Rainflow

Rainflow counting, or the rainflow method, is a widely used technique in fatigue analysis for reducing an irregular stress history into a set of simple stress-reversal cycles. By converting a fluctuating load into a histogram of cycle ranges and mean stresses, it supports life prediction using S-N curves, energy methods, or damage summation rules such as Miner’s rule. The method helps to identify the significance of different stress ranges and to distinguish full cycles from partial or half cycles that arise from non-monotonic loading.

The basic idea is to take a time history of stress, extract turning points (local maxima and minima), and process them in sequence to form cycles. Turning points are paired according to a rainflow criterion, typically using a stack or pairing rule that compares current ranges with previous unpaired points. When the current range is large enough relative to earlier unpaired ranges, a complete cycle is counted and the paired point is removed from consideration; otherwise, the point is kept for possible future pairing. The result is a set of cycles with associated ranges and mean stresses. Output commonly includes a distribution of cycle counts by range (and optionally by mean stress), which can then be used with fatigue life models.

Applications and considerations: rainflow counting is standard in aerospace, automotive, and civil engineering for estimating fatigue life from complex loading histories. It is implemented in many software tools and fatigue analysis workflows. Limitations include sensitivity to noise and sampling resolution, which may require smoothing or filtering, and the need to choose appropriate preprocessing and mean-stress corrections to reflect the material behavior accurately.