Convenient Stress Concentration Formula Useful for Any Shape of Fillet. Tension of a Stepped Round Bar with Fillet.

Abstract

In this work, stress concentration factors (SCFs) of a round bar with fillet Kt are considered on he basis of exact solutions now available for special cases and accurate numerical results. First, for he limiting cases of large and small values of the step including fillets, the body force method is used to calculate the SCFs ; then the formulas are obtained as Ktd and Kts. Here, Ktd is a SCF of a deep shoulder fillet and Kts is a SCF of a shoulder fillet in semi-infinite plate. On the one hand, upon comparison of Kt and Ktd, it is found that Kt is nearly equal to Ktd if the step is large or the radius of the fillet is small. On the other hand, if the step is small or the radius of the fillet is large, Kt is mainly controlled by Kts and the relative step length. The fillet shape is classified into several groups according as the fillet radius and the step length ; 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 fillet in a round test specimen are proposed. The formulas yield SCFs for any shape of notch with less than 1% error in most cases.