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Max-Planck-Institut für Eisenforschung GmbH Investigation of the texture and microstructure evolution around a nanoindent close to an individual grain boundary. David Mercier 1 C. Zambaldi 1, P. Eisenlohr 2 M. A. Crimp 2, T. R. Bieler 2 1 Max-Planck-Institut für Eisenforschung, Düsseldorf, Germany 2 Michigan State University, East Lansing, MI 48824, USA 17 th 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. Indentation experiments are often used to characterize plasticity of single crystal… MERCIER David2 Motivation of this work Inverse pole figure of pile-up topographies of cp-Ti 1 Misorientation maps underneath the indentation at different cross sections, comparison between experimental and simulation results 2 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 Zaafarani N. “On the origin of deformation-induced rotation patterns below nanoindents.”, Acta Mater., 2008, 56, pp But, missing element to predict polycrystal mechanics…

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Micromechanical behavior of grain boundaries. EBSD and indentations close to grain boundaries are performed in alpha-Ti quasi bi-crystal deformation MERCIER David3 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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MERCIER David4 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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MERCIER David Bicrystal definition 5 DOF 1.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, Crystallographic description 3 Geometrical description 1,2 5 1.Euler angles of grains (by EBSD) Or 2.Misorientation axis / angle [uvw] (by EBSD or TEM) Trace of the grain boundary (GB) Crystal 1 Crystal 2 GB n GB 1.GB inclination (by serial polishing or by FIB) and GB trace (by EBSD ) Or GB normal n GB 2.Step between grains after polishing / Rougness (by AFM)

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Crystal Plasticity of alpha-Titanium (hcp) Large number of dislocation slip and twinning systems. Slip systems Twin systems MERCIER David

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MERCIER David Criteria to predict the slip transmission m’ factor (from Luster & Morris) 2 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 N factor (from Livingston & Chalmers) 1 Residual Burgers vector 3 Schmid Factor, resolved shear stress… 4 Outgoing slipIncoming slip Outgoing slipIncoming slip

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Strain Transfer parameters implemented in the toolbox MERCIER David

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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 1 st slip transmission analysis via the MATLAB Toolbox/GUI Creation of output files for CPFEM using 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 results and the MATLAB Toolbox/GUI Cross sectional view of GB Experiments Modeling MERCIER David

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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. MERCIER David10 1.Seal J. R. et al., Mater. Sci. and Eng. A 552, 2012, pp 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 MERCIER David

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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… MERCIER David12 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 GB Gr. BGr. A

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MERCIER David13 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 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 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. 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 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 Flow rule given by Kalidindi’s constitutive model 1,2,3 Only Prismatic 1 st order, Basal and Pyramidal 1 st order MERCIER David Gr. B Gr. A

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MERCIER David15 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. A Gr. B Gr. A Local Misorientation from EBSD measurement vs CPFEM results. EBSD CPFEM CPFEM results (2/3) MERCIER David

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Gr. A Accumulated basal shear Accumulated prism. 1 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 and basal, low RBV, high LRB…). MERCIER David

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Advantages of the GUI MERCIER David18 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 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 Cu bi-crystal Tensile test of Aluminum oligocrystal “dogbone” 1. Straining test and TEM 3. µ-pillar compression test and µ-cantilever bending test

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Results from in situ straining test in TEM (Kacher et al. 2012) MERCIER David19 “In situ and tomographic analysis of dislocation/grain boundary interactions in - 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

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Results from polycrystal tensile test (Patriarca et al. 2014) MERCIER David20 “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

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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 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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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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