Department MTM

NANOSPD 2014 Metz

1

A subdivision model for CP Ti during the first pass

of ECAP at room temperature

Dep. of Materials Engineering, KU Leuven, Belgium

Xiaodong Guo, Marc Seefeldt

Department MTM

Content

2

Backgrounds

Modeling Strategy

Results & Discussions

Conclusion Future Plans

Department MTM

Backgrounds

3

Ti C Fe N H O

wt% Base 0.04 0.14 0.006 0.0015 0.36

Nano Titanium Implant®, produced in Timplant, Czech

∅ = 90°

𝛹 = 0°

𝑇 = 298𝐾

∆𝜀 = 1.15

𝜀 = 10−4/𝑠

ViNaT Project under FP7: Virtual NanoTitanium

Properties required for biomedical materials:

Biocompatibility

Non-Toxic

Strength

Ductility

Persistency

…

Nanosized Ti by ECAP can improve biocompatibility, strength, persistency while keeping the ductility

This subdivision model couples with VPSC, simulates a

grain’s (orientation) behavior during the first pass of

ECAP at room temperature. The effect of grain

subdivision on texture evolution will be the future work.

Department MTM

Modeling Strategy

4

Deformation Substructure

Prismatic, Basal, Pyramidal

Twins: type of reorientation bands

defect densities

Δε

microscopic mesoscopic

Deformation Texture

VPSC Model

(Simple Shear Mode)

orientations

Δε

Velocity

Gradient

Tensor

Dislocation

Elementary

Processes

macroscopicnanoscopic

)(s CRSS

)(w

Department MTM

Reorientation bands formation

5

Compression Direction

Dorothe′e Dorner, Yoshitaka Adachi, Kaneaki Tsuzaki, Scripta Materialia 57, 2007

Fe-3%Si

Compression to 36% strain

Room Temperature

Slip bands in grain A impose shear steps at grain boundary, then trigger microband groups

with periodic orientation change in grain C

How and where does the misorientation arise?

Department MTM

Reorientation bands formation

6

Prismatic slip bands in grain 1 impose shear on grain boundary, triggering twinning in grain 2

L. Wang, Y. Yang, P. Eisenlohr, T.R. Bieler, M.A. Crimp, D.E. Mason, Meta.& Mater. Trans. A, Vol 41A, 2010

Pure Titanium

Tension to 1.5% strain

Room Temperature

Department MTM

Graphical Scenario

7

∆𝛾 =𝑏

ℎ𝑐𝑟Primary dislocation slip bandsNo misorientation

Grain Boundary

Reorientation BandsHave misorientation with matrix

• Forest dislocations

• Mobile dislocations

• Slip band formation

• Excess shear at GB

• Shear transmitted into its neighbor

• Misorientation generated

• Growth of band tip by capturing

mobile dislocation

𝜔 = ∆𝛾

Department MTM

Forest Dislocations

8

• Three slip modes (Prismatic, Basal, Pyramidal) are considered;

• Edge and screw dislocations are considered;

• Vacancy assisted climb is neglected;

• Shear rates & specific Taylor factor for 3 slip modes are deduced from slip activities in VPSC

( i ) ( i )fs ( tot ) ( i )s

f s fs

dy

dt b

( i ) ( i )fe ( tot ) ( i )e

f e fe

dy

dt b

𝛽: Storage Coefficient, 𝛽 = 0.1 for current simulation

0

(i)(i)

sM

(i)

cs

c

:‘critical shear stress ratio’

Department MTM

Nucleation of Mobile Dislocations

9

‘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

Department MTM

Density of Mobile Dislocations

10

2

1( i ) ( i ) ( i )transfer ( j i )s s

eff eff fs

f

dnq( ) q( )

dt b b

hhCSeff cr

ffq s

w

CS

CSCSv

d

l

bPf 0

)1(

s

cr

CS

CShhv

h

l

bPf

cr 0

)2(exp

Cross-slip getting activated

Return to primary plane

𝑞(𝜏𝑒𝑓𝑓): A possibility coefficient indicating a screw dislocation undergoes a double cross slip event.

