modify document for ConstitutivePhenoPowerLaw

This commit is contained in:
Yun Jo Ro 2009-06-15 08:09:49 +00:00
parent caf568eb89
commit 204e296ecd
7 changed files with 5273 additions and 4100 deletions

View File

@ -175,7 +175,7 @@ hex (hcp)
placement tbph placement tbph
wide false wide false
sideways false sideways false
status collapsed status open
\begin_layout Plain Layout \begin_layout Plain Layout
\align center \align center
@ -607,7 +607,7 @@ reference "Fig:twinSystemHCP"
\begin_inset Float figure \begin_inset Float figure
wide false wide false
sideways false sideways false
status open status collapsed
\begin_layout Plain Layout \begin_layout Plain Layout
\align center \align center
@ -676,8 +676,15 @@ Drawing for twin system for HCP (
\end_inset \end_inset
- Ti). - Ti).
Twin directions are not scaled yet. Twin directions are not scaled because the
\begin_inset Quotes eld
\end_inset
twin Burgers vector
\begin_inset Quotes erd
\end_inset
magnitude is too small to show in the current figures.
\end_layout \end_layout
\end_inset \end_inset
@ -699,6 +706,382 @@ name "Fig:twinSystemHCP"
\end_inset \end_inset
\begin_inset Newpage clearpage
\end_inset
\end_layout
\begin_layout Standard
The Table
\begin_inset CommandInset ref
LatexCommand ref
reference "Tab:TwinBurgersVector"
\end_inset
shows the twin Burgers vector and its maganitude.
The magnitude of twin Burgers vector for each system is not shown in Figure
\begin_inset CommandInset ref
LatexCommand ref
reference "Fig:twinSystemHCP"
\end_inset
since the scale of twin Burgers vector is too small to put in figures.
\end_layout
\begin_layout Standard
\begin_inset Float table
placement tbph
wide false
sideways false
status open
\begin_layout Plain Layout
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="5" columns="5">
<features>
<column alignment="center" valignment="middle" width="0">
<column alignment="center" valignment="middle" width="0">
<column alignment="center" valignment="middle" width="0">
<column alignment="center" valignment="middle" width="0">
<column alignment="center" valignment="middle" width="0">
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
Twin Burgers vector
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
Magnitude
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
twin system
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
tensile (T1)
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $\left\{ 10\bar{1}2\right\} \left\langle \bar{1}011\right\rangle $
\end_inset
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $b_{T}=\frac{3-\left(\frac{c}{a}\right)^{2}}{3+\left(\frac{c}{a}\right)^{2}}\left\langle \bar{1}011\right\rangle $
\end_inset
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $|b_{T}|=\frac{3-\left(\frac{c}{a}\right)^{2}}{\sqrt{3+\left(\frac{c}{a}\right)^{2}}}\cdot a$
\end_inset
, 0.20
\begin_inset Formula $\cdot a$
\end_inset
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
compressive (C1)
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $\left\{ 11\bar{2}2\right\} \left\langle 11\bar{2}\bar{3}\right\rangle $
\end_inset
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $b_{T}=\frac{\left(\frac{c}{a}\right)^{2}-2}{3\cdot\left(\left(\frac{c}{a}\right)^{2}+1\right)}\left\langle 11\bar{2}\bar{3}\right\rangle $
\end_inset
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $|b_{T}|=\frac{\left(\frac{c}{a}\right)^{2}-2}{\sqrt{\left(\frac{c}{a}\right)^{2}+1}}\cdot a$
\end_inset
, 0.30
\begin_inset Formula $\cdot a$
\end_inset
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
tensile (T2)
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $\left\{ 11\bar{2}1\right\} \left\langle \bar{1}\bar{1}26\right\rangle $
\end_inset
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $b_{T}=\frac{1}{3\cdot\left(4\cdot\left(\frac{c}{a}\right)^{2}+1\right)}\left\langle \bar{1}\bar{1}26\right\rangle $
\end_inset
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $|b_{T}|=\frac{1}{\sqrt{1+4\cdot\left(\frac{c}{a}\right)^{2}}}\cdot a$
\end_inset
, 0.24
\begin_inset Formula $\cdot a$
\end_inset
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
compressive (C1)
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $\left\{ 10\bar{1}1\right\} \left\langle 10\bar{1}\bar{2}\right\rangle $
\end_inset
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $b_{T}=\frac{4\cdot\left(\frac{c}{a}\right)^{2}-9}{4\cdot\left(\frac{c}{a}\right)^{2}+3}\left\langle 10\bar{1}\bar{2}\right\rangle $
\end_inset
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $|b_{T}|=\frac{\sqrt{2}\cdot\left(4\cdot\left(\frac{c}{a}\right)^{2}-9\right)}{\sqrt{3\cdot\left(4\cdot\left(\frac{c}{a}\right)^{2}+3\right)}}\cdot a$
\end_inset
, 0.28
\begin_inset Formula $\cdot a$
\end_inset
\end_layout
\end_inset
</cell>
</row>
</lyxtabular>
\end_inset
\end_layout
\begin_layout Plain Layout
\begin_inset Caption
\begin_layout Plain Layout
Twin Burgers vector,
\begin_inset Formula $\frac{c}{a}=1.587$
\end_inset
.
Equations in Table are adopted from reference
\begin_inset CommandInset citation
LatexCommand citet
key "Christian1995"
\end_inset
.
\end_layout
\end_inset
\begin_inset CommandInset label
LatexCommand label
name "Tab:TwinBurgersVector"
\end_inset
\end_layout
\begin_layout Plain Layout
\end_layout
\end_inset
\end_layout \end_layout
\begin_layout Standard \begin_layout Standard

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@ -310,6 +310,20 @@
url = {http://www.sciencedirect.com/science/article/B6TXD-4TY9MS1-3/2/18f90a633e0d7cf464c6f03b8a0e698d} url = {http://www.sciencedirect.com/science/article/B6TXD-4TY9MS1-3/2/18f90a633e0d7cf464c6f03b8a0e698d}
} }
@ARTICLE{Christian1995,
author = {Christian, J. W. and Mahajan, S.},
title = {Deformation twinning},
journal = {Progress in Materials Science},
year = {1995},
volume = {39},
pages = {1--157},
number = {1-2},
issn = {0079-6425},
owner = {yj.ro},
timestamp = {2009.06.15},
url = {http://www.sciencedirect.com/science/article/B6TX1-3YRSGDH-1/2/9c86a05bd8433ef810e649a7cfd53862}
}
@ARTICLE{CHURCHMAN1953, @ARTICLE{CHURCHMAN1953,
author = {CHURCHMAN, A. T.}, author = {CHURCHMAN, A. T.},
title = {Preparation of Single Crystals of Titanium and their Mode of Deformation}, title = {Preparation of Single Crystals of Titanium and their Mode of Deformation},

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