holes loaded longitudinally, a solution taken from the literature as a test case. These results lead to the conclusion that Neuber's criterion, supplemented with the newly disclosed depth reduction factor, can be applied to periodic notches of whatever geometry under normal stresses.