“…In general, for both low-and high-frequency fatigue tests, the classical temperature evolution of a material that undergoes fatigue straining and damage up to failure consists of three main stages: the first stage is an initial increase at the beginning of the test, the second stage is associated with a steady-state or a slight increase and the last stage is a final sharp increase that is related to fracture initiation (see, for example, [13,16,20]). Ranc et al [20] observed that ferritic-pearlitic C45 steel that was loaded cyclically at 20 kHz did not follow this classical thermal response and exhibited a steep increase in temperature up to a few hundreds of degrees, which did not lead to a final rupture.…”