High Cycle Fatigue: A Mechanics of Materials Perspective part 26. The nomenclature used in this book may differ somewhat from what is considered standard or common usage. In such instances, this has been noted in a footnote. Additionally, units of measurement are not standard in many cases. While technical publications typically adhere to SI units these days, much of the work published by the engine manufacturers in the United States is presented using English units (pounds, inches, for example), because these are the units used as standard practice in that industry. The graphs and calculations came in those units and no attempt was made to convert. | 236 Effects of Damage on HCF Properties Mean stress ksi Figure . Smooth and notch fatigue data from 22 and methods for representing the notch curve. It is often tempting to take a small amount of data that includes inherent scatter and postulate a new or modified theory that will fit the data better than existing models. So not heeding my own advice I offer the following as a method for fitting notch data based on the results shown in Figure . Following the concepts presented above that were put forth by Bell and Benham 18 the modification for the value of kf is further modified slightly for the following reasons. If the notch behavior is purely elastic then the value of kf should not change for a given notch geometry. This region on a Haigh diagram will cover values of mean stress from zero until the value at which the maximum stress Smax equals the yield stress Sy or in terms of mean and alternating stress Sm sm when Sm Sa Sy where sm is defined as a transition mean stress. For values of Sm below sm the fatigue notch factor is constant and equal to the value of kf at R -1 or zero mean stress which we denote by kf0. For mean stress values above Sm we can allow the value of kf to decrease linearly up to the ultimate strength Su. This can be expressed by the equation which I will modestly call the Nicholas equation as kf kro 1 Sm - Sm Su - Sm Sm V Sm Su - Sm In the above the transition mean stress is calculated from Equation based on the assumption that for a mild notch kf is approximately equal to kt . In reality kt relates the peak stress to the average stress so that kt will govern when first yielding occurs Notch Fatigue 237 based on average stress values. Then first yielding would occur as per Equation which is based on smooth bar values. The concept behind proposed Equation is that when the ultimate strength of the material with a notch is approached the notch and the smooth bar ultimate strengths are nearly the same because .
