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University of Illinois at Urbana Champaign
1
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 Paderborn, Germany ICOMAT-2011, September 6, 2011
Funded by NSF- Division of Materials Research
1
University of Illinois at Urbana Champaign
2
Presentation Outline • Detwinning mechanism of Type II-1 twin in
Martensitic NiTi • Compound twinning in Martensite (001),
(100) and Modes • Twinning in Austenite (112) and (114)
Modes • Slip in B2 NiTi
(201)
University of Illinois at Urbana Champaign
3
Fault Energy Measurement: Example with FCC
2( )mJm
γ
2116
xua ⎡ ⎤⎣ ⎦
Perfect fcc Unstable Stable stacking fault
is linked to Dislocation Nucleation
GSFE GPFE
2116
xua ⎡ ⎤⎣ ⎦
is the energy barrier to overcome during Twin Nucleation
usγ
isfγ
UTγ
2layertwinγ
TMγ
usγ
is the barrier to overcome during Twin growth
TMγ
Unstable Twin fault 2 layer twin
UTγ
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]
University of Illinois at Urbana Champaign
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Detwinning and Twinning of NiTi Martensite
Adapted from Ishida et al.,2006
University of Illinois at Urbana Champaign
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Type II-1 twins
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)
University of Illinois at Urbana Champaign
6
Fault Energy in Type II twin
Ezaz -Sehitoglu., APL, 2011
TMth b
γτ π=
University of Illinois at Urbana Champaign
• Detwinning mechanism of Type II-1 twin in Martensitic NiTi
• Compound twinning in Martensite (001), (100) and
• Twinning in Austenite, (112) and (114)
(201)
Outline
• VASP-PAW-GGA
• 9x9x9 k-point mesh with 273.2 eV energy cutoff.
• Convergence assessed with increasing L
University of Illinois at Urbana Champaign
8
(001) Compound Twin
(001) Twin boundary
(001) Twin boundary
Twin formation due to glide of twinning partial a/2 [100]
University of Illinois at Urbana Champaign
9
(001) Compound Twin-GSFE and GPFE
2TM = 7.6mJ /mγ
2UT = 24mJ / mγ
2
mJ
m! " #$ %& '
Generalized planar fault energy (GPFE)
xua
2
mJ
m! " #$ %& '
Generalized stacking fault energy (GSFE)
220 /us mJ mγ =
xua 2.884a A= & a aa[100] = [100]+ [100]
2 2Ezaz, Sehitoglu, Acta. Mat, 2011
University of Illinois at Urbana Champaign
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2
mJm
γ ⎛ ⎞⎜ ⎟⎝ ⎠
xuc
4.66= &c A
(100) Compound Twin
Onda et al., 33,354,1992, JIM, Mats. Trans.
[ ]100
[ ]001
[ ]010 Ti Ni
Generalized stacking fault energy (GSFE)
No Metastable Position,
Barrier too high
University of Illinois at Urbana Champaign
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Energy Barrier of (100) Twin
2
mJm
γ ⎛ ⎞⎜ ⎟⎝ ⎠
xuc
241TMEmJm
γ =
[ ]00113.5
=M
cc
Generalized planar fault energy (GPFE) [ ]100
[ ]001
[ ]010
Ti Ni 0.46 A Shuffle in Ti
0.23 A Shuffle in Ni
3. [001]9a
B19’ 3 layer twin aMer only shear 3 layer twin aMer shuffle
following shear
Shear Direction
University of Illinois at Urbana Champaign
Two different Twin growth mechanism
Ledge Ledge
Matrix
Twin
Matrix
[100] [100] [100]2 2a aa → +
[100]
(001]
Displacement
Faul
t Ene
rgy
Shear
Shuffle
[001]
(100]
Aided by twinning partial
No twinning partial, combined shear and shuffle
Displacement
Faul
t Ene
rgy
Without shuffle
With shuffle
Displacement
University of Illinois at Urbana Champaign
Compound Twin (201)
(201)
[102]
[201]
Faul
t Ene
rgy
(mJ/
m2 )
| 102 |xu
Generalized Stacking Fault Energy (GSFE)
University of Illinois at Urbana Champaign
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Energy Barrier of Twin
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
Shu
ffle.h
