The EUROMAT conferences have been held every two years since 1989, and have an increased record of bringing together up to 2000 researchers, scientists, trainees, and students from both academia and industry to discuss critical developments and perspectives in the field of materials science and technology and their applications. In 2015, the symposia within the conference will be grouped under the main headings: (A) Functional Materials, (B) Structural Materials, (C) Processing, (D) Characterization and Modelling, (E) Energy and Environment, and (F) Biomaterials and Healthcare, and there will be additional contributions on (G) Education, Technology Transfer and Strategic Materials.

1. Department MTM
EUROMAT 2013 SEVILLE
1
Multiscale Modelling of Grain Subdivision During
Severe Plastic Deformation of CP Titanium
Dep. of Metalluary and Materials Engineering (MTM)
KU Leuven, Belgium
Xiaodong Guo, Marc Seefeldt
In framework of Project of ViNaT – Virtual NanoTitanium

2. Department MTM
ViNaT Backgrounds
2
• EU: FP7-NMP-2011-EU-Russia, NMP.2011.1.4-5,
contract no. 295322
• RUS: Russian Ministry of Education and Science,
state contract no. 16.523.12.3002
Nano Titanium Processing and Modelling for Biomedical application

3. Department MTM
Content
3
Backgrounds
Overview & Theory Basis
Results & Discussions
Conclusion

4. Department MTM
Application & Why We Need Nano-Ti?
4
Best of CP Ti & its alloys
Better for Nano grains
Requirements
Formability
StrengthBiocompatibility
Improved with Nano grains
Nice of CP Ti than alloys
Maintained with Nano grains
Hip, Knee Joints etc.
Screws for teeth, heart surgery
Nano grains Normal grains
*Ruslan Z. Valiev et al. ADVANCED BIOMATERIALS 2008
Nano Ti Matrix
Large Ti Matrix
Mice Tissue
Composition Ti C Fe N H O
wt% Base 0.04 0.14 0.006 0.0015 0.36

5. Department MTM
SPD Methods for Nano Ti
5
ECAP HPT
* R.Z. Valiev et al. MSE A137 (1991)
ARB
* Y. Saito et al. Scripta Mater, 39 (1998)
SPD Methods
∅ = 𝟗𝟎°, 𝜳 = 𝟎°, 𝑻 = 𝟎℃ & 𝟐𝟎𝟎℃, ∆𝜺 = 𝟏. 𝟏𝟓
Our Research
𝐄𝐂𝐀𝐏 − 𝐂

6. Department MTM
Hierarchical Multiscale Modelling
6
Deformation Substructure
- Prismatic, Basal, Pyramidal
- Twins not considered
defect densities
Δε
microscopic scale mesoscopic
Deformation Texture
VPSC Model
orientations
Δε
Velocity
Gradient
Tensor
Dislocation
Elementary
Processes
macroscopicnanoscopic
)(s
 CRSS
)(w

* cp. G. Winther, 1998; B. Peeters, M. Seefeldt, P. Van Houtte et al.; M. Seefeldt et al., 2001

7. Department MTM 7
Texture Simulation for CP Ti in ECAP-C

8. Department MTM
Slip & Twinning in α-Titanium
8
{0001}<11-20> {10-10}<11-20>
{11-22}
{10-11}<11-23> {11-22}<11-23>
Basal Prismatic <a> Pyramidal <a> Pyramidal <c+a> I Pyramidal <c+a> II
Slip Modes
Twinning Modes
{11-21}{10-12}
{10-11}<11-20>
 Prismatic and Basal <a> glide prevail, as well as Tensile and Compressive Twins
 3 slip modes and 2 twin modes are considered

9. Department MTM
Texture Evolution
9
1 PASS 2 PASS
4 PASS 8 PASS
ED
ND
NSD SD
 Strong C texture (c-axis 10o rotated from ND around TD CW) due to high activity of both C.T and T.T twins
 Prismatic, Basal, Pyramidal slip result in texture along NSD (c-axis // NSD)
TD
Max: 7.06 Max: 2.46 Max: 8.14 Max: 2.83
Max: 11.68 Max: 3.31 Max: 12.6 Max: 3.42
* VPSC Codes from Los-Alamos * MTEX

10. Department MTM 10
Go to the subdivision simulation…

11. Department MTM
Grain Subdivision
11
* S. Van Boxel, Universtity of Manchester
Band Structure Checkerboard Structure
Orientation Gradient Core & Shell
4 General Types of Grain Subdivision:
 Simultaneous activation of prismatic, basal and twinning results in Band or Checkerboard type substructure
due to interaction of misorientation bands
 Misorientation bands are delimited by Dislocation Rotation Boundaries (DRB) which are strongly directional
and affect texture development.

