An Advanced Perspective on Twin Growth and Slip in NiTi Huseyin - - PowerPoint PPT Presentation
University of Illinois at Urbana Champaign An Advanced Perspective on Twin Growth and Slip in NiTi Huseyin Sehitoglu, Tawhid Ezaz, H.J.Maier Department of Mechanical Science & Engineering University of Illinois, Urbana University of
University of Illinois at Urbana Champaign
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Huseyin Sehitoglu, Tawhid Ezaz, H.J.Maier Department of Mechanical Science & Engineering University of Illinois, Urbana University of Paderborn, Germany ICOMAT-2011, September 6, 2011 Funded by NSF- Division of Materials Research
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University of Illinois at Urbana Champaign
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University of Illinois at Urbana Champaign
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( ) mJ m γ 211 6
x
u a ⎡ ⎤ ⎣ ⎦
Perfect fcc Unstable Stable stacking fault
is linked to Dislocation Nucleation
GSFE GPFE
211 6
x
u a ⎡ ⎤ ⎣ ⎦
is the energy barrier to
during Twin Nucleation
us
γ
isf
γ
UT
γ
2layertwin
γ
TM
γ
us
γ
is the barrier to overcome during Twin growth
TM
γ
Unstable Twin fault 2 layer twin
UT
γ
FCC is the Simplest!
A B C A A B C B C A B C A A B C A A B C B C A B C A B C B A B A C A B C A B
b b/2 1.5b 2b
[111]
[211]
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Adapted from Ishida et al.,2006
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Liu, ¡Van ¡Humbeeck, ¡46, ¡1998, ¡Acta ¡Mat. ¡ Xie,Liu,84,3497,2004, ¡Acta ¡Mat. ¡
Phenomenological Theory provides twinning plane to be irrational (0.7205 1 1) Experimentally evidence of rational ledges and steps
(1 1 1)
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Ezaz -Sehitoglu., APL, 2011
TM th
b γ τ π =
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in Martensitic NiTi
(001), (100) and
(201)
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(001) Twin boundary (001) Twin boundary Twin formation due to glide of twinning partial a/2 [100]
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2 TM = 7.6mJ / m
γ
2 UT = 24mJ / m
γ
2
mJ m ! " # $ % & '
Generalized planar fault energy (GPFE)
x
u a
2
mJ m ! " # $ % & '
Generalized stacking fault energy (GSFE)
2
20 /
us
mJ m γ =
x
u a 2.884 a A = &
a a a[100] = [100]+ [100] 2 2
Ezaz, Sehitoglu, Acta. Mat, 2011
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2
mJ m γ ⎛ ⎞ ⎜ ⎟ ⎝ ⎠
x
u c
4.66 = & c A
Onda ¡et ¡al., ¡33,354,1992, ¡JIM, ¡
[ ]
100
[ ]
001
[ ]
010
Ti ¡ Ni ¡ Generalized stacking fault energy (GSFE)
No Metastable Position, Barrier too high
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2
mJ m γ ⎛ ⎞ ⎜ ⎟ ⎝ ⎠
x
u c
2
41
TME
mJ m γ =
[ ]
001 13.5 =
M
c c
Generalized planar fault energy (GPFE)
[ ]
100
[ ]
001
[ ]
010
Ti ¡ Ni ¡
0.46 ¡A ¡Shuffle ¡ in ¡Ti ¡ 0.23 ¡A ¡Shuffle ¡ in ¡Ni ¡
3. [001] 9 a
B19’ ¡
3 ¡layer ¡twin ¡aMer ¡ ¡only ¡shear ¡ 3 ¡layer ¡twin ¡aMer ¡shuffle ¡ following ¡shear ¡
Shear Direction ¡
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Ledge Ledge
Matrix Twin Matrix
[100] [100] [100] 2 2 a a a → +
[100] (001]
Displacement Fault Energy
Shear Shuffle
[001] (100]
Aided by twinning partial No twinning partial, combined shear and shuffle
Displacement Fault Energy Without shuffle With shuffle Displacement
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(201)
[102] [201]
Fault Energy (mJ/m2)
| 102 |
x
u
Generalized Stacking Fault Energy (GSFE)
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Gives the exact coupling of Shear and shuffle
Computationally extensive!
1st Energy Barrier Metastable position
0,0 0.5,0 1,1 0.5,1 0,1
3 layer twin 4 layer twin Metastable position
Shear, e Shuffle.h Fault Energy (mJ/m2) Reaction path along MEP
1st Energy Barrier 2nd Energy Barrier 2nd Energy Barrier
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Twin Migration Energy gTM (mJ/m2)
ux/b
(001)[100] (100)[001 ] (201)[102] K1 η1
(τ shear)ideal = δγ δux max (MPa)
{ }
( )
/ τ π γ =
TMideal TM twin
b (MPa) (001) [100] 277 165 (100) [001] 4530 1790 (201) [102] 107060 3900
Twin growth stress is proportional to the twin migration energy
Ishida et al., 2005
3 layer Twin 4 layer Twin 5 layer Twin
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Digital Image Correlation Results displaying Multiple Twin Modes During Deformation of Martensite
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(112) Twin (114) Twin (112) And (114) are the mostly observed twin systems Nishida et al., 2003
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3b 4b
2
mJ m γ ⎛ ⎞ ⎜ ⎟ ⎝ ⎠ [ ]
111 6
x
u a
Ni – In Plane ¡ Ti – In Plane ¡ Ni – Out of Plane ¡ Ti – Out of Plane ¡
/ 6 111 b a =
Shear ¡Magnitude ¡ Shear ¡Direc0on ¡ 1 2 s =
211 ⎡ ⎤ ⎣ ⎦
[ ]
111
No metastable position, and labeled as ‘impossible’.
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1 2 s =
s 4 layer twin 5 layer twin Application of only shear
Ortho structure
211 ⎡ ⎤ ⎣ ⎦
[ ]
111
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4 layer Twin 5 layer Twin
2
mJ m γ ⎛ ⎞ ⎜ ⎟ ⎝ ⎠
Reaction coordinate along MEP
4 layer Twin 5 layer Twin Pseudotwin
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Different Shuffle Possibilities
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Normalized displacement / | 221 |
x
u a Fault Energy (mJ/m2) Fault Energy (mJ/m2) Reaction Coordinate along MEP
shuffle.
= /18[221] b a
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!
Sharp Boundaries Further Lower the Energy Barriers
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2
mJ m γ ⎛ ⎞ ⎜ ⎟ ⎝ ⎠
[100]
x
u a
[111]
x
u a
(011)[111]
Most observed slip system in B2 NiTi, Chumlyakov, 2004, Norfleet et al., 2010, Delville et al. , 2010
Not presented in early work, lower barrier energy in (1-11) direction
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(011)[111]
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30 ¡ Slip Plane Slip Direction
max
( )
shear ideal x
u δγ τ δ = (MPa) (011) [100] 1034 (011) [111] 726 ( 211) [111] 7430 (100) [010] 9320
Summary of Slip Systems
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Summary
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