Transcript Ductility Plasticity of TiAl in the light of deformation

Piling-up behavior during axisymmetric
indentation and its relation to the activated
deformation mechanisms in -TiAl
C. Zambaldi, F. Roters, D. Raabe
Department of Microstructure Physics and Metal Forming
Düsseldorf, Germany
[email protected]
2010-11-30
MRS Fall 2010
Overview
• Introduction
• Experiments: nanoindentation, AFM,
EBSD
• Crystal plasticity finite element (CP-FEM)
simulation of anisotropic flow during
nanoindentation
• Comparison of experiment and simulation
• Anisotropic hardness of γ-TiAl
C. Zambaldi, F. Roters, D. Raabe
Max-Planck-Institut für Eisenforschung
Nanoindentation
• Instrumented indentation is a simple and potentially
highly accurate materials testing method
• Mechanical characterization from nano to macro
• Uniaxial testing: 1-d flow curve;
Indentation: load-displacement curve (1-d)
as well as pile-up (2-d).
• Complex 3-dimensional deformation
• Crystal-Plasticity-FEM (CPFEM) capable to
describe the orientation dependency during
indentation; orientation information needed
C. Zambaldi, F. Roters, D. Raabe
Max-Planck-Institut für Eisenforschung
Crystal plasticity of γ-TiAl
Deformation modes
• 4 systems for {111} 1-10] slip by
ordinary dislocations, b=1/2 110]
• 8 systems for {111} -101] slip by
superdislocations, b= 101]
• 4 twinning systems of type {111}11-2]
unidirectional with a fixed amount of shear
(1/sqrt(2)), b= 1/6 11-2]
(110)
(111)
C. Zambaldi, F. Roters, D. Raabe
Max-Planck-Institut für Eisenforschung
3
γ-TiAl , indentation experiments
[Göken & Kempf, 2001, 2002]
Pronounced orientation
dependency
during
indentation, e.g. pile-up
C. Zambaldi, F. Roters, D. Raabe
[Göken & Kempf, 2001, 2002]
[111] indentation
Order variants result in
3-fold symmetry of pile-up
during 111 indentation
Max-Planck-Institut für Eisenforschung
Identification of order domains by EBSD
120°@[111]
x x
x x x
o
o o
x
x
o o
o o
x
x
x
o
o o o
o o o
o o o
o o o
o
o
x x
x
x
x
x
o
o
o
Fit-rank EBSD indexing
Zambaldi, Zaefferer, Wright; J. Appl Cryst. (Dec 2009)
C. Zambaldi, F. Roters, D. Raabe
Max-Planck-Institut für Eisenforschung
Nanoindentation & EBSD & AFM
• γ-TiAl single crystals cannot be grown in the specific
compositions Nanoindentation in fine microstructures
• Characterization by AFM & EBSD
C. Zambaldi, F. Roters, D. Raabe
Max-Planck-Institut für Eisenforschung
Elasto-viscoplastic CPFEM model of -TiAl
Continuum mechanics: F*  FF P
1
T  CE
*
*


1 *T *
with E  F F  1
2
*
F P  LP F P
Crystal plasticity:
LP   γ α S α0
with S α0  m α0  n α0
α
γ α  f(τ α , τ αcrit ) with τ α  T*  S α0
ταcrit  gγ, γ 
τ
γ  γ 0 α
τ crit
α
Strain rate law:
Hardening law:
α
τ
α
crit
  h γ ,
αβ
β
β
1m
 
