ESDU 75033 gives a method of deriving a double radius fillet that gives a lower stress concentration than a single radius fillet where that is constrained geometrically (either by the height of the shoulder or by the length available along the shaft). A double radius fillet has two maximum stress points@ on the circumferential line where it runs out on the shaft@ and on the circumferential line where the two radii intersect. The lowest stress concentration occurs when those two maxima are equal and curves defining the geometry for that case are provided for radii ratios of 3 and 6. Also given are curves showing the maximum reduction in stress concentration attainable by use of the double radius fillet over the single radius fillet for the cases when either the height or length of fillet is constrained.
ESDU 75033-1975 history
1975ESDU 75033-1975 Elastic stress concentration factors. Double radius fillets in shouldered shafts in torsion.