Real components rarely experience one perfectly repeated stress cycle. Their loads vary in amplitude and mean value, so fatigue analysis needs a way to reduce a complex history to damaging cycles.

Cycle counting

Rainflow counting decomposes an irregular stress history into equivalent stress cycles with defined ranges and mean stresses.

This does not predict damage by itself; it converts a time history into cycle categories that can be compared with fatigue data.

Mean-stress corrections

A tensile mean stress generally reduces fatigue life for a given alternating stress. Relations such as Goodman-type corrections map combinations of mean and alternating stress to an equivalent fatigue severity.

Miner's rule

A simple cumulative-damage model assigns each group of cycles a damage fraction

$$D_i=\frac{n_i}{N_i},$$

where $n_i$ cycles occurred and $N_i$ is the fatigue life at that cycle severity.

Miner's rule estimates total damage as

$$D=\sum_i\frac{n_i}{N_i},$$

with failure often approximated near $D=1$.

This is an engineering model rather than a fundamental law: sequence effects and changing crack behaviour can make real fatigue more complicated.