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+#LyX 1.6.2 created this file. For more info see http://www.lyx.org/
+\lyxformat 345
+\begin_document
+\begin_header
+\textclass scrartcl
+\use_default_options true
+\begin_modules
+endnotes
+foottoend
+hanging
+linguistics
+logicalmkup
+minimalistic
+braille
+theorems-std
+\end_modules
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+\author ""
+\author ""
+\end_header
+
+\begin_body
+
+\begin_layout Title
+Summary of constitutive_phenoPowerlaw
+\end_layout
+
+\begin_layout Author
+YUN JO RO
+\end_layout
+
+\begin_layout Standard
+This document contains information for constitutive_phenoPowerlaw.f90.
+ This constitutive subroutine is modified from the current contitutive_phenomeno
+logical.f90.
+ We introduce slip and twin family as additional index (or input) for each
+ crystal structure in lattice.f90 subroutine (e.g., for HCP crystal: slip and
+ twin system has four faimilies, respectively).
+ The current State variables in constitutive_phenoPowerlaw are
+\begin_inset Quotes eld
+\end_inset
+
+slip resistance
+\begin_inset Formula $\left(s^{\alpha}\right)$
+\end_inset
+
+
+\begin_inset Quotes erd
+\end_inset
+
+,
+\begin_inset Quotes erd
+\end_inset
+
+twin resistance
+\begin_inset Formula $\left(s^{\beta}\right)$
+\end_inset
+
+
+\begin_inset Quotes erd
+\end_inset
+
+,
+\begin_inset Quotes eld
+\end_inset
+
+cumulative shear strain
+\begin_inset Formula $\left(\gamma^{\alpha}\right)$
+\end_inset
+
+
+\begin_inset Quotes erd
+\end_inset
+
+, and
+\begin_inset Quotes eld
+\end_inset
+
+twin volume fraction
+\begin_inset Formula $\left(f^{\beta}\right)$
+\end_inset
+
+
+\begin_inset Quotes erd
+\end_inset
+
+.
+ Superscript
+\begin_inset Formula $\alpha$
+\end_inset
+
+ and
+\begin_inset Formula $\beta$
+\end_inset
+
+ denote to slip and twin systems, respectively, in this entire document.
+ Table
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "Flo:DeformationSystemTable"
+
+\end_inset
+
+ lists slip/twin systems for the
+\begin_inset Quotes eld
+\end_inset
+
+hex (hcp)
+\begin_inset Quotes erd
+\end_inset
+
+ case.
+\begin_inset VSpace medskip
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+\end_layout
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+\end_layout
+
+\end_inset
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+
+\begin_layout Plain Layout
+tensile (T1)
+\end_layout
+
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+compressive (C1)
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+\begin_layout Plain Layout
+tensile (T2)
+\end_layout
+
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+ |
+
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+
+\begin_layout Plain Layout
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+
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+
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+ |
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+ |
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+
+\begin_layout Plain Layout
+compressive (C1)
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
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+
+
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+ |
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+
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+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Implemented deformation mechanims in
+\begin_inset Formula $\alpha$
+\end_inset
+
+-Ti
+\end_layout
+
+\end_inset
+
+
+\begin_inset CommandInset label
+LatexCommand label
+name "Flo:DeformationSystemTable"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+Slip/twin system for HCP are illustrated in Figures
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "Fig:slipSystemHCP"
+
+\end_inset
+
+ and
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "Fig:twinSystemHCP"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figures/slipSystemForHCP.jpg
+ lyxscale 20
+ scale 25
+ clip
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Drawing for slip system for HCP.
+ Burgers vectors were scaled.
+\end_layout
+
+\end_inset
+
+
+\begin_inset CommandInset label
+LatexCommand label
+name "Fig:slipSystemHCP"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figures/twinSystemForHCP.jpg
+ lyxscale 20
+ scale 25
+ clip
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Drawing for twin system for HCP (
+\begin_inset Formula $\alpha$
+\end_inset
+
+- Ti).
+ Twin directions are not scaled yet.
+
+\end_layout
+
+\end_inset
+
+
+\begin_inset CommandInset label
+LatexCommand label
+name "Fig:twinSystemHCP"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Newpage clearpage
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Kinetics
+\end_layout
+
+\begin_layout Standard
+Shear strain rate due to slip is described by following eqation
+\begin_inset CommandInset citation
+LatexCommand citet
+key "Salem2005,Wu2007"
+
+\end_inset
+
+:
+\begin_inset Formula \begin{equation}
+\dot{\gamma}^{\alpha}=\dot{\gamma_{o}}\left|\frac{\tau^{\alpha}}{s^{\alpha}}\right|^{n}sign\left(\tau^{\alpha}\right)\label{eq:slipStrainRate}\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+, where
+\begin_inset Formula $\dot{\gamma}^{\alpha}$
+\end_inset
+
+; shear strain rate,
+\begin_inset Formula $\dot{\gamma}_{o}$
+\end_inset
+
+; reference shear strain rate,
+\begin_inset Formula $\tau^{\alpha}$
+\end_inset
+
+; resolved shear stress on the slip system,
+\begin_inset Formula $n$
+\end_inset
+
+; stress exponent, and
+\begin_inset Formula $s^{\alpha}$
+\end_inset
+
+; slip resistance.
+\end_layout
+
+\begin_layout Standard
+Twin volume fraction rate is described by following eqation
+\begin_inset CommandInset citation
+LatexCommand citet
+key "Salem2005,Wu2007"
+
+\end_inset
+
+:
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \begin{equation}
+\dot{f}^{\beta}=\frac{\dot{\gamma_{o}}}{\gamma^{\beta}}\left|\frac{\tau^{\beta}}{s^{\beta}}\right|^{n}\mathbb{\mathcal{H}}\left(\tau^{\beta}\right)\label{eq:twinVolrate}\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+, where
+\begin_inset Formula $\dot{f}^{\beta}$
+\end_inset
+
+; twin volume fraction rate,
+\begin_inset Formula $\dot{\gamma}_{o}$
+\end_inset
+
+; reference shear strain rate,
+\begin_inset Formula $\gamma^{\beta}$
+\end_inset
+
+;shear strain due to mechanical twinning,
+\begin_inset Formula $\tau^{\beta}$
+\end_inset
+
+; resolved shear stress on the twin system, and
+\begin_inset Formula $s^{\beta}$
+\end_inset
+
+; twin resistance.
+
+\begin_inset Formula $\mathcal{H}$
+\end_inset
+
+ is Heaviside function.
+
+\end_layout
+
+\begin_layout Section
+Structure Evolution
+\end_layout
+
+\begin_layout Standard
+In this present section, we attempt to show how we establish the relationship
+ between the evolutoin of slip/twin resistance and the evolution of shear
+ strain/twin volume fraction.
+
+\end_layout
+
+\begin_layout Subsection
+Interaction matrix.
+
+\end_layout
+
+\begin_layout Standard
+Conceptual relationship between the evolution of state and kinetic variables
+ is shown in Equation
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "eq:InteractionMatrix"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \begin{equation}
+\left[\begin{array}{c}
+\dot{s}^{\alpha}\\
+\dot{s}^{\beta}\end{array}\right]=\left[\begin{array}{cc}
+M_{\mathrm{slip-slip}} & M_{\mathrm{slip-twin}}\\
+M_{\mathrm{twin-slip}} & M_{\mathrm{twin-twin}}\end{array}\right]\left[\begin{array}{c}
+\dot{\gamma}^{\alpha}\\
+\dot{f}^{\beta}\end{array}\right]\label{eq:InteractionMatrix}\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Four interaction martices are followings; i) slip-slip interaction matrix
+
+\begin_inset Formula $\left(M_{\mathrm{{\scriptstyle slip-slip}}}\right)$
+\end_inset
+
+, ii) slip-twin interaction matrix
+\begin_inset Formula $\left(M_{\mathrm{slip-twin}}\right)$
+\end_inset
+
+, iii) twin-slip interaction matrix
+\begin_inset Formula $\left(M_{\mathrm{twin-slip}}\right)$
+\end_inset
+
+, and iv) twin-twin interaction matrix
+\begin_inset Formula $\left(M_{\mathrm{twin-twin}}\right)$
+\end_inset
+
+.
+
+\end_layout
+
+\begin_layout Standard
+Detailed interaction type matrices in Equation
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "eq:InteractionMatrix"
+
+\end_inset
+
+ will be further discussed in the following Section.
+\end_layout
+
+\begin_layout Subsection
+Interaction type matrix
+\end_layout
+
+\begin_layout Standard
+Following sections are sparated into four based on each interaction type
+ matrix alluded.
+ Numbers in Tables
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "Flo:SlipSlipIntTypeTable"
+
+\end_inset
+
+,
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "Flo:SlipTwinIntTypeTable"
+
+\end_inset
+
+,
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "Flo:TwinSlipIntTypeTable"
+
+\end_inset
+
+, and
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "Flo:TwinTwinIntTypeTable"
+
+\end_inset
+
+ denote the type of interaction between deformation systems (The first column
+ vs.
+ The first row).
+\end_layout
+
+\begin_layout Subsubsection
+Slip-Slip interaction type matrix
+\end_layout
+
+\begin_layout Itemize
+There are 20 types of slip-slip interaction as shown in Table
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "Flo:SlipSlipIntTypeTable"
+
+\end_inset
+
+.
+
+\end_layout
+
+\begin_layout Itemize
+In Table
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "Flo:SlipSlipIntTypeTable"
+
+\end_inset
+
+, types of latent hardening among slip systems are listed.
+
+\end_layout
+
+\begin_layout Itemize
+Actual slip-slip interaction type matrix,
+\begin_inset Formula $M_{\mathrm{slip-slip}}^{'}$
+\end_inset
+
+, is listed in Equation
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "eq:SlipSlipIntMatrix"
+
+\end_inset
+
+.
+\end_layout
+
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+\begin_inset Text
+
+\begin_layout Plain Layout
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+
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+
+
+
+\end_inset
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+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Slip-slip interaction type
+\end_layout
+
+\end_inset
+
+
+\begin_inset CommandInset label
+LatexCommand label
+name "Flo:SlipSlipIntTypeTable"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \begin{equation}
+M_{\mathrm{slip-slip}}^{'}=\left[\begin{array}{ccc|ccc|cccccc|cccccccccccc}
+1 & 5 & 5 & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot\\
+ & 1 & 5 & \cdot & 9 & \cdot & \cdot & \cdot & 12 & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & 14 & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot\\
+ & & 1 & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot\\
+\hline \cdot & \cdot & \cdot & 2 & 6 & 6 & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot\\
+\cdot & 15 & \cdot & & 2 & 6 & \cdot & \cdot & 10 & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & 13 & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot\\
+\cdot & \cdot & \cdot & & & 2 & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot\\
+\hline \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & 3 & 7 & 7 & 7 & 7 & 7 & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot\\
+\cdot & \cdot & \cdot & \cdot & \cdot & \cdot & & 3 & 7 & 7 & 7 & 7 & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot\\
+\cdot & \cdot & \cdot & \cdot & \cdot & \cdot & & & 3 & 7 & 7 & 7 & \cdot & \cdot & \cdot & \cdot & \cdot & 11 & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot\\
+\cdot & 18 & \cdot & \cdot & 16 & \cdot & & & & 3 & 7 & 7 & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot\\
+\cdot & \cdot & \cdot & \cdot & \cdot & \cdot & & & & & 3 & 7 & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot\\
+\cdot & \cdot & \cdot & \cdot & \cdot & \cdot & & & & & & 3 & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot\\
+\hline \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & 4 & 8 & 8 & 8 & 8 & 8 & 8 & 8 & 8 & 8 & 8 & 8\\
+\cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & & 4 & 8 & 8 & 8 & 8 & 8 & 8 & 8 & 8 & 8 & 8\\
+\cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & & & 4 & 8 & 8 & 8 & 8 & 8 & 8 & 8 & 8 & 8\\
+\cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & & & & 4 & 8 & 8 & 8 & 8 & 8 & 8 & 8 & 8\\
+\cdot & 20 & \cdot & \cdot & 19 & \cdot & \cdot & \cdot & 17 & \cdot & \cdot & \cdot & & & & & 4 & 8 & 8 & 8 & 8 & 8 & 8 & 8\\
+\cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & & & & & & 4 & 8 & 8 & 8 & 8 & 8 & 8\\
+\cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & & & & & & & 4 & 8 & 8 & 8 & 8 & 8\\
+\cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & & & & & & & & 4 & 8 & 8 & 8 & 8\\
+\cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & & & & & & & & & 4 & 8 & 8 & 8\\
+\cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & & & & & & & & & & 4 & 8 & 8\\
+\cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & & & & & & & & & & & 4 & 8\\
+\cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & & & & & & & & & & & & 4\end{array}\right]\label{eq:SlipSlipIntMatrix}\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace vfill
+\end_inset
+
+
+\begin_inset VSpace vfill
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsubsection
+Slip-Twin interaction type matrix
+\end_layout
+
+\begin_layout Itemize
+There are 16 types of slip-twin interaction in Table
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "Flo:SlipTwinIntTypeTable"
+
+\end_inset
+
+.
+
+\end_layout
+
+\begin_layout Itemize
+Meaning of T1, C1, T2, C2 is listed in Table
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "Flo:DeformationSystemTable"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Itemize
+Actual slip-twin interaction type matrix,
+\begin_inset Formula $M_{\mathrm{slip-twin}}^{'}$
+\end_inset
+
+, is listed in Equation
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "eq:SlipTwinIntMatrix"
+
+\end_inset
+
+.