12. Department MTM
How subdivision happens?
12
 Prismatic slip band in grain 1 triggers twinning in grain 2
* L. WANG et.al – MMTA - 2009 * T. B. Britton, Angus J. Wilkinson – Acta - 2012
 Slip band from the top grain triggers a 30o rotation about a
shared c axis in bottom grain
 Reorientation bands or rigid body rotation arise due to a force applied from slip bands in
neighboring grains

13. Department MTM
Graphical Scenario
13
∆𝛾 =
𝑏
ℎ 𝑐𝑟Primary dislocation slip bands
No misorientation
Boundary
Reorientation Bands
Forest Dislocation • Homogeneous slip background
• Kocks-Mecking Balance equations
Nucleation of Mobile
Dislocations
• Double cross slip & Frank-Read Source
• Nucleation site density
Fragmentation &
Misorientation • Disclination

14. Department MTM
Forest Dislocations on Homogeneous Slip
14
 Three slip systems (Prismatic, Basal, Pyramidal c+a 1st ) are considered,
twinning is neglected; Vacancy assisted climb is neglected
 Driving storage and recovery balance equations for forest dislocations
  b
y
dt
d i
si
fssannihil
tot
f
i
fs
)(
)(
,
)(
)(


 

  b
y
dt
d i
ei
feeannihil
tot
f
i
fe
)(
)(
,
)(
)(


 

𝛽: 𝑆𝑡𝑜𝑟𝑎𝑔𝑒 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡
𝑦 𝑎𝑛𝑛𝑖ℎ𝑖𝑙: 𝐴𝑛𝑛𝑖ℎ𝑖𝑙𝑎𝑡𝑖𝑜𝑛 𝑙𝑒𝑛𝑔𝑡ℎ 𝑓𝑜𝑟 𝑒𝑑𝑔𝑒 𝑎𝑛𝑑 𝑠𝑐𝑟𝑒𝑤 𝑟𝑒𝑠𝑝𝑒𝑐𝑡𝑖𝑣𝑒𝑙𝑦

15. Department MTM
Mobile Dislocations from DCS
15
 ‘ℎ’ : a minimum critical distance for FR source effectively generated
 Slip band forms when a bunch of parallel primary slip planes undergo this process
(1) (2) (3)
Double Cross Slip event

16. Department MTM
Modelling Nucleation from DCS
16
  b
q
b
q
dt
dn i
sij
fseff
i
s
f
eff
i
transfer
)(
)(
)(
2
)(
)(
1
)(

















  hhCSeff cr
ffq  s
w
CS
CSCS
v
d
l
b
Pf 0
)1(








s
cr
CS
CShh
v
h
l
b
Pf cr 0
)2(
exp 
cross-slip getting activated
Return to primary plane
 𝑞(𝜏 𝑒𝑓𝑓): Breeding coefficient is one important parameter, because it directly affect
the generation of dislocations, and then fragmentation process for different slip
systems
 𝑞 𝜏 𝑒𝑓𝑓 is sensitive to SFE, temperature, atomistic parameters etc.
* Marc Seefeldt, 2004; * Bonneville & Escaig,1983

17. Department MTM
Generation of Mobile Dislocations
17
)(
)()(
0
)()(
2
i
e
i
me
i
e
s
i
transfer
i
ms
L
v
L
dt
dn
dt
d  



)(
)()(
0
)()(
2
i
s
i
ms
i
s
e
i
transfer
i
me
L
v
L
dt
dn
dt
d  



b ⊥
⊥
evev
sv
sv
eL
sL
Firstly generated from DCS Later increase from Loop expansion

18. Department MTM
Slip Band Growth & Transmission
18
sLa 2
crith
b

Slip Band:
Localised shear, but no misorientation with
respect to matrix
Excess Shear:
Width:
Misorientation Band:
Realising a similar localised shear in
another slip mode
crith
b
Shear Transmissed:
Transmission Factor: 100% now
sLa 2Width:

19. Department MTM
Growth by Tip Propagation
19
* A.E. Romanov, Ioffe St. Petersburg
• Terminating boundaries grow by
– end stresses
– capturing mobile dislocations,
– attaching them,
– thus shifting the boundaries’ ends
Partial Disclination Dipole

20. Department MTM
Results: Dislocation Density
20
Prismatic Screw
Prismatic Edge
Basal Screw
Basal Edge
- Prismatic and Basal have a similar dislocation density which meets well with
experimental value 5.8 × 1014
/𝑚2
in total after one ECAP-C pass by Gunderov et al.
MSEA 2013

