Fatigue Life Estimate (S-N, Basquin)

What is fatigue?

A part can break at a stress well below its yield strength if the load is applied over and over. This is fatigue, and it accounts for most failures of machine parts. Fatigue strength is described by the S-N (Wöhler) curve, which relates stress amplitude to the number of cycles to failure.

The Basquin relation

In the finite life region the S-N curve is close to a straight line on logarithmic axes. That line is written as the Basquin relation: σ_a = σ_f' × (2N)^b. Here σ_a is the stress amplitude, N the number of cycles, σ_f' the fatigue strength coefficient and b the fatigue strength exponent. Life follows as N = ½ × (σ_a / σ_f')^(1/b).

If you do not know the parameters you can enter two points on the curve, and the tool fits S = A × N^B through them.

Mean stress

When the load does not swing equally about zero there is a mean stress. A tensile mean stress shortens life. The Goodman correction turns the stress state into an equivalent fully reversed amplitude: σ_ar = σ_a / (1 − σ_m / S_u).

Example

On a curve with σ_f' = 1000 MPa and b = −0.1, a fully reversed amplitude of 400 MPa gives 2N = 0.4^(−10) = 9537, so N = 4768 cycles. On the same curve an amplitude of 300 MPa with a mean stress of 200 MPa and a tensile strength of 800 MPa is equivalent to 400 MPa, and the life is the same.

Why is this only a preliminary estimate?

Life is extremely sensitive to stress: a small error in stress changes life many times over. Notches, surface finish, part size, welds, corrosion and variable loading decide the real life and are not in this tool. Test data also scatter widely. Use the result as an order of magnitude only. For safety relevant parts, design must be carried out by a qualified engineer to the relevant standard.