Manson, S., Nachtigall, A., Ensign, C., and Freche, J., "Further Investigation of a Relation for Cumulative Fatigue Damage in Bending," SAE Technical Paper 640498, 1964, doi:10.4271/640498.
The fatigue behavior of several steels, AISI 4130, E52100, and 304 ELC stainless, as well as that of a nonferrous alloy, 5456-H311, was investigated in rotating bending fatigue after these materials were subjected to a prestress for different cyclic histories. The data obtained corroborated the hypothesis proposed by the authors that lines representing the S - log N relation of a material prestressed in varying amounts will intersect the S - log N line of the original material near a common point.A correlation was found between the stress at this intersection point and the ultimate tensile strength. Thus, the only requirements for establishing the fatigue behavior of a prestressed material in the range of stresses where the S -log N line is inclined are the S - log N line of the original material and the ultimate tensile strength.The importance of determining the new endurance limit of a material after prestressing was shown analytically. The omission from cycle ratio summations of cyclic histories applied below the original, but above the new endurance limit of a material, was shown for an illustrative example to result in a cycle ratio summation less than unity, which leads to unconservative estimates of fatigue life. Cyclic histories so applied can produce damage and must be taken into account. A new hypothesis based upon actual fatigue behavior and incorporating a cycle-ratio - modified-stress-ratio factor is suggested, which holds promise for more accurately predicting the new endurance limit than most existing methods. Extensive additional tests are required to verify this concept