21. Department MTM
Slip Nucleation Density
21
- Highly activated prismatic nucleation sites, in this case, around 1 to 3 successful slip
banding nucleation sites per grain (initial grain size is 10 𝜇𝑚)
- Explains why mostly observed slip bands are prismatic
Prismatic
Basal

22. Department MTM
Cell & Fragment Size & Misorientation
22
𝒅 𝒄
𝒅 𝒇 * Gunderov et al., MSEA 2013
* T.R. Cass, Oxford, 1966
Mean Cell & Fragment Size
𝑑 𝑐 =
𝐾𝑐
𝜌𝑡𝑜𝑡
𝑑 𝑓 ≈
𝐾𝑓
𝜃𝑖
Mean Misorientation of New Band Boundary

23. Department MTM
Temperature Effect
23
- Temperature effect is well interpreted by Nucleation Site Density

24. Department MTM
Conclusion
24
 On the basis of orientation fragmentation, mechanisms of slip
patterning, slip concentration , “transformation” of slip bands into
misorientation bands, misorientation band nucleation and growth from
view of disclination are talked.
 Balance equations for dislocations and partial disclinations,
corresponding excess slip superimposed to homogeneous slip, excess
slip “translated” into upper bound misorientation
 Strong dependence on atomistic parameters!

25. Department MTM
Project Calendar
25
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
2012 1st
2nd
RW1
MS2 RW2
2013 3rd MS3
Pre-
Doct
MS4
DL1
4th RW3
2014
VNT
END
2015
2016
PHD
END
MS: Milestone Report Submission
RW: Review Report Submission
DL: Deliverable Report Submission
Meetings: GLADD : Gent, Kerkrade, Leuven; Caen Texture Symposium; Moscow, Israel Project Meetings; Tribute to PVH;
ICCMNM Frankfurt 2013; EuroMat 2013 Sevilla

26. Department MTM
Appendix
26

27. Department MTM
Work Packages in ViNaT
27
 WP1: Multiscale modeling of mechanical behavior of biocompatible NanoTi
 WP2: Modeling of biocompatible nano SMA and superelastic alloys
 WP3: Modeling of biocompatibility of NanoTi and Ti-alloys
 WP4: Modeling of nanoidentation and mechanism of localized deformation of Nano Ti
 WP 1: Multiscale modeling of mechanical behavior and strength of biocompatible nanostructured titanium
 T1.1. atomistic modeling of NanoTi (FIAS)
 T1.2. Crystal/dislocation modeling (IMDEA)
 T1.3. (Micro) Texture Evolution (KUL)
 T1.4. Grain boundary sliding (Technion)
 T1.5. Micromechanics of NanoTi (DTU)
 T1.6. Experimental validation (USATU)
 T1.7 Severe plastic deformation (USATU)
 T1.8. TEM, SEM (USATU, NM)

28. Department MTM 28
Grain Subdivision
Low to medium strains:
 Cell walls (IDB): 𝜽 < 𝟒°
 DDW (GND): 𝟒° < 𝜽 < 𝟐𝟎°
 Microband: 𝟓° < 𝜽 < 𝟓𝟎°
Large strains:
 Kink Bands, shear bands
Banding
Gradient
Checkerboard
Core + Shell
Incidental Dislocation Boundary
No misorientation
Composed of Incidental Stored Dislocation
Geometrical Dislocation Boundary
Medium misorientation
Composed of Geometrical Dislocation Boundary
Microbands
Transition bands
inbetween
Microbands highly
misorientation
transition bands have
orientation gradient
Cell Interior
Negligible dislocation
density

