Miner's rule

Remarks

The rule assumes that each cycle at amplitude $\sigma_i$ uses up the fraction $1/N_i$ of the life, independently of the order of the cycles and of the damage already present. It is an engineering hypothesis, not a theorem, and tests show failure at values of $D$ that can be well below or above $1$. In particular it ignores sequence effects: a high-amplitude block followed by a low-amplitude block usually causes failure at $D < 1$. Example: let $N_1 = 10^5$ cycles at a high amplitude and $N_2 = 10^6$ cycles at a low amplitude. If the part has seen $5 \times 10^4$ cycles at the high amplitude, the rule allows $5 \times 10^5$ more cycles at the low amplitude, since $0.5 + 0.5 = 1$. For random loadings, the cycles are first counted by a method such as rainflow counting and then summed by the rule.

Going deeper

For a student

Miner's rule is the simplest damage accumulation law, used with S–N curves to estimate fatigue life under variable amplitude loading. It corresponds to a scalar damage variable that grows linearly with cycles, which is a very special case of continuum damage mechanics. Nonlinear damage rules and crack growth laws such as Paris' law give more accurate predictions when the loading sequence matters.