Plotting the Wöhler Curves
Plotting S-N curve includes plotting initial strain against life to failure. In the laboratory, a sinusoidal stress is applied and the process is known as the Coupon Testing process. These curves are also known as a Stress-Life diagram. For example, let us consider fatigue behavior of compression members like springs. The following figure has been divided into three different regions. Region 1 denotes the area of ogilocyclic fatigue. In this region, rupture occurs at very small alternations and the material is often subjected to plastic deformations.
Region 2 denotes the area of limited endurance.
Region 3 is known as the security zone under low constraint.
Now let us consider an ideal S-N curve, which would be a straight line. By approximating a stress curve, we can calculate the value of stress amplitude. The curve is used to determine the Basquin Slope. N1 = N2 (S1 / S2)1/b is the general relationship between two failure cycles at different time intervals.
and the Basquin Slope is determined by the equation:
b = -[(logS1 – logS2)/ (log N2 - logN1)], where
S1, S2 are stress values for corresponding number of failure cycles denoted by N1 and N2. b denotes slope of the S-N curve.
Once slope of the curve is determined, it becomes very easy to find out the value of stress amplitude for any two S-N values on the curve.
Wöhler Curves can also be used to determine the values of fatigue ratio for different materials. Fatigue Limit can be defined as ratio of ultimate strength (Su) and endurance limit (Se) of a material. The value of fatigue limit usually varies between 0.25 and 0.60.
For instance, steel's fatigue ratio is expressed as Se = 0.55 Su.