## Rainflow count method

The rainflow ( “rain-flow counting method”) is used in the analysis of fatigue in order to reduce a spectrum of varying stress into a set of simple stress reversals. Its importance is that it allows the application of Miner’s rule in order to assess the fatigue life of a structure subject to complex loading.

procedure:

1. Reduce the time history to a sequence of (tensile) peaks and (compressive) troughs.
2. Imagine that the time history is a template for a rigid sheet (pagoda roof).
3. Turn the sheet clockwise 90° (earliest time to the top).
4. Each tensile peak is imagined as a source of water that “drips” down the pagoda.
5. Count the number of half-cycles by looking for terminations in the flow occurring when either:
1. It reaches the end of the time history;
2. It merges with a flow that started at an earlier tensile peak; or
3. It flows opposite a tensile peak of greater magnitude.
6. Repeat step 5 for compressive troughs.
7. Assign a magnitude to each half-cycle equal to the stress difference between its start and termination.
8. Pair up half-cycles of identical magnitude (but opposite sense) to count the number of complete cycles. Typically, there are some residual half-cycles.

Example

• The stress history in Figure 2 is reduced to peaks and troughs in Figure 3.
• Half-cycle (A) starts at tensile peak (1) and terminates opposite a greater tensile stress, peak (2). Its magnitude is 16 MPa.
• Half-cycle (B) starts at tensile peak (4) and terminates where it is interrupted by a flow from an earlier peak, (3), Its magnitude is 17 MPa.
• Half-cycle (C) starts at tensile peak (5) and terminates at the end of the time history.
• Similar half-cycles are calculated for compressive stresses (Figure 4) and the half-cycles are then matched.
 Stress (MPa) Whole cycles Half cycles 10 2 0 13 0 1 16 0 2 17 0 2 19 1 0 20 0 1 22 0 1 24 0 1 27 0 1

For simple periodic loadings, such as Figure 1, rainflow counting is unnecessary. In case the structure’s life can be estimated from a simple application of the relevant S-N curve.

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