A simple surrogate model for the rainflow fatigue damage arising from processes with bimodal spectra

•New formula for fatigue damage due to a bimodal process.•Function of variance of high freq component, freq ratio, and exponent of S–N curve.•Formula is simple and can be implemented in spreadsheets or design codes.•Predicted damage is very precise when benchmarked against numerical simulation.•Formula yields the exact theoretical result under several limiting conditions.

There are many applications, in particular offshore engineering, in which the load process comprises a high frequency and a low frequency component, and each component can be regarded as a narrowband process. Many researchers have proposed spectral methods for evaluating the rainflow fatigue damage for such bimodal processes, nevertheless the accuracies of these methods still have room for improvement. Recently, the author has developed an analytical approach that compares well with numerical simulation; unfortunately, the approach is intricate and difficult to implement. This paper presents a new formula that is accurate, and yet simple enough for adoption in standard spreadsheets and design codes. The formula is valid for a wide range of parameter values and yields the exact theoretical result under several limiting conditions. The formula is calibrated based on extensive numerical simulations, and the database of results are fully presented herein so that they may be used directly in design, or for further studies.