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Presentation of STABiX in MTEX workshop .

Authors:

Abstract

Invited talk about the presentation of STABiX in MTEX workshop 2016.
Max-Planck-Institut für Eisenforschung GmbH
Grain Boundaries and Plasticity
David Mercier1,2 (d.mercier@mpie.de), C. Zambaldi1, P. Eisenlohr3
M. A. Crimp3, T. R. Bieler3 and Raúl Sánchez Martín4
1Max-Planck-Institut für Eisenforschung, 40237 Düsseldorf, Germany
2CRM Group, 4000, Liège, Belgium
3Michigan State University, East Lansing, MI 48824, USA
4IMDEA Materials Institute, C/ Eric Kandel 2, 28906 Getafe, Madrid, Spain
Chemnitz MTEX Workshop 2016
26/02/2015
2
Introduction to NI and to my work
Grain Boundaries and Plasticity
Motivation
SX plasticity vs polyX plasticity
The Matlab STABiX toolbox
BX geometry
Crystal plasticity – Slip systems
Slip transmission functions
Visualization of EBSD Datasets and GBs color coding
Data transfer to CPFE modelling
Some results with cp-Ti and Ti alloy samples
SX nanoindentation - CRSS estimation
BX nanoindentation and strain transfer analysis
CPFE modelling
Analysis of datasets from the literature
Outlook: 3D EBSD, Scratch experiment
Collaboration, Network, GitHub…
Conclusion
Plan
SX Vickers nanoindentation
in cp-Ti
polyX tensile test in cp-Ti
3
Nanoindentation technique
Scheme of the Nano Indenteur® Displacement (h)
Load (F)
Continuous Stiffness
Measurement
See in Fischer-Cripps A. C., “Nanoindentation – 2nd Edition.”, Springer, 2004.
dh
dF
S
=
c
a
S
E
2
'
=
2
c
a
F
H
π
=
4
Nanoindentation applied to thin films
AFM for indent
topography and
roughness
4µm
Influence of underlying layers…
From Chen X. and Vlassak J.J. - J. Mater. Res., Vol. 16, No. 10, Oct 2001
Mencik J. et al. - Mater. Res.,
Vol. 12, No. 9, Sep 1997
Au
Ti
SiO2
Si
520nm
565nm
529nm
SEM / FIB / EBSD for film
thickness and microstructure
5
NIMS Matlab toolbox
Toolbox to plot and to analyze (nano)indentation data (obtained
with conical indenters) for bulk material or multilayer sample.
Open Source Code : https://github.com/DavidMercier/NIMS
Generation of
parameterized
FEM model…
6
« Crème brûlée
» model…
Elastic-Plastic substrate (Al)
Brittle thin film (Al2O3)
2cm
Al
Spherical
indenter (radius
R)t
Al2O3
Fracture mechanisms of amorphous Alumina
Cracks
Applied load (mN)
Indentation depth / Alumina
thickness
Pop-in
R/t = 125
Pop-in correlated to nucleation of
dislocation and fracture event
crack
Homogeneous
loop
σ
xx
σ
xx
SX with oxide layer1
1Kramer D. E. et al., “Surface constrained
plasticity: Oxide rupture and the yield point
process.”, Phil. Mag. A, 2001, 81(8), pp. 2033.
7
PopIn Matlab toolbox
Toolbox to plot (nano)indentation data and to analyze pop-in
events distribution.
Open Source Code : https://github.com/DavidMercier/PopIn
8
STABiX Matlab toolbox
9
Grain Boundaries
And
Plasticity
Plasticity of Single Crystal is “well understood”.
10
Plasticity of Single Crystal
Critical resolved shear stress1,2
Schmid factor
1. Schmid E. and Boas W. – “Plasticity of crystals, with special reference to metals” (1968)
2. Reid C.N. – “Deformation geometry for materials scientists” (1973)
3. Uchihc M. D. et al., “Plasticity of Micrometer-Scale Single Crystals in Compression” (2009).
Slip lines on the surface of a
compressed crystal of niobium2.
Slip plane
SEM image of a 5-μm-diameter microcrystal
sample of pure Ni oriented for single slip
after compression.3
Micropillar compression modelling
with TRIDIS.
