Demir, E.

Ma, D.

Raabe, D.

Roters, F.

Weber, F.

Zaafarani, N.

Zaefferer, S.

English

MPG.PuRe

3D EBSD analysis of mechanical size effects during indentation: EBSD tomography and crystal plasticity FEM

3D EBSD analysis of mechanical size effects during indentation:EBSD tomography and crystal plasticity FEME. Demir, N. Zaafarani, F. Weber, D. Ma, S. Zaefferer, F. Roters, D. RaabeDepartment of Microstructure Physics and Metal FormingDüsseldorf, GermanyJanuary 07th, 2009; PLASTICITY 2009, St Thomas, Virgin Islands, USAd.raabe@mpie.de1Dierk Raabe, PLASTICITY 2009, Jan. 2009, d.raabe@mpie.de Motivation and approach Sample preparation Deformation experiments Characterization Orientation gradients Dislocation analysis Results Other examples: Wire bending, pillar compression ConclusionsOverview2Dierk Raabe, PLASTICITY 2009, Jan. 2009, d.raabe@mpie.deOverview Motivation and approach Sample preparation Deformation experiments Characterization Orientation gradients Dislocation analysis Results Other examples: Wire bending, pillar compression Conclusions3Dierk Raabe, PLASTICITY 2009, Jan. 2009, d.raabe@mpie.deOverviewChallenges in size dependent mechanics• Theoretical concept (GND, gradients, sources, hardening, localization, …)• Experiments asking a specific question• Homogeneity of the microstructure• Boundary conditions of the experimenthallenges in size dependent echanics• Theoretical concept ( , gradients, sources, hardening, localization, )• Experi ents asking a specific question• o ogeneity of the icrostructure• oundary conditions of the experi ent4Dierk Raabe, PLASTICITY 2009, Jan. 2009, d.raabe@mpie.de3% 8%15%Microstructure not homogeneousBoundary conditions essentialMicrostructure not homogeneousBoundary conditions essentialHomogeneity and boundary conditions – large scaleM. Sachtleber, Z. Zhao, D. Raabe: Mater. Sc. Engin. A 336 (2002) 81D. Raabe, M. Sachtleber, Z. Zhao, F. Roters, S. Zaefferer: Acta Mater. 49 (2001) 3433–34415Dierk Raabe, PLASTICITY 2009, Jan. 2009, d.raabe@mpie.de1mm21mm8mm5mm 5mmCrystal plasticity FEM, grain scale mechanics (3D)Z. Zhao, M. Ramesh, D. Raabe, A. Cuitino, R. Radovitzky: Intern. J. Plast. 24 (2008) 2278–2297orientationvM strain6Dierk Raabe, PLASTICITY 2009, Jan. 2009, d.raabe@mpie.de[-110][11-2][111]Homogeneity and boundary conditions – small scale7Dierk Raabe, PLASTICITY 2009, Jan. 2009, d.raabe@mpie.de Relationship between ISE and GND: hardness and GND in the same experiment Indents of different depths, Cu single crystal High resolution 3D EBSD Determine plastic volume beneath indents Calculate GNDs around indents from 3D orientationgradients and plastic volume Also: Wire bending; pillar compressionMotivation and approach: specific8Dierk Raabe, PLASTICITY 2009, Jan. 2009, d.raabe@mpie.deOverview Motivation and approach Sample preparation Deformation experiments Characterization Orientation gradients Dislocation analysis Results Other examples: Wire bending, pillar compression Conclusions9Dierk Raabe, PLASTICITY 2009, Jan. 2009, d.raabe@mpie.deNanoindentation[-110][11-2][111]Y. Wang, D. Raabe, C. Klüber, F. Roters: Acta Mater. 52 (2004) 222960° conical, tip radius 1μm, loading rate 1.82mN/s, loads of 4000μN, 6000μN, 8000μN and 10000μN10Dierk Raabe, PLASTICITY 2009, Jan. 2009, d.raabe@mpie.de3D electron microscopy, 3D EBSD, tomographyJ. Konrad, S. Zaefferer, D. Raabe, Acta Mater. 54 (2006) 1369S. Zaefferer, S. I. Wright, D. Raabe, Metall. Mater. Trans. A 39A (2008) 37411Dierk Raabe, PLASTICITY 2009, Jan. 2009, d.raabe@mpie.deCrystal Mechanics FEM (General)DFT, ultrasonicsDDD, TEM, single crystal testsCrystallography, MD, Peierls analysisEBSD, RVE,….Kinematics in CPFEMStatistical dislocation-basedhardening law in CPFEMD. Raabe, P. Klose, B. Engl, K.