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\begin{document}

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



\author[1]{Rosa De Finis}%
\author[1]{Davide Palumbo}%
\author[1]{Umberto Galietti}%
\affil[1]{Politecnico di Bari}%


\vspace{-1em}



  
  \date{May 06, 2024}


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\selectlanguage{english}
\begin{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, 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 stabilisation. 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 stabilisation.%
\end{abstract}%



\sloppy


Rosa De Finis

Politecnico di Bari

Via Orabona 4,

Bari, Italy, 70125

\emph{rosa.definis@poliba.it}{]}

Professor Y. Hong,

Editor-in-Chief

\emph{Fatigue \& Fracture of Engineering Materials \& Structures}

May 12, 2021

Dear Editor,

I am pleased to submit an original research article entitled ``On the
relationship between mechanical energy rate and heat dissipated rate
during fatigue for a C45 steel depending on stress ratio'' by Rosa De
Finis, Davide Palumbo and Umberto Galietti for consideration for
publication in the \emph{Fatigue \& Fracture of Engineering Materials \&
Structures} . We previously presented a new procedure to analyze
temperature data acquired during a rapid fatigue test and to evaluate
the endurance limit of different stainless steels and this manuscript
builds on our prior study to investigate more in depth, in frequency
domain, the thermal signal acquired during a rapid, stepwise fatigue
test. In particular, we focus on the second amplitude harmonic (SAH) of
thermal signal, a very well-known parameter to estimate the damage under
specific test conditions (fully-reversed applied load). We investigate
the capability of SAH of temperature signal to represent an useful
parameter to estimate the heat dissipated energy at different stress
ratio conditions (R=-1 and R=0.1). In addition, we study the frequency
spectrum of the strain energy rate, as well, in order to understand the
energy distribution among the harmonics for different stress ratios.

In this manuscript, \textbf{we show that in presence of the mean stress
in the load, the frequency spectrum of the strain energy density rate
presents different harmonic components (not just one as occurs at R=-1 )
while heat dissipated energy rate spectrum presents different harmonics,
so that the SAH is not the only one but it can be used to estimate the
heat dissipated energy. In addition, we show that} \textbf{the second
amplitude harmonic (SAH) of the heat energy rate dissipated by a unit
volume of material is linearly related to the SAH of strain energy
density rate. Such a relationship depends only on material and do not
depend on loading conditions or damage level. The relationship is also
valid, independently on signal stabilisation.}

We believe that this manuscript is appropriate for publication by
the\emph{Fatigue \& Fracture of Engineering Materials \&
Structures}because it regards the use of innovative characterization
methods associated with fatigue such as the energy-based methods for
carrying out the damage monitoring of the C45 steel. Our manuscript can
create a paradigm for future studies for the understanding of the
relationship between mechanical energy rate and heat dissipated rate
during fatigue tests under different loading conditions.

This manuscript has not been published and is not under consideration
for publication elsewhere. We have no conflicts of interest to disclose.

Thank you for your consideration.

Sincerely,

Rosa De Finis, PhD

Post doctoral research fellow, Department of Mechanical Mathematics and
Management

Politecnico di Bari-Via Orabona 4, 70125-Bari, Italy\selectlanguage{english}
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