+\end_layout
+
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+
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+ |
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+\begin_layout Plain Layout
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+ |
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+\begin_inset Text
+
+\begin_layout Plain Layout
+15
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+
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+ |
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+\begin_inset Text
+
+\begin_layout Plain Layout
+16
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+
+\end_inset
+ |
+
+
+
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+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Slip-twin interaction type
+\end_layout
+
+\end_inset
+
+
+\begin_inset CommandInset label
+LatexCommand label
+name "Flo:SlipTwinIntTypeTable"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \begin{equation}
+M_{\mathrm{slip-twin}}^{'}=\left[\begin{array}{c|c|c|c}
+1 & 2 & 3 & 4\\
+\hline 5 & 6 & 7 & 8\\
+\hline 9 & 10 & 11 & 12\\
+\hline 13 & 14 & 15 & 16\end{array}\right]\label{eq:SlipTwinIntMatrix}\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsubsection
+Twin-Slip interaction type matrix
+\end_layout
+
+\begin_layout Itemize
+There 16 types of twin-slip interaction in Table
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "Flo:TwinSlipIntTypeTable"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Itemize
+Meaning of T1, C1, T2, C2 is listed in Table
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "Flo:DeformationSystemTable"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Itemize
+Actual twin-slip interaction type matrix,
+\begin_inset Formula $M_{\mathrm{twin-slip}}^{'}$
+\end_inset
+
+, is listed in Equation
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "eq:TwinSlipIntMatrix"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float table
+placement H
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
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+
+
+
+
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+
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+
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+
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+
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+
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+
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+
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+
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+
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+\begin_inset Text
+
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+14
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+
+\end_inset
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+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
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+\end_layout
+
+\end_inset
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+
+\begin_inset Text
+
+\begin_layout Plain Layout
+3
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+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
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+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
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+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+15
+\end_layout
+
+\end_inset
+ |
+
+
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+C2
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+4
+\end_layout
+
+\end_inset
+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
+8
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+
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+ |
+
+\begin_inset Text
+
+\begin_layout Plain Layout
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+
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+ |
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+\begin_inset Text
+
+\begin_layout Plain Layout
+16
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+
+\end_inset
+ |
+
+
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Twin-slip interaction type
+\end_layout
+
+\end_inset
+
+
+\begin_inset CommandInset label
+LatexCommand label
+name "Flo:TwinSlipIntTypeTable"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \begin{equation}
+M_{\mathrm{twin-slip}}^{'}=\left[\begin{array}{c|c|c|c}
+1 & 5 & 9 & 13\\
+\hline 2 & 6 & 10 & 14\\
+\hline 3 & 7 & 11 & 15\\
+\hline 4 & 8 & 12 & 16\end{array}\right]\label{eq:TwinSlipIntMatrix}\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsubsection
+Twin-twin interaction type matrix
+\end_layout
+
+\begin_layout Itemize
+There are 20 types of twin-twin interaction as shown in Table
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "Flo:TwinTwinIntTypeTable"
+
+\end_inset
+
+.
+
+\end_layout
+
+\begin_layout Itemize
+In Table
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "Flo:TwinTwinIntTypeTable"
+
+\end_inset
+
+, types of latent hardening among twin systems are listed.
+
+\end_layout
+
+\begin_layout Itemize
+Actual twin-twin interaction type marix,
+\begin_inset Formula $M_{\mathrm{twin-twin}}^{'}$
+\end_inset
+
+, is listed in Equation
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "eq:TwinTwinIntMatrix"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float table
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+sideways false
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+
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+
+\begin_layout Plain Layout
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+
+\begin_layout Plain Layout
+Twin-twin interaction type
+\end_layout
+
+\end_inset
+
+
+\begin_inset CommandInset label
+LatexCommand label
+name "Flo:TwinTwinIntTypeTable"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \begin{equation}
+M_{\mathrm{twin-twin}}^{'}=\left[\begin{array}{cccccc|cccccc|cccccc|cccccc}
+1 & 5 & 5 & 5 & 5 & 5 & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot\\
+ & 1 & 5 & 5 & 5 & 5 & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot\\
+ & & 1 & 5 & 5 & 5 & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot\\
+ & & & 1 & 5 & 5 & \cdot & \cdot & \cdot & 9 & \cdot & \cdot & \cdot & \cdot & \cdot & 12 & \cdot & \cdot & \cdot & \cdot & \cdot & 14 & \cdot & \cdot\\
+ & & & & 1 & 5 & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot\\
+ & & & & & 1 & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot\\
+\hline \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & 2 & 6 & 6 & 6 & 6 & 6 & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot\\
+\cdot & \cdot & \cdot & \cdot & \cdot & \cdot & & 2 & 6 & 6 & 6 & 6 & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot\\
+\cdot & \cdot & \cdot & \cdot & \cdot & \cdot & & & 2 & 6 & 6 & 6 & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot\\
+\cdot & \cdot & \cdot & 15 & \cdot & \cdot & & & & 2 & 6 & 6 & \cdot & \cdot & \cdot & 10 & \cdot & \cdot & \cdot & \cdot & \cdot & 13 & \cdot & \cdot\\
+\cdot & \cdot & \cdot & \cdot & \cdot & \cdot & & & & & 2 & 6 & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot\\
+\cdot & \cdot & \cdot & \cdot & \cdot & \cdot & & & & & & 2 & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot\\
+\hline \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & 3 & 7 & 7 & 7 & 7 & 7 & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot\\
+\cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & & 3 & 7 & 7 & 7 & 7 & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot\\
+\cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & & & 3 & 7 & 7 & 7 & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot\\
+\cdot & \cdot & \cdot & 18 & \cdot & \cdot & \cdot & \cdot & \cdot & 16 & \cdot & \cdot & & & & 3 & 7 & 7 & \cdot & \cdot & \cdot & 11 & \cdot & \cdot\\
+\cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & & & & & 3 & 7 & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot\\
+\cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & & & & & & 3 & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot\\
+\hline \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & 4 & 8 & 8 & 8 & 8 & 8\\
+\cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & & 4 & 8 & 8 & 8 & 8\\
+\cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & & & 4 & 8 & 8 & 8\\
+\cdot & \cdot & \cdot & 20 & \cdot & \cdot & \cdot & \cdot & \cdot & 19 & \cdot & \cdot & \cdot & \cdot & \cdot & 17 & \cdot & \cdot & & & & 4 & 8 & 8\\
+\cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & & & & & 4 & 8\\
+\cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & \cdot & & & & & & 4\end{array}\right]\label{eq:TwinTwinIntMatrix}\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Prefactor (nonlinear factor)
+\end_layout
+
+\begin_layout Subsubsection
+Prefactors for slip resistance
+\begin_inset Formula $\left(s^{\alpha}\right)$
+\end_inset
+
+;
+\begin_inset Formula $M_{\mathrm{slip-slip}}$
+\end_inset
+
+ and
+\begin_inset Formula $M_{\mathrm{slip-twin}}$
+\end_inset
+
+
+\begin_inset CommandInset citation
+LatexCommand citet
+key "Wu2007"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $M_{\mathrm{slip-slip}}$
+\end_inset
+
+ and
+\begin_inset Formula $M_{\mathrm{slip-twin}}$
+\end_inset
+
+ use for slip resistance evolution
+\begin_inset Formula $\left(\dot{s}^{\alpha}\right)$
+\end_inset
+
+.
+ Equation
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "eq:SlipResisEvolutionEq"
+
+\end_inset
+
+ is for a slip resistance rate evolution.
+ This currently shows the prefactor for
+\begin_inset Quotes eld
+\end_inset
+
+slip-slip interaction matrix,
+\begin_inset Formula $M_{\mathrm{slip-slip}}$
+\end_inset
+
+
+\begin_inset Quotes erd
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\noun off
+\color none
+\begin_inset Formula \begin{equation}
+M_{\mathrm{slip-slip}}=h_{\mathrm{slip}}\left(1+C\cdot F^{b}\right)\left(1-\frac{s^{\alpha}}{s_{so}^{\alpha}+s_{\mathrm{pr}}\cdot\sqrt{F}}\right)\cdot M_{\mathrm{slip-slip}}^{'}\label{eq:SlipResisEvolutionEq}\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+, where
+\begin_inset Formula $h_{\mathrm{slip}}$
+\end_inset
+
+represent a hardening rate, and
+\begin_inset Formula $S_{\mathrm{so}}^{\alpha}$
+\end_inset
+
+ saturation slip resistance for slip system without mechanical twinning
+
+\begin_inset Formula $\left(\sum_{\beta}f^{\beta}=0\right)$
+\end_inset
+
+, respectively.
+ And,
+\begin_inset Formula $F$
+\end_inset
+
+ is
+\begin_inset Formula $\sum_{\beta}f^{\beta}$
+\end_inset
+
+, and
+\begin_inset Formula $N^{S}$
+\end_inset
+
+is the total number of slip system.
+\begin_inset Formula $C$
+\end_inset
+
+,
+\begin_inset Formula $s_{\mathrm{pr}}$
+\end_inset
+
+, and
+\begin_inset Formula $b$
+\end_inset
+
+ are coefficients to introduce the effect of interaction between slip and
+ mechanical twin in Equation
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "eq:SlipResisEvolutionEq"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Itemize
+Slip-twin interaction matrix,
+\begin_inset Formula $M_{\mathrm{slip-twin}}$
+\end_inset
+
+, has not been implemented with any prefactor in the present version.
+
+\end_layout
+
+\begin_layout Subsubsection
+Prefactors for twin resistance
+\begin_inset Formula $\left(s^{\beta}\right)$
+\end_inset
+
+;
+\begin_inset Formula $M_{\mathrm{twin-slip}}$
+\end_inset
+
+ and
+\begin_inset Formula $M_{\mathrm{twin-twin}}$
+\end_inset
+
+
+\begin_inset CommandInset citation
+LatexCommand citet
+key "Salem2005"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $M_{\mathrm{twin-sli}p}$
+\end_inset
+
+ and
+\begin_inset Formula $M_{\mathrm{twin-twin}}$
+\end_inset
+
+ use for twin resistance evolution
+\begin_inset Formula $\left(\dot{s}^{\beta}\right)$
+\end_inset
+
+.
+ Twin-twin and twin-slip interaction matrices are described in Equations
+
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "eq:TwinTwinContributionToTwinResis"
+
+\end_inset
+
+ and
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "eq:TwinSlipContributionToTwinResis"
+
+\end_inset
+
+.
+
+\begin_inset VSpace medskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \begin{equation}
+M_{\mathrm{twin-twin}}=h_{\mathrm{tw}}\cdot F^{d}\cdot M_{\mathrm{twin-twin}}^{'}\label{eq:TwinTwinContributionToTwinResis}\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+,where
+\begin_inset Formula $h_{\mathrm{tw}}$
+\end_inset
+
+ and
+\begin_inset Formula $d$
+\end_inset
+
+ are coefficients for twin-twin contribution.
+
+\begin_inset Formula $F$
+\end_inset
+
+ is
+\begin_inset Formula $\sum_{\beta}f^{\beta}$
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset VSpace medskip
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \begin{equation}
+M_{\mathrm{twin-slip}}=h_{\mathrm{tw-sl}}\cdot\Gamma^{e}\cdot M_{\mathrm{twin-slip}}^{'}\label{eq:TwinSlipContributionToTwinResis}\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+,where
+\begin_inset Formula $h_{\mathrm{tw-sl}}$
+\end_inset
+
+ and
+\begin_inset Formula $e$
+\end_inset
+
+ are coefficients for twin-slip contribution
+\family roman
+\series medium
+\shape up
+\size normal
+\emph off
+\bar no
+\noun off
+\color none
+, and
+\begin_inset Formula $\Gamma=\sum_{\alpha}\gamma^{\alpha}$
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Newpage clearpage
+\end_inset
+
+
+\end_layout
+
+\begin_layout Section
+Material Parameters (Material Configuration file)
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+placement tbph
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+ filename figures/ExpectedMaterialConfigFile.jpg
+ lyxscale 30
+ scale 80
+ clip
+
+\end_inset
+
+
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Expected of phenomenological modelling parameters.
+\end_layout
+
+\end_inset
+
+
+\begin_inset CommandInset label
+LatexCommand label
+name "Fig:ModelParameters"
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Itemize
+The sequence for hardening coefficients in Figure
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "Fig:ModelParameters"
+
+\end_inset
+
+ is the sequence of numbering in Tables
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "Flo:SlipSlipIntTypeTable"
+
+\end_inset
+
+,
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "Flo:SlipTwinIntTypeTable"
+
+\end_inset
+
+,
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "Flo:TwinSlipIntTypeTable"
+
+\end_inset
+
+, and
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "Flo:TwinTwinIntTypeTable"
+
+\end_inset
+
+ above.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Newpage clearpage
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset CommandInset bibtex
+LatexCommand bibtex
+bibfiles "MPIEyjr"
+options "bibtotoc,plain"
+
+\end_inset
+
+
+\end_layout
+
+\end_body
+\end_document
diff --git a/trunk/documentation/ConstitutiveLaw/powerLaw/ConstitutivePhenoPowerLaw.pdf b/trunk/documentation/ConstitutiveLaw/powerLaw/ConstitutivePhenoPowerLaw.pdf
new file mode 100644
index 000000000..adf6c4a92
Binary files /dev/null and b/trunk/documentation/ConstitutiveLaw/powerLaw/ConstitutivePhenoPowerLaw.pdf differ
diff --git a/trunk/documentation/ConstitutiveLaw/powerLaw/MPIEyjr.bib b/trunk/documentation/ConstitutiveLaw/powerLaw/MPIEyjr.bib
new file mode 100644
index 000000000..2d52724a4
--- /dev/null
+++ b/trunk/documentation/ConstitutiveLaw/powerLaw/MPIEyjr.bib
@@ -0,0 +1,2031 @@
+% This file was created with JabRef 2.4.2.
+% Encoding: Cp1252
+
+@ARTICLE{Ahn2006,
+ author = {D.C. Ahn and P. Sofronis and R. Minich},
+ title = {On the micromechanics of void growth by prismatic-dislocation loop
+ emission},
+ journal = {Journal of the Mechanics and Physics of Solids},
+ year = {2006},
+ volume = {54},
+ pages = {735 - 755},
+ number = {4},
+ doi = {DOI: 10.1016/j.jmps.2005.10.011},
+ issn = {0022-5096},
+ keywords = {Void growth},
+ owner = {yj.ro},
+ timestamp = {2009.02.26},
+ url = {http://www.sciencedirect.com/science/article/B6TXB-4HTBMD1-2/2/5390a456c470a8def2420f78bcdcc7ac}
+}
+
+@ARTICLE{Akhtar1975,
+ author = {Akhtar, A.},
+ title = {Basal slip and twinning in alpha-titanium single crystals},
+ journal = {Metallurgical and Materials Transactions A},
+ year = {1975},
+ volume = {6},
+ pages = {1105--1113},
+ number = {4},
+ month = apr,
+ owner = {yj.ro},
+ timestamp = {2009.01.22},
+ url = {http://dx.doi.org/10.1007/BF02645537}
+}
+
+@ARTICLE{Akhtar1975a,
+ author = {Akhtar, A. and Teghtsoonian, E.},
+ title = {Prismatic slip in alpha-titanium single crystals},
+ journal = {Metallurgical and Materials Transactions A},
+ year = {1975},
+ volume = {6},
+ pages = {2201--2208},
+ number = {12},
+ month = dec,
+ owner = {yj.ro},
+ timestamp = {2009.01.22},
+ url = {http://dx.doi.org/10.1007/BF02818644}
+}
+
+@ARTICLE{Asgari1997,
+ author = {Asgari, Sirous and El-Danaf, Ehab and Kalidindi, Surya and Doherty,
+ Roger},
+ title = {Strain hardening regimes and microstructural evolution during large
+ strain compression of low stacking fault energy fcc alloys that form
+ deformation twins},
+ journal = {Metallurgical and Materials Transactions A},
+ year = {1997},
+ volume = {28},
+ pages = {1781--1795},
+ number = {9},
+ month = sep,
+ abstract = {Abstract Constant true strain rate simple compression tests
+ were conducted on annealed, polycrystalline samples of α-brass and
+ MP35N, and the evolution of the true stress (σ)-true strain (ε)
+ response was documented. From these data, the strain hardening rate
+ was numerically computed, normalized with shear modulus (G), and
+ plotted against both (σ − σ 0)/G (σ0 being the initial yield
+ strength of the alloy) and ε. Such normalized plots for α-brass
+ and MP35N were found to be almost identical to each other, and revealed
+ four distinct stages of strain hardening: stage A, with a steadily
+ decreasing strain hardening rate up to a true strain of about −0.08;
+ stage B, with an almost constant strain hardening rate up to a true
+ strain of about −0.2; stage C, with a steadily decreasing strain
+ hardening rate up to a true strain of about −0.55; and a final
+ stage D, again with an almost constant strain hardening rate. Optical
+ microscopy and transmission electron microscopy (TEM) were performed
+ on deformed samples. The results suggested that stage A corresponded
+ to stage III strain hardening (dynamic recovery) of higher stacking
+ fault energy (SFE) fcc metals such as copper. The onset of stage
+ B correlated with the first observation of deformation twins in the
+ microstructure. Further straining in stage B was found to produce
+ clusters of parallel twins in an increasing number of grains. Stage
+ C correlated with the development of severe inhomogeneity of deformation
+ within most grains, and with the development of significant misorientation
+ between the twin/matrix interface and the {111} plane in the matrix
+ of the grain, i.e., the matrix/twin interface lost coherency with
+ continued deformation. Stage D correlated with extensive formation
+ of secondary twins that resulted in twin intersections in many grains.
