Max-Planck-Institut für Eisenforschung GmbH
Investigation of the texture and microstructure evolution around
a nanoindent close to an individual grain boundary.
David Mercier1 (d.mercier@mpie.de),
C. Zambaldi1, P. Eisenlohr2
M. A. Crimp2, T. R. Bieler2
1Max-Planck-Institut
2Michigan
für Eisenforschung, 40237 Düsseldorf, Germany
State University, East Lansing, MI 48824, USA
17th International Conference on Textures of Materials
August 24-29, 2014 | Dresden, Germany
Gr. A
Gr. B
Motivation of this work
Plasticity of Single Crystal is well understood.
 Indentation experiments are often used to characterize
plasticity of single crystal…
Inverse pole figure of pile-up topographies of cp-Ti1
1. Zambaldi C. “Orientation informed nanoindentation of atitanium: Indentation pileup in hexagonal metals
deforming by prismatic slip.”, J. Mater. Res., 2012,
27(1), pp. 356-367.
2. Zaafarani N. “On the origin of deformation-induced
rotation patterns below nanoindents.”, Acta Mater.,
2008, 56, pp. 31-42.
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Misorientation maps underneath the indentation at different
cross sections, comparison between experimental and
simulation results2
But, missing element to predict
polycrystal mechanics…
MERCIER David
2
Motivation of this work (2/2)
Micromechanical behavior of grain boundaries.
EBSD and indentations close to grain boundaries
are performed in alpha-Ti  quasi bi-crystal deformation.
Gr. A
Comparison of experimental
results (residual topography,
texture around indent…) to
simulated indentations as
predicted by
3D CPFE modeling.
Gr. B
Start to model the slip
transmission and GB
mechanic…
2014-08-25
AFM topography of residual indent in
Ti-5Al-2.5Sn, close to a grain boundary.
MERCIER David
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Strategy  Creation of a toolbox
GB and
Bicrystal
definition
Crystal
Plasticity
Slip
transmission
model
MATLAB Toolbox and
Graphical User Interfaces (GUIs)
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Bicrystal definition  5 DOF
Trace of the grain
boundary (GB)
Geometrical description1,2
1. GB inclination (b) (by serial
polishing or by FIB) and GB
trace (a) (by EBSD )
a
b
Crystal 1
𝛗𝟏 𝛟𝛗𝟐
nGB
Or
GB normal (nGB)
GB
2. Step between grains after
polishing / Rougness (by AFM)
Crystal 2
𝟏
𝛗𝟏 𝛟𝛗𝟐
𝟐
𝒖𝒗𝒘 𝝎
Crystallographic description3
1.
Randle V. “Five-parameter’ analysis of grain boundary networks
by electron backscatter diffraction.”, J. Microscopy, 2005, 222,
pp. 69-75.
2.
Randle V. “A methodology for grain boundary plane assessment
by single-section trace analysis.”, Scripta Mater., 2001, 44, pp.
2789-2794
3.
Morawiec A., “Orientations and Rotations: Computations in
Crystallographic Textures.”, Springer, 2004.
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MERCIER David
1. Euler angles of grains
(12 3) (by EBSD)
Or
2. Misorientation axis / angle
[uvw] / w (by EBSD or TEM)
5
Crystal Plasticity of alpha-Titanium (hcp)
 Slip systems
Basal <a>
{𝟎𝟎𝟎𝟏} <𝟏𝟏𝟐𝟎>
Prism. 1st ord. <a>
{𝟏𝟎𝟏𝟎} < 𝟏𝟏𝟐𝟎 >
Prism. 2nd ord. <a>
{𝟏𝟏𝟐𝟎} <𝟏𝟏𝟎𝟎>
Pyr. 1st ord. <a>
{𝟏𝟎𝟏𝟏} < 𝟏𝟏𝟐𝟎 >
Pyr. 1st ord. <c+a>
{𝟏𝟎𝟏𝟏} <𝟏𝟏𝟐𝟑>
Pyr. 2nd ord. <c+a>
{𝟏𝟏𝟐𝟐} <𝟏𝟏𝟐𝟑>
 Twin systems
Large number of
dislocation slip and
twinning systems.
Tensile twinning
{𝟏𝟎𝟏𝟐} < 𝟏𝟎𝟏𝟏>
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Tensile twinning
{𝟏𝟏𝟐𝟏} < 𝟏𝟏𝟐𝟔>
Compr. twinning
{𝟏𝟎𝟏𝟏} < 𝟏𝟎𝟏𝟐>
Compr. twinning
{𝟏𝟏𝟐𝟐} < 𝟏𝟏𝟐𝟑>
MERCIER David
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Criteria to predict the slip transmission
N factor (from Livingston & Chalmers)1
N  (nin  nout )* (din  dout )  (nin  dout )* (nout  din )
m’ factor (from Luster &
1.