11
Plasticity of Polycrystal
Micromechanics of GBs ?
Need of experimental data…
Slip transmission / Strain transfer
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. Lim H. et al., “Grain-scale Experimental Validation of Crystal Plasticity Finite Element Simulations of Tantalum Oligocrystals.”,
International Journal of Plasticity 60, 2014, pp. 1-18.
Experimental
(HR-DIC)
CP-FEM
Simulation
Experimental (DIC)
CP-FEM Simulation
2008
Tensile test @ RT on Al (FCC) oligocrystal
2014
Tensile test @ RT on Ta (BCC) oligocrystal
Solution ?
12
Micromechanics of GBs ?
Solution ?
1. Dewald M. et al., Modelling Simul. Mater. Sci. Eng. 19, (2011).
2. Kacher J.P. et al. - Scripta Materialia 64 (2011) 677–680
3. Britton T.B. et al., J. Mater. Res., 2009, 24(3), pp 607-615.
4. Guo Y. et al., Acta Materialia 76 (2014) 1-12
5. Patriarca L. et al., Mater. Sci. & Eng. A 588 (2013).
6. Bieler T.R. et al., Current Opinion in Solid State and Materials
Scienc, Volume 18, Issue 4, August 2014, Pages 212–226
7. Reuber C. et al., Acta Materialia 71 (2014) 333–34
Our solution : Combination of (3D-)EBSD and SX or BX nanoindentation ?
Coupled atomistic
discrete dislocation (CADD)1
Mechanical test on pX + DIC5
Mechanical test on pX + EBSD6
Mechanical test on pX +
HR-EBSD4
CPFEM7
Straining test in situ TEM/SEM2
Nanoindentation test + EBSD/AFM3
Indentation experiments are often used to characterize
plasticity of single crystal… (more than 100 papers/PhD thesis)
1. Osmond F. et al. “Les figures de pression et de percussion
sur les métaux plastiques cristallisés.” (1905).
2. Kwon J. et al., Acta Materialia (2013).
5mm
Indentation with a needle (15N) on single
crystals of a steel sample3.
Vickers indent on cp-Ti
Indentation of Single Crystal
Secondary electron SEM (a, c, e) and STEM (b, d, f) images of the
deformation structures observed for indents on the second-order
prismatic planes, in Ti alloy.2
13
14
Indentation of Single Crystal and EBSD
IPF of pile-up topographies and maximum indentation depth
(hardness) of cp-Ti2
Misorientation maps underneath the
indentation at different cross
sections, comparison between
experimental and simulation results1
1. Zaafarani N. et al., Acta Mater., 2008, 56, pp. 31-42.
2. Zambaldi C. et al., J. Mater. Res., 2012, 27(1), pp. 356-367
3. Zambladi C. et al., Acta Materialia 91 (2015) 267–2
IPF of pile-up topographies of Mg3
Indentation experiments are often used to
capture / quantify GB strengthening…
(~40 papers)
15
Indentation close to a GB
1. Wo R.C. and Ngan A.H.W.,, J. Mater. Res., 2004,
19(1), pp 189-201.
2. Soer W.A., Mater. Letters 59 (2005) 3192 – 3195
3. Britton T.B. et al., J. Mater. Res., 2009, 24(3), pp
607-615.
4. Lawrence S.K. et al., JOM, Vol. 66, No. 8, 2014.
5. Pathak S. et al., . Mater. Res., 2012, 47,(2), pp
815-823.
6. Kalidindi S.R. et al., Current Opinion in Solid
State and Materials Science (2014), 18(4), pp.
196-204.
Berkovich indentations in Ni3Al1, in Fe-14%Si2 and in copper3.
60° / radius 150nm conical
indentation in Ni-2014 Sphero-conical indentation in Fe–3%Si5 and in Al6
Increase of hardness close to the GB ?
16
1. Soifer Ya. M. et al., Scripta Materialia 47 (2002) 799–804
2. Soer W.A., Mater. Letters 59 (2005) 3192 – 3195
Indentation with AFM tip
(apex angle of 90°) in Cu1.
Berkovich indentation (CSM )in BCC
materials (Fe-14%Si and Mo)2.
