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Investigation of the texture and microstructure evolution around a nanoindent close to an individual grain boundary. David Mercier1 C. Zambaldi1, P. Eisenlohr2 M. A. Crimp2, T. R. Bieler2 1Max-Planck-Institut für Eisenforschung, Düsseldorf, Germany 2Michigan State University, East Lansing, MI 48824, USA 17th International Conference on Textures of Materials August 24-29, 2014 | Dresden, Germany Gr. A Gr. B

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**Plasticity of Single Crystal is well understood.**

Motivation of this work Plasticity of Single Crystal is well understood. Indentation experiments are often used to characterize plasticity of single crystal… More complex, but faster, and possible to probe rapidly a lot of GBs, lot of data in a afternoon… 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 Zambaldi C. “Orientation informed nanoindentation of a-titanium: Indentation pileup in hexagonal metals deforming by prismatic slip.”, J. Mater. Res., 2012, 27(1), pp Zaafarani N. “On the origin of deformation-induced rotation patterns below nanoindents.”, Acta Mater., 2008, 56, pp But, missing element to predict polycrystal mechanics… MERCIER David

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**Micromechanical behavior of grain boundaries.**

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. 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. More complex, but faster, and possible to probe rapidly a lot of GBs, lot of data in a afternoon… Start to model the slip transmission and GB mechanic… MERCIER David

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**MATLAB Toolbox and Graphical User Interfaces (GUIs)**

Strategy Creation of a toolbox MATLAB Toolbox and Graphical User Interfaces (GUIs) Slip transmission model GB and Bicrystal definition Crystal Plasticity MERCIER David

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**a b nGB Bicrystal definition 5 DOF Geometrical description1,2**

Trace of the grain boundary (GB) Geometrical description1,2 GB inclination (b) (by serial polishing or by FIB) and GB trace (a) (by EBSD ) Or GB normal (nGB) Step between grains after polishing / Rougness (by AFM) a b nGB Crystal 1 GB 𝛗 𝟏 𝛟 𝛗 𝟐 𝟏 Crystal 2 𝛗 𝟏 𝛟 𝛗 𝟐 𝟐 𝒖𝒗𝒘 𝝎 Crystallographic description3 Euler angles of grains (12 3) (by EBSD) Or Misorientation axis / angle [uvw] / w (by EBSD or TEM) Randle V. “Five-parameter’ analysis of grain boundary networks by electron backscatter diffraction.”, J. Microscopy, 2005, 222, pp Randle V. “A methodology for grain boundary plane assessment by single-section trace analysis.”, Scripta Mater., 2001, 44, pp Morawiec A., “Orientations and Rotations: Computations in Crystallographic Textures.”, Springer, 2004. MERCIER David

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**Large number of dislocation slip and twinning systems.**

Crystal Plasticity of alpha-Titanium (hcp) Slip systems Pyr. 2nd ord. <c+a> {𝟏𝟏 𝟐 𝟐} <𝟏𝟏 𝟐 𝟑> Basal <a> {𝟎𝟎𝟎𝟏} <𝟏𝟏 𝟐 𝟎> Prism. 1st ord. <a> {𝟏𝟎 𝟏 𝟎} < 𝟏𝟏 𝟐 𝟎 > Prism. 2nd ord. <a> {𝟏𝟏 𝟐 𝟎} < 𝟏 𝟏𝟎𝟎> Pyr. 1st ord. <a> {𝟏𝟎 𝟏 𝟏} < 𝟏𝟏 𝟐 𝟎 > Pyr. 1st ord. <c+a> {𝟏𝟎 𝟏 𝟏} <𝟏𝟏 𝟐 𝟑> Twin systems Tensile twinning {𝟏𝟎 𝟏 𝟐} < 𝟏𝟎 𝟏 𝟏 > Tensile twinning {𝟏𝟏 𝟐 𝟏} < 𝟏𝟏 𝟐 𝟔 > Compr. twinning {𝟏𝟎 𝟏 𝟏} < 𝟏 𝟎𝟏𝟐> Compr. twinning {𝟏𝟏 𝟐 𝟐} < 𝟏𝟏 𝟐 𝟑 > Large number of dislocation slip and twinning systems. MERCIER David

