# How to Calculate High Cycle Fatigue Strength of Steel without Using S-N curve

Plotting the S-N curve requires actual fatigue testing of the specimen, and that is why it may not always possible to have an exact S-N diagram for the component of your design interest. Fortunately, there is an work around, an analytical (relatively less accurate) method of calculation for the high cycle fatigue analysis of the components made out of steel.

We will discuss the analytical method with the help of the following fatigue stress design calculation problem:

Calculate the approximate fatigue strength of a steel component at 10^4 cycles. The following input data is available:

The ultimate tensile strength of the steel (Sut)= 85 Kpsi

Solution:

Step-1- calculate the endurance strength (S’e): The endurance strength (S’e) can be calculated from the following equations:
S’e = 0.5*Sut for Sut<=200 Kpsi
=
100 Kpsi for Sut >200 Kpsi

For our example, Sut=85 Kpsi. So, endurance strength for our problem is

S’e=0.5*85 = 42.5 Kpsi

Step-2Calculate the fatigue strength coefficient (σ’f): The fatigue strength coefficient is the true stress corresponding to the fracture of the component in one reversal of the loading cycle. The fatigue strength coefficient can be calculated from the following equation:

σ’f = Sut+50 kpsi

For our example, Sut=85 Kpsi. So, the fatigue strength coefficient for our problem is

σ’f = 85+50 =135 kpsi

Step-3Calculate the fatigue strength exponent (b): Smaller the fatigue strength exponent of the component, larger the fatigue life of the component. Typically, the values of b for the common materials lies in the range of -0.12 to -0.05. The fatigue strength exponent can be calculated from the following equation:

b= -[log(σf )/(S’e)]/[log(2*Ne)]

Where,

σ’f = fatigue strength coefficient = 135 Kpsi in our example

S’e = Endurance strength = 42.5 Kpsi in our example

Ne = Number of loading cycles corresponding to the endurance limit = 1000000

So, by putting all the above values, for our example,

b = -0.079

Step4Calculate fatigue strength (S’f): The fatigue strength of the component corresponding to the particular number of loading cycles can be calculated from the following equation:

Sf = (σ’f)* (2n )^b

Where,

σ’f =fatigue strength coefficient=135Kpsi in our example

n = The number of loading cycle for which the fatigue strength need to be calculated = 10000 for our example as given in the problem statement

b = Fatigue strength exponent = -0.079

So, by putting all the above values, for our example, the fatigue strength of the component at 10000 cycles is:

S ′f = 61.33 Kpsi

The fatigue stress design calculation explained here is useful for a design engineer in case she don’t have a S-N diagram for the material of her design interests. However, the method has the following limitations:

• It should only be used for the component of steel
• It produces reasonable results only for the high cycle fatigue strength analysis