While SN curve is clear and straight forward on addressing the service life under fatigue, its accuracy leaves some room to be improved. Partially because of the statistical nature of fatigue and Partially because of the difference between laboratory experiments and the reallife practice.
For example, most SN curves are constructed based on zero mean stress. However, it is more often the timevarying stresses are oscillating near a nonzero mean stress. Multiple SN curves are determined by a several sets of fatigue experiments. Each curve represents a specific mean stress of that particular material.
The nonzero mean stress SN relation requires huge amount of experiments to obtain the required data and form the mesh over a wide range of mean stresses. There are two approaches to present the data. The first is to present it in a diagram format. The second is to resemble the data with a formula based on the zeromean stress SN curve.
A more popular diagram for design purposes is called master diagram which accumulates fatigue data under different mean stresses and presents each line as the fatigue life under the net of maximum and minimum stresses in addition to mean stress and alternating stress as the reference axises. An example of master diagram of AISI 4340 steel is enclosed for your reference.
Users may check the maximum and minimum stress directly. Define R is the ratio of minimum stress to the maximum stress. Alternatively, define A is the ratio of alternating stress to mean stress.
An approximation based on the zeromean stress SN curve proposed by Goodman and Gerber is written as
where 
is the amplitude of allowable stress (alternating stress).

is the stress at fatigue fracture when the material under zero mean stress cycled loading.

_{m} is the mean stress of the actual loading.

_{u} is the tensile strength of the material.

r = 1 is called Goodman line which is close to the results of notched specimens.
r = 2 is the Gerber parabola which better represents ductile metals.

Please note that the SN curve and its elaborated master diagram require a lot of experiments to accumulate the necessary data. On the other hand, Goodman and Gerber's approximations, although simple, they might not properly represent the specific material. Finally, they are only good for uniform mean and alternating stresses.
