# Stress-life (S-N) Approach

The stress-life method works well in predicting fatigue life when the stress level in the structure falls mostly in the elastic range.

When the cyclical strains extend into plastic strain range, the fatigue endurance of the structure typically decreases significantly; this is characterized as low-cycle fatigue, more details about it can be found in the next section.

The generally accepted transition point between high-cycle and low-cycle fatigue is around 10,000 loading cycles.

## S-N Curve

The S-N curve, first developed by Wöhler, defines a relationship between stress and number of cycles to failure.

Typically, the S-N curve (and other fatigue properties) of a material is obtained from experiment through fully reversed rotating bending tests. Due to the large amount of scatter that usually accompanies test results, statistical characterization of the data should also be provided (certainty of survival is used to modify the S-N curve according to the standard error of the curve and a higher reliability level requires a larger certainty of survival).
When S-N testing data is presented in a log-log plot of alternating nominal stress amplitude Sa versus cycles to failure N, the relationship between S and N can be described by straight line segments. Normally, a one or two segment idealization is used.
(1)(1)
$S=S1{\left({N}_{f}\right)}^{b1}$
for segment 1 (1)
Where:
• S is the nominal stress amplitude
• Nf are the fatigue cycles to failure
• b1 is the first fatigue strength exponent
• S1 is the fatigue strength coefficient
• Nc1 is cyclic limit of endurance

The S-N approach is based on elastic cyclic loading, inferring that the S-N curve should be confined, on the life axis, to numbers greater than 1000 cycles. This ensures that no significant plasticity is occurring. This is commonly referred to as high-cycle fatigue.