Peterson Notch Sensitivity Index

Peterson [12-14] introduced a notch sensitivity index q, or simply q factor, defined 

The reason to subtract unity from both numerator and denominator in Eq. (7.4) is to provide a scale for q that ranges from zero for no notch effect to unity for fiiU notch effect. In this latter case kf is exactly equal to kf. A deep analysis of fatigue limit experimental data brought Peterson to make the hypothesis that fatigue damage became critical in relation to the stress level Opeak at a small distance b below the surface of notch root where the stress gradient is very steep 

Assuming a linear decrease of the notch tip stress field, Peterson [13] formulated an empirical expression 

For medium-high strength steels (t7 560 MPa) the ap values can be approximated by the following formulas 

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