Stress Concentration Factor Formulas Useful for All Notch Shapes in a Flat Test Specimen Under Tension and Bending

In this work, stress concentration factors Ktfor a flat bar with circular-arc or V-shaped notches are considered based on the exact solutions for special cases and accurate numerical results. Then, a set of Ktformulas useful for any notch shape is proposed. The conclusions can be summarized as follows. For the limiting cases of deep (d) and shallow (s) notches, the body force method is used to calculate the Ktvalues. Then, the formulas are obtained as Ktdand Kts. Next, 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/Ktdand Kt/Kts. Finally, convenient formulas are proposed that are useful for any notch shape in a flat test specimen. The formulas yield stress concentration factors with less than 1% error for any notch shape in a flat test specimen.