Indentation close to a GB
17
2nd pop-in Slip transmission?
Berkovich indentation in BCC materials
(Fe-14%Si and Mo)1.
GB description and
GB geometry ?
1. Han F. et al. Materials Science and Engineering: A (2015), 625(11), pp. 28–35.
2. Soer W.A., Mater. Letters 59 (2005) 3192 – 3195.
CPFE simulation of bicrystal indentation2.
Indentation close to a GB
EBSD and spherical indentations close to
GBs are performed in α-Ti
quasi bi-crystal deformation
18
AFM topography of residual indent in
Ti-5Al-2.5Sn, close to a grain boundary.
Gr. A
Gr. B
Comparison of residual topography
and texture around indent to
simulated indentations as predicted
by 3D CPFE modeling.
Start to model slip transmission
and GB mechanic…
Our strategy
Bicrystal definition
Crystal plasticity
Slip transmission model
Matlab
Toolbox
19
The Matlab STABiX toolbox
Bicrystal definition 5 DOF
1. Randle V. “Five-parameteranalysis 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.
Crystallographic
description3
Geometrical description1,2
20
1. Euler angles of grains
(ϕ1Φ2ϕ 3 ) (by EBSD)
Or
3. Misorientation axis / angle
[uvw] / ω (by EBSD or TEM)
Trace of the grain
boundary (GB)
Crystal 1
Crystal 2
GB
nG
B
1. GB inclination (
β
) (by
serial polishing or by FIB) and
GB trace (
α
) (by EBSD )
Or
GB normal (nGB)
3. Step between grains after
polishing / Rougness (by AFM)
βα
21
GB inclination measurement
1. Randle V. “A methodology for grain boundary plane assessment by single-section trace analysis.”, Scripta Mater., 2001, 44, pp. 2789-2794
2. Konijnenberg P. J. et al., “Analysis of 3D-EBSD Datasets Obtained by FIB Tomography”, Microsc. Microanal. 19 (Suppl 2), 2013.
3. Chapman M. et al., “Can EBSD Patterns Be Used for Determination of Grain Boundary Inclination?”, Microscopy and Microanalysis, 2015.
Determination of sub-surface grain
boundary inclination angle from
EBSD line scans ?3
Combining Monte Carlo electron
trajectory simulations and dynamical
Electron Backscatter Diffraction Pattern
(EBSP).
EBSD measurements on sample sides1.
FIB/SEM observation – Courtesy of Y. Su
3D EBSD2
22
GB inclination measurement
Serial polishing, with
a combination of
Vickers indentation and
SEM observations…
Matlab GUI included
in the STABiX toolbox…
( )
α
=90tan
d
h
=
h
d
GB
GB
inc
tan
Crystal Plasticity of hcp sample
Large number of
dislocation slip and
twinning systems.
Database saved in a
Matlab function…
Slip systems
Twin systems
Pyr. 1st ord. <a>
{} < >
Pyr. 1st ord. <c+a>
{} <>
Tensile twinning
{} < >
Tensile twinning
{} < >
Compr. twinning
{} < >
Compr. twinning
{} < >
Prism. 1st ord. <a>
{} < >
Basal <a>
{} <>
Pyr. 2nd ord. <c+a>
{} <>
Prism. 2nd ord. <a>
{} <>
23
DAMASK documentation : https://damask.mpie.de/Documentation/CrystalLattice
24
Slip activity / Slip trace identification
Examples of surface topography measured by
AFM in grain after deformation2
Examples of surface topography measured by
AFM in grain after deformation2
1. Li H. et al., Philosophical Magazine, 2013.
2. Yang Y. et al., Metal. And Mater. Trans. A, 42A (2011), pp. 636-644.
3. Zhang J.I. et al., Materials Science & Engineering A, 2015.
ECCI of discrete dislocation patterns, imaging conditions
(displayed in simulated EC patterns) and stereographic
projections for the indents into a crystal with {100} surface
normal.3
Slip transmission
25
Possible strain transfer across grain boundaries (GB).
From Sutton and Balluffi, , “Interfaces in Crystalline Materials.”,
OUP Oxford (1995).