-P. Imlau, F. Friedel, F. Roters: Adv. Eng. Mater. 4 (2002) 169-18012Dierk Raabe, PLASTICITY 2009, Jan. 2009, d.raabe@mpie.deflow law1ee:−= FFLe &1ppp :~ −= FFL &1epep~: −= FLFLDefinitions:constitutive reduction of DOF:ααααγ ndL ~~~121p ⊗=∑=&),,(),,(θτγθττγαααααρ&& c PhenomenologicalDislocation density laws1: −= FFL &F* :  elastic and rotation deformation gradientF   :  total deformation gradientFp :  plastic deformation gradientLp :  plastic velocity  gradientLe :  elastic velocity gradientMultiplicative Decomposition ofthe Deformation GradientbvtZbXxnt md1ddd ργγ ===&Crystal Plasticity FEM (constitutive laws)13Dierk Raabe, PLASTICITY 2009, Jan. 2009, d.raabe@mpie.dedyadic flow law based on dislocation rate theoryPhysics-based constitutive laws: mean field theoryplastic gradients, size scale and orientation gradients (implicit)11. set internalvariables2grain boundaries32. set internalvariables3. set internalvariablesTTTTTTTTTaylor, Kocks, Mecking, Estrin, Kubin,...Nye, Ashby, Kröner,....activation concept:energy of formation upon slip penetration: conservation lawMa, Roters, Raabe: Acta Mater. 54 (2006) 2169; Ma, Roters, Raabe: Acta Mater. 54 (2006) 2181; Ma, Roters, Raabe: Intern. J Sol. Struct. 43 (2006) 728714Dierk Raabe, PLASTICITY 2009, Jan. 2009, d.raabe@mpie.deDislocation classes¾ Mobile dislocationsaccommodate the external plastic deformation¾ Immobile dislocations (cell interior, cell walls)work hardening, including locks and dipoles¾ Geometrically necessary dislocationspreserve the lattice continuity15Dierk Raabe, PLASTICITY 2009, Jan. 2009, d.raabe@mpie.deSSDIISSDISSDIISSDISSD )()()()(−−++ +++= ρρρρρ &&&&&Rate equationsRate equations are formulated for the immobile dislocation densities:Four mechanisms:mechanism 1 :  lock formationmechanism 2 : dipole formationmechanism 3 : athermal annihilationmechanism 4 : thermally activated annihilation by climbA. Ma F. Roters D. Raabe: Acta Mater. 54 (2006) 216916Dierk Raabe, PLASTICITY 2009, Jan. 2009, d.raabe@mpie.deAl Bicrystals, low angle g.b. [112] 7.4°, v Mises strainSSD10%               20%               30%               40%   50%experimentviscoplasticphenomen.modeldislocation-based model;g.b. model von Misesstrain [1]A. Ma F. Roters D. Raabe: Acta Mater. 54 (2006) 218117Dierk Raabe, PLASTICITY 2009, Jan. 2009, d.raabe@mpie.deOverview Motivation and approach Sample preparation Deformation experiments Characterization Orientation gradients Dislocation analysis Results Other examples: Wire bending, pillar compression Conclusions18Dierk Raabe, PLASTICITY 2009, Jan. 2009, d.raabe@mpie.de[-110][111][11-2]Misorientation angle0°20°Crystal orientation distribution around nanoindentsZaafarani, Raabe, Singh, Roters, Zaefferer: Acta Mater. 54 (2006) 1707;            Zaafarani, Raabe, Roters, Zaefferer: Acta Mater. 56 (2008) 3119Dierk Raabe, PLASTICITY 2009, Jan. 2009, d.raabe@mpie.descan7scan8scan9Comparison, crystal rotations about [11-2] axisphenomenologicalCPFEMexperiment3D EBSDdislocation-basedCPFEMexperimentsimulationN. Zaafarani D. Raabe, R. N. Singh, F. Roters, S. Zaefferer: Acta Mater. 54 (2006) 1707N. Zaafarani, D. Raabe, F. Roters and S. Zaefferer: Acta Mater. 56 (2008) 31[-110][111][11-2]20Dierk Raabe, PLASTICITY 2009, Jan. 2009, d.raabe@mpie.deSimplify21Dierk Raabe, PLASTICITY 2009, Jan. 2009, d.raabe@mpie.dePattern quality, rotation field, indents of different size22Dierk Raabe, PLASTICITY 2009, Jan. 2009, d.raabe@mpie.deOverview Motivation and approach Sample preparation Deformation experiments Characterization Orientation gradients Dislocation analysis Results Other examples: Wire bending, pillar compression Conclusions23Dierk Raabe, PLASTICITY 2009, Jan. 2009, d.raabe@mpie.deLocal misorientation analysis24Dierk Raabe, PLASTICITY 2009, Jan. 2009, d.raabe@mpie.deFrom local misorientations to GNDsmisorientationorientation differenceorientation gradient(spacing d from EBSD scan)25Dierk Raabe, PLASTICITY 2009, Jan. 2009, d.raabe@mpie.deFrom local misorientations to GNDsdistortion(sym, a-sym)dislocation tensor (GND)J. F. Nye. Some geometrical relations in dislocated crystals. Acta Metall. 1:153, 1953.E. Demir, D. Raabe, N. Zaafarani, S. Zaefferer: Acta Mater. 57 (2009) 559–569E. Kröner. Kontinuumstheorie der Versetzungen und Eigenspannungen (in German). Springer, Berlin, 1958.E. Kröner. Physics of defects, chapter Continuum theory of defects, p.217. North-Holland Publishing, Amsterdam, Netherlands, 1981.26Dierk Raabe, PLASTICITY 2009, Jan. 2009, d.raabe@mpie.deFrom local misorientations to GNDsFrank loop through area rDDT in terms of 18 b,t combinationsDDT in terms of 9 b,t combinationsE. Demir, D. Raabe, N. Zaafarani, S. Zaefferer: Acta Mater. 57 (2009) 559–56927Dierk Raabe, PLASTICITY 2009, Jan. 2009, d.raabe@mpie.deOverview Motivation and approach Sample preparation Deformation experiments Characterization Orientation gradients Dislocation analysis Results Other examples: Wire bending, pillar compression Conclusions28Dierk Raabe, PLASTICITY 2009, Jan. 2009, d.raabe@mpie.deDistribution of GNDs for different gradient resolutionscenter section, 2D analysis, color code: GND density (decadic log. (1/m2) )50 nm100 nm200 nm29Dierk Raabe, PLASTICITY 2009, Jan. 2009, d.raabe@mpie.deReference volumes (red color) indicates the plastic volume using lower threshold of GNDs of 1014/m2Identification of the plastic volumedepth[μm]center section, 2D analysis, color code: GND density (decadic log. (1/m2) )E. Demir, D. Raabe, N. Zaafarani, S. Zaefferer: Acta Mater. 57 (2009) 559–56930Dierk Raabe, PLASTICITY 2009, Jan. 2009, d.raabe@mpie.deExtract geometrically necessary dislocationsE. Demir, D. Raabe, N. Zaafarani, S. Zaefferer: Acta Mater. 57 (2009) 559–56931Dierk Raabe, PLASTICITY 2009, Jan. 2009, d.raabe@mpie.de Motivation and approach Sample preparation Deformation experiments Characterization Orientation gradients Dislocation analysis Results Other examples: Wire bending, pillar compression ConclusionsOverview32Dierk Raabe, PLASTICITY 2009, Jan. 2009, d.raabe@mpie.deSimilar experiment for bendingF. Weber, I. Schestakow, D. Raabe, F. Roters: Adv. Engin. Mater. 10 (2008) 737-74133Dierk Raabe, PLASTICITY 2009, Jan. 2009, d.raabe@mpie.deParameter study: frictionMetallic micropillar deformationD. Raabe, D. Ma, F. Roters: Acta Mater. 55 (2007) 4567–458334Dierk Raabe, PLASTICITY 2009, Jan. 2009, d.raabe@mpie.deParameter study: individual slip activity and heterogeneityMetallic micropillar deformationD. Raabe, D. Ma, F. Roters: Acta Mater. 55 (2007) 4567–458335Dierk Raabe, PLASTICITY 2009, Jan. 2009, d.raabe@mpie.decorresponding experiments by : Robert Maaß, Steven Van Petegem, Julien Zimmermann, Daniel Grolimund, Helena Van SwygenhovenSimulation resultsMetallic micropillar deformation36Dierk Raabe, PLASTICITY 2009, Jan. 2009, d.raabe@mpie.deOverview Motivation and approach Sample preparation Deformation experiments Characterization Orientation gradients Dislocation analysis Results Other examples: Wire bending, pillar compression Conclusions37Dierk Raabe, PLASTICITY 2009, Jan. 2009, d.raabe@mpie.de The GNDs have an inhomogeneous distribution underneath the indentswith very high local density