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 für Eisenforschung, 40237 Düsseldorf, Germany2Michigan State University, East Lansing, MI 48824, USA

17th International Conference on Textures of MaterialsAugust 24-29, 2014 | Dresden, Germany

Gr. A

Gr. B

Plasticity of Single Crystal is well understood. Indentation experiments are often used to characterize

plasticity of single crystal…

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Motivation of this work

Inverse pole figure of pile-up topographies of cp-Ti1

Misorientation maps underneath the indentation at different cross sections, comparison between experimental and

simulation results2

1. Zambaldi C. “Orientation informed nanoindentation of a-titanium: 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.

But, missing element to predict polycrystal mechanics…

Micromechanical behavior of grain boundaries.EBSD and indentations close to grain boundariesare performed in alpha-Ti quasi bi-crystal deformation.

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AFM topography of residual indent in Ti-5Al-2.5Sn, close to a grain boundary.

Gr. A

Gr. B

Comparison of experimental results (residual topography, texture around indent…) to simulated indentations as

predicted by 3D CPFE modeling.

Start to model the slip transmission and GB

mechanic…

Motivation of this work (2/2)

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Strategy Creation of a toolbox

MATLAB Toolbox and Graphical User Interfaces (GUIs)

Slip transmission

model

GB and Bicrystal definition

Crystal Plasticity

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Bicrystal definition 5 DOF

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.

Crystallographic description3

Geometrical description1,2

5

1. Euler angles of grains (12 3) (by EBSD)

Or

2. Misorientation axis / angle[uvw] / w (by EBSD or TEM)

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Trace of the grain boundary (GB)

Crystal 1

Crystal 2

GB

(𝛗𝟏𝛟𝛗𝟐 )𝟏(𝛗𝟏𝛟𝛗𝟐 )𝟐

[𝒖𝒗𝒘 ] /𝝎

nGB

1. GB inclination (b) (by serial polishing or by FIB) and

GB trace (a) (by EBSD )

OrGB normal (nGB)

2. Step between grains after polishing / Rougness (by AFM)

b

a

Crystal Plasticity of alpha-Titanium (hcp)

Large number of dislocation slip and twinning systems.

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>{} <>

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Criteria to predict the slip transmission

m’ factor (from Luster & Morris)21. 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.

coscos' m

7

outinr bbb

N factor (from Livingston & Chalmers)1

Residual Burgers vector3

inoutoutinoutinoutin dndnddnnN **

Schmid Factor, resolved shear stress…4

Outgoing slip Incoming slip

Outgoing slip Incoming slip

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Strain Transfer parameters implemented in the toolbox

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Outline

Acquisition of EBSD map of the sample

Selection of interesting GBusing the MATLAB Toolbox/GUI

Spherical indentation close to the chosen GBs

Measurement of the topography by AFM and of the lattice rotation by EBSD

Inclination of GB measured by FIB or serial polishing

1st slip transmission analysis viathe MATLAB Toolbox/GUI

Creation of output files for CPFEMusing the MATLAB Toolbox/GUI

3D CPFE modeling

AFM topography of a residual indent

EBSD map

CPFEM displacement result after bicrystal

indentation

Slip transmission model using CPFEM resultsand the MATLAB Toolbox/GUI

Cross sectional view of GB

Exp

erim

ents

Mo

del

ing

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EBSD on Ti–5Al–2.5Sn (wt%) sample

EBSD orientation map with IPF coloring scheme of Ti–5Al–2.5Sn (wt.%) sample.

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The sample exhibited a near- (HCP) microstructure with the body centered cubic (BCC) phase located primarily at α phase grain boundaries1.

Mean grain diameter : (34 ± 16)µm

1. Seal J. R. et al., Mater. Sci. and Eng. A 552, 2012, pp. 61-68.

• 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.

MATLAB Toolbox/GUI

Outputs from OIM™ Data Analysis

Grain file type 2 and

Reconstructed Boundaries file

Loading and Plot of EBSD data

Loading of EBSD files.

Setting of the coordinate system.

Plot of the GBs segments.

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Introduction to the MATLAB toolbox

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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…

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Indentation experiments

Gr. A

Gr. B

AFM topography of residual indent in Ti-5Al-2.5Sn, close to a grain boundary with profiles of pile-up surrounding the indent.

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GB

Gr. B Gr. A

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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.

CPFE model generation from the GUI

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Few details about CPFE model

Generation of a CPFE model with the MATLAB Toolbox/GUI

References1. 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

• 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/

• Flow rule given by Kalidindi’s constitutive model1,2,3

• Only Prismatic 1st order <a>, Basal <a> and Pyramidal 1st order <c+a>

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Gr. B

Gr. A

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CPFEM results (1/3)

•Small discrepancy between experimental and simulated pile-up topographies indicate strain transfer is mainly controlled by geometrical consideration.

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.

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•The CPFE model with no strengthening effect from grain boundaries seems to predict almost correctly the plasticity transfer.

Gr. B

Gr. AGr. B Gr. A

Local Misorientation from EBSD measurement vs CPFEM results.

EBSDCPFEM

CPFEM results (2/3)

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Gr. A

Accumulated basal shear

Accumulated prism. 1<a>

shear

Gr. B

Isosurfaces of accumulated shear int the bicrystal obtained by CPFEM.

CPFEM results (3/3)

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

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•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

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.

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Results from in situ straining test in TEM (Kacher et al. 2012)

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“In situ and tomographic analysis of dislocation/grain boundary interactions in a-titanium.”, 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)

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“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 ?

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d.mercier@mpie.de

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