Prediction of slip transmission ?
Criteria to predict the slip transmission
m’ factor 1
1. 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.
2. Livingston J.D . & Chalmers B., “Multiple
slip in bicrystal deformation”, Acta Met.
1957,5, pp. 322-327.
3. Z. Shen et al., “Dislocation pile-up and
grain boundary interactions in 304
stainless steel.”, Scripta Metallurgica
(1986), 20(6), pp. 921–926.
4. Marcinkowski M. J. & Tseng W. F.,
“Dislocation behavior at tilt boundaries of
infinite extent.”, Metallurgical
Transactions, 1970, 1(12), pp. 3397-
3401.
26
N factor2
Residual Burgers vector4
LRB factor3
m’ mapping
κψ
coscos'
=
m
outinr
bbb
=
δγκψ
coscoscoscos +=N
κθ
coscos
=
LRB
27
Criteria to predict the slip transmission
λ function from Werner and Prantl1
With this function, slip transmission is expected to occur only when the angle ψ
between slip plane normal directions is lower than a given critical value (ψc=15°) and
the angle κ between slip directions is lower than a given critical value (κc=45°).
1. E. Werner and W. Prantl, “Slip transfer across grain and phase boundaries.”, Acta Metallurgica et Materialia (1990), 38(3), pp. 533-537.
3D pseudo-view
of λ maps…
28
Criteria to predict the slip transmission
Critical resolved shear stress1,2
Schmid factor
1. Schmid E. and Boas W. – “Plasticity of crystals, with special reference to metals” (1968).
2. Reid C.N. – “Deformation geometry for materials scientists” (1973).
3. Abuzaid W.Z. et al., “Slip transfer and plastic strain accumulation across grain boundaries in Hastelloy X.”, J. of
the Mech. and Phys. of Sol. (2012), 60(6) ,pp. 1201–1220.
Slip plane
GB Schmid Factor3
Generalized Schmid Factor2
The generalized Schmid factor, which
describes the shear stress on a given slip
system, can be computed from any stress tensor
.
29
Combination of criteria ?
Bayerschen E. et al., “Review on slip
transmission criteria in experiments and
crystal plasticity models“, 2015.
Bieler T. R. et al.,
Current Opinion in Solid
State and Materials
Science, 2014.
The Ti alloy sample exhibited a near-α
(HCP) microstructure with the body
centered cubic (BCC) β phase located
primarily at α phase grain boundaries1.
EBSD measurement
EBSD orientation map with IPF coloring scheme
of Ti–5Al–2.5Sn (wt.%) sample.
30
1. Seal J. R. et al., Mater. Sci. and Eng. A 552, 2012, pp. 61-68.
MATLAB Toolbox/GUI
Outputs from EBSD measurement
Loading and Plot of EBSD data
Loading of EBSD
files.
Setting of the
coordinate system.
Plot of the GBs
segments.
Average orientation of each grains
Euler angles (phi1, PHI, phi2);
Phase of material;
Average positions of grains;
GB trace coordinates;
Trace length and trace angle.
For TSL-OIM data
Grain File type
2 and Reconstructed Boundaries
files or use of MTEX toolbox to
load/convert ang. file…
Introduction to the MATLAB toolbox
31
Isolate a specific GB.
Data transfer from EBSD map into a
new window in order to analyze in
detail the given bicrystal…
Selection of a specific grain boundary…
32
33
Possibility to tune the indenter geometry (tip radius, apex
angle…), sample geometry (GB inclination, sample size…), the mesh
parameters (bias, number of elements…)…
Generation of mesh procedure file and material config. file using
Python scripts. Generation of a .inp file for some indenter’s
geometry (Berkovich, AFM topography…etc.).
CPFE model generation from the GUI (1/2)
34
Some results
with cp-Ti and Ti alloy
samples
35
Sample description
cp α-Ti
(Optical microscope)
α-Ti-5Al-2.5Sn (wt%)
(SEM)
10µm
High specific strength, good corrosion resistance, and
good ability to resist at high temperature ( Aerospace
industry …)
Large number of dislocation slip and twinning systems.
