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Factor of Strength (FOS) vs Fatigue Reserve Factor (FRF) in FE-SAFE

While using FE-SAFE for fatigue analysis, users come across two different types of fatigue safety factors. It is common to get confused on which one to use. Let us take a quick look into both safety factors.

Understanding them would help us to use the right safety factor for our fatigue analysis. It should be noted here that both these safety factors are based on the assumption that fatigue loading defined by the user is linear and elastic since a scale factor is being applied to those loading definitions.

Factor of Strength (FOS)

As a general definition, FOS can be termed as a factor which, when applied to the elastic stresses from FEA at a node, will produce the corresponding design life at the node. The significant advantage of using FOS comes from the ability of user to calculate safety factor based on target life of the component. To be more specific on how FE-SAFE calculates FOS; it uses an iterative procedure as defined below:

  1. For a given elastic stress at a node, the fatigue life is calculated
  2. This fatigue life is compared with the design life or target life specified by the user
  3. The elastic stresses at the node are scaled
    1. By a factor less than 1.0, if the calculated life is lower than design life
    2. By a factor greater than 1.0, if the calculated life is greater than design life

Elastic stress history is recalculated using scaled stress. The fatigue life is then recalculated. This process is repeated with different scale factors until it finds the scale factor to give the required design life. This makes the method more generic and broadens its application to complex loading history and low cycle fatigue analysis. The method takes longer computational time but is more accurate. It can be applied to calculate safety factor for both target life as well as infinite life of the material. This method is unique to FE-SAFE.

Fatigue Reserve Factor (FRF)

FRF is a linear scale factor obtained from mean stress corrections such as Goodman, Gerber etc. They are used to calculate stress based fatigue safety factors (FRF) for a calculated life against infinite life of the material or a target life specified by user.

FRF allows the user to specify an envelope of infinite life for the component (target life) or for the material as function of stress/strain cycle amplitude and mean stress (Haigh diagram). The ratio of the distance to the infinite life line and the distance to the cycle (Sa, Sm) is calculated for each extracted cycle, to produce four FRF types – horizontal, vertical, radial and the worst of the three. FRF analyses can be applicable when used for infinite life of the material or for finite life with constant amplitude load. This is rarely the case. As in real world problem, the loading is complex and the fatigue life calculation many a times be done for finite life with loading variation. FRF over predicts safety factors specially when used with variable amplitude loading and user defined target life due to the inability of the FRF to rescale the elastic stresses hence never be used in that scenario. 


To summarize, FOS is more accurate in predicting the safety factor given the realistic scenario of complex loading and user defined target life. FRF on the other hand works well only when the loading is constant amplitude for a user specified target life or when loading is variable amplitude but against endurance limit of the material.

Although FOS is expensive than FRF, it is the most recommended method in FE-SAFE because is applicable to both complex and constant amplitude loading and to both target life and infinite life or endurance limit of the material.

We hope this gives general guideline on using FOS and FRF for fatigue analysis with FE-SAFE. Further information can be found at Section: 17 Factor of strength and probability-based fatigue methods in the FE-SAFE User Guide, or contact us.