Faul
t Ene
rgy
(mJ/
m2 )
Reaction path along MEP
1st Energy Barrier
2nd Energy Barrier
2nd Energy Barrier
(201)
University of Illinois at Urbana Champaign
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(001), (100), Compound Twins
Twin
Mig
ratio
n E
nerg
y g T
M (m
J/m
2 )
ux/b
(001)[100](100)[001](201)[102]
K1
η1
(τ shear )ideal =
δγδux max
(MPa) { }( )/τ π γ=TMideal TM twinb (MPa)
(001) [100] 277 165
(100) [001] 4530 1790
(201) [102] 107060 3900
Twin growth stress is proportional to the twin migration energy
(201)
Ishida et al., 2005 3 layer Twin
4 layer Twin
5 layer Twin
University of Illinois at Urbana Champaign
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Digital Image Correlation Results displaying Multiple Twin Modes During Deformation of Martensite
University of Illinois at Urbana Champaign
• Introduction to NiTi – Applications – Shape Memory Behavior
• Detwinning mechanism of Type II twin in Martensitic NiTi
• Compound twinning in Martensite (001), (100) and
• Twinning in Austenite, (112) and (114)
(201)
Outline
University of Illinois at Urbana Champaign
(112) and (114) Twin in Austenite
(112) Twin (114) Twin
(112) And (114) are the mostly observed twin systems
Nishida et al., 2003 18
University of Illinois at Urbana Champaign
(112) Pseudotwinning in B2 NiTi 3b 4b
2
mJm
γ ⎛ ⎞⎜ ⎟⎝ ⎠
[ ]1116
xua
Ni – In Plane Ti – In Plane
Ni – Out of Plane Ti – Out of Plane [ ]/ 6 111b a=
Shear Magnitude
Shear Direc0on
12
s =
211⎡ ⎤⎣ ⎦
[ ]111
No metastable position, and labeled as ‘impossible’.
University of Illinois at Urbana Champaign
Coupled shear and shuffle mechanism during (112) twin growth
[ ]1116ab= 1
2s =
s
4 layer twin 5 layer twin Application of only shear
Ortho
structure
211⎡ ⎤⎣ ⎦
[ ]111
University of Illinois at Urbana Champaign
PES and MEP of (112) Twin
4 layer Twin
5 layer Twin
2
mJm
γ ⎛ ⎞⎜ ⎟⎝ ⎠
Reaction coordinate along MEP 4 layer Twin
5 layer Twin
Pseudotwin
University of Illinois at Urbana Champaign
PES and MEP in (114) twinning
Normalized displacement / | 221 |xu a
Faul
t Ene
rgy
(mJ/
m2 )
Faul
t Ene
rgy
(mJ/
m2 )
Reaction Coordinate along MEP
• No Energy well at
• Twinning combines shear and shuffle.
• Barrier energy of 148 mJ/m2
= / 18[221]b a
University of Illinois at Urbana Champaign
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Presentation Outline • Detwinning mechanism of Type II-1 twin in
Martensitic NiTi • Compound twinning in Martensite (001),
(100) and Modes • Twinning in Austenite (112) and (114)
Modes • Slip in B2 NiTi
(201)
University of Illinois at Urbana Champaign
Slip Systems in B2 NiTi
2
mJm
γ ⎛ ⎞⎜ ⎟⎝ ⎠
[100]xu a [111]xu a
(011)[100] (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
University of Illinois at Urbana Champaign
Experimental observation of novel [111](011) system systems
(011)[100] (011)[111]
University of Illinois at Urbana Champaign
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Slip
Plane
Slip
Direction max
( )shear idealxu
δγτδ
= (MPa)
(011) [100] 1034
(011) [111] 726
( 211) [111] 7430
(100) [010] 9320
Summary of Slip Systems
University of Illinois at Urbana Champaign
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Conclusions • Twinning is favored over slip in the case B19’ martensite
(a key reason why shape memory works). • Shuffles play a significant role in Type II-1, (100), (201)
twinning in martensite. • (112) and (114) twinning in B2 NiTi has to overcome
much lower barrier with shear and shuffle with comparable
• [111](011) slip has been shown to be significant in B2 NiTi along with [100](011) slip both with experiments and simulations.