β-phase
(BCC)
Grain size ≈ (114±40)µm Grain size ≈ (35±15)µm
α-phase
36
Spherical indentation on a polycristal
37
Indentation in cp-Ti and in Ti-5Al-2.5Sn (wt%) at RT
Ti-5Al-2.5Sn
@293K
cp-Ti
@293K
Global Schmid factor
distribution of slip systems1
Tensile test on polycrystal
Inverse pole figure of pile-up
topographies2
Nanoindentation on single crystal
1. Li H. et al. , Phil. Mag. (2013), pp. 1-21.
2. Zambaldi C. et al., J. Mater. Res., 2012, 27(1), pp. 356-367.
Basal activity in
Ti-5Al-2.5Sn (wt%) ?
No twin
observed
38
Spherical indentation in Ti-5Al-2.5Sn (wt%) at RT
CRSS values ?
Basal activity in
Ti-5Al-2.5Sn (wt%) confirmed !
And no twin observed…
Identification of the crystal plasticity hardening parameters
1. S.R. Kalidindi and L. Anand, Int. J. Mech. Sci. 34(4) (1992) pp. 309-329.
2. A.A. Salem et al., Acta Materialia 53(12) (2005) pp. 3495-3502.
3. X. Wu et al., Acta Materialia, 55(2) (2007) pp. 423-432J.
Flow rule given by Kalidindi’s
constitutive model1,2,3 DAMASK
(http://damask.mpie.de/)
Only Prismatic 1st order <a>,
Basal <a> and Pyramidal 1st order
<c+a>4.
39
Type τo (MPa) τsat (MPa) CRSS
ratio
Prismatic <a>-glide 150 ± 4 1502 ± 125 1
Basal <a>-glide 349 ± 10 568 ± 17 2.3
Pyramidal <c+a>-glide 1107 ± 39 3420 ± 202 7.4
4. Zambaldi C. et al., J. of Mater. Res., 2012, 27(01), pp. 356-367.
5. Sun Q.Y. and Gu H.C., Mat. Sc. and Eng. A, 2001, 316(01-02), pp. 80-86.
Type τo (MPa) τsat (MPa) CRSS
ratio
Prismatic <a>-glide 320 1000 1
Basal <a>-glide 360 1000 1.1
Pyramidal <c+a>-glide 1200 3500 3.8
cp-Ti4 Ti-5Al-2.5Sn (wt%)
Nonlinear optimization4 Comparison between experiments and CPFEM simulation,
of the surface topography of the indent and the indentation load-displacement curve.
Solid solution hardening by Al and Sn elements.5
40
Comparison with the literature
1. Williams J. C. et al., Metallurgical and Materials Transactions A (2002), 33A, pp. 837-850.
Type τo (MPa) τsat (MPa) CRSS
ratio
Prismatic <a>-glide 320 1000 1
Basal <a>-glide 360 1000 1.1
Pyramidal <c+a>-glide 1200 3500 3.8
Ti-5Al-2.5Sn (wt%) Williams et al. (2002)1
Ti-5Al (wt%) @ 293K
Basal slip
Prismatic <a> slip
Type τo (MPa) τsat (MPa) CRSS
ratio
Prismatic <a>-glide 150 1
Basal <a>-glide 180 1.2
Indentation close to GBs ?
Direct correlation between slip transmission and 2nd pop-in !
Good agreement between strain transfer and m’ value !
AFM topography AFM profiles Load-displacement
curves
m’ = 0.98
m’ = 0.38
Quantitative study of spherical indentation in cp-Ti
…Courtesy of Y. Su (MSU, East Lansing, USA)
41
42
Statistical analysis of slip transmission in cp-Ti (hcp)
Lee’s criterion1
1. T.C. Lee, et al. Scr.
Metall. 23, 799 (1989).
Mainly prism<a> to
prism<a> transfer ?
Strain transfer occurs
at GB in cp-Ti for :
Geometric consideration
m’ > 0.7
Low CRSS
1. Guo Y. et al., Acta Materialia 76 (2014) 1-12
Transmission map in cp-Ti after pX compression test
and HR-EBSD measurement.1
43
Recent results – Yang et al. (soon published) (1/2)
Discrepancies between experimental and simulated are explained by the
reverse plasticity after large plastic deformation.
