Lab1 / main

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\begin{document}

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\addcontentsline{toc}{section}{\it W.-J. Kim et al. / Scripta Materialia 54 (2006) 1745-1750}
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\begin{figure}[h]
\captionsetup{font=scriptsize}
\includegraphics [scale=0.7] {./fig/1.png}
\caption{\label{fig:ris1}  Tensile stress-strain curves for the unECAPed and ECAPed Ti samples.}
\end{figure}
\footnotesize
\noindent and correspondingly large elongation. After ECAP, the
ultimate tensile strength is increased by 60%. This result is
attributed to considerable grain refinement through severe
deformation by ECAP. The tensile elongation was, how-
ever, drastically decreased, by 31%. This result is related
to the decrease of strain hardening capability after ECAP,
which commonly occurs in many metallic alloys after
ECAP [2].
\par\smallskip
\noindent\textit{3.3. Fatigue properties}
\par\smallskip
Fig. \ref{fig:ris2} shows the S-N curves for unECAPed and
ECAPed Ti with and without notches. Their S-N curves
can be described by the following equations

$\sigma_a=311  \times N^{-0.023}_f$ for plain specimens (unECAPed);\\
\parindent = 0pt
%\centering
$R=0.92$  \flushright (2)
\flushleft
$\sigma_a=306  \times N^{-0.043}_f$ for notched specimens (unECAPed);

\begin{equation}
R=0.91
\end{equation}

$\sigma_a=654 \times N^{-0.041}_f$ for plain specimens (ECAPed);

\begin{equation}
R=0.95
\end{equation}

$\sigma_a=552 \times N^{-0.080}_f$ for notched specimens (ECAPed);

\begin{equation}
R=0.99
\end{equation}

The result of the smooth bar tests will be discussed first.
According to Fig. \ref{fig:ris2}, the fatigue limit $\sigma_e$ of the pure Ti
increased from 210 and 350 MPa after ECAP, which is a
factor of 1.67 increase. This result indicates that a signifi-
cant improvement in high-cycle fatigue life can be achieved
by applying ECAP on pure Ti. This is in contrast to the
cases for the Al and Mg alloys after ECAP where little

\begin{figure}[t]
\captionsetup{font=scriptsize}
\includegraphics [scale=0.7] {./fig/2.png}
\caption{\label{fig:ris2} $S-N$ curves for the unECAPed and ECAPed samples.}
\end{figure}

enhancement in high-cycle fatigue performance was
observed [5,6]. The fatigue limit of 350 MPa is comparable
to that of the ECAPed Ti (=380 MPa) with the same grain
size studied by Valiev et al. [4]. The tensile and fatigue test
results of the unECAPed and ECAPed Ti are summarized
in Table 1, together with the data from other investigators
for pure Ti [4,7-9].

The fatigue notch factor, $K_f$ , is defined as follows:
\begin{equation}
K_F=\dfrac{\sigma_e}{\sigma_{en}}
\end{equation}

where $\sigma_e$ and $\sigma_{en}$ are the nominal fatigue limit of the mini-
mum cross-sectional area for plain and notched specimens,
respectively. Based on the data in Fig. \ref{fig:ris2}, the values of $K_F$ for
the ECAPed and unECAPed samples were computed. The
values were 2.12 and 1.28, respectively. The theoretical
stress concentration factor $K_t$ for the notched specimen
\begin{table}[h]
\label{lab1:table1}
\noindent Table 1:
\newline
Mechanical properties and grain size of pure Ti
\newline \noindent
\scalebox{0.8}{
\begin{tabular}{lllllll}
\hline
\footnotesize
Material  & $\sigma_{UTS}$ & $\sigma_{UTS}$ & $\sigma_{UTS}$ & $\sigma_{UTS}$ & $d$ & Elongation \\
   & (MPa) & (MPa) & (MPa) &   & (${\mu}m$) & (\%) \\
\hline

UnECAPed & 418 & 248 & 210 & 0.50 & 105 & 47.2\\
ECAPed & 669 & 635 & 350 & 0.52 & 0.3 & 32.5\\
ECAPed[4] & 810 & 650 & 380 & 0.47 & 0.3 & 15\\
ECAPed[7] & 1050 & 970 & 420 & 0.4 & 0.15 & 8\\
UnECAPed: & 460 & 380 & 238 & 0.52 & 15 & 26\\
cold reduction &  &  &  &  &  & \\
a[8] &  &  &  &  &  & \\
UnECAPed: &  440 & 315 & 235 & 0.53 & 9 & N.A.\\
annealed [9] &  &  &  &  &  & \\
UnECAPed: & 380 & 248 & 190 & 0.5 & 32 & N.A.\\
annealed[9] &  &  &  &  &  & \\
UnECAPed: & 377 & 190 & 178 & 0.47 & 100 & N.A.\\
annealed [9] &  &  &  &  &  & \\

\hline
\end{tabular}}
\end{table}
\end{document}