Yoshinaga’s Jog Pair cross slip model: for High SFE

* Marc Seefeldt, 2004* Yoshinaga, 1964

Nucleation site density for mobile dislocations

Breeding Coefficient

Nucleation Site Density of FR source

Department MTM

Density of Mobile Dislocations

11

)(

)()(

0

)()( 2i

e

i

me

i

es

i

transferi

ms

L

vL

dt

dn

dt

d

)(

)()(

0

)()( 2i

s

i

ms

i

se

i

transferi

me

L

vL

dt

dn

dt

d

Firstly generated from DCS Later increase from Loop expansion

b ⊥⊥

evev

sv

sveL

sL

Department MTM

Transmission & Growth of Reorientation Bands

12

sLa 2

crit

b

h

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

bShear Transmissed:

Transmission Factor: 100% now

sLa 2Width:

Terminating boundaries grow

• End stress at the tip

• Capturing mobile dislocations

• Attaching mobile dislocations

• Shift the end of the boundary’s tip

Department MTM

Results: Dislocation Density

13

- Prismatic and Basal slip modes have a similar forest dislocation density

- Excess dislocations depend on nucleation site densities

- Experimental value of 5 × 1014/m2 after one ECAP-C pass, see Gunderov et al. MSEA, 2013

Dislocation Density Nucleation Site Density

Department MTM

Cell & Fragment Size Prediction

14

* Gunderov et al., MSEA 2013

* T.R. Cass, Oxford, 1966

Mean Cell & Fragment Size

𝑑𝑐 =𝐾𝑐𝜌𝑡𝑜𝑡

𝑑𝑓 ≈𝐾𝑓

𝜃𝑖

0.0 0.1 0.2 0.3 0.4 0.5

0

1

2

3

4

5

Cell

Fragment

True Equivalent Strain(1)Si

ze o

f C

ell &

Fra

gmen

ts (𝜇𝑚

)

Department MTM 15

Mean Misorientation

0.0 0.2 0.4 0.6 0.8 1.0 1.22.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

Mean Misorientation

Me

an

Mis

orie

nta

tio

n(o

)

True Equivalent Strain(1)

Misorientation & Hardening

0

50

100

150

200

250

300

350

400

0 0.2 0.4 0.6 0.8 1 1.2

True Equivalent Strain (1)

Tru

e Eq

uiv

alen

t S

tres

s (M

Pa)

Simulated

Experimental from Simple Shear test

- Hardening due to

• Dislocation forest hardening: ∆𝜎𝑓 = 𝑀𝛼𝜌𝐺𝑏 𝜌 𝑡𝑜𝑡

• Long-range stress hardening due to mismatch stresses around FB triple junctions: ∆𝜎𝜔 = 𝑀𝛼𝜃𝐺𝜔

• Texture hardening due to the evolving average Taylor factor 𝑀

10

14

18

Mis

mat

ch S

tres

s (M

pa)

∆𝜎𝜔

Department MTM

Conclusion & Future Plans

16

We introduced a grain subdivision model for the first pass of ECAP of CP Ti at room

temperature. The generation of reorientation bands is triggered by the stimulation

of slip bands from neighboring grain. Defect densities, cell size and fragment

spacing, hardening behavior are simulated.

One future plan is to combine this subdivision model with plasticity model in order

to study the effect of grain subdivision on texture evolution.

A simple shear test for CP Ti is in process to study more detailed parameters like

evolution of cell and fragment size, transmission factor at grain boundaries and its

orientation dependence, texture evolution etc. which can provide useful

information to the ECAP deformation of metals.

Department MTM

Grain rotation

17

Slip band from the top grain triggers a 30° rotation about a shared c axis in bottom grain

T. Benjamin Britton, Angus J. Wilkinson, Acta Materialia Vol. 60, 2012

Grade 1 Pure Titanium

Tension to 2.5% strain

Room Temperature