+ Early in stage D, some strain localization in the form of shear bands
+ was observed. Although formation of these shear bands had no detectable
+ effect on the macroscopic strain hardening rate, it did correlated
+ with a marked change in texture evolution. Based on these experimental
+ observations, we have developed and presented a physical description
+ of the microstructural phenomena responsible for the various strain
+ hardening stages observed in low SFE fcc alloys.},
+ owner = {yj.ro},
+ timestamp = {2009.04.09},
+ url = {http://dx.doi.org/10.1007/s11661-997-0109-3}
+}
+
+@ARTICLE{Battaini2007,
+ author = {Battaini, M. and Pereloma, E.V. and Davies, C.H.J.},
+ title = {Orientation Effect on Mechanical Properties of Commercially Pure
+ Titanium at Room Temperature},
+ journal = {Metallurgical and Materials Transactions A},
+ year = {2007},
+ volume = {38},
+ pages = {276--285},
+ number = {2},
+ month = feb,
+ owner = {yj.ro},
+ timestamp = {2009.02.26},
+ url = {http://dx.doi.org/10.1007/s11661-006-9040-2}
+}
+
+@ARTICLE{Beevers1969,
+ author = {Beevers, C. J. and Halliday, M. D.},
+ title = {The role of twinning in the fatigue behaviour of alpha-titanium},
+ journal = {Czechoslovak Journal of Physics},
+ year = {1969},
+ volume = {19},
+ pages = {343--346},
+ number = {3},
+ month = mar,
+ owner = {yj.ro},
+ timestamp = {2009.03.12},
+ url = {http://dx.doi.org/10.1007/BF01712874}
+}
+
+@ARTICLE{Berfield2007,
+ author = {Berfield, T. and Patel, J. and Shimmin, R. and Braun, P. and Lambros,
+ J. and Sottos, N.},
+ title = {Micro- and Nanoscale Deformation Measurement of Surface and Internal
+ Planes via Digital Image Correlation},
+ journal = {Experimental Mechanics},
+ year = {2007},
+ volume = {47},
+ pages = {51--62},
+ number = {1},
+ month = feb,
+ abstract = {Abstract The digital image correlation (DIC) technique
+ is successfully applied across multiple length scales through the
+ generation of a suitable speckle pattern at each size scale. For
+ microscale measurements, a random speckle pattern of paint is created
+ with a fine point airbrush. Nanoscale displacement resolution is
+ achieved with a speckle pattern formed by solution deposition of
+ fluorescent silica nanoparticles. When excited, the particles fluoresce
+ and form a speckle pattern that can be imaged with an optical microscope.
+ Displacements are measured on the surface and on an interior plane
+ of transparent polymer samples with the different speckle patterns.
+ Rigid body translation calibrations and uniaxial tension experiments
+ establish a surface displacement resolution of 1 μm over a
+ 56 mm scale field of view for the airbrushed samples and 17 nm
+ over a 100100 μm scale field of view for samples with the fluorescent
+ nanoparticle speckle. To demonstrate the capabilities of the method,
+ we characterize the internal deformation fields generated around
+ silica microspheres embedded in an elastomer under tensile loading.
+ The DIC technique enables measurement of complex deformation fields
+ with nanoscale precision over relatively large areas, making it of
+ particular relevance to materials that possess multiple length scales.},
+ owner = {yj.ro},
+ timestamp = {2009.04.09},
+ url = {http://dx.doi.org/10.1007/s11340-006-0531-2}
+}
+
+@ARTICLE{Beyerlein2008,
+ author = {I.J. Beyerlein and C.N. Tom},
+ title = {A dislocation-based constitutive law for pure Zr including temperature
+ effects},
+ journal = {International Journal of Plasticity},
+ year = {2008},
+ volume = {24},
+ pages = {867 - 895},
+ number = {5},
+ doi = {DOI: 10.1016/j.ijplas.2007.07.017},
+ issn = {0749-6419},
+ keywords = {A. Dislocations},
+ owner = {yj.ro},
+ timestamp = {2009.05.04},
+ url = {http://www.sciencedirect.com/science/article/B6TWX-4PFDDMC-1/2/2e4d625f58cc8d631f6240ab9c34edaf}
+}
+
+@ARTICLE{Biallas2007,
+ author = {G. Biallas and H.J. Maier},
+ title = {In-situ fatigue in an environmental scanning electron microscope
+ - Potential and current limitations},
+ journal = {International Journal of Fatigue},
+ year = {2007},
+ volume = {29},
+ pages = {1413 - 1425},
+ number = {8},
+ doi = {DOI: 10.1016/j.ijfatigue.2006.11.008},
+ issn = {0142-1123},
+ keywords = {In situ fatigue},
+ owner = {yj.ro},
+ timestamp = {2009.04.09},
+ url = {http://www.sciencedirect.com/science/article/B6V35-4MSY8H6-1/2/ac32b32e9a08bcbf0c6d6ca03252225b}
+}
+
+@ARTICLE{Biget1989,
+ author = {Biget, M. P. and Saada, G.},
+ title = {Low-temperature plasticity of high-purity α-titanium single crystals},
+ journal = {Philosophical Magazine A},
+ year = {1989},
+ volume = {59},
+ pages = {747--757},
+ number = {4},
+ owner = {yj.ro},
+ publisher = {Taylor \& Francis},
+ timestamp = {2009.04.23},
+ url = {http://www.informaworld.com/10.1080/01418618908209818}
+}
+
+@ARTICLE{Cai2008,
+ author = {Shengqiang Cai and Ziran Li and Yuanming Xia},
+ title = {Evolution equations of deformation twins in metals--Evolution of
+ deformation twins in pure titanium},
+ journal = {Physica B: Condensed Matter},
+ year = {2008},
+ volume = {403},
+ pages = {1660 - 1665},
+ number = {10-11},
+ doi = {DOI: 10.1016/j.physb.2007.09.091},
+ issn = {0921-4526},
+ keywords = {Gibbs free energy},
+ owner = {yj.ro},
+ timestamp = {2009.01.22},
+ url = {http://www.sciencedirect.com/science/article/B6TVH-4PT7X4N-1/2/8208076d98499b7efcf88b3df2d87d7b}
+}
+
+@ARTICLE{Capolungo2009,
+ author = {L. Capolungo and I.J. Beyerlein and G.C. Kaschner and C.N. Tom},
+ title = {On the interaction between slip dislocations and twins in HCP Zr},
+ journal = {Materials Science and Engineering: A},
+ year = {2009},
+ volume = {513-514},
+ pages = {42 - 51},
+ doi = {DOI: 10.1016/j.msea.2009.01.035},
+ issn = {0921-5093},
+ keywords = {Zirconium},
+ owner = {yj.ro},
+ timestamp = {2009.05.04},
+ url = {http://www.sciencedirect.com/science/article/B6TXD-4VF56W9-1/2/96559a17e0128c846012b89d57e96762}
+}
+
+@ARTICLE{Capolungo2009a,
+ author = {L. Capolungo and I.J. Beyerlein and C.N. Tom},
+ title = {Slip-assisted twin growth in hexagonal close-packed metals},
+ journal = {Scripta Materialia},
+ year = {2009},
+ volume = {60},
+ pages = {32 - 35},
+ number = {1},
+ doi = {DOI: 10.1016/j.scriptamat.2008.08.044},
+ issn = {1359-6462},
+ keywords = {Twinning},
+ owner = {yj.ro},
+ timestamp = {2009.02.24},
+ url = {http://www.sciencedirect.com/science/article/B6TY2-4TG9J13-1/2/b8a6d947d7ec88bacf253bd3b717146d}
+}
+
+@ARTICLE{Capolungo2008,
+ author = {L. Capolungo and I. J. Beyerlein},
+ title = {Nucleation and stability of twins in hcp metals},
+ journal = {Physical Review B (Condensed Matter and Materials Physics)},
+ year = {2008},
+ volume = {78},
+ pages = {024117},
+ number = {2},
+ eid = {024117},
+ doi = {10.1103/PhysRevB.78.024117},
+ keywords = {dislocation nucleation; magnesium; nucleation; twin boundaries; twinning;
+ zirconium},
+ numpages = {19},
+ owner = {yj.ro},
+ publisher = {APS},
+ timestamp = {2009.01.22},
+ url = {http://link.aps.org/abstract/PRB/v78/e024117}
+}
+
+@ARTICLE{Cho2002,
+ author = {J. R. Cho and D. Dye and K. T. Conlon and M. R. Daymond and R. C.
+ Reed},
+ title = {Intergranular strain accumulation in a near-alpha titanium alloy
+ during plastic deformation},
+ journal = {Acta Materialia},
+ year = {2002},
+ volume = {50},
+ pages = {4847 - 4864},
+ number = {19},
+ doi = {DOI: 10.1016/S1359-6454(02)00354-3},
+ issn = {1359-6454},
+ owner = {yj.ro},
+ timestamp = {2009.02.25},
+ url = {http://www.sciencedirect.com/science/article/B6TW8-473MNHB-G/2/3113572716f9931937bb701bedc74e18}
+}
+
+@ARTICLE{Choi2009,
+ author = {Jae-Man Choi and Chung-Youb Kim and Ji-Ho Song},
+ title = {Noise reduction for fatigue crack growth test data under random loading},
+ journal = {Materials Science and Engineering: A},
+ year = {2009},
+ volume = {505},
+ pages = {163 - 168},
+ number = {1-2},
+ doi = {DOI: 10.1016/j.msea.2008.11.005},
+ issn = {0921-5093},
+ keywords = {Fatigue crack growth},
+ owner = {yj.ro},
+ timestamp = {2009.02.20},
+ url = {http://www.sciencedirect.com/science/article/B6TXD-4TY9MS1-3/2/18f90a633e0d7cf464c6f03b8a0e698d}
+}
+
+@ARTICLE{CHURCHMAN1953,
+ author = {CHURCHMAN, A. T.},
+ title = {Preparation of Single Crystals of Titanium and their Mode of Deformation},
+ journal = {Nature},
+ year = {1953},
+ volume = {171},
+ pages = {706--706},
+ number = {4355},
+ month = apr,
+ comment = {10.1038/171706a0},
+ owner = {yj.ro},
+ timestamp = {2009.04.17},
+ url = {http://dx.doi.org/10.1038/171706a0}
+}
+
+@ARTICLE{Cojocaru2009,
+ author = {D. Cojocaru and A.M. Karlsson},
+ title = {Assessing plastically dissipated energy as a condition for fatigue
+ crack growth},
+ journal = {International Journal of Fatigue},
+ year = {2009},
+ volume = {31},
+ pages = {1154 - 1162},
+ number = {7},
+ doi = {DOI: 10.1016/j.ijfatigue.2008.12.009},
+ issn = {0142-1123},
+ keywords = {Finite element method},
+ owner = {yj.ro},
+ timestamp = {2009.04.17},
+ url = {http://www.sciencedirect.com/science/article/B6V35-4V7MSHM-2/2/76871f554c14db78d71577fa55be9e78}
+}
+
+@ARTICLE{Conrad1981,
+ author = {Hans Conrad},
+ title = {Effect of interstitial solutes on the strength and ductility of titanium},
+ journal = {Progress in Materials Science},
+ year = {1981},
+ volume = {26},
+ pages = {123 - 403},
+ number = {2-4},
+ doi = {DOI: 10.1016/0079-6425(81)90001-3},
+ issn = {0079-6425},
+ owner = {yj.ro},
+ timestamp = {2009.02.04},
+ url = {http://www.sciencedirect.com/science/article/B6TX1-48KNRFW-2H/2/d6c48f18ceac9719a02ff8b58f9697a9}
+}
+
+@ARTICLE{Crostack2001,
+ author = {Crostack, H.-A. and Fischer, G. and Soppa, E. and Schmauder, S. and
+ Liu, Y.-L.},
+ title = {Localization of strain in metal matrix composites studied by a scanning
+ electron microscope-based grating method},
+ journal = {Journal of Microscopy},
+ year = {2001},
+ volume = {201},
+ pages = {171--178},
+ number = {2},
+ owner = {yj.ro},
+ timestamp = {2009.03.25},
+ url = {http://dx.doi.org/10.1046/j.1365-2818.2001.00772.x}
+}
+
+@ARTICLE{Dargusch2008,
+ author = {Dargusch, M.S. and Zhang, M.-X. and Palanisamy, S. and Buddery,
+ A.J.M. and StJohn, D.H.},
+ title = {Subsurface Deformation After Dry Machining of Grade 2 Titanium},
+ journal = {Advanced Engineering Materials},
+ year = {2008},
+ volume = {10},
+ pages = {85--88},
+ number = {1-2},
+ owner = {yj.ro},
+ timestamp = {2009.04.20},
+ url = {http://dx.doi.org/10.1002/adem.200700233}
+}
+
+@ARTICLE{Donoso1977,
+ author = {Donoso, J. and Reed-Hill, R.},
+ title = {Static strain-aging in commercial purity alpha titanium},
+ journal = {Metallurgical and Materials Transactions A},
+ year = {1977},
+ volume = {8},
+ pages = {945--948},
+ number = {6},
+ month = jun,
+ owner = {yj.ro},
+ timestamp = {2009.03.12},