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**Criteria to predict the slip transmission**

N factor (from Livingston & Chalmers)1 Livingston J.D . & Chalmers B., “Multiple slip in bicrystal deformation”, Acta Met. 1957,5, pp 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 Marcinkowski M. J. & Tseng W. F., “Dislocation behavior at tilt boundaries of infinite extent.”, Metallurgical Transactions, 1970, 1(12), pp 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 m’ factor (from Luster & Morris)2 Outgoing slip Incoming slip Residual Burgers vector3 Outgoing slip Incoming slip Schmid Factor, resolved shear stress…4 MERCIER David

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**Strain Transfer parameters implemented in the toolbox**

MERCIER David

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**Experiments Modeling Outline**

Acquisition of EBSD map of the sample Selection of interesting GB using 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 via the MATLAB Toolbox/GUI Creation of output files for CPFEM 3D CPFE modeling EBSD map Experiments AFM topography of a residual indent Cross sectional view of GB Modeling Slip transmission model using CPFEM results and the MATLAB Toolbox/GUI CPFEM displacement result after bicrystal indentation MERCIER David

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**Reconstructed Boundaries file**

EBSD on Ti–5Al–2.5Sn (wt%) sample Loading and 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. Grain file type 2 and Reconstructed Boundaries file Loading of EBSD files. Setting of the coordinate system. Plot of the GBs segments. EBSD orientation map with IPF coloring scheme of Ti–5Al–2.5Sn (wt.%) sample. The sample exhibited a near-𝜶 (HCP) microstructure with the body centered cubic (BCC) phase located primarily at α phase grain boundaries1. Mean grain diameter : (34 ± 16)µm MATLAB Toolbox/GUI Seal J. R. et al., Mater. Sci. and Eng. A 552, 2012, pp MERCIER David

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**Introduction to the MATLAB toolbox**

MERCIER David

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**Selection of a specific grain boundary… Indentation experiments**

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… 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…)… Generation of mesh procedure file and material config. file using Python scripts. MERCIER David

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**Few details about CPFE model**

Generation of a CPFE model with the MATLAB Toolbox/GUI Flow rule given by Kalidindi’s constitutive model1,2,3 Only Prismatic 1st order <a>, Basal <a> and Pyramidal 1st order <c+a> Gr. B 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 References 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 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 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 J. 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 MERCIER David

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**Calculated topography from CPFEM of spherical indent close to a GB.**

CPFEM results (1/3) Gr. A Gr. B Gr. A Gr. B AFM topography of residual indent in Ti-5Al-2.5Sn, close to a grain boundary. To do this process many times…. (statistics…) 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. MERCIER David

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**Local Misorientation from EBSD measurement vs CPFEM results.**

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. MERCIER David

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CPFEM results (3/3) Accumulated prism. 1<a> shear Gr. A Accumulated basal shear Gr. B 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…). MERCIER David

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**Fast transfer of experimental data into simulation input files :**

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 Cu bi-crystal Straining test and TEM3. 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 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). Shen Z. et al., “Dislocation and grain boundary interactions in metal.”, Acta Metal., 1988, 36(12), pp Tensile test of Aluminum oligocrystal “dogbone”1. µ-pillar compression test and µ-cantilever bending test 2. MERCIER David

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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 a-titanium.”, Phil. Mag., 2014, pp Good agreement in term of residual Burgers vector calculated with the MATLAB Toolbox and values given in Kacher’s paper. MERCIER David

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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 Good agreement in term of residual Burgers vector calculated with the MATLAB Toolbox and values given in Patriarca’s paper. MERCIER David

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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…) 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… MERCIER David

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**Thanks for your attention…. d.mercier@mpie.de**

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 ? MERCIER David

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