On the relationship between mechanical energy rate and heat dissipated rate during fatigue for a C45 steel depending on stress ratio

Abstract

This work deals with the analysis in the frequency domain of the temperature signal and mechanical energy rate of C45 steel under two different fatigue stepwise loading series at stress ratios of 0.1 and −1. It was first investigated the energy distribution among the harmonic components of the signals to understand possible variations caused by a different stress ratio. In addition, the second amplitude harmonic (SAH) of heat dissipated and mechanical energy rates have been considered in the analysis, and their relationship was investigated. It has been shown as it depends only on the material, and hence, it is valid whatever the kind of the test is without any assumption on the energy supplied to the material or material hysteresis loop stabilization. The adopted approach allows the analysis of intrinsic dissipations by means of rapid, full‐field, and contactless techniques without any specific requirement on loading condition or temperature signal stabilization.

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

“…This denomination might, though, be misleading since it does not consider the contribution to the second harmonic from the thermoelastic source, as predicted by the second order theory. Following previous works [24,26,36] the irreversible heat is produced near each peak and trough of a loading cycle, and the corresponding temperature has a fundamental frequency at 2f L . The SH harmonic component of dissipation is here written as:…”

“…It is therefore useful to propose temperature metrics related with temperature changes at specific loading frequencies. A number of works, including the present one, have then propsed to investigate the influence of the heat sources on the temperature modulation by means of frequency domain signal processing strategies [2,6,7,9,10,16,18,[20][21][22][23][24][25][26][31][32][33].…”

Estimating the intrinsic dissipation using the second‐harmonic temperature signal in the tension–tension fatigue

“…Moreover, a typical strain ratcheting is observed, as found in tension-tension fatigue of C45 steel. 7,44,[61][62][63] After setting the reference coordinate system at the lower tips of the hysteresis loops, the K 0 and n 0 material parameters are evaluated by individually best fitting the loading branch of the measured hysteresis loop at each load step according to the Ramberg-Osgood equation:…”

“…Moreover, the figure shows that ΔT 1ps is greater than ΔT 2 for lower R and n 0 values; therefore, in tension-tension fatigue, ΔT 2 may no longer convey most of the information. 44 Thanks to the assumption of a Ramberg-Osgood description of the branches of the hysteresis loop (Figure 2), comparing the plastic strain energy density W with the hysteresis energy density, W hyst , is valuable. W can be evaluated by integrating Equation ( 12) over one loading cycle:…”

“…40,41 This phenomenon is why several evaluations of the intrinsic dissipation, Q p , in tension-compression fatigue tests start from the range of the second-harmonic temperature signal ΔT 2 . [40][41][42][43][44] Recently, De Finis et al 44 extended the analysis to the case of tension-tension (R > 0) fatigue and investigated the relationship between mechanical energy and heat dissipation; the outcome of the investigation is an empirical linear correlation between the second harmonic of the mechanical energy rate and the second harmonic of the heat dissipation rate.…”