Stress concentrations in periodic notches: a critical investigation of Neuber's method

The work investigates the stress concentrations produced by periodic notches (i. e. uniformly repeated) in elastic solids under different loading conditions. Neuber's criterion, which likens the effect of a periodic notch to a single notch of similar profile but lesser depth, is critically examined. The criterion simply correlates the depth reduction factor to the ratio between the depth and the pitch of the original periodic notch, regardless of its shape. By examining literature results in periodic notches on circular bars and plane strips under torsion or axial loads, the work proves the accuracy of the Neuber's method for the ideal configuration of a sharp and shallow notch under shear stresses. By contrast, for real notches with a large root radius and finite depth, the accuracy is very poor, in particular for normal stresses. However, it is found that by simply ‘repairing’ the expression of the depth reduction factor and distinguishing between notches under shear or normal stresses, the criterion provides very accurate results, and becomes quite useful for real geometries.