Rainflow stress cycle counting

Rainflow stress cycles counting is the most common and practical form of stress cycle counting. Rainflow counting is used to measure the likely impact of the most damaging stress cycles. It is only applicable for stress cycles in a single and constant direction (i.e. uniaxial loading). While theories have been advanced to extend the method to multiaxial loading, these are not generally accepted.

There is a certain elegance in the rainflow method. Chronological information is discarded as are minor "noise" cycles as being irrelevant. Megabytes of raw stress data is reduced to a few hundred bytes of hopefully good qualitative information. In addition, the rainflow method is fairly easy to implement in computer code - most of which is derived from the original work of Downing and Socie in the late 1970's.

Question: What is a stress cycle? Answer: A closed loop in "load space" that can be completely defined by the amplitude and the mid-value. Helpful? Probably not!

"Load space" is a two dimensional region with stress (i.e. force) on one axis and strain (i.e. movement) on the other axis. Idea materials would move only on a fixed straight line in this space, however, there is no such thing as the ideal material. Real materials move in a curve and to add to the complexity, on a difference curve when moving in the opposite direction. So a stress cycle is the movement along these curves until a loop is closed. Whenever a loop is closed, its amplitude and mid-value (sometime call mean) are determined, and the result recorded by incrementing a count in a bin of a two dimensional histogram of cycle amplitude vs mid-value.

As a matter of interest and understanding, the area within the stress loop represents an energy loss. The stored potential energy of the "spring" is not all returned. Some of this energy is absorbed by the crack forming process and remainder goes to heat generation. As a matter of further interest, this heat can be detected by thermal imaging, providing an effective but expensive method of identifying dynamically stressed areas.

References

Downing, S. D., and Socie, D. F., Simple Rainflow Counting Algorithms,
International Journal of Fatigue, Vol. 4, N. 1, 1982, pp. 31-40.

ASME 1985, Standard Practices for Cycle Counting in Fatigue Analysis, ASTM E1049-85(1997),
American Society of Mechanical Engineers, USA.