+ url = {http://dx.doi.org/10.1007/BF02661577}
+}
+
+@ARTICLE{Dunne2007,
+ author = {F.P.E. Dunne and D. Rugg and A. Walker},
+ title = {Lengthscale-dependent, elastically anisotropic, physically-based
+ hcp crystal plasticity: Application to cold-dwell fatigue in Ti alloys},
+ journal = {International Journal of Plasticity},
+ year = {2007},
+ volume = {23},
+ pages = {1061 - 1083},
+ number = {6},
+ doi = {DOI: 10.1016/j.ijplas.2006.10.013},
+ issn = {0749-6419},
+ keywords = {Crystal plasticity},
+ owner = {yj.ro},
+ timestamp = {2009.03.18},
+ url = {http://www.sciencedirect.com/science/article/B6TWX-4MY0TTV-2/2/91f50c6886693aeee08d190770cdf5b2}
+}
+
+@ARTICLE{Dunne2007a,
+ author = {Dunne, F.P.E and Walker, A and Rugg, D},
+ title = {{A systematic study of hcp crystal orientation and morphology effects
+ in polycrystal deformation and fatigue}},
+ journal = {Proceedings of the Royal Society A: Mathematical, Physical and Engineering
+ Science},
+ year = {2007},
+ volume = {463},
+ pages = {1467-1489},
+ number = {2082},
+ doi = {10.1098/rspa.2007.1833},
+ eprint = {http://rspa.royalsocietypublishing.org/content/463/2082/1467.full.pdf+html},
+ owner = {yj.ro},
+ timestamp = {2009.03.17},
+ url = {http://rspa.royalsocietypublishing.org/content/463/2082/1467.abstract}
+}
+
+@ARTICLE{DUNNE2008,
+ author = {DUNNE, F. P. E. and RUGG, D.},
+ title = {On the mechanisms of fatigue facet nucleation in titanium alloys},
+ journal = {Fatigue \& Fracture of Engineering Materials \& Structures},
+ year = {2008},
+ volume = {31},
+ pages = {949--958},
+ number = {11},
+ owner = {yj.ro},
+ timestamp = {2009.03.18},
+ url = {http://dx.doi.org/10.1111/j.1460-2695.2008.01284.x}
+}
+
+@ARTICLE{Evans2009,
+ author = {A.G. Evans and M.Y. He and A. Suzuki and M. Gigliotti and B. Hazel
+ and T.M. Pollock},
+ title = {A mechanism governing oxidation-assisted low-cycle fatigue of superalloys},
+ journal = {Acta Materialia},
+ year = {2009},
+ volume = {57},
+ pages = {2969 - 2983},
+ number = {10},
+ doi = {DOI: 10.1016/j.actamat.2009.02.047},
+ issn = {1359-6454},
+ keywords = {Low-cycle fatigue},
+ owner = {yj.ro},
+ timestamp = {2009.05.07},
+ url = {http://www.sciencedirect.com/science/article/B6TW8-4W01WM6-5/2/1229ce6be9bcf2168669f3dd827a1b1e}
+}
+
+@ARTICLE{Fromm2009,
+ author = {Bradley S. Fromm and Brent L. Adams and Sadegh Ahmadi and Marko Knezevic},
+ title = {Grain size and orientation distributions: Application to yielding
+ of [alpha]-titanium},
+ journal = {Acta Materialia},
+ year = {2009},
+ volume = {57},
+ pages = {2339 - 2348},
+ number = {8},
+ doi = {DOI: 10.1016/j.actamat.2008.12.037},
+ issn = {1359-6454},
+ keywords = {Texture},
+ owner = {yj.ro},
+ timestamp = {2009.04.17},
+ url = {http://www.sciencedirect.com/science/article/B6TW8-4VV0DMW-1/2/872cc58c52a9f293fa825c2f95fb19b0}
+}
+
+@ARTICLE{Goods1979,
+ author = {S.H. Goods and L.M. Brown},
+ title = {Overview No. 1: The nucleation of cavities by plastic deformation},
+ journal = {Acta Metallurgica},
+ year = {1979},
+ volume = {27},
+ pages = {1 - 15},
+ number = {1},
+ doi = {DOI: 10.1016/0001-6160(79)90051-8},
+ issn = {0001-6160},
+ owner = {yj.ro},
+ timestamp = {2009.02.26},
+ url = {http://www.sciencedirect.com/science/article/B7598-48JJK9X-7B/2/387d3e5470e76cb432f44838a15e10d6}
+}
+
+@ARTICLE{Gray1997,
+ author = {Gray, G. T.},
+ title = {Influence of Strain Rate and Temperature on the Structure. Property
+ Behavior of High-Purity Titanium},
+ journal = {Le Journal de Physique IV},
+ year = {1997},
+ volume = {07},
+ pages = {C3-423-C3-428},
+ number = C3,
+ month = {aug},
+ doi = {10.1051/jp4:1997373},
+ owner = {yj.ro},
+ timestamp = {2009.03.17},
+ url = {http://dx.doi.org/10.1051/jp4:1997373}
+}
+
+@ARTICLE{Grujicic2001,
+ author = {Grujicic, M. and Batchu, S.},
+ title = {A crystal plasticity materials constitutive model for polysynthetically-twinned
+ γ-TiAl + α2-Ti3Al single crystals},
+ journal = {Journal of Materials Science},
+ year = {2001},
+ volume = {36},
+ pages = {2851--2863},
+ number = {12},
+ month = jun,
+ abstract = {Deformation behavior of polysynthetically-twinned lamellar γ-TiAl
+ + α2-Ti3Al single crystals has been analyzed using a three-dimensional,
+ isothermal, rate-dependent, large-strain, crystal-plasticity based
+ materials constitutive model. Within the model it is assumed that
+ plastic deformation parallel to the γ-TiAl/α2-Ti3Al lamellar boundaries
+ is controlled by the softer γ-TiAl phase while deformation which
+ contains a component normal to these boundaries is dominated by the
+ harder α2-Ti3Al phase. The parameters appearing in the crystal-plasticity
+ materials constitutive relations are assessed using the available
+ experimental information pertaining to the active slip systems, their
+ deformation resistances and hardening and rate behavior of the two
+ constitutive phases both in their single-crystalline and in polysynthetically-twinned
+ lamellar forms. The constitutive relations are implemented in a Vectorized
+ User Material Subroutine (VUMAT) of the commercial finite element
+ program Abaqus/Explicit within which the material state is integrated
+ during loading using an explicit Euler-forward formulation. The results
+ obtained suggest that the adopted crystal-plasticity model and the
+ parameters assessed in the present work account quite well for the
+ observed room-temperature deformation behavior of polysynthetically-twinned
+ lamellar γ-TiAl + α2-Ti3Al single crystals.},
+ owner = {yj.ro},
+ timestamp = {2009.04.09},
+ url = {http://dx.doi.org/10.1023/A:1017942117952}
+}
+
+@ARTICLE{Haicheng1994,
+ author = {Gu Haicheng and Guo Huifang and Chang Shufen and Campbell Laird},
+ title = {Orientation dependence of cyclic deformation in high purity titanium
+ single crystals},
+ journal = {Materials Science and Engineering: A},
+ year = {1994},
+ volume = {188},
+ pages = {23 - 36},
+ number = {1-2},
+ doi = {DOI: 10.1016/0921-5093(94)90352-2},
+ issn = {0921-5093},
+ owner = {yj.ro},
+ timestamp = {2009.04.23},
+ url = {http://www.sciencedirect.com/science/article/B6TXD-48FKKVP-3/2/e3627502c857c5240f3ab05bfaec89ed}
+}
+
+@ARTICLE{Hu1993,
+ author = {Hu, Xiaoyu and Wei, Chao and Margolin, Harold and Nourbakhsh, Said},
+ title = {The stresses in a face-centered cubic single crystal under uniaxial
+ tension},
+ journal = {Metallurgical and Materials Transactions A},
+ year = {1993},
+ volume = {24},
+ pages = {875--881},
+ number = {4},
+ month = apr,
+ owner = {yj.ro},
+ timestamp = {2009.03.06},
+ url = {http://dx.doi.org/10.1007/BF02656508}
+}
+
+@ARTICLE{Huez1998,
+ author = {Huez, J. and Helbert, A. and Feaugas, X. and Guillot, I. and Clavel,
+ M.},
+ title = {Damage process in commercially pure},
+ journal = {Metallurgical and Materials Transactions A},
+ year = {1998},
+ volume = {29},
+ pages = {1615--1628},
+ number = {6},
+ month = jun,
+ owner = {yj.ro},
+ timestamp = {2009.02.26},
+ url = {http://dx.doi.org/10.1007/s11661-998-0085-2}
+}
+
+@ARTICLE{Hultgren1999,
+ author = {Hultgren, Carl and Ankem, Sreeramaurthy and Greene, Charles},
+ title = {Time-dependent twinning during ambient temperature compression creep
+ of alpha Ti-0.4Mn alloy},
+ journal = {Metallurgical and Materials Transactions A},
+ year = {1999},
+ volume = {30},
+ pages = {1675--1679},
+ number = {6},
+ month = jun,
+ owner = {yj.ro},
+ timestamp = {2009.04.27},
+ url = {http://dx.doi.org/10.1007/s11661-999-0106-9}
+}
+
+@ARTICLE{Kalidindi1998,
+ author = {Surya R. Kalidindi},
+ title = {Incorporation of deformation twinning in crystal plasticity models},
+ journal = {Journal of the Mechanics and Physics of Solids},
+ year = {1998},
+ volume = {46},
+ pages = {267 - 271},
+ number = {2},
+ doi = {DOI: 10.1016/S0022-5096(97)00051-3},
+ issn = {0022-5096},
+ keywords = {A. twinning},
+ owner = {yj.ro},
+ timestamp = {2009.01.22},
+ url = {http://www.sciencedirect.com/science/article/B6TXB-3SYYM0T-4/2/88bce8557651ce28dee790b39c9bd8ef}
+}
+
+@ARTICLE{Kirane2008,
+ author = {Kedar Kirane and Somnath Ghosh},
+ title = {A cold dwell fatigue crack nucleation criterion for polycrystalline
+ Ti-6242 using grain-level crystal plasticity FE Model},
+ journal = {International Journal of Fatigue},
+ year = {2008},
+ volume = {30},
+ pages = {2127 - 2139},
+ number = {12},
+ doi = {DOI: 10.1016/j.ijfatigue.2008.05.026},
+ issn = {0142-1123},
+ keywords = {Ti-6242},
+ owner = {yj.ro},
+ timestamp = {2009.03.10},
+ url = {http://www.sciencedirect.com/science/article/B6V35-4SRKMJM-2/2/66058d22d6e2fde0cd799873a11003be}
+}
+
+@ARTICLE{Kocks1970,
+ author = {Kocks, U.},
+ title = {The relation between polycrystal deformation and single-crystal deformation},
+ journal = {Metallurgical and Materials Transactions B},
+ year = {1970},
+ volume = {1},
+ pages = {1121--1143},
+ number = {5},
+ month = may,
+ owner = {yj.ro},
+ timestamp = {2009.02.26},
+ url = {http://dx.doi.org/10.1007/BF02900224}
+}
+
+@ARTICLE{Kolluri2007,
+ author = {Kedarnath Kolluri and M. Rauf Gungor and Dimitrios Maroudas},
+ title = {Void nucleation in biaxially strained ultrathin films of face-centered
+ cubic metals},
+ journal = {Applied Physics Letters},
+ year = {2007},
+ volume = {90},
+ pages = {221907},
+ number = {22},
+ eid = {221907},
+ doi = {10.1063/1.2744477},
+ keywords = {metallic thin films; voids (solid); nucleation; relaxation; slip;
+ vacancies (crystal); molecular dynamics method},
+ numpages = {3},
+ owner = {yj.ro},
+ publisher = {AIP},
+ timestamp = {2009.02.26},
+ url = {http://link.aip.org/link/?APL/90/221907/1}
+}
+
+@ARTICLE{Kouchmeshky2009,
+ author = {Babak Kouchmeshky and Nicholas Zabaras},
+ title = {Modeling the response of HCP polycrystals deforming by slip and twinning
+ using a finite element representation of the orientation space},
+ journal = {Computational Materials Science},
+ year = {2009},
+ volume = {In Press, Corrected Proof},
+ pages = { - },
+ doi = {DOI: 10.1016/j.commatsci.2009.01.009},
+ issn = {0927-0256},
+ keywords = {Polycrystal plasticity},
+ owner = {yj.ro},
+ timestamp = {2009.02.20},
+ url = {http://www.sciencedirect.com/science/article/B6TWM-4VKVBTN-2/2/0b7244c1ddc2cee3517d7798f8b70c22}
+}
+
+@ARTICLE{Kuhlmann-Wilsdorf1995,
+ author = {Kuhlmann-Wilsdorf, Doris},
+ title = {Modelling of plastic deformation via segmented voce curves, linked
+ to characteristic LEDS's which are generated by LEDS transformations
+ between workhardening stages},
+ journal = {Physica Status Solidi (a)},
+ year = {1995},
+ volume = {149},
+ pages = {131--153},
+ number = {1},
+ owner = {yj.ro},
+ timestamp = {2009.02.12},
+ url = {http://dx.doi.org/10.1002/pssa.2211490110}
+}
+
+@ARTICLE{Lederich1978,
+ author = {R.J. Lederich and S.M.L. Sastry and J.E. O'Neal and B.B. Rath},
