Glossary term
Miner Rule
A linear cumulative damage model used to predict fatigue failure under variable amplitude loading.
Definition
methodThe Miner rule is a linear cumulative damage hypothesis that predicts fatigue failure under variable amplitude loading by summing the fractional damage contributions from each stress level, with failure occurring when the total reaches unity.
Real engineering components rarely experience constant-amplitude cyclic loading. Vehicle suspensions, aircraft wings, wind turbine blades, pressure equipment, and offshore structures are subjected to load spectra whose amplitudes and mean stresses vary throughout service. The Miner rule, also called the Palmgren-Miner rule, gives a practical linear estimate of cumulative fatigue damage from those spectra using S-N curve data.
Under constant-amplitude loading, fatigue life can be read directly from an S-N curve: for a given stress amplitude, the curve gives the number of cycles to failure. Under variable-amplitude loading, no single point on the S-N curve represents the whole service history. The Miner rule converts the load history into damage fractions and adds them.
The damage summation
For each stress-amplitude bin i, the component experiences n_i cycles. The relevant S-N curve gives N_i, the number of cycles to failure if that stress level were applied alone. The cumulative damage is:
The simplest design interpretation is that fatigue failure becomes expected when:
Values below one are treated as consumed fractions of fatigue life. This formulation is linear: the same set of cycles gives the same damage sum regardless of sequence, spacing, crack state, or interaction between high and low amplitudes. That assumption is useful for engineering calculation, but it is also the main limitation of the method.
Cycle counting
Before applying the rule, an irregular stress or strain history must be decomposed into counted cycles. Rainflow counting is commonly used because it extracts closed hysteresis loops from a time history and produces amplitudes, mean stresses, and counts. The resulting table is combined with material S-N data, surface finish factors, size factors, notch effects, residual stress assumptions, and mean-stress correction methods such as Goodman or Gerber when required by the design basis.
For welded structures and many code-based checks, the stress range is often the primary variable. For machined components, local stress concentration, mean stress, material condition, and surface state can dominate. The same raw load history can therefore produce different Miner sums depending on how the fatigue detail is classified.
Limits and interpretation
The Miner rule does not model crack initiation, crack closure, overload retardation, residual-stress relaxation, corrosion fatigue, or load-sequence effects. High-amplitude cycles early in life can create damage that makes later low-amplitude cycles more severe than the linear rule predicts. Low-amplitude cycles below an endurance limit are often omitted, but that can be unsafe when occasional overloads have already initiated a crack or when the material has no true endurance plateau.
Despite these weaknesses, the rule remains widely used because it is transparent, compatible with test-based S-N data, and easy to audit in design codes. A high-quality fatigue assessment states the load spectrum source, cycle-counting method, stress definition, S-N curve family, correction factors, safety factors, and inspection assumptions. The Miner sum should be read as an engineering damage index, not as a physical measurement of microscopic damage.
Common mistakes
A common mistake is to report only the final damage value without showing which stress ranges dominate it. Another is to apply a laboratory S-N curve to a notched, corroded, welded, or thermally affected part without adjusting the fatigue class. For critical components, Miner calculations should be supported by sensitivity studies, inspection planning, fracture-mechanics checks, or test evidence when the consequences of failure are high.