29. Department MTM
U. F. Kocks – Transaction of the ASME - 1976
 Mechanistic Interpretation of hardening law
𝑑𝜌 = 𝑑𝜌 𝑆𝑇𝑂𝑅. − 𝑑𝜌 𝑅𝐸𝐶𝑂𝑉.
= 𝜌 𝑚
𝑑𝑥
Λ
− 𝐿 𝑅 𝜌𝑑𝑎/𝑉
=
𝜌𝑑𝛾
𝑏𝛽
− 𝐿 𝑅 𝜌𝑑𝛾/𝑏
𝑑𝜌 𝑆𝑇𝑂𝑅. = 𝜌 𝑚
𝑑𝑥
Λ
𝑉𝑑𝜌 𝑅𝐸𝐶𝑂𝑉. = 𝐿 𝑅 𝜌𝑑𝑎
Λ = 𝛽/ 𝜌 : Λ is mean free path
𝑑𝛾 = 𝜌 𝑚 𝑏𝑑𝑥 = 𝑏𝑑𝑎/𝑉
𝑑𝜌
𝑑𝛾
=
𝜌
𝑏𝛽
−
𝜌𝐿 𝑅
𝑏
𝐿 𝑅: 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑎𝑛𝑛𝑖ℎ𝑖𝑙𝑡𝑎𝑖𝑜𝑛 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑑𝑖𝑠𝑙𝑜𝑐𝑎𝑡𝑖𝑜𝑛𝑠
𝑏: 𝐵𝑢𝑟𝑔𝑒𝑟𝑠 𝑣𝑒𝑐𝑡𝑜𝑟
𝛽: 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑓𝑟𝑜𝑚 Λ
𝑑𝜌+
=
2
𝐿𝑏
𝑑𝛾
𝑑𝜌−
= 2𝜌𝑐𝑦
𝑑𝛾
𝑏
𝑑𝜌
𝑑𝛾
=
2
𝐿𝑏
−
2𝜌𝑐𝑦
𝑏
U. Essmann and H. Mughrabi – Philosophical Magazine - 1979
Dilsocation Evolution

30. Department MTM
Deformation Modes in ECAP
30
* V.M. Segal, MSE A197 (1995) 157 * VIrene J. Beyerlein, Carlos N. Tomé, MSE A197 (2004)
Central Fan Deformation Zone Two Part Deformation ZoneSimple Shear Modes

31. Department MTM
Texture Components in ECAP CP-Ti
31

32. Department MTM
CRSS Value by H. Conrad
32
Composition Ti C Fe N H O [O]%
wt.% Base 0.04 0.14 0.006 0.0015 0.36 0.4
As-received:
Prismatic vs Temp. vs [O]% Basal vs [O]%
CP Ti – Grade 4
0.1wt% [O%] 0.4%wt [O%]
Prismatic <a> 20 ~35
Basal <a> 30 ~65
* Hans Conrad, Progress in Materials Science, 26 (1981) 123-403.
(MN/m2)
CRSS of T = 473K
Basal vs Temp.
T = 300 K
Ci%=0.05At.%
Basal
Basal
500K
Also affirmed by S. Naka’s work in 1988

33. Department MTM
Twinning CRSS Value by H. Conrad
33
300K 500K
T. T. {10-12} 49.4 70~75
T. T. {11-21} 40.6 65~70
C. T. {11-22} 70~75 140~150
Conclusion of Twins CRSS Value by Literatures
 If we estimate 3 twinning systems as linearly increasing at 473K under compression
(MN/m2)
It needs further confirmation by fitting of experiments and modelling works

34. Department MTM 34

35. Department MTM 35

36. Department MTM 36
Pass 5 Pass 6 Pass 7 Pass 8

37. Department MTM
Results & Challenges
37
 Texture Modeling using VPSC
- Deformation mechanism in CP Ti, CRSS values etc.
- Texture evolution during ECAP-C, with slip activity, Taylor factor evolution etc.
- Intensity in pole figure is higher than experiment value
 Substructure Modeling:
- Cell structure developed based on balance equation of dislocations, including generation,
immobilization, annihilation terms.
- Fragmentation in representation of partial disclination
- Large variation of SFE in literatures, effect on slip banding, cross slip, screw annihilation
length etc.
- Incorporation of vacancy-assisted climb
- Transmission of shear between two neighboring grains

38. Department MTM
CRSS Selection
𝒔 𝝉 𝟎 𝝉 𝟏 𝜽 𝟎 𝜽 𝟏 𝒉∗,𝑷𝒓
𝒉∗,𝑩
𝒉∗,𝑷𝒚
𝒉∗,𝑪 𝒉∗,𝑻
𝑇 = 298𝐾
Prismatic 120 150 300 0 1 1 1 1 1
Basal 150 100 400 0 1 1 1 1 1
Pyramidal 300 200 600 0 1 1 1 1 1
Tens. Twin 0.167 150 0 1 10 1 1 1 1 1
Com. Twin 0.225 300 0 1 20 1 1 1 1 1
𝑇 = 473𝐾
Prismatic 35 200 300 0 1 1 1 1 1
Basal 65 150 400 0 1 1 1 1 1
Pyramidal 200 300 600 0 1 1 1 1 1
Tens. Twin 0.167 150 0 1 10 1 1 1 1 1
Com. Twin 0.225 300 0 1 20 1 1 1 1 1
Comp. Ti C Fe N H O
Wt% Base 0.04 0.14 0.006 0.0015 0.36
 As-received composition
 CRSS values we use

39. Department MTM 39
Texture Simulation Substructure Simulation
Ti Products by NanoSPD