+ title = {The effect of grain size on yield stress and work hardening of polycrystalline
+ titanium at 295 K and 575 K},
+ journal = {Materials Science and Engineering},
+ year = {1978},
+ volume = {33},
+ pages = {183 - 188},
+ number = {2},
+ doi = {DOI: 10.1016/0025-5416(78)90171-4},
+ issn = {0025-5416},
+ owner = {yj.ro},
+ timestamp = {2009.03.17},
+ url = {http://www.sciencedirect.com/science/article/B759M-48HS2M2-10X/2/e7887d8060588932b522294b5a95ff05}
+}
+
+@ARTICLE{Li2009,
+ author = {B. Li and E. Ma},
+ title = {Zonal dislocations mediating twinning in magnesium},
+ journal = {Acta Materialia},
+ year = {2009},
+ volume = {57},
+ pages = {1734 - 1743},
+ number = {6},
+ doi = {DOI: 10.1016/j.actamat.2008.12.016},
+ issn = {1359-6454},
+ keywords = {Magnesium},
+ owner = {yj.ro},
+ timestamp = {2009.03.02},
+ url = {http://www.sciencedirect.com/science/article/B6TW8-4VDY40S-2/2/6d536cdd6e9b59eebf68bc5e14b2c684}
+}
+
+@ARTICLE{Li2008,
+ author = {Li, N. and Sutton, M. and Li, X. and Schreier, H.},
+ title = {Full-field Thermal Deformation Measurements in a Scanning Electron
+ Microscope by 2D Digital Image Correlation},
+ journal = {Experimental Mechanics},
+ year = {2008},
+ volume = {48},
+ pages = {635--646},
+ number = {5},
+ month = oct,
+ abstract = {Abstract Using recently developed methods for application
+ of a nano-scale random pattern having high contrast during SEM imaging,
+ baseline full-field thermal deformation experiments have been performed
+ successfully in an FEI Quanta SEM using 2D-DIC methods. Employing
+ a specially redesigned commercial heating plate and control system,
+ with modified specimen attachment procedures to minimize unwanted
+ image motions, recently developed distortion correction procedures
+ were shown to be effective in removing both drift and spatial distortion
+ fields under thermal heating. 2D-DIC results from heating experiments
+ up to 125°C on an aluminum specimen indicate that (a) the fully
+ corrected displacement components have nearly random variability
+ and a standard deviation of 0.02 pixels (≈25 nm at 200×
+ and ≈0.5 nm at 10,000×) in each displacement component and
+ (b) the unbiased measured strain fields have a standard deviation
+ ≈150 × 10−6 and a mean value that is in good agreement with
+ independent measurements, confirming that the SEM-DIC based method
+ can be used for both micro-scale and nano-scale thermal strain measurements.},
+ owner = {yj.ro},
+ timestamp = {2009.03.25},
+ url = {http://dx.doi.org/10.1007/s11340-007-9107-z}
+}
+
+@ARTICLE{Love2001,
+ author = {Love, J. Christopher and Wolfe, Daniel B. and Jacobs, Heiko O. and
+ Whitesides, George M.},
+ title = {Microscope Projection Photolithography for Rapid Prototyping of Masters
+ with Micron-Scale Features for Use in Soft Lithography},
+ journal = {Langmuir},
+ year = {2001},
+ volume = {17},
+ pages = {6005-6012},
+ number = {19},
+ doi = {10.1021/la010655t},
+ eprint = {http://pubs.acs.org/doi/pdf/10.1021/la010655t},
+ owner = {yj.ro},
+ timestamp = {2009.04.09},
+ url = {http://pubs.acs.org/doi/abs/10.1021/la010655t}
+}
+
+@ARTICLE{Lu2005,
+ author = {Lu, Gang and Kaxiras, Efthimios},
+ title = {Hydrogen Embrittlement of Aluminum: The Crucial Role of Vacancies},
+ journal = {Phys. Rev. Lett.},
+ year = {2005},
+ volume = {94},
+ pages = {155501--},
+ number = {15},
+ month = apr,
+ owner = {yj.ro},
+ publisher = {American Physical Society},
+ refid = {10.1103/PhysRevLett.94.155501},
+ timestamp = {2009.05.20},
+ url = {http://link.aps.org/abstract/PRL/v94/e155501}
+}
+
+@ARTICLE{Lubarda2004,
+ author = {V. A. Lubarda and M. S. Schneider and D. H. Kalantar and B. A. Remington
+ and M. A. Meyers},
+ title = {Void growth by dislocation emission},
+ journal = {Acta Materialia},
+ year = {2004},
+ volume = {52},
+ pages = {1397 - 1408},
+ number = {6},
+ doi = {DOI: 10.1016/j.actamat.2003.11.022},
+ issn = {1359-6454},
+ keywords = {Voids},
+ owner = {yj.ro},
+ timestamp = {2009.02.26},
+ url = {http://www.sciencedirect.com/science/article/B6TW8-4B8K8R7-4/2/3f5b9aeddae77894d75f14fe8cd0cb46}
+}
+
+@ARTICLE{Lynch2009,
+ author = {S.P. Lynch},
+ title = {Comments on } # A # unified # model # of # environment-assisted #
+ cracking,
+ journal = {Scripta Materialia},
+ year = {2009},
+ volume = {61},
+ pages = {331 - 334},
+ number = {3},
+ doi = {DOI: 10.1016/j.scriptamat.2009.02.031},
+ issn = {1359-6462},
+ keywords = {Liquid-metal embrittlement},
+ owner = {yj.ro},
+ timestamp = {2009.05.20},
+ url = {http://www.sciencedirect.com/science/article/B6TY2-4VNH488-C/2/5c8d9cb463e7be2080ca2cb8ea20adac}
+}
+
+@ARTICLE{Lynch2007,
+ author = {S.P. Lynch},
+ title = {Progression markings, striations, and crack-arrest markings on fracture
+ surfaces},
+ journal = {Materials Science and Engineering: A},
+ year = {2007},
+ volume = {468-470},
+ pages = {74 - 80},
+ note = {The McEvily Symposium: Fatigue and Fracture of Traditional and Advanced
+ Materials, TMS 2006},
+ doi = {DOI: 10.1016/j.msea.2006.09.083},
+ issn = {0921-5093},
+ keywords = {Fractography},
+ owner = {yj.ro},
+ timestamp = {2009.03.06},
+ url = {http://www.sciencedirect.com/science/article/B6TXD-4M9H3SM-6/2/64673c73023c0f8d688ff2b425c60c81}
+}
+
+@ARTICLE{Matsunaga2009,
+ author = {Tetsuya Matsunaga and Kohei Takahashi and Tatsuya Kameyama and Eiichi
+ Sato},
+ title = {Relaxation mechanisms at grain boundaries for ambient-temperature
+ creep of h.c.p. metals},
+ journal = {Materials Science and Engineering: A},
+ year = {2009},
+ volume = {510-511},
+ pages = {356 - 358},
+ note = {11th International Conference of Creep and Fracture of Engineering
+ Materials and Structures, CREEP 2008},
+ doi = {DOI: 10.1016/j.msea.2008.06.055},
+ issn = {0921-5093},
+ keywords = {Ambient-temperature creep},
+ owner = {yj.ro},
+ timestamp = {2009.04.27},
+ url = {http://www.sciencedirect.com/science/article/B6TXD-4V76251-1F/2/39d115978086373d4b1488039556104f}
+}
+
+@ARTICLE{McHargue1953,
+ author = {C.J McHargue and J.P Hammond},
+ title = {Deformation mechanisms in titanium at elevated temperatures},
+ journal = {Acta Metallurgica},
+ year = {1953},
+ volume = {1},
+ pages = {700 - 701, 703-705},
+ number = {6},
+ doi = {DOI: 10.1016/0001-6160(53)90028-5},
+ issn = {0001-6160},
+ owner = {yj.ro},
+ timestamp = {2009.02.12},
+ url = {http://www.sciencedirect.com/science/article/B7598-48KNTHY-2R/2/66321d3f4813c79a684cc9f116956d58}
+}
+
+@ARTICLE{Mendelson1970,
+ author = {S. Mendelson},
+ title = {Dislocation Dissociations in hcp Metals},
+ journal = {Journal of Applied Physics},
+ year = {1970},
+ volume = {41},
+ pages = {1893-1910},
+ number = {5},
+ doi = {10.1063/1.1659139},
+ owner = {yj.ro},
+ publisher = {AIP},
+ timestamp = {2009.04.17},
+ url = {http://link.aip.org/link/?JAP/41/1893/1}
+}
+
+@ARTICLE{Minonishi1985,
+ author = {Y. Minonishi and S. Morozumi and H. Yoshinaga},
+ title = {Accommodation around {101} twins in titanium},
+ journal = {Scripta Metallurgica},
+ year = {1985},
+ volume = {19},
+ pages = {1241 - 1245},
+ number = {10},
+ doi = {DOI: 10.1016/0036-9748(85)90246-7},
+ issn = {0036-9748},
+ owner = {yj.ro},
+ timestamp = {2009.01.22},
+ url = {http://www.sciencedirect.com/science/article/B759T-48N5N1J-7Y/2/888ba516ef4fcd5ef922d1ef539c238b}
+}
+
+@ARTICLE{Minonishi1982,
+ author = {Y. Minonishi and S. Morozumi and H. Yoshinaga},
+ title = {{112} <23> slip in titanium},
+ journal = {Scripta Metallurgica},
+ year = {1982},
+ volume = {16},
+ pages = {427 - 430},
+ number = {4},
+ doi = {DOI: 10.1016/0036-9748(82)90166-1},
+ issn = {0036-9748},
+ owner = {yj.ro},
+ timestamp = {2009.02.12},
+ url = {http://www.sciencedirect.com/science/article/B759T-48JCSWN-362/2/b33203f2ef53d4755d7cb1eafbfd6637}
+}
+
+@ARTICLE{Morris1995,
+ author = {Morris, J. R. and Ye, Y. Y. and Ho, K. M. and Chan, C. T. and Yoo,
+ M. H.},
+ title = {Structures and energies of compression twin boundaries in hcp
+ Ti and Zr},
+ journal = {Philosophical Magazine A},
+ year = {1995},
+ volume = {72},
+ pages = {751--763},
+ number = {3},
+ owner = {yj.ro},
+ publisher = {Taylor \& Francis},
+ timestamp = {2009.04.17},
+ url = {http://www.informaworld.com/10.1080/01418619508243798}
+}
+
+@ARTICLE{Moskalenko1998,
+ author = {V. A. Moskalenko and A. R. Smirnov},
+ title = {Temperature effect on formation of reorientation bands in [alpha]-Ti},
+ journal = {Materials Science and Engineering A},
+ year = {1998},
+ volume = {246},
+ pages = {282 - 288},
+ number = {1-2},
+ doi = {DOI: 10.1016/S0921-5093(97)00713-2},
+ issn = {0921-5093},
+ keywords = {Ti},
+ owner = {yj.ro},
+ timestamp = {2009.05.25},
+ url = {http://www.sciencedirect.com/science/article/B6TXD-3TJBBWH-11/2/018d9d8a90570743f40c4eb3e89ae206}
+}
+
+@ARTICLE{Moskalenko2002,
+ author = {V. A. Moskalenko and A. R. Smirnov and V. N. Kovaleva and V. D. Natsik},
+ title = {Staged work hardening of polycrystalline titanium at low temperatures
+ and its relation to substructure evolution},
+ journal = {Low Temperature Physics},
+ year = {2002},
+ volume = {28},
+ pages = {935-941},
+ number = {12},
+ doi = {10.1063/1.1531398},
+ keywords = {titanium; work hardening; plastic deformation; dislocation structure;
+ tensile strength; electron microscopy; optical microscopy; twinning;
+ crystal microstructure},
+ owner = {yj.ro},
+ publisher = {AIP},
+ timestamp = {2009.04.22},
+ url = {http://link.aip.org/link/?LTP/28/935/1}
+}
+
+@ARTICLE{Mullins1981,
+ author = {Mullins, S. and Patchett, B.},
+ title = {Deformation microstructures in titanium sheet metal},
+ journal = {Metallurgical and Materials Transactions A},
+ year = {1981},
+ volume = {12},
+ pages = {853--863},
+ number = {5},
+ month = may,
+ abstract = {Abstract A metallographic study has been made of the microstructures
+ produced by room temperature deformation of 0.6mm thick commercially
+ pure titanium sheet metal in uniaxial, plane strain and biaxial tension.
+ Deformation twinning becomes increasingly important as the deformation
+ mode changes from uniaxial through plane strain to equibiaxial tension,
+ and is more significant for strain transverse to the rolling direction
+ than for strain in the longitudinal direction. In uniaxial tension,
+ 1122 twins are dominant in longitudinal straining, while 1012 twins
+ dominate in transverse straining. In plane strain and equibiaxial
+ straining, 1012 twinning is suppressed and largely replaced by 1122
+ twinning. The observed changes in twin occurrence and type are attributed
+ to the interaction of the imposed stress system and the crystallographic
+ texture of the rolled sheet, which alters the distribution of the
+ grain basal-plane poles with respect to the operative stress axes.
