In almost all cases the material fatigue curves are generated using a completely alternating stress; i.e., the average stress component is zero. Research has shown that the magnitude of the mean stress can have an effect on the endurance strength of a material, the trend of which is shown below:
Note that as the mean stress increases the maximum permissible absolute stress (Sa + Sm) increases, while the permissible alternating stress decreases. The relationship between the allowable alternating stress and the average stress is described by the Soderberg line, which correlates fairly well with test data for ductile materials. The equation for the Soderberg line is:
Sa (Allowed) = Sa (for R = -l) x (1 - Sm / SYieid )
Where:
R= Smin / Smax Sa = (Smax - Smin) / 2 Sm = (Smax + Smin) / 2
Note that during the development of the ASME Boiler and Pressure Vessel Code Section III rules and procedures for analysis of nuclear piping, the Special Committee to Review Code Stress Basis concluded that the required adjustments to a strain-controlled fatigue data curve based on zero mean stress, occur only for a large number of cycles (i.e. N > 50,000 -100,000)cycles for carbon and low-alloy steels, and are insignificant for 18-8 stainless steels and nickel-chrome-iron alloys. Since these materials constitute the majority of the piping materials in use, and since most cyclic loading events comprise much fewer than 50,000 cycles, the effects of mean stress on fatigue life are negligible for piping materials with ultimate strengths below 100,000 psi. For materials with an ultimate strength equal to or greater than 100,000 psi, such as high strength bolting, mean stress can have a considerable effect on fatigue strength and should be considered when performing a fatigue analysis.
For a piping application, the implication of the Soderberg line on the fatigue allowable is implemented in a conservative manner. The sustained stress (i.e., weight, pressure, etc.) can be considered to be the mean component of the stress range after system relaxation, and as such is used to reduce the allowable stress range:
SE <= F f (Syc + Syh - Ssus)
Where:
Se = expansion stress range, psi F = factor of safety, dimensionless Syc = material yield stress at cold (installed) temperature, psi Syh = material yield stress at hot (operating) temperature, psi
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