The Physical Origin of the Coffin-Manson Law in Low-Cycle Fatigue

According to Coffin and Manson, the number NR of cycles to fracture in the low-fatigue regime is related to the amplitude of the applied cyclic plastic deformation Δεp by the famous empirical relation NRΔεpβ = C named after them, where β = 2 is found remarkably universal in single-phased metallic materials, whatever their atomic and/or polycrystalline structure. Here, we propose a theory of the Coffin-Manson law which is based upon the observation that the “mesoscopic” grain scale, intermediate between the dislocation scale and the macroscopic crack scale, plays a fundamental role. In addition, we get the dependence of NR on the grain size and sample size as well as a quantitative description of mesocrack clusters distribution prior to rupture, which can be tested in future experiments.