Concentration of shear stresses in shallow periodic notches

Abstract

The torsional stresses in straight round bars with periodic U-shaped shallow grooves are calculated numerically (boundary elements) taking advantage of a computationally efficient thermal analogy. Neuber’s theory is scrutinized, which equates the stress concentration factor in the periodic notch to the stress concentration factor in the single notch of like profile and lower depth. (Corrected depth = original depth times a depth reduction factor, which is a function of the depth-to-pitch aspect ratio of the periodic notch.) The results disclose a depth correction function in close agreement with Neuber’s theory for ideally sharp notches. For a wide range of rounded notches, which are more likely to occur in practice, the paper shows that Neuber’s depth correction grossly overestimates the stresses. By modifying the expression of the depth correction factor, however, Neuber’s conceptual equivalence works well for engineering purposes. Comparison with former results by the authors indicates that the optimal depth correction function is different for notches affected by shear stresses (as in this paper) or by normal stresses.