CCF modelling with use of a two-timescale homogenization model

When dealing with simultaneous two-frequency periodic loads, classical methods tend to establish the relationship between the cross-correlations of transient loadings and those of fatigue criteria in order to evaluate the associated fatigue strength. What appears to be a more robust and coherent approach is to use a two-timescale homogenization strategy. First, two different time scales are identified: a fast one associated with the high frequency loading and a slow one associated with the low frequency loading. It is then assumed that the ratio of the periods associated with the fast and slow time scales respectively is small enough so that we can write asymptotic developments of the mechanical quantities to be calculated. Separating these two time scales enables to compute the evolution of homogenized variables at the slow time scale instead of accurately computing the complete problem at the fast time scale. This method was successfully applied to academic as well as actual specimens in the case of quasistatic behaviour, and its extension to dynamic cases is straightforward.