Two-timescale homogenization method for the modeling of material fatigue

Abstract

When dealing with Combined Cycle Fatigue (CCF), characterized by two simultaneous periodic loads with different frequencies, what appears to be a more robust and coherent approach than classical methods is to use a two-timescale homogenization strategy. First, two different time scales are identified: a fast one and a slow one associated with the high frequency and low frequency loadings respectively. It is then assumed that the ratio of the periods associated with the two time scales is small enough so that asymptotic developments of the mechanical quantities to be calculated can be written. The method was applied to the study of academic as well as actual specimens, considering a quasi-static behavior or a dynamic behavior. We conclude that separating the two time scales allows to compute the evolution at the slow time scale of homogenized variables instead of accurately computing the problem at the fast time scale. With such a method it is then possible to calculate the fatigue strength under CCF conditions without any further assumption than the asymptotic decomposition.