Practical expressions for the notch stress concentration factors of round bars under torsion

Stress concentration factors and generalised stress intensity factors of round bars weakened by different kind of notches are analysed under torsion loading. An exact, closed-form relationship correlating the generalised stress intensity factors of classic notches (parabolic, semi-elliptic and hyperbolic), characterized by an exact mathematical profile, and pointed V-notches is obtained by using in combination the analytical expressions already available in the literature and some new equations developed in the present contribution. Afterwards this link is discussed with reference to U- and blunt V-shaped notches. This allows us to provide a new analytical relationship between the generalised notch stress intensity factor (NSIF) and the maximum shear stress at the notch tip. By taking advantage of the new developed frame, simple but accurate expressions for the stress concentration factors, valid for a large bulk of different configurations changing the notch acuity, from shallow to deep, are developed. For some opening angles an explicit comparison between the new expressions and those proposed by Noda and Takase (Int J Fatigue, 2006;28:151–163) has been carried out, considering deep and shallow notches.