On the correlation of temperature harmonic content with energy dissipation in C45 steel samples under fatigue loading

Fatigue damage onset involves a transformation of mechanical energy. This is in part spent into work of plastic deformation and fracture and in part transformed into heat. Therefore, different thermomechanical heat sources are activated during a fatigue loading cycle, resulting in a temperature modulation that can be characterized by its frequency content. Several studies have monitored the temperature on samples undergoing high-cycle fatigue, measuring specific thermomechanical metrics which could serve as indicators of damage evolution. The present work evaluates the harmonic content of temperature, to investigate its correlation with the material dissipation. The harmonic terms investigated are the amplitude and phase of temperature at the loading frequency (First Harmonic) and at twice the loading frequency (Second Harmonic). The paper reviews the mechanisms linking the evolution of heat dissipation to changes in these four parameters. The theoretical analysis is supported by an experimental campaign carried out on C45 steel tensile specimen subject to R=-1 and R=0.01 loading ratios. The harmonic metrics are evaluated analyzing both their spatially averaged value and their spatial dispersion, to check for the formation of localized heat dissipation zones in early fatigue life. The study shows that the phase of the Second Harmonic signal has a peculiar bimodal distribution that can be correlated to either a thermoelastic or dissipative prevailing effect. This behavior evolves towards a unimodal dissipative behavior when the load amplitude is increased, thus proposing the Second Harmonic phase parameter as an effective indicator for monitoring internal intrinsic dissipation in the material.