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Poster presented at "Indentation 2014" Conference in Strasbourg (France) (December 2014). Spherical indentation and crystal plasticity modeling near grain boundaries in alpha‐Ti.
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Max-Planck-Institut für
Eisenforschung GmbH
Düsseldorf/Germany
CPFEM model [12]
Flow rule given by Kalidindi’s
constitutive model;
Only 3 slip families are
introduced into the model :
Prismatic 1st order <a>, Basal
<a>, Pyramidal 1st order
<c+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.
[1] Sutton A.P. and Balluffi R.W. , “Interfaces in Crystalline Materials.”, (1995).
[2] Randle V., J. Microscopy, 2005, 222, pp. 69-75.
[3] Livingston J.D. and Chalmers B., Acta Metall. (1957), 5(6), pp. 322-327.
[4] Shen Z. et al., Scripta Metallurgica (1986), 20(6), pp. 921–926.
[5] Luster J. et al., Metall. Mater. Trans. A26 (1995) p.1745-1756.
[6] Marcinkowski M.J. et al.., Metal. Trans. (1970), 1(12), pp. 3397-3401.
[7] Reid C.N., Pergamon Press, Oxford, United Kingdom, 1973.
[8] MTEX code : http://mtex-toolbox.github.io/
[9] Guo Y. et al., Acta Mater. (2014), 76, pp. 1-12.
[10] Kacher J. and Robertson I.M., Phil. Mag. (2014), 94(8), pp. 814-829.
[11] Lee T.C. et al. Scr. Metall. 23, 799 (1989).
[12] Zambaldi C. et al., J. Mater. Res. (2012), 27(01), pp. 356-367.
[13] Patriarca L. et al., Mater. Sci. & Eng. (2013), A588, pp. 308317.
D. Mercier1 (d.mercier@mpie.de), C. Zambaldi1, P. Eisenlohr2, Y. Su2, M. Crimp2, T. R. Bieler2.
1Max-Planck-Institut für Eisenforschung, 40237 Düsseldorf, Germany
2Chemical Engineering and Materials Science, Michigan State University, East Lansing 48824 MI, USA
Microstructure Physics
and Alloy Design
Prof. Dr. D. Raabe
Theory and Simulation
Dr. Franz Roters
Motivation and Strategy
Spherical indentation and crystal plasticity modeling
near grain boundaries in alpha
Ti.
Figure 4 : EBSD
orientation map with
IPF coloring scheme of
Ti5Al–2.5Sn (wt.%)
sample.
Matlab Toolbox Bridge between experiments and modeling (for BCC, FCC and HCP materials, with 1 or 2 phases).
The development of pile-up topographies across GBs are affected by the geometrical compatibility of the 2 grains and
not inherent GB resistance to slip.
CPFE 3D models are necessary to accurately predict spatial distribution of shear per slip system.
Other functions to implement and other CPFEM models -pillar compression or bending test of cantilever…).
Mercier D., Zambaldi, C. and Bieler T.R. (2014). “A Matlab toolbox to analyze slip transfer through grain
boundaries.” DOI: http://doi.org/10.5281/zenodo.11561
Gr. A
Gr. B
Plasticity of single crystal is well
understood... But, missing element to
predict polycrystal mechanics !
Micromechanics of grain
boundaries (GB) ?
1) Combination of EBSD and strain
experiments on bicrystal sample.
2) Analysis of slip transmission using
the Matlab Toolbox STABiX.
3) 3D Crystal Plasticity Finite
Element (CPFE) modeling
4) Model the slip transmission and
GB mechanic
5 macroscopic degrees of freedom are
required to characterize a GB [1-2]:
3 for the rotation between the 2 crystals
(by EBSD or TEM characterizations);
2 for the orientation of the GB plane
defined by its normal n (inclination by
serial polishing or FIB sectioning and
trace by EBSD).
The rotation between the 2 crystals is defined by the
rotation angle and the rotation axis common to
both crystals uvw . Knowing Euler angles 
of each crystal (from EBSD), a misorientation matrix
 is calculated. Figure 2 : Possible strain transfer
across a GB [1].
Figure 1 : Schematic of a bicrystal.
Slip transmission parameters implemented in the toolbox:
What is a bicrystal ?
Quantification of slip transmission
Figure 3 : Geometrical
description of the slip
transfer.