+ In uniaxial tension parallel to the longitudinal direction, twins
+ favored by ‘c’ axis compression are produced, while in the transverse
+ direction twins favored by ‘c’ axis tension appear. In plane
+ strain and biaxial tension the dominant stress is through-thickness
+ compression, which produces twins favored by ‘c’ axis compression
+ in nearly all cases. The alterations in twin orientation and numbers
+ are associated with changes in stress-strain behavior. As twin volume
+ fraction increases and twins are aligned more closely to the principal
+ stress axis, the instantaneous work-hardening rate tends to stabilize
+ at a nearly constant value over a large strain range.},
+ owner = {yj.ro},
+ timestamp = {2009.01.22},
+ url = {http://dx.doi.org/10.1007/BF02648350}
+}
+
+@ARTICLE{Munroe1997,
+ author = {Norman Munroe and Xiaoli Tan and Haicheng Gu},
+ title = {Orientation dependence of slip and twinning in HCP metals},
+ journal = {Scripta Materialia},
+ year = {1997},
+ volume = {36},
+ pages = {1383 - 1386},
+ number = {12},
+ doi = {DOI: 10.1016/S1359-6462(97)00048-1},
+ issn = {1359-6462},
+ owner = {yj.ro},
+ timestamp = {2009.04.20},
+ url = {http://www.sciencedirect.com/science/article/B6TY2-3X2B4HD-6P/2/025a748a25f377371bd212b4a224e2d6}
+}
+
+@ARTICLE{Naka1983,
+ author = {Naka, S. and Lasalmonie, A.},
+ title = {Cross-slip on the first order pyramidal plane (10 1) of a-type dislocations
+ [1 10] in the plastic deformation of α-titanium single crystals},
+ journal = {Journal of Materials Science},
+ year = {1983},
+ volume = {18},
+ pages = {2613--2617},
+ number = {9},
+ month = sep,
+ abstract = {The nature of the cross-slip plane was determined by electron microscopy
+ observations of α-titanium single crystal specimens, oriented for
+ single prismatic slip (10},
+ owner = {yj.ro},
+ timestamp = {2009.03.25},
+ url = {http://dx.doi.org/10.1007/BF00547577}
+}
+
+@ARTICLE{Naka1982,
+ author = {S. Naka and A. Lasalmonie},
+ title = {Prismatic slip in the plastic deformation of [alpha]-Ti single crystals
+ below 700 K},
+ journal = {Materials Science and Engineering},
+ year = {1982},
+ volume = {56},
+ pages = {19 - 24},
+ number = {1},
+ doi = {DOI: 10.1016/0025-5416(82)90178-1},
+ issn = {0025-5416},
+ owner = {yj.ro},
+ timestamp = {2009.03.25},
+ url = {http://www.sciencedirect.com/science/article/B759M-48FMBBG-TC/2/6880ebb60dec693c2e0bda33ee94a139}
+}
+
+@ARTICLE{Naka1988,
+ author = {Naka, S. and Lasalmonie, A. and Costa, P. and Kubin, L. P.},
+ title = {The low-temperature plastic deformation of alpha-titanium and the
+ core structure of a-type screw dislocations},
+ journal = {Philosophical Magazine A},
+ year = {1988},
+ volume = {57},
+ pages = {717--740},
+ number = {5},
+ owner = {yj.ro},
+ publisher = {Taylor \& Francis},
+ timestamp = {2009.03.02},
+ url = {http://www.informaworld.com/10.1080/01418618808209916}
+}
+
+@ARTICLE{Newman2009,
+ author = {John A. Newman and Stephen W. Smith and Robert S. Piascik},
+ title = {Kmax effects on the near-threshold fatigue crack growth of powder-metallurgy
+ aluminum alloys},
+ journal = {International Journal of Fatigue},
+ year = {2009},
+ volume = {31},
+ pages = {1237 - 1245},
+ number = {8-9},
+ doi = {DOI: 10.1016/j.ijfatigue.2009.01.002},
+ issn = {0142-1123},
+ keywords = {Fatigue crack growth},
+ owner = {yj.ro},
+ timestamp = {2009.05.25},
+ url = {http://www.sciencedirect.com/science/article/B6V35-4VD9X5H-1/2/02fcc42b39b99f90f0b0ba3a25b49605}
+}
+
+@ARTICLE{Numakura1986,
+ author = {H. Numakura and Y. Minonishi and M. Koiwa},
+ title = { slip in titanium polycrystals at room temperature},
+ journal = {Scripta Metallurgica},
+ year = {1986},
+ volume = {20},
+ pages = {1581 - 1586},
+ number = {11},
+ doi = {DOI: 10.1016/0036-9748(86)90399-6},
+ issn = {0036-9748},
+ owner = {yj.ro},
+ timestamp = {2009.02.12},
+ url = {http://www.sciencedirect.com/science/article/B759T-48JCNSN-1YV/2/a3866fca2d50ef8c06f1088c78931e39}
+}
+
+@ARTICLE{Odegard1974,
+ author = {Odegard, Ben and Thompson, Anthony},
+ title = {Low temperature creep of Ti-6 Al-4 V},
+ journal = {Metallurgical and Materials Transactions B},
+ year = {1974},
+ volume = {5},
+ pages = {1207--1213},
+ number = {5},
+ month = may,
+ abstract = {Abstract Creep tests were conducted at 295 K on Ti-6 Al-4
+ V in the solution treated and aged (4 h at 815 K) condition, and
+ in the as-welded condition. Some aged specimens were tested after
+ pre-straining. Creep stresses ranged from 40 to 90 pct of the aged
+ material yield strength. Results showed that creep was of the primary
+ or transient kind in all cases, and was much greater in welded than
+ in aged material. In general, pre-strains reduced creep, although
+ a strain larger than 10-3 was needed to do this at the highest creep
+ stress. Activation areas A* were between 10 and 20 b2, and thus were
+ similar to tensile results on titanium and its alloys. The microstructural
+ rationale applied to Ti-5 Al-2.5 Sn in earlier work, based on the
+ character of dislocation sources, proved successful in understanding
+ the effects of prestrain in this work.},
+ owner = {yj.ro},
+ timestamp = {2009.04.27},
+ url = {http://dx.doi.org/10.1007/BF02644335}
+}
+
+@ARTICLE{Oh2009,
+ author = {Oh, Sang Ho and Legros, Marc and Kiener, Daniel and Dehm, Gerhard},
+ title = {In situ observation of dislocation nucleation and escape in a submicrometre
+ aluminium single crystal},
+ journal = {Nat Mater},
+ year = {2009},
+ volume = {8},
+ pages = {95--100},
+ number = {2},
+ month = feb,
+ comment = {10.1038/nmat2370},
+ issn = {1476-1122},
+ owner = {yj.ro},
+ publisher = {Nature Publishing Group},
+ timestamp = {2009.01.28},
+ url = {http://dx.doi.org/10.1038/nmat2370}
+}
+
+@ARTICLE{PARTRIDGE1964,
+ author = {PARTRIDGE, P. G.},
+ title = {Distribution of Twins around a Microhardness Indenter in Close-packed
+ Hexagonal Metals},
+ journal = {Nature},
+ year = {1964},
+ volume = {203},
+ pages = {634--635},
+ number = {4945},
+ month = aug,
+ comment = {10.1038/203634a0},
+ owner = {yj.ro},
+ timestamp = {2009.04.22},
+ url = {http://dx.doi.org/10.1038/203634a0}
+}
+
+@ARTICLE{Pochettino1992,
+ author = {A.A. Pochettino and N. Gannio and C.Vial Edwards and R. Penelle},
+ title = {Texture and pyramidal slip in Ti, Zr and their alloys},
+ journal = {Scripta Metallurgica et Materialia},
+ year = {1992},
+ volume = {27},
+ pages = {1859 - 1863},
+ number = {12},
+ doi = {DOI: 10.1016/0956-716X(92)90033-B},
+ issn = {0956-716X},
+ owner = {yj.ro},
+ timestamp = {2009.04.20},
+ url = {http://www.sciencedirect.com/science/article/B6TY3-48F4Y9W-DK/2/3aa6de3d1a288fe10992b4225b6ca3e9}
+}
+
+@ARTICLE{Ramesh2002,
+ author = {Ramesh, K.},
+ title = {Effects of high rates of loading on the deformation behavior and
+ failure mechanisms of hexagonal close-packed metals and alloys},
+ journal = {Metallurgical and Materials Transactions A},
+ year = {2002},
+ volume = {33},
+ pages = {927--935},
+ number = {3},
+ month = mar,
+ abstract = {Abstract A substantial amount of work has been performed
+ on the effect of high rates of loading on the deformation and failure
+ of fcc and bcc metals. In contrast, the influence of high strain
+ rates and temperature on the flow stress of hcp metals has received
+ relatively little attention, and the modes of dynamic failure of
+ these materials are poorly characterized. The low symmetry of these
+ materials and the development of twinning lead to a particularly
+ rich set of potential mechanisms for deformation and failure at high
+ rates. This article reviews results of high-strain-rate deformation
+ and dynamic failure studies on hcp metals, with a focus on titanium,
+ Ti-6Al-4V, and hafnium. Strain rates as high as 105},
+ owner = {yj.ro},
+ timestamp = {2009.01.22},
+ url = {http://dx.doi.org/10.1007/s11661-002-0162-x}
+}
+
+@ARTICLE{Rao1979,
+ author = {Y.Krishna Mohan Rao and V.Kutumba Rao and P.Rama Rao},
+ title = {Fracture mechanism maps for titanium},
+ journal = {Scripta Metallurgica},
+ year = {1979},
+ volume = {13},
+ pages = {851 - 856},
+ number = {9},
+ doi = {DOI: 10.1016/0036-9748(79)90173-X},
+ issn = {0036-9748},
+ owner = {yj.ro},
+ timestamp = {2009.02.04},
+ url = {http://www.sciencedirect.com/science/article/B759T-48JCMPY-1JC/2/7c54e81f2fd43c5999f9ac47b882cff0}
+}
+
+@ARTICLE{Salem2003,
+ author = {Ayman A. Salem and Surya R. Kalidindi and Roger D. Doherty},
+ title = {Strain hardening of titanium: role of deformation twinning},
+ journal = {Acta Materialia},
+ year = {2003},
+ volume = {51},
+ pages = {4225 - 4237},
+ number = {14},
+ abstract = {The purpose of this study is to investigate the role of deformation
+ twinning in the strain-hardening behavior of high purity, polycrystalline
+ [alpha]-titanium in a number of different deformation modes. Constant
+ strain rate tests were conducted on this material in simple compression,
+ plane-strain compression and simple shear, and the true stress ([sigma])-true
+ strain ([var epsilon]) responses were documented. From the measured
+ data, the strain hardening rates were numerically computed, normalized
+ by the shear modulus (G), and plotted against both normalized stress
+ and [var epsilon]. These normalized strain hardening plots exhibited
+ three distinct stages of strain hardening that were similar to those
+ observed in previous studies on low stacking fault energy fcc metals
+ (e.g. 70/30 brass) in which deformation twinning has been known to
+ play an important role. Optical microscopy and Orientation imaging
+ microscopy were conducted on samples deformed to different strain
+ levels in the various deformation paths. It was found that the onset
+ of deformation twinning correlated with a sudden increase in strain
+ hardening rate in compression tests. The falling strain hardening
+ rate correlated with saturation in the twin volume fraction. In shear
+ testing a much lower rate of strain hardening was found, at all strains,
+ and this correlated with a lower density of deformation twinning.},
+ doi = {DOI: 10.1016/S1359-6454(03)00239-8},
+ issn = {1359-6454},
+ keywords = {Titanium},
+ url = {http://www.sciencedirect.com/science/article/B6TW8-48VTB43-2/2/950c31f7658f3f4c0f4d9c8d67e54da4}
+}
+
+@ARTICLE{Salem2006,
+ author = {Salem, A. and Kalidindi, S. and Doherty, R. and Semiatin, S.},
+ title = {Strain hardening due to deformation twinning in alpha-titanium:
+ Mechanisms},
+ journal = {Metallurgical and Materials Transactions A},
+ year = {2006},
+ volume = {37},
+ pages = {259--268},
+ number = {1},
+ month = jan,
+ abstract = {Abstract Novel experiments were conducted to elucidate
+ the effect of deformation twinning on the mechanical response of
+ high-purity α-titanium deformed at room temperature. Orientation-imaging
+ microscopy (OIM), microhardness, and nanohardness evaluations were
+ employed in conjunction with optical microscopy and quasi-static
+ compression testing to obtain insight into the deformation mechanisms.
+ Hardness measurements revealed that the newly formed deformation
+ twins were harder than the matrix. This observation is perhaps the
+ first experimental evidence for the Basinski mechanism for hardening
+ associated with twinning, arising from the transition of glissile
+ dislocations to a sessile configuration upon the lattice reorientation
+ by twinning shear. This work also provided direct evidence for two
+ competing effects of deformation twinning on the overall stress-strain
+ response: (1) hardening via both a reduction of the effective slip
+ length (Hall-Petch effect) and an increase in the hardness of twinned
+ regions (Basinski mechanism) and (2) softening due to the lattice
+ reorientation of the twinned regions.},
+ owner = {yj.ro},
+ timestamp = {2009.01.22},
+ url = {http://dx.doi.org/10.1007/s11661-006-0171-2}
+}
+
+@ARTICLE{Salem2005,
+ author = {A.A. Salem and S.R. Kalidindi and S.L. Semiatin},
+ title = {Strain hardening due to deformation twinning in [alpha]-titanium:
+ Constitutive relations and crystal-plasticity modeling},
+ journal = {Acta Materialia},
+ year = {2005},
+ volume = {53},
+ pages = {3495 - 3502},
+ number = {12},
+ abstract = {The mechanisms governing twin-induced strain hardening of high-purity
+ [alpha]-titanium at room temperature were incorporated into constitutive
+ laws to describe the evolution of both twin and slip resistance due
+ to deformation twinning. The proposed equations were incorporated
+ in a Taylor-type crystal plasticity model to predict mechanical behavior
+ and texture evolution for different deformation paths. Model predictions
+ for the overall stress-strain response and texture evolution compared
+ well with the experimental results. Specifically, the model captured
+ the three stages of strain hardening for uniaxial-compression and
+ plane-strain-compression testing of [alpha]-titanium. In addition,
+ predicted texture evolution due to the reorientation of twinned area
+ showed excellent agreement with the observations. These findings
+ proved the necessity of incorporating twinning and its associated
+ hardening mechanisms in realistic constitutive descriptions to account
+ for anisotropic strain-hardening behavior and texture evolution in
+ materials that deform by both slip and twinning.},
+ doi = {DOI: 10.1016/j.actamat.2005.04.014},
+ issn = {1359-6454},
+ keywords = {Texture},
+ owner = {yj.ro},
+ timestamp = {2009.01.22},
+ url = {http://www.sciencedirect.com/science/article/B6TW8-4G94J1C-2/2/9745b826d50791e36598ba02e5b0d4e1}
+}
+
+@ARTICLE{Santhanam1970,
+ author = {A. T. Santhanam and R. E. Reed-Hill},
+ title = {Work hardening peaks in [alpha]-titanium},
+ journal = {Scripta Metallurgica},
+ year = {1970},
+ volume = {4},
+ pages = {529 - 531},
+ number = {7},
+ doi = {DOI: 10.1016/0036-9748(70)90010-4},
+ issn = {0036-9748},
+ owner = {yj.ro},
+ timestamp = {2009.03.12},
+ url = {http://www.sciencedirect.com/science/article/B759T-48J027T-DJ/2/ca4f3b94f041545b1151e6f45505ffec}
+}
+
+@ARTICLE{Schroeter2003,
+ author = {Brian M. Schroeter and David L. McDowell},
+ title = {Measurement of deformation fields in polycrystalline OFHC copper},
+ journal = {International Journal of Plasticity},
+ year = {2003},
+ volume = {19},
+ pages = {1355 - 1376},
+ number = {9},
+ doi = {DOI: 10.1016/S0749-6419(02)00040-2},
+ issn = {0749-6419},
+ keywords = {Polycrystalline materials},
+ owner = {yj.ro},
+ timestamp = {2009.04.09},
+ url = {http://www.sciencedirect.com/science/article/B6TWX-46YXJ7T-6/2/b748033823db97fbbe1b560258cbdb1b}
+}
+
+@ARTICLE{Scrivens2007,
+ author = {Scrivens, W. and Luo, Y. and Sutton, M. and Collette, S. and Myrick,
+ M. and Miney, P. and Colavita, P. and Reynolds, A. and Li, X.},
+ title = {Development of Patterns for Digital Image Correlation Measurements
+ at Reduced Length Scales},
+ journal = {Experimental Mechanics},
+ year = {2007},
+ volume = {47},
+ pages = {63--77},
+ number = {1},
+ month = feb,
+ abstract = {Abstract Methods for patterning metal thin films at the
+ microscale and nanoscale by applying the patterns to metallic and
+ polymeric materials for use in shape and deformation measurements
+ in a scanning electron microsope (SEM) or other high magnification
+ imaging system are described. In one approach, thin films of metallic
+ materials (e.g., Au, Ag, Cu, and Cr) are applied to a variety of
+ substrates. The coated samples are then placed into a reaction vessel,
+ where the specimens are heated and exposed to a nitrogen atmosphere
+ saturated with selected volatile chemicals. This process results
+ in nano-scale remodeling of the metallic films, thereby affording
+ high contrast random patterns with different morphologies. In a second
+ approach, thin films of metallic materials, including gold and silver,
+ also have been applied using a simplified UV photolithographic method
+ requiring a minimum amount of laboratory preparation. Using selected
+ substrates, both methods have been used successfully to transfer
+ patterns onto polymeric and metallic materials ranging from 50–500
+ nanometers with chemical vapor rearrangement and 2 to 20 microns
+ with UV photolithography, providing a pattern that can be used with
+ digital image correlation to quantify both the surface profile and
+ also surface deformations at reduced length scales.},
+ owner = {yj.ro},
+ timestamp = {2009.03.25},
+ url = {http://dx.doi.org/10.1007/s11340-006-5869-y}
+}
+
+@ARTICLE{Semiatin1985,
+ author = {Semiatin, S. and Ghosh, A. and Jonas, J.},
+ title = {A simplified numerical analysis of the sheet tensile test},
+ journal = {Metallurgical and Materials Transactions A},
+ year = {1985},
+ volume = {16},
+ pages = {2291--2298},
+ number = {12},
+ month = dec,
+ abstract = {Abstract A simplified numerical analysis of the tensile
+ test for sheet metal specimens is presented with particular emphasis
+ on the relationship between plastic flow parameters and tensile ductility.
