Miner's Rule

The ratio nᵢ/Nᵢ compares the cycles actually applied at one stress amplitude with the cycles that stress level can withstand under constant-amplitude fatigue conditions. This normalizes different loading blocks to a common damage measure, allowing their contributions to be added and providing a practical estimate of cumulative fatigue exposure.

Each stress amplitude is evaluated separately using its corresponding constant-amplitude fatigue life. The cycles experienced at that level are converted into a fraction of that life, and the fractions are summed across the complete loading history. This makes the rule suitable for variable-amplitude service conditions rather than only one repeated stress level.

The linear summation treats damage fractions as additive and does not account for how one loading block may influence the effect of a later block. Consequently, different arrangements of the same stress amplitudes can produce different physical fatigue behavior even when their calculated sum is identical. The rule therefore provides an estimate rather than a complete description of fatigue progression.

Miner’s Rule may overlook changes in mean stress and interactions between different damage mechanisms. These factors can alter how fatigue damage develops during service, while the basic linear model combines damage fractions without explicitly representing such interactions. Engineers should therefore recognize that the calculated failure condition may not capture every feature of the component’s actual loading history.

The loading history must be separated into blocks, with each block defined by its stress amplitude and cycle count nᵢ. A corresponding constant-amplitude fatigue life Nᵢ is then obtained from stress-life data for every stress level. Dividing each cycle count by its matching life and summing the resulting fractions gives the cumulative damage estimate.

Stress-life data provide the constant-amplitude fatigue lives required for each stress amplitude in the service history. Without those corresponding Nᵢ values, the cycle counts cannot be converted into comparable damage fractions. Using the data in this way connects the recorded or expected loading spectrum to an estimate of cumulative fatigue exposure for the component.

The rule is useful when a component experiences repeated service loads at different stress amplitudes and engineers need a practical first estimate of fatigue accumulation. Its result can support design evaluations and maintenance planning by indicating when the summed damage approaches or exceeds the model’s failure criterion. Because its assumptions are limited, the estimate should be interpreted accordingly.