Slip transmission parameter Function Ref.
(C-axis) Misorientation angle () =    1 2
[1]
factor from Livingston and Chamlers
= cos cos +cos cos [3]
 factor from Shen et al.  = cos cos [4]
parameter from Luster and Morris = cos cos [5]
Residual Burgers vector () =   -   [6]
Resolved Shear Stress () or
Schmid Factor (
) = :
with
= [7]
Generalized Schmid Factor ()  =   [7]
100µm
Analysis of CPFE results
GB
Gr. B Gr. A
Figure 5 : AFM topography
of residual indent close to a
GB and profile of pile-up
surrounding the indent. Figure 6 : EBSD map GUI.
Figure 7 : Bicrystal GUI. Figure 8 : preCPFE bicrystal GUI.
Accumulated
basal shear
Accumulated
prism. 1 <a>
shear
Gr. B
Gr. A
Gr. B Gr. A
EBSD CPFEM
Validation on literature data
Conclusion
EBSD data are
required: average
grain orientations and
grain boundaries
positions.
Figure 10 : Calculated
topography from CPFEM.
Figure 11 : Local misorientation from
EBSD measurement and CPFEM results.
Figure 12 : Isosurfaces of
accumulated shear in the
bicrystal obtained by CPFEM.
https://github.com/stabix/stabix
Gr. A
Gr. B
IPF from
MTEX [8]
Figure 13 : Comparison of results obtained with the toolbox and
results from a) Kachers paper [10] and b) Patriarca’s paper [13].
a) b)
Bicrystal meshing Single crystal meshing
Gr. A
Gr. B
Indentation 2014
10 au 12 décembre 2014 - Strasbourg
Mainly prism.<a> to prism.<a> transfer for cp
α
-Tiour study, 9, 10.
Competition between prism.<a> to prism.<a> and prism.<a> to
basal<a> transfers for
α
-Ti alloy.
The strain transfer across grain boundaries (GB)
can be defined by 4 mechanisms :
Strain transfer across GBs
a) direct transfer and GB is
transparent to dislocations
(no strengthening effect);
b) direct transmission leaving
a residual dislocations;
c) indirect transmission
leaving a residual
boundary dislocations;
d) no transfer and the GB acts
as an impenetrable
boundary, which implies
stress accumulations,
localized rotations, pile-up
of dislocations…
STABiX workflow: from EBSD data to CPFEM model in 3 steps
1
2
3
Figure 9 : preCPFE single crystal GUI.
Transmission in cp-Ti
No transmission in cp-Ti
Strain transfer occurs at GB in cp-Ti for :
geometric consideration
m> 0.7 and low RBV
low critical resolved shear stress
Lee’s
criterion11
Ti alloy
Strain transfer
in cp-Ti
References
ResearchGate has not been able to resolve any citations for this publication.
Article
The tensile deformation of bicrystal specimens with longitudinal grain boundaries has been considered, both from the point of view of macroscopic plasticity and from that of dislocation theory. Emphasis has been on the multiple slip associated with the interaction between the two crystals at the boundary. It has been shown that macroscopic continuity at the boundary will in general require the crystals of a bicrystal to deform on at least four slip systems between them, distributed either with two in each crystal or with three in one crystal and one in the other. A model employing the pile-up of dislocations at a grain boundary has led to a method of predicting which additional slip systems will operate in a given bicrystal. Experimental observations of slip lines on twenty-four aluminum bicrystals deformed in tension have supported the predictions made by this method.
  • Z Shen
Shen Z. et al., Scripta Metallurgica (1986), 20(6), pp. 921-926.
  • J Luster
Luster J. et al., Metall. Mater. Trans. A26 (1995) p.1745-1756.
  • M J Marcinkowski
Marcinkowski M.J. et al.., Metal. Trans. (1970), 1(12), pp. 3397-3401.
  • Y Guo
Guo Y. et al., Acta Mater. (2014), 76, pp. 1-12.
  • T C Lee
Lee T.C. et al. Scr. Metall. 23, 799 (1989).
  • C Zambaldi
Zambaldi C. et al., J. Mater. Res. (2012), 27(01), pp. 356-367.
  • L Patriarca
Patriarca L. et al., Mater. Sci. & Eng. (2013), A588, pp. 308-317.