si gn τ α
h
αβ
β 
q h , h
αβ
β 
aβ
 τ 
 h 1 

τ 

β
0
β
crit
β
s
Kalidindi et al. (1992) J. Mech. Phys. Solids; Roters et. al. Acta Mater. 2010 (Review)
C. Zambaldi, F. Roters, D. Raabe
Max-Planck-Institut für Eisenforschung
3-dimensional simulation of nanoindentation
Meshing, contact, strong gradients, numerical robustness,…
Ti
C. Zambaldi, F. Roters, D. Raabe
Max-Planck-Institut für Eisenforschung
Al
Iterative fitting of tip geometry
Comparison of remaining impression shape
with simulated indent
C. Zambaldi, F. Roters, D. Raabe
Max-Planck-Institut für Eisenforschung
Piling-up / sinking-in behavior
Influence of hardening parameters
Pile-up Sink-in
Sink-in
τc
Pile-up
shear strain γ
C. Zambaldi, F. Roters, D. Raabe
Max-Planck-Institut für Eisenforschung
Study of orientation dep. pile-up
Near-equidistant directions
8°~9° misorientation
C. Zambaldi, F. Roters, D. Raabe
Improper rotation leads to
change in handedness of
the pile-up
Max-Planck-Institut für Eisenforschung
Displaying pile-up topographies
A convention for in-plane rotation of pile-up topographies
Simulation: use convention to choose orientations directly
Experiment: backrotate topographies with arbitrary in-plane
orientation into the unique position
C. Zambaldi, F. Roters, D. Raabe
Max-Planck-Institut für Eisenforschung
Simulated pile-up profiles
Pile-up IPF
from 51 orientations
approx. resol. 9°
Zambaldi & Raabe, Acta Mater. 2010
C. Zambaldi, F. Roters, D. Raabe
Max-Planck-Institut für Eisenforschung
Simulated pile-up profiles
[110]
Pile-up IPF
High symmetry
orientations
[111]
[001]
[101]
Zambaldi & Raabe, Acta Mater. 2010
C. Zambaldi, F. Roters, D. Raabe
Max-Planck-Institut für Eisenforschung
[100]
Comparison AFM / CP-FEM topography
Experiment
C. Zambaldi, F. Roters, D. Raabe
Simulation
Max-Planck-Institut für Eisenforschung
[u v w]=[3 1 4] indentation
[3 1 4]
C. Zambaldi, F. Roters, D. Raabe
[1 1 1]
Max-Planck-Institut für Eisenforschung
[101] indentation in γ-TiAl
C. Zambaldi, F. Roters, D. Raabe
Max-Planck-Institut für Eisenforschung
Relative strengths of slip systems
(Ti-50Al)
Cu, Al, Au, Ag,…
Predicted
for Ti-55Al
[101] indentation indicates relative
strengths of ordinary and super
dislocation glide in TiAl
C. Zambaldi, F. Roters, D. Raabe
Max-Planck-Institut für Eisenforschung
Extension to hexagonal α2-Ti3Al
22 orientations after the
developed convention
Prismatic <a>-slip is easy to activate  22 CPFEM simulations
C. Zambaldi, F. Roters, D. Raabe
Max-Planck-Institut für Eisenforschung
Pile-up IPF & AFM result close to [2-1-1 0]
2 µm
α2-Ti3Al
C. Zambaldi, F. Roters, D. Raabe
Max-Planck-Institut für Eisenforschung
Conclusions
• Ordinary dislocation glide in near-stoichiometric
γ-TiAl is an intrinsic property, i.e. not interfacerelated
• Twinning contributes to deformation to a minor
extent during single phase indentation of γ-TiAl
• Nanoindentation combined with AFM, EBSD and
CP-FEM can characterize activation of individual
slip systems in single crystal indentation
• Method based on highest accuracy values: P, h
• Axisymmetric indenters need to be employed to
make the method efficient
C. Zambaldi, F. Roters, D. Raabe
Max-Planck-Institut für Eisenforschung
Samples were provided by
G. Behr, W. Löser (IFW Dresden)
U. Hecht (ACCESS e.V. Aachen)
Support by the European Union FP6 project
IMPRESS (Intermetallic Materials Processing
in Relation to Earth and Space Solidification)
is gratefully acknowledged.
Vielen Dank.
C. Zambaldi, F. Roters, D. Raabe
Max-Planck-Institut für Eisenforschung
References
C. Zambaldi, D. Raabe, Plastic anisotropy of gamma-TiAl revealed by
axisymmetric indentation, Acta Materialia 58 (9) (2010) 3516–3530,
doi:10.1016/j.actamat.2010.02.025
C. Zambaldi, S. Zaefferer, S. Wright, Characterization of order domains
in gamma-TiAl by orientation microscopy based on electron backscatter
diffraction, Journal of Applied Crystallography 42 (6) (2009) 1092–1101,
doi:10.1107/S0021889809036498, pdf:http://edoc.mpg.de/439331
N. Zaafarani D. Raabe, R. N. Singh, F. Roters, S. Zaefferer: Acta Mater. 54 (2006) 1863–1876
Three dimensional investigation of the texture and microstructure below a nanoindent in a Cu single
crystal using 3D EBSD and crystal plasticity finite element simulations
E. Demir, D. Raabe, N. Zaafarani, S. Zaefferer: Acta Mater. 57 (2009) 559–569
Experimental investigation of geometrically necessary dislocations beneath small indents of different
depths using EBSD tomography
Y. Wang, D. Raabe, C. Klüber, F. Roters: Acta Mater. 52 (2004) 2229-2238
Orientation dependence of nanoindentation pile-up patterns and of nanoindentation microtextures in
copper single crystals
N. Zaafarani, D. Raabe, F. Roters and S. Zaefferer: Acta Mater. 56 (2008) 31-42
On the origin of deformation-induced rotation patterns below nanoindents
F. Roters, P. Eisenlohr, L. Hantcherli, D.D. Tjahjanto, T.R. Bieler, D. Raabe: Acta Materialia 58 (2010)
1152–1211
Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity
finite-element modeling: Theory, experiments, applications
C. Zambaldi, F. Roters, D. Raabe
Max-Planck-Institut für Eisenforschung