+ This analysis is based on a one-dimensional, “long wavelength?
+ approximation in which the stress state is assumed to be uniaxial
+ throughout the deformation. To account for the influence of necking
+ and triaxiality on the flow behavior, however, an extended Bridgman
+ correction for sheet specimens deformed under conditions of plane
+ stress is employed. The governing equilibrium equation and boundary
+ conditions are discretized to obtain computer solutions. Engineering
+ stress-strain curves and strain distributions in deformed tensile
+ specimens are compared to results from a more complex formulation
+ previously published in the technical literature and show good agreement
+ with it.},
+ owner = {yj.ro},
+ timestamp = {2009.03.10},
+ url = {http://dx.doi.org/10.1007/BF02670429}
+}
+
+@ARTICLE{Song1995,
+ author = {S. G. Song and G. T. Gray},
+ title = {Structural interpretation of the nucleation and growth of deformation
+ twins in Zr and Ti--I. Application of the coincidence site lattice
+ (CSL) theory to twinning problems in h.c.p. structures},
+ journal = {Acta Metallurgica et Materialia},
+ year = {1995},
+ volume = {43},
+ pages = {2325 - 2337},
+ number = {6},
+ abstract = {A step-wise nucleation and growth mechanism based on the coincidence
+ site lattice (CSL) theory is proposed for deformation twinning in
+ h.c.p. structures. Lattice transformation during twinning is accomplished
+ by a coordinated movement of a large number of atoms between two
+ lattice match planes from the matrix to twin positions rather than
+ a layer by layer movement through twinning dislocations as proposed
+ for twinning dislocation theories. The sidewise propagation and thickening
+ of a twin lamella proceeds in a step-wise manner with lattice match
+ planes being the coherent boundaries between the matrix and twins.
+ This model predicts that twinning in h.c.p. lattices can occur at
+ a high velocity close to the sound speed, which is impossible according
+ to twinning dislocation theories. The proposed mechanism is also
+ consistent with other observations such as lack of critical-resolved-shear-stress
+ for twinning, emissary dislocations, and insensitivity to temperature.
+ Dislocation reactions may be involved in twinning although they are,
+ at high stresses, not required.},
+ doi = {DOI: 10.1016/0956-7151(94)00433-1},
+ issn = {0956-7151},
+ owner = {yj.ro},
+ timestamp = {2009.01.22},
+ url = {http://www.sciencedirect.com/science/article/B7599-49FY37T-9M/2/74a19901a871a83da911616d5f2993da}
+}
+
+@ARTICLE{Song1995a,
+ author = {S. G. Song and G. T. Gray},
+ title = {Structural interpretation of the nucleation and growth of deformation
+ twins in Zr and Ti--II. Tem study of twin morphology and defect reactions
+ during twinning},
+ journal = {Acta Metallurgica et Materialia},
+ year = {1995},
+ volume = {43},
+ pages = {2339 - 2350},
+ number = {6},
+ abstract = {A TEM study of mechanical twinning in Ti and Zr was performed. A large
+ number of [0001]-dislocations which are rarely seen in the matrix,
+ and a new type of stacking fault were found within deformation twins
+ in both materials. Matrix dislocations were observed to actively
+ interact with the tips of twin embryos and step ledges of growing
+ twin lamellae. Twin embryos bounded by straight coherent and inclined
+ semi-coherent boundaries were observed. These results as well as
+ the morphological variation of twin lamellae during deformation do
+ not agree with twinning dislocation theories but support a step-wise
+ nucleation and growth mechanism proposed for deformation twinning
+ in h.c.p. structures. Extended discussions are provided to address
+ unanswered questions in the literature concerning deformation twinning.},
+ doi = {DOI: 10.1016/0956-7151(94)00434-X},
+ issn = {0956-7151},
+ owner = {yj.ro},
+ timestamp = {2009.01.22},
+ url = {http://www.sciencedirect.com/science/article/B7599-49FY37T-9N/2/8d2f35458aeb7062e85e4b4456a953c7}
+}
+
+@ARTICLE{Stanford2008,
+ author = {Stanford, N. and Carlson, U. and Barnett, M.R.},
+ title = {Deformation Twinning and the Hall–Petch Relation in Commercial
+ Purity Ti},
+ journal = {Metallurgical and Materials Transactions A},
+ year = {2008},
+ volume = {39},
+ pages = {934--944},
+ number = {4},
+ month = apr,
+ abstract = {Abstract The effect of grain size and deformation temperature
+ on the behavior of wire-drawn α-Ti during compression has been examined.
+ At strains of 0.3, the flow stress exhibited a negative Hall–Petch
+ slope. This is proposed to result from the prevalence of twinning
+ during the compressive deformation. Electron backscattered diffraction
+ revealed that $$ \{ 10\ifmmode\expandafter\bar\else\expandafter\=\fi{1}2\}
+ $$ was the most prolific twin type across all the deformation temperatures
+ and grain sizes examined. Of the twinning modes observed, $$ \{ 11\ifmmode\expandafter\bar\else\expandafter\=\fi{2}2\}
+ $$ twinning was the most sensitive to the grain size and deformation
+ temperature. The range of morphologies exhibited by deformation twins
+ is also described.},
+ owner = {yj.ro},
+ timestamp = {2009.05.04},
+ url = {http://dx.doi.org/10.1007/s11661-007-9442-9}
+}
+
+@ARTICLE{Stroh1954,
+ author = {Stroh, A. N.},
+ title = {The Formation of Cracks as a Result of Plastic Flow},
+ journal = {Proceedings of the Royal Society of London. Series A. Mathematical
+ and Physical Sciences},
+ year = {1954},
+ volume = {223},
+ pages = {404--414},
+ number = {1154},
+ date = {May 6, 1954},
+ owner = {yj.ro},
+ timestamp = {2009.03.18},
+ url = {http://rspa.royalsocietypublishing.org/content/223/1154/404.abstract}
+}
+
+@ARTICLE{Sun2001,
+ author = {Q. Y. Sun and X. P. Song and H. C. Gu},
+ title = {Cyclic deformation behaviour of commercially pure titanium at cryogenic
+ temperature},
+ journal = {International Journal of Fatigue},
+ year = {2001},
+ volume = {23},
+ pages = {187 - 191},
+ number = {3},
+ doi = {DOI: 10.1016/S0142-1123(00)00089-X},
+ issn = {0142-1123},
+ keywords = {Titanium},
+ owner = {yj.ro},
+ timestamp = {2009.04.20},
+ url = {http://www.sciencedirect.com/science/article/B6V35-42992CH-1/2/4083b6ebaa36adb6aa78ccbfb126ae29}
+}
+
+@ARTICLE{Sutton2007,
+ author = {Sutton, M. and Li, N. and Garcia, D. and Cornille, N. and Orteu,
+ J. and McNeill, S. and Schreier, H. and Li, X. and Reynolds, A.},
+ title = {Scanning Electron Microscopy for Quantitative Small and Large Deformation
+ Measurements Part II: Experimental Validation for Magnifications
+ from 200 to 10,000},
+ journal = {Experimental Mechanics},
+ year = {2007},
+ volume = {47},
+ pages = {789--804},
+ number = {6},
+ month = dec,
+ abstract = {Abstract A combination of drift distortion removal and
+ spatial distortion removal are performed to correct Scanning Electron
+ Microscope (SEM) images at both �200 and �10,000 magnification.
+ Using multiple, time-spaced images and in-plane rigid body motions
+ to extract the relative displacement field throughout the imaging
+ process, results from numerical simulations clearly demonstrate that
+ the correction procedures successfully remove both drift and spatial
+ distortions with errors on the order of �0.02 pixels. A series
+ of 2D translation and tensile loading experiments are performed in
+ an SEM for magnifications at �200 and �10,000, where both the
+ drift and spatial distortion removal methods described above are
+ applied to correct the digital images and improve the accuracy of
+ measurements obtained using 2D-DIC. Results from translation and
+ loading experiments indicate that (a) the fully corrected displacement
+ components have nearly random variability with standard deviation
+ of 0.02 pixels (≈25 nm at �200 and ≈0.5 nm at
+ �10,000) in each displacement component and (b) the measured strain
+ fields are unbiased and in excellent agreement with expected results,
+ with a spatial resolution of 43 pixels (≈54 μm at �200
+ and ≈1.1 μm at �10,000) and a standard deviation on the
+ order of 6 � 10−5 for each component.},
+ owner = {yj.ro},
+ timestamp = {2009.03.25},
+ url = {http://dx.doi.org/10.1007/s11340-007-9041-0}
+}
+
+@ARTICLE{Sutton2007a,
+ author = {Sutton, M. and Li, N. and Joy, D. and Reynolds, A. and Li, X.},
+ title = {Scanning Electron Microscopy for Quantitative Small and Large Deformation
+ Measurements Part I: SEM Imaging at Magnifications from 200 to 10,000},
+ journal = {Experimental Mechanics},
+ year = {2007},
+ volume = {47},
+ pages = {775--787},
+ number = {6},
+ month = dec,
+ abstract = {Abstract A series of baseline displacement measurements
+ have been obtained using 2D Digital Image Correlation (2D-DIC) and
+ images from Scanning Electron Microscopes (SEM). Direct correlation
+ of subsets from a reference image to subsets in a series of uncorrected
+ images is used to identify the presence of non-stationary step-changes
+ in the measured displacements. Using image time integration and recently
+ developed approaches to correct residual drift and spatial distortions
+ in recorded images, results clearly indicate that the corrected SEM
+ images can be used to extract deformations with displacement accuracy
+ of �0.02 pixels (1 nm at magnification of 10,000) and mean
+ value strain measurements that are consistent with independent estimates
+ and have point-to-point strain variability of �1.5 � 10−4.},
+ owner = {yj.ro},
+ timestamp = {2009.03.25},
+ url = {http://dx.doi.org/10.1007/s11340-007-9042-z}
+}
+
+@ARTICLE{Takahashi2009,
+ author = {Yoshimasa Takahashi and Masaki Tanaka and Kenji Higashida and Hiroshi
+ Noguchi},
+ title = {Hydrogen-induced slip localization around a quasi-brittle fatigue
+ crack observed by high-voltage electron microscopy},
+ journal = {Scripta Materialia},
+ year = {2009},
+ volume = {61},
+ pages = {145 - 148},
+ number = {2},
+ doi = {DOI: 10.1016/j.scriptamat.2009.03.020},
+ issn = {1359-6462},
+ keywords = {TEM},
+ owner = {yj.ro},
+ timestamp = {2009.05.20},
+ url = {http://www.sciencedirect.com/science/article/B6TY2-4VW558T-1/2/8155f0b3726238215bc70e8372a4fa06}
+}
+
+@ARTICLE{Tan1998,
+ author = {Tan, X. and Gu, H. and Laird, C. and Munroe, N.},
+ title = {Cyclic deformation behavior of high-purity titanium single crystals:
+ Part I. Orientation dependence of stress-strain response},
+ journal = {Metallurgical and Materials Transactions A},
+ year = {1998},
+ volume = {29},
+ pages = {507--512},
+ number = {2},
+ month = feb,
+ abstract = {Abstract Randomly oriented single crystals of high-purity
+ titanium were prepared by strain annealing and were subjected to
+ multiple-step fatigue testing under strain-controlled conditions,
+ in order to determine their cyclic stress-strain curves (CSSCs).
+ These were found to fall into three groups, depending on orientation
+ and the extent of slip and twinning. For those crystals oriented
+ for single prismatic slip, a plateau was observed in the CSSCs, persistent
+ slip bands (PSBs) occurred, and the plateau stress was 38 MPa. In
+ a second group, oriented for prismatic slip but for which cross-slip
+ and twinning was favored, the plateau was suppressed and the flow
+ stresses were higher. In a third group, connected with orientations
+ on the borders of the unit triangle, extensive hardening occurred,
+ the CSSCs were steep, and there were multiple cases of slip and twinning.
