What does rainflow counting actually do?

It turns a messy variable-amplitude stress history into a list of closed hysteresis loops — each with an amplitude and a mean — so that constant-amplitude S–N or strain–life data can be applied. It is the standard way to extract "how many cycles of what size" from real measured loading.

Is failure really at a damage sum of 1.0?

Palmgren–Miner assumes linear damage accumulation and predicts failure at D = 1. In reality, observed failure sums scatter from roughly 0.3 to 3 depending on load sequence, so many codes apply a usage factor (e.g. design to D ≤ 0.5) or use sequence-aware methods for critical parts.

When do I need a mean-stress correction?

Whenever cycles have a non-zero mean stress. A tensile mean stress shortens life; Goodman, Gerber and Soderberg lines convert each cycle to an equivalent fully reversed amplitude before the S–N lookup. Compressive means are often (conservatively) treated as zero mean.

Fatigue · guide

Rainflow counting and cumulative fatigue damage

Real structures rarely see constant-amplitude loading. The standard assessment chain is: rainflow-count the history into cycles, correct each for mean stress, look up damage on an S–N curve, and sum it with Miner's rule. Here is each step and where the conservatism lives.

Step 1 — rainflow counting

A measured load–time signal is a tangle of large and small reversals. Rainflow counting (Matsuishi and Endo, 1968) pairs peaks and valleys into closed hysteresis loops, each described by an amplitude and a mean. The result is a histogram — a count of how many cycles occur at each amplitude/mean bin — which is exactly the input constant-amplitude fatigue data expects.

Step 2 — the S–N (Basquin) curve

The allowable number of cycles at a given stress amplitude comes from an S–N curve, commonly a power law on log–log axes:

N = ( σ_a / A )^(1/b) ⇔ σ_a = A · N^b

where σ_a is the stress amplitude and A, b are material/detail constants. Welded joints use standardised detail classes (e.g. the BS 7608 / Eurocode FAT classes) instead of a polished-specimen curve.

Step 3 — mean-stress correction

A tensile mean stress is damaging. The classic lines convert a cycle with amplitude σ_a and mean σ_m into an equivalent fully reversed amplitude σ_ar. Goodman (linear to the ultimate strength σ_u):

σ_ar = σ_a / ( 1 − σ_m / σ_u )

Gerber uses a parabola in (σ_m/σ_u) and fits ductile steels better; Soderberg references the yield strength and is the most conservative. Pick the one your code or data set assumes.

Step 4 — Miner’s rule

Linear cumulative damage sums the fractional life used by each bin:

D = Σ ( n_i / N_i ) → failure predicted at D = 1

n_i is the applied cycle count in a bin and N_i the allowable count for that bin's corrected amplitude. Because real failure sums scatter widely, design practice usually targets a damage budget below 1.

Open the calculatorRainflow + Miner fatigue calculator →Paste a load history, rainflow-count it, apply Goodman/Gerber and an S–N curve, and get the Miner damage sum with the cycle histogram and Haigh diagram.

Pitfalls

Watch the sequence assumption (Miner ignores load order), the endurance-limit treatment (variable-amplitude loading can damage below a nominal limit, so many codes slope the curve down rather than cutting it off), and the difference between nominal, structural (hot-spot) and notch stress when choosing an S–N class.

Frequently asked

What does rainflow counting actually do?: It turns a messy variable-amplitude stress history into a list of closed hysteresis loops — each with an amplitude and a mean — so that constant-amplitude S–N or strain–life data can be applied. It is the standard way to extract "how many cycles of what size" from real measured loading.
Is failure really at a damage sum of 1.0?: Palmgren–Miner assumes linear damage accumulation and predicts failure at D = 1. In reality, observed failure sums scatter from roughly 0.3 to 3 depending on load sequence, so many codes apply a usage factor (e.g. design to D ≤ 0.5) or use sequence-aware methods for critical parts.
When do I need a mean-stress correction?: Whenever cycles have a non-zero mean stress. A tensile mean stress shortens life; Goodman, Gerber and Soderberg lines convert each cycle to an equivalent fully reversed amplitude before the S–N lookup. Compressive means are often (conservatively) treated as zero mean.

References

M. Matsuishi, T. Endo, "Fatigue of metals subjected to varying stress," Japan Society of Mechanical Engineers, 1968 (rainflow method).
ASTM E1049, "Standard Practices for Cycle Counting in Fatigue Analysis."
M.A. Miner, "Cumulative Damage in Fatigue," J. Applied Mechanics 12, 1945.
BS 7608, "Guide to fatigue design and assessment of steel products," BSI.

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