Stress concentration formula useful for all notch shape in a round bar (comparison between torsion, tension and bending)

In this work, stress concentration factors (SCFs, Kt) of a round bar with a circular-arc or V-shaped notch are considered under torsion, tension and bending. First, for the limiting cases of deep and shallow notches, the body force method is used to calculate the SCFs; then, the formulas are obtained as Ktd and Kts. On the one hand, upon comparison between Kt and Ktd, it is found that Kt is nearly equal to Ktd if the notch is deep or blunt. On the other hand, if the notch is sharp or shallow, Kt is mainly controlled by Kts and the notch depth. The notch shape is classified into several groups according to the notch radius and notch depth; then, the least squares method is applied for calculation of Kt/Ktd and Kt/Kts. Finally, a set of convenient formulas useful for any shape of notch in a round test specimen is proposed. The formulas yield SCFs with less than 1% error for any shape of notch. The effect of notch opening angle on the SCF is also considered for the limiting cases of deep and shallow notches.