Quantitative study of spherical indentation in single crystal of cp-Ti
44
Recent results – Yang et al. (soon published) (2/2)
Discrepancies between experimental and simulated are explained by the
absence of the grain boundary mechanism in the current model.
Quantitative study of spherical indentation in bicrystal of cp-Ti
45
Gr. A
Gr. B
GB
Gr. B Gr. A
Prism<a> to Basal ?
Slip transmission in Ti-5Al-2.5Sn (wt%) at RT
Some details about CPFE model…
1. S.R. Kalidindi and L. Anand, Int. J. Mech. Sci. 34(4) (1992) pp. 309-329.
2. A.A. Salem et al., Acta Materialia 53(12) (2005) pp. 3495-3502.
Flow rule given by Kalidindi’s
constitutive model1,2,3 DAMASK
(http://damask.mpie.de/)
Only Prismatic 1st order <a>, Basal
<a> and Pyramidal 1st order <c+a>4.
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 GB.
46
Gr. B
Gr. A
Type τo (MPa) τsat (MPa) CRSS
ratio
Prismatic <a>-glide 150 ± 4 1502 ± 125 1
Basal <a>-glide 349 ± 10 568 ± 17 2.3
Pyramidal <c+a>-glide 1107 ± 39 3420 ± 202 7.4
3. X. Wu et al., Acta Materialia, 55(2) (2007) pp. 423-432J.
4. Zambaldi C. et al., J. of Mater. Res., 2012, 27(01), pp. 356-367
Type τo (MPa) τsat (MPa) CRSS
ratio
Prismatic <a>-glide 320 1000 1
Basal <a>-glide 360 1000 1.1
Pyramidal <c+a>-glide 1200 3500 3.8
cp-Ti Ti-5Al-2.5Sn (wt%)
47
Small discrepancy between experimental and
simulated pile-up topographies.
Gr. A
Gr. B
AFM topography of residual indent in Ti-5Al-2.5Sn,
close to a grain boundary.
Gr. A
Gr. B
Calculated topography from CPFEM of spherical
indent close to a GB.
AFM CPFEM
3D CPFE of bicrystal indentation in Ti-5Al-2.5Sn (wt%)
48
Gr. B
Gr. A
Gr. B Gr. A
Local Misorientation from EBSD
measurement vs CPFEM results.
EBSD
CPFEM
The CPFE model with no strengthening effect from
grain boundaries seems to predict almost correctly
the plasticity transfer.
3D CPFE of bicrystal indentation in Ti-5Al-2.5Sn (wt%)
Gr. A
Accumulated
basal shear
Accumulated
prism. 1<a>
shear
Gr. B
Isosurfaces of accumulated shear int the bicrystal
obtained by CPFEM.
Slip transfer seems to be based on the
geometrical compatibility of the 2 grains.
high m’ value (prism. 1 <a> and basal)
49
Prism<a> to Basal ?
3D CPFE of bicrystal indentation in Ti-5Al-2.5Sn (wt%)
Outlook : 3D EBSD ?
50
Analysis of datasets from
the literature
51
Kacher J. et al., “In situ and tomographic analysis
of dislocation/grain boundary interactions in
α
-
titanium.”, Phil. Mag., 2014, pp. 1-16.
Validation on literature data
Patriarca L. et al., “Slip transmission in bcc FeCr
polycrystal.”, Materials Science and Engineering:
A, 2014, 588, pp. 308-317.
52
Outlook:
3D EBSD, Scratch experiment…
53
3D EBSD technique
FIB/EBSD tomography is performed by removing successive layers of material using gallium ions in grazing incidence.
EBSD-based mapping of orientations is performed between each milling steps.
The microstructure is then reconstructed using the post-processing software QUBE [1].
[1] Konijnenberg, P. J. et al., Materials Science Forum, 702-703, 475-478, 2012
sample in cutting
position
(36° tilt)
e-
x-rays
e-
sample in EBSD
position
(70° tilt)
FIB column
EBSD
camera
EDX
detector
SEM objective
lens
Ga+
…Courtesy of Dr. S. Zaefferer
(MPIE, Düsseldorf, Germany)
54
3D EBSD on nanoindent close to GB in Ti-5Al-2.5Sn (wt%)
Pile-up#2
Pile-up#1
Problem : Minimum step size = 50nm vs indent size ≈ 1µm (↔20 px) !