+ The results are interpreted in terms of maps in the stereographic
+ projection recording the Schmid factors for the various deformation
+ modes.},
+ owner = {yj.ro},
+ timestamp = {2009.04.23},
+ url = {http://dx.doi.org/10.1007/s11661-998-0131-0}
+}
+
+@ARTICLE{Tanaka1972,
+ author = {T Tanaka and H Conrad},
+ title = {Deformation kinetics for {101[combining macron]0}<112[combining macron]0>
+ slip in titanium single crystals below 0.4Tm},
+ journal = {Acta Metallurgica},
+ year = {1972},
+ volume = {20},
+ pages = {1019 - 1029},
+ number = {8},
+ abstract = {The deformation kinetics for {101[combining macron]0}<112[combining
+ macron]0> slip in zone refined titanium single crystals of ~0.05
+ at.% Oeq total interstitial content were investigated in tension
+ over the temperature range of 4.2-650K. Using the thermally activated
+ approach, values of the usual activation parameters were determined
+ and found to be in good agreement with those reported previously
+ for polycrystalline titanium with total interstitial contents ranging
+ from 0.05 to 1 at.% Oeq. This agreement supports the earlier conclusion
+ that the deformation kinetics in polycrystalline titanium are associated
+ with slip on the first-order prism planes. Also, the present data
+ support the earlier proposal that the rate controlling dislocation
+ mechanism during the low temperature deformation of titanium is thermally
+ activated overcoming of interstitial solute obstacles. Comparison
+ of the single crystal results with those on polycrystals yielded
+ a value of 5 for the Taylor factor relating resolved shear stress
+ to the tensile stress in titanium polycrystals.},
+ doi = {DOI: 10.1016/0001-6160(72)90136-8},
+ issn = {0001-6160},
+ owner = {yj.ro},
+ timestamp = {2009.01.22},
+ url = {http://www.sciencedirect.com/science/article/B7598-48KNY87-WK/2/941561542f234ab354d026145908eba2}
+}
+
+@ARTICLE{Tonda2002,
+ author = {Tonda, Hideki and Ando, Shinji},
+ title = {Effect of temperature and shear direction on yield stress by 11},
+ journal = {Metallurgical and Materials Transactions A},
+ year = {2002},
+ volume = {33},
+ pages = {831--836},
+ number = {3},
+ month = mar,
+ abstract = {Abstract The yield shear stress τ},
+ owner = {yj.ro},
+ timestamp = {2009.02.12},
+ url = {http://dx.doi.org/10.1007/s11661-002-0152-z}
+}
+
+@ARTICLE{Tong2005,
+ author = {Tong, Wei and Tao, Hong and Zhang, Nian and Jiang, Xiquan and Marya,
+ Manuel and Hector, Louis and Gayden, Xiaohong},
+ title = {Deformation and fracture of miniature tensile bars with resistance-spot-weld
+ microstructures},
+ journal = {Metallurgical and Materials Transactions A},
+ year = {2005},
+ volume = {36},
+ pages = {2651--2669},
+ number = {10},
+ month = oct,
+ abstract = {Abstract Plastic deformation of miniature tensile bars
+ generated from dual-phase steel weld microstructures (i.e., fusion
+ zone, heat-affected zone, and base material) was investigated up
+ to final rupture failure. Uniaxial tensile true stress-strain curves
+ beyond diffuse necking were obtained with a novel strain-mapping
+ technique based on digital image correlation (DIC). Key microstructural
+ features (including defects) in each of these three metallurgical
+ zones were examined to explore the material influence on the plastic
+ deformation and failure behavior. For weld fusion zones with minimal
+ defects, diffuse necking was found to begin at 6 pct strain and continue
+ up to 55 to 80 pct strain. The flow stresses of the weld fusion zones
+ were at least twice those of the base material, and fracture strains
+ exceeded 100 pct for both materials. The heat-affected zones exhibited
+ a range of complex deformation behaviors, as expected from their
+ microstructural variety. Only those fusion zones with substantial
+ defects (e.g., shrinkage voids, cracks, and contaminants) failed
+ prematurely by edge cracking, as signaled by their highly irregular
+ strain maps.},
+ owner = {yj.ro},
+ timestamp = {2009.03.25},
+ url = {http://dx.doi.org/10.1007/s11661-005-0263-4}
+}
+
+@ARTICLE{Ungar2008,
+ author = {T. Ungr and M.G. Glavicic and L. Balogh and K. Nyilas and A.A. Salem
+ and G. Ribrik and S.L. Semiatin},
+ title = {The use of X-ray diffraction to determine slip and twinning activity
+ in commercial-purity (CP) titanium},
+ journal = {Materials Science and Engineering: A},
+ year = {2008},
+ volume = {493},
+ pages = {79 - 85},
+ number = {1-2},
+ note = {Mechanical Behavior of Nanostructured Materials, a Symposium Held
+ in Honor of Carl Koch at the TMS Annual Meeting 2007, Orlando, Florida},
+ doi = {DOI: 10.1016/j.msea.2007.06.096},
+ issn = {0921-5093},
+ keywords = {Titanium},
+ owner = {yj.ro},
+ timestamp = {2009.03.25},
+ url = {http://www.sciencedirect.com/science/article/B6TXD-4RBYD2M-5/2/1dcd434111b67d44cb6d074cd4d9e544}
+}
+
+@ARTICLE{Wang2009,
+ author = {L. Wang and S.R. Daniewicz and M.F. Horstemeyer and S. Sintay and
+ A.D. Rollett},
+ title = {Three-dimensional finite element analysis using crystal plasticity
+ for a parameter study of fatigue crack incubation in a 7075 aluminum
+ alloy},
+ journal = {International Journal of Fatigue},
+ year = {2009},
+ volume = {31},
+ pages = {659 - 667},
+ number = {4},
+ abstract = {Three-dimensional finite element analysis of a bicrystal using a crystal
+ plasticity constitutive theory was performed to compute the maximum
+ plastic shear strain range in the matrix, at the particle/matrix
+ interface, and at the bicrystal boundary. Using the finite element
+ analysis results, a design of experiments (DOE) technique was employed
+ to understand and quantify the effects of seven parameters on fatigue
+ crack incubation: applied displacement, load ratio, particle modulus,
+ the number of initially active slip systems, the relative crystallographic
+ misorientation at the grain boundary, the particle aspect ratio,
+ and the normalized particle size. The simulations clearly showed
+ that the applied displacement is the most influential parameter.
+ In most cases, particles were found to be more significant than bicrystal
+ boundaries for incubation. The number of initially active slip systems,
+ the particle aspect ratio, and the normalized particle size showed
+ some influences on fatigue incubation. The particle modulus was the
+ least influential parameter.},
+ doi = {DOI: 10.1016/j.ijfatigue.2008.03.022},
+ issn = {0142-1123},
+ keywords = {Crystal plasticity},
+ owner = {yj.ro},
+ timestamp = {2009.05.04},
+ url = {http://www.sciencedirect.com/science/article/B6V35-4S4TNY3-1/2/19b9e03f31d80e2c188e041dade66004}
+}
+
+@ARTICLE{Williams1968,
+ author = {Williams, J. C. and Blackburn, M. J.},
+ title = {The identification of a Non-Basal slip vector in titanium and Titanium-Aluminum
+ alloys},
+ journal = {Physica Status Solidi (b)},
+ year = {1968},
+ volume = {25},
+ pages = {K1-K3},
+ number = {1},
+ owner = {yj.ro},
+ timestamp = {2009.02.12},
+ url = {http://dx.doi.org/10.1002/pssb.19680250146}
+}
+
+@ARTICLE{Wu2007,
+ author = {Xianping Wu and Surya R. Kalidindi and Carl Necker and Ayman A. Salem},
+ title = {Prediction of crystallographic texture evolution and anisotropic
+ stress-strain curves during large plastic strains in high purity
+ [alpha]-titanium using a Taylor-type crystal plasticity model},
+ journal = {Acta Materialia},
+ year = {2007},
+ volume = {55},
+ pages = {423 - 432},
+ number = {2},
+ abstract = {A new Taylor-type polycrystalline model has been developed to simulate
+ the evolution of crystallographic texture and the anisotropic stress-strain
+ response during large plastic deformation of high purity [alpha]-titanium
+ at room temperature. Crystallographic slip, deformation twinning
+ and slip inside twinned regions were all considered as contributing
+ mechanisms for the plastic strain in the model. This was accomplished
+ by treating the dominant twin systems in a given crystal as independent
+ grains once the total twin volume fraction in that crystal reached
+ a predetermined saturation value. The newly formed grains were allowed
+ to independently undergo further slip and the concomitant lattice
+ rotation, but further twinning was prohibited. New descriptions have
+ been established for slip and twin hardening and the complex coupling
+ between them. Good predictions were obtained for the overall anisotropic
+ stress-strain response and texture evolution in three different monotonic
+ deformation paths on annealed, initially textured samples of high
+ purity [alpha]-titanium.},
+ doi = {DOI: 10.1016/j.actamat.2006.08.034},
+ issn = {1359-6454},
+ keywords = {Twinning},
+ owner = {yj.ro},
+ timestamp = {2009.01.22},
+ url = {http://www.sciencedirect.com/science/article/B6TW8-4M63RXJ-6/2/b13d16ac5a205e5218141b1a25b85a27}
+}
+
+@ARTICLE{Xiao2005,
+ author = {Lin Xiao},
+ title = {Twinning behavior in the Ti-5at.% Al single crystals during cyclic
+ loading along [0001]},
+ journal = {Materials Science and Engineering A},
+ year = {2005},
+ volume = {394},
+ pages = {168 - 175},
+ number = {1-2},
+ doi = {DOI: 10.1016/j.msea.2004.11.039},
+ issn = {0921-5093},
+ keywords = {Titanium single crystal},
+ owner = {yj.ro},
+ timestamp = {2009.04.20},
+ url = {http://www.sciencedirect.com/science/article/B6TXD-4F60NFD-3/2/4a198451bf43350ecccd7a9f36b12608}
+}
+
+@ARTICLE{Xiao2003,
+ author = {Xiao, L. and Umakoshi, Y.},
+ title = {Cyclic deformation behaviour and saturation bundle structure in Ti–5 at.% Al
+ single crystals deforming by single prism slip},
+ journal = {Philosophical Magazine},
+ year = {2003},
+ volume = {83},
+ pages = {3407--3426},
+ number = {30},
+ owner = {yj.ro},
+ publisher = {Taylor \& Francis},
+ timestamp = {2009.04.22},
+ url = {http://www.informaworld.com/10.1080/14786430310001603454}
+}
+
+@ARTICLE{Xiao2002,
+ author = {Xiao, L. and Umakoshi, Y.},
+ title = {Cyclic deformation behaviour and dislocation structure of Ti-5 at.%
+ Al single crystals oriented for double prism slip},
+ journal = {Philosophical Magazine A},
+ year = {2002},
+ volume = {82},
+ pages = {2379--2396},
+ number = {12},
+ owner = {yj.ro},
+ publisher = {Taylor \& Francis},
+ timestamp = {2009.04.22},
+ url = {http://www.informaworld.com/10.1080/01418610208240042}
+}
+
+@ARTICLE{Yoo2002,
+ author = {Yoo, M. and Morris, J. and Ho, K. and Agnew, S.},
+ title = {Nonbasal deformation modes of HCP metals and alloys: Role of dislocation
+ source and mobility},
+ journal = {Metallurgical and Materials Transactions A},
+ year = {2002},
+ volume = {33},
+ pages = {813--822},
+ number = {13},
+ month = mar,
+ abstract = {Abstract A review is presented on the role of dislocation
+ cores and planar faults in activating the nonbasal deformation modes,
+ <c + a> pyramidal slip and deformation twinning, in hcp metals
+ and alloys and in D019 intermetallic compounds. Material-specific
+ mechanical behavior arises from a competition between alternate defect
+ structures that determine the deformation modes. We emphasize the
+ importance of accurate atomistic modeling of these defects, going
+ beyond simple interatomic energy models. Recent results from both
+ experiments and theory are summarized by discussing specific examples
+ of Ti and Mg single crystals; Ti-, Zr-, and Mg-base alloys; and Ti3Al
+ ordered alloys. Remaining key issues and directions for future research
+ are also discussed.},
+ owner = {yj.ro},
+ timestamp = {2009.01.22},
+ url = {http://dx.doi.org/10.1007/s11661-002-1013-5}
+}
+
+@ARTICLE{Yoo1991,
+ author = {Yoo, M. H. and Lee, J. K.},
+ title = {Deformation twinning in h.c.p. metals and alloys},
+ journal = {Philosophical Magazine A},
+ year = {1991},
+ volume = {63},
+ pages = {987--1000},
+ number = {5},
+ issn = {0141-8610},
+ owner = {yj.ro},
+ publisher = {Taylor \& Francis},
+ timestamp = {2009.01.22},
+ url = {http://www.informaworld.com/10.1080/01418619108213931}
+}
+
+@ARTICLE{Zeng2009,
+ author = {Zhipeng Zeng and Yanshu Zhang and Stefan Jonsson},
+ title = {Microstructure and texture evolution of commercial pure titanium
+ deformed at elevated temperatures},
+ journal = {Materials Science and Engineering: A},
+ year = {2009},
+ volume = {513-514},
+ pages = {83 - 90},
+ doi = {DOI: 10.1016/j.msea.2009.01.065},
+ issn = {0921-5093},
+ keywords = {Commercial pure titanium},
+ owner = {yj.ro},
+ timestamp = {2009.05.04},
+ url = {http://www.sciencedirect.com/science/article/B6TXD-4VJ4WS3-1/2/b0fdaa847bc30ee8800b21baf24a500d}
+}
+
+@ARTICLE{Zhang2007,
+ author = {M. Zhang and J. Zhang and D.L. McDowell},
+ title = {Microstructure-based crystal plasticity modeling of cyclic deformation
+ of Ti-6Al-4V},
+ journal = {International Journal of Plasticity},
+ year = {2007},
+ volume = {23},
+ pages = {1328 - 1348},
+ number = {8},
+ doi = {DOI: 10.1016/j.ijplas.2006.11.009},
+ issn = {0749-6419},
+ keywords = {Crystal plasticity},
+ owner = {yj.ro},
+ timestamp = {2009.03.18},
+ url = {http://www.sciencedirect.com/science/article/B6TWX-4MY0TTV-1/2/ec2eaa204c6c095020809303280674e3}
+}
+
+@ARTICLE{Zhang1997,
+ author = {Zhang, Z. and Gu, H. and Tan, X.},
+ title = {Influence of low cycle fatigue on deformation twins in commercial
+ purity titanium},
+ journal = {Journal of Materials Science Letters},
+ year = {1997},
+ volume = {17},
+ pages = {211--214},
+ number = {3},
+ month = feb,
+ owner = {yj.ro},
+ timestamp = {2009.04.17},
+ url = {http://dx.doi.org/10.1023/A:1006532227698}
+}
+
+@ARTICLE{Zhou2008,
+ author = {A.G. Zhou and S. Basu and M.W. Barsoum},
+ title = {Kinking nonlinear elasticity, damping and microyielding of hexagonal
+ close-packed metals},
+ journal = {Acta Materialia},
+ year = {2008},
+ volume = {56},
+ pages = {60 - 67},
+ number = {1},
+ doi = {DOI: 10.1016/j.actamat.2007.08.050},
+ issn = {1359-6454},
+ keywords = {Compression test},
+ owner = {yj.ro},
+ timestamp = {2009.04.17},
+ url = {http://www.sciencedirect.com/science/article/B6TW8-4R2H229-1/2/412f7e7fa0b2d6534d30cd704f3187db}
+}
+
+@ARTICLE{Aaob1975,
+ author = {Šob, M. and Kratochvíl, J. and Kroupa, F.},
+ title = {Theory of strengthening of alpha titanium by interstitial solutes},
+ journal = {Czechoslovak Journal of Physics},
+ year = {1975},
+ volume = {25},
+ pages = {872--890},
+ number = {8},
+ month = aug,
+ abstract = {It is assumed that the core structure of screw dislocations in the
+ h.c.p. lattice of a-Ti can be described by a sessile splitting on
+ the prism plane and on the first order pyramidal plane simultaneously
+ and that slip can proceed after its transformation into a glissile
+ configuration on the prism plane. The strengthening by interstitial
+ solutes O, N, C is explained by their impeding role in these sessile-glissile
+ transformations. A good agreement between the theoretical temperature
+ dependences of the effective stress for different interstitial content
+ and the experimental values can be reached if the effect of impurities
+ on the stacking fault energies is also taken into account. The similarity
+ between the role of screw dislocations in the low temperature deformation
+ of h.c.p. metals with more slip systems operating and of b.c.c. metals
+ is stressed.},
+ owner = {yj.ro},
+ timestamp = {2009.03.25},
+ url = {http://dx.doi.org/10.1007/BF01589305}
+}
+
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