Livingston J.D . & Chalmers B., “Multiple slip in
bicrystal deformation”, Acta Met. 1957,5, pp.
322-327.
2.
Luster J. & Morris M.A., “Compatibility of
deformation
in
two-phase
Ti-Al
alloys:
Dependence on microstructure and orientation
relationships.”, Metallurgical and Materials
Transactions A, 1995, 26(7), pp. 1745-1756.
3.
Marcinkowski M. J. & Tseng W. F., “Dislocation
behavior at tilt boundaries of infinite extent.”,
Metallurgical Transactions, 1970, 1(12), pp.
3397-3401.
4.
Bieler T. R. et al., “The role of heterogeneous
deformation on damage nucleation at grain
boundaries
in
single
phase
metals.”,
International Journal of Plasticity, 2009, 25(9),
pp. 1655-1683.
Morris)2
m'  cos  cos 
Outgoing slip
Incoming slip
Residual Burgers vector3
br  bin  bout
Outgoing slip
Incoming slip
Schmid Factor, resolved shear stress…4
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Strain Transfer parameters implemented in the toolbox
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Outline
Selection of interesting GB
using the MATLAB Toolbox/GUI
EBSD map
Spherical indentation close to the chosen GBs
Measurement of the topography
by AFM and of the lattice rotation by EBSD
AFM topography of a
residual indent
Inclination of GB measured by FIB or serial polishing
1st slip transmission analysis via
the MATLAB Toolbox/GUI
Modeling
Experiments
Acquisition of EBSD map of the sample
Cross sectional view of GB
Creation of output files for CPFEM
using the MATLAB Toolbox/GUI
3D CPFE modeling
 Slip transmission model using CPFEM results
and the MATLAB Toolbox/GUI
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MERCIER David
CPFEM displacement
result after bicrystal
indentation
9
EBSD onand
Ti–5Al–2.5Sn
(wt%)
sample
Loading
Plot of EBSD
data
Outputs from OIM™ Data Analysis
• Grains number;
• Average orientation of each grains
 Euler angles (phi1, PHI, phi2);
• Phase of material;
• Average positions and diameters of grains;
• GB numbers;
• GB trace coordinates ;
• Trace length and trace angle.
 Loading of EBSD
EBSD orientation map with IPF coloring scheme
files.
of Ti–5Al–2.5Sn (wt.%) sample.
The
Setting
the a near- 𝜶 (HCP)
sample of
exhibited
coordinate system.
microstructure
with the body centered
cubic (BCC) b phase located primarily at α
phase
Plot grain
of boundaries
the GBs 1.
segments.
 Mean grain diameter : (34 ± 16)µm
1.
Grain file type 2
and
Reconstructed Boundaries file
MATLAB
Toolbox/GUI
Seal J. R. et al., Mater. Sci. and Eng. A 552, 2012, pp. 61-68.
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Introduction to the MATLAB toolbox
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Selection
Indentation
of experiments
a specific grain boundary…
Gr. A
Gr. B
GB
Gr. B
Gr. A
 Isolate a specific GB.
 Data transfer from EBSD map into a
new window in order to analyze in
detail the given bicrystal…
2014-08-25
AFM topography of residual indent in Ti-5Al-2.5Sn, close to a grain
boundary with profiles of pile-up surrounding the indent.
MERCIER David
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CPFE model generation from the GUI
 Possibility to tune the indenter geometry (tip radius, apex
angle…), sample geometry (GB inclination, sample size…),
the mesh parameters (bias, number of elements…)…

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Generation of mesh procedure file and material config.
file using Python scripts.
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Few details about CPFE model
Generation of a CPFE model with the MATLAB Toolbox/GUI
•
•
Gr. B
Flow rule given by Kalidindi’s
constitutive model1,2,3
Only Prismatic 1st order <a>,
Basal <a> and Pyramidal 1st
order <c+a>
Gr. A
•
The CPFE model used is purely local formulation, and includes only the
changes in slip system alignment across the boundary, but no
strengthening effect from grain boundaries.
•
DAMASK  http://damask.mpie.de/
References
1. S.R. Kalidindi and L. Anand, “An approximate procedure for predicting the evolution of crystallographic texture in bulk deformtion processing of FFC metals.”, Int. J. Mech. Sci. 34(4)
(1992) pp. 309-329.
2. A.A. Salem et al., “Strain hardening due to deformation twinning in alpha-titanium: Constitutive relations and crystal-plasticity modeling.”, Acta Materialia 53(12) (2005) pp. 3495-3502.
3. X. Wu et al., “Prediction of crystallographic texture evolution and anisotropic stress-strain curves during large plastic strains in high purity alpha-titanium using a taylor-type crystal
plasticity model.”, Acta Materialia, 55(2) (2007) pp. 423-432J.
4. Zambaldi C. et al. “Orientation informed nanoindentation of α-titanium: Indentation pileup in hexagonal metals deforming by prismatic slip.”, J. of Mater. Res., 2012, 27(01), pp. 356-367
2014-08-25
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CPFEM results (1/3)
Gr. A
Gr. A
Gr. B
Gr. B
AFM topography of residual indent in Ti-5Al-2.5Sn,
close to a grain boundary.
Calculated topography from CPFEM of spherical
indent close to a GB.
• Small discrepancy between experimental and simulated pile-up
topographies indicate strain transfer is mainly controlled by
geometrical consideration.
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CPFEM results (2/3)
CPFEM
EBSD
Gr. B
Gr. A
Gr. A
Gr. B
Local Misorientation from EBSD measurement vs CPFEM results.
• The CPFE model with no strengthening effect from grain boundaries
seems to predict almost correctly the plasticity transfer.
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CPFEM results (3/3)
Accumulated
prism. 1<a>
shear
Accumulated
basal shear
Isosurfaces of accumulated shear int the bicrystal
obtained by CPFEM.
Slip transfer is based on the
geometrical compatibility of the two
grains (high m’ value for prism. 1 <a>
and basal, low RBV, high LRB…).
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Advantages of the GUI
• Analysis of all GBs in a map (and color coded results), then
selection of interesting ones
• Fast transfer of experimental data into simulation input files :
 SX indentation
 BX indentation
• Reduction of possible sources of error in analysis by visualization,
standardized workflow and automated data I/O
• Readily extendible to other experiments :




Polycrystal tensile test
µ-cantilever bending test
µ-pillar compression test
Straining test and TEM
Tensile test of Aluminum
oligocrystal “dogbone”1.
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Straining test and TEM3.
Cu bi-crystal
µ-pillar compression test and
µ-cantilever bending test 2.
MERCIER David
1.
Zhao Z. et al., “Investigation of three-dimensional
aspects of grain-scale plastic surface deformation of
an aluminum oligocrystal.”, International Journal of
Plasticity 24, 2008, pp. 2278-2297.
2.
Dehm G. et al., “Plasticity and Fracture at Small
Length Scales: from Single Crystals towards
Interfaces.”, Workshop on Mechanical Behaviour of
Systems – 4, 2013 (India).
3.
Shen Z. et al., “Dislocation and grain boundary
interactions in metal.”, Acta Metal., 1988, 36(12), pp.
3231-3242.
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Results from in situ straining test in TEM (Kacher et al. 2012)
 “In situ and tomographic analysis of dislocation/grain boundary interactions in atitanium.”, Phil. Mag., 2014, pp. 1-16.
Good agreement in term of residual Burgers vector
calculated with the MATLAB Toolbox and values given in
Kacher’s paper.
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Results from polycrystal tensile test (Patriarca et al. 2014)
 “Slip transmission in bcc FeCr polycrystal.”, Materials Science and
Engineering: A, 2014, 588, pp. 308-317.
Good agreement in term of
residual
Burgers
vector
calculated with the MATLAB
Toolbox and values given in
Patriarca’s paper.
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Conclusion and Outlook
•
MATLAB Toolbox / GUI = “Bridge between EBSD and CPFEM”
 For bcc, fcc and hcp materials and for 1 or 2 phase materials
 Slip trace analysis
 Many functions implemented to analyze and to quantify the potential
for slip transmission at GBs
 Interfaced with Python code to rapidly generate CPFE simulation
input files for indentation experiments
 Possibility to implement new functions and new CPFE models for
other experiments (µ-cantilever, µ-pillar, straining test…)
 http://github.com/czambaldi/stabix
 Proceedings paper on ICOTOM17 conference
• Preliminary results : CPFE model with no strengthening effect from grain
boundaries seems to predict almost correctly the plasticity transfer.
•
More indentation and 3D EBSD experiments to do…
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Acknowledgments and Questions
Dr. P. Eisenlohr, Dr. M. Crimp and
Y. Su are acknowledged.
Materials World Network grant references NSF: DFG: ZA523/3-1
Thanks for your attention….
Questions ?
d.mercier@mpie.de
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