Problem : High lattice rotation EBSD conditions not respected !
55
3D EBSD on nanoindent close to GB in Ti-5Al-2.5Sn (wt%)
Grain 1
Grain 2
Pile-up
Pile-up
Residual
indent
56
3D EBSD on nanoindent close to GB in Ti-5Al-2.5Sn (wt%)
KAM distribution GND
Useful for a comparison with a physical
model (non-local)…
57
Outlook : continuous dislocations dynamics…
Non-local CPFEM implemented in DAMASK1,2
“… physics-based constitutive model of dislocation glide in metals that explicitly
accounts for the redistribution of dislocations due to their motion.”
“… promising application of the model is the analysis of grain/phase boundary
behavior with respect to dislocation glide by altering the transmissivity property of
interfaces according to e.g. the orientation relationship at the boundary.”
1. Reuber C. et al., “Dislocation density distribution around an indent in single-crystalline nickel: Comparing nonlocal crystal plasticity
finite-element predictions with experiments”, Acta Materialia, 2014, pp. 333-348.
2. Kords C., “”, PhD thesis, Aachen University (2013).
Scratch test on Austenite (bcc) (1/2)
Z-displacement (µm)
CPFEM with flow rule given by
Kalidindi’s constitutive model
SEM observations
58
…Courtesy of Dr. S. Brinckmann
(MPIE, Düsseldorf, Germany)
Scratch test on Austenite (bcc) (2/2)
Z-displacement (µm)
CPFEM with flow rule given by
Kalidindi’s constitutive model
SEM observations
59
…Courtesy of Dr. S. Brinckmann
(MPIE, Düsseldorf, Germany)
60
Collaboration, Network, GitHub…
61
List of STABiX users
Max-Planck-Institut für Eisenforschung GmbH
Düsseldorf / Germany
Department of Chemical Engineering and Materials
Science / Michigan State University
East Lansing, MI / USA
IMDEA Materials Institute
Madrid / Spain
Australian Nuclear Science and Technology
Organization
Sydney / Australia
Physikalische Metallkunde (PhM), TU Darmstadt
Darmstadt / Germany
RWTH Aachen University
Aachen / Germany
Solanki Research Group, Arizona State University
Tempe / USA
STABiX in GitHub https://github.com/stabix/stabix
62
Documentation =
http://stabix.readthedocs.org/en/latest/
MTEX and STABiX…
Use of MTEX in STABiX
Plots of IPF / ODF
Grains statistics…
Use of import_wizard
Outlook
Visualization of EBSD map
Crystallographic function (vector3d,
rotation, orientation, Miller…)
Collaboration about slip system
definition, slip transmission functions…
Transfer to MTEX ?
63
Gr. A
Gr. B
200
7
m
Titanium (Alpha)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
64
Conclusion
65
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 and BX indentation
SX and BX scratch test
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
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.
Cu bi-crystal
Tensile test of Aluminum
oligocrystal “dogbone”1.
Straining test and TEM3.
µ-pillar compression test and
µ-cantilever bending test 2.
Advantages of the toolbox
https://github.com/stabix/stabix
66
Conclusion and Outlook
Slip transmission analysis done with STABiX using EBSD data.
Slip transfer based on the geometrical compatibility of the two
grains (high m’ value for prism. 1 <a> for cp-Ti and prism. 1 <a> /
basal for Ti-5Al-2.5Sn (wt%) low RBV, high LRB…
Small discrepancy between experimental and simulated pile-up
topographies using 3D-CPFEM. But no GB strengthening !
Outlook : 3D-EBSD + Use of the non-local model to assess GND
distributions and GB resistance…
STABiX toolbox = “Bridge between EBSD and CPFEM”
For bcc, fcc and hcp materials / for 1 or 2 phases
CPFEM models for Mentat and Abaqus :
SX / BX indentation and scratch test (and compression of µ-pillar soon)
Open Source Software on GitHub / Use of MTEX toolbox
Questions ?
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