Department of Microstructure Physics and Metal Forming Düsseldorf, Germany Piling-up behavior during axisymmetric indentation and its relation to the activated deformation mechanisms in  -TiAl C. Zambaldi, F. Roters, D. Raabe MRS Fall 2010

Max-Planck-Institut für Eisenforschung C. Zambaldi, F. Roters, D. Raabe Overview Introduction Experiments: nanoindentation, AFM, EBSD Crystal plasticity finite element (CP-FEM) simulation of anisotropic flow during nanoindentation Comparison of experiment and simulation Anisotropic hardness of γ -TiAl

Max-Planck-Institut für Eisenforschung C. Zambaldi, F. Roters, D. Raabe Nanoindentation Instrumented indentation is a simple and potentially highly accurate materials testing method Mechanical characterization from nano to macro Uniaxial testing: 1-d flow curve; Indentation: load-displacement curve (1-d) as well as pile-up (2-d). Complex 3-dimensional deformation Crystal-Plasticity-FEM (CPFEM) capable to describe the orientation dependency during indentation; orientation information needed

Max-Planck-Institut für Eisenforschung C. Zambaldi, F. Roters, D. Raabe Crystal plasticity of γ -TiAl 3 Deformation modes 4 systems for {111}  1-10] slip by ordinary dislocations, b=1/2  110] 8 systems for {111}  -101] slip by superdislocations, b=  101] 4 twinning systems of type {111}  11-2] unidirectional with a fixed amount of shear (1/sqrt(2)), b= 1/6  11-2] (110) (111)

Max-Planck-Institut für Eisenforschung C. Zambaldi, F. Roters, D. Raabe γ- TiAl, indentation experiments [Göken & Kempf, 2001, 2002] Order variants result in 3-fold symmetry of pile-up during  111  indentation [111] indentation [Göken & Kempf, 2001, 2002] Pronounced orientation dependency during indentation, e.g. pile-up

Max-Planck-Institut für Eisenforschung C. Zambaldi, F. Roters, D. Raabe Identification of order domains by EBSD x x x x x x x x x x x x x x x x o o o o o o o o o o o o o o o o o o o o o o o o o Fit-rank EBSD indexing Zambaldi, Zaefferer, Wright; J. Appl Cryst. (Dec 2009)

Max-Planck-Institut für Eisenforschung C. Zambaldi, F. Roters, D. Raabe Nanoindentation & EBSD & AFM γ -TiAl single crystals cannot be grown in the specific compositions  Nanoindentation in fine microstructures Characterization by AFM & EBSD

Max-Planck-Institut für Eisenforschung C. Zambaldi, F. Roters, D. Raabe Elasto-viscoplastic CPFEM model of  -TiAl Continuum mechanics: Crystal plasticity: Strain rate law: Hardening law: Kalidindi et al. (1992) J. Mech. Phys. Solids; Roters et. al. Acta Mater (Review)

Max-Planck-Institut für Eisenforschung C. Zambaldi, F. Roters, D. Raabe 3-dimensional simulation of nanoindentation Ti Al Meshing, contact, strong gradients, numerical robustness,…

Max-Planck-Institut für Eisenforschung C. Zambaldi, F. Roters, D. Raabe Iterative fitting of tip geometry Comparison of remaining impression shape with simulated indent

Max-Planck-Institut für Eisenforschung C. Zambaldi, F. Roters, D. Raabe Piling-up / sinking-in behavior Influence of hardening parameters τcτc shear strain γ Sink-in Pile-up Pile-up Sink-in

Max-Planck-Institut für Eisenforschung C. Zambaldi, F. Roters, D. Raabe Study of orientation dep. pile-up Near-equidistant directions 8°~9° misorientation Improper rotation leads to change in handedness of the pile-up

Max-Planck-Institut für Eisenforschung C. Zambaldi, F. Roters, D. Raabe Displaying pile-up topographies A convention for in-plane rotation of pile-up topographies Simulation: use convention to choose orientations directly Experiment: backrotate topographies with arbitrary in-plane orientation into the unique position

Max-Planck-Institut für Eisenforschung C. Zambaldi, F. Roters, D. Raabe Simulated pile-up profiles Pile-up IPF from 51 orientations approx. resol. 9° Zambaldi & Raabe, Acta Mater. 2010

Max-Planck-Institut für Eisenforschung C. Zambaldi, F. Roters, D. Raabe Simulated pile-up profiles Pile-up IPF High symmetry orientations [001] [101] [100] [110] [111] Zambaldi & Raabe, Acta Mater. 2010

Max-Planck-Institut für Eisenforschung C. Zambaldi, F. Roters, D. Raabe Comparison AFM / CP-FEM topography ExperimentSimulation

Max-Planck-Institut für Eisenforschung C. Zambaldi, F. Roters, D. Raabe [u v w]=[3 1 4] indentation [3 1 4] [1 1 1]

Max-Planck-Institut für Eisenforschung C. Zambaldi, F. Roters, D. Raabe [101] indentation in γ -TiAl

Max-Planck-Institut für Eisenforschung C. Zambaldi, F. Roters, D. Raabe Relative strengths of slip systems (Ti-50Al) Cu, Al, Au, Ag,… Predicted for Ti-55Al [101] indentation indicates relative strengths of ordinary and super dislocation glide in TiAl

Max-Planck-Institut für Eisenforschung C. Zambaldi, F. Roters, D. Raabe Extension to hexagonal α 2 -Ti 3 Al 22 orientations after the developed convention Prismatic -slip is easy to activate  22 CPFEM simulations

Max-Planck-Institut für Eisenforschung C. Zambaldi, F. Roters, D. Raabe Pile-up IPF & AFM result close to [ ] 2 µm α 2 -Ti 3 Al

Max-Planck-Institut für Eisenforschung C. Zambaldi, F. Roters, D. Raabe Conclusions Ordinary dislocation glide in near-stoichiometric γ- TiAl is an intrinsic property, i.e. not interface- related Twinning contributes to deformation to a minor extent during single phase indentation of γ -TiAl Nanoindentation combined with AFM, EBSD and CP-FEM can characterize activation of individual slip systems in single crystal indentation Method based on highest accuracy values: P, h Axisymmetric indenters need to be employed to make the method efficient

Max-Planck-Institut für Eisenforschung C. Zambaldi, F. Roters, D. Raabe Vielen Dank. Samples were provided by G. Behr, W. Löser (IFW Dresden) U. Hecht (ACCESS e.V. Aachen) Support by the European Union FP6 project IMPRESS (Intermetallic Materials Processing in Relation to Earth and Space Solidification) is gratefully acknowledged.

Max-Planck-Institut für Eisenforschung C. Zambaldi, F. Roters, D. Raabe References C. Zambaldi, D. Raabe, Plastic anisotropy of gamma-TiAl revealed by axisymmetric indentation, Acta Materialia 58 (9) (2010) 3516–3530, doi: /j.actamat /j.actamat C. Zambaldi, S. Zaefferer, S. Wright, Characterization of order domains in gamma-TiAl by orientation microscopy based on electron backscatter diffraction, Journal of Applied Crystallography 42 (6) (2009) 1092–1101, doi: /S , pdf: N. Zaafarani D. Raabe, R. N. Singh, F. Roters, S. Zaefferer: Acta Mater. 54 (2006) 1863–1876 Three dimensional investigation of the texture and microstructure below a nanoindent in a Cu single crystal using 3D EBSD and crystal plasticity finite element simulations E. Demir, D. Raabe, N. Zaafarani, S. Zaefferer: Acta Mater. 57 (2009) 559–569 Experimental investigation of geometrically necessary dislocations beneath small indents of different depths using EBSD tomography Y. Wang, D. Raabe, C. Klüber, F. Roters: Acta Mater. 52 (2004) Orientation dependence of nanoindentation pile-up patterns and of nanoindentation microtextures in copper single crystals N. Zaafarani, D. Raabe, F. Roters and S. Zaefferer: Acta Mater. 56 (2008) On the origin of deformation-induced rotation patterns below nanoindents F. Roters, P. Eisenlohr, L. Hantcherli, D.D. Tjahjanto, T.R. Bieler, D. Raabe: Acta Materialia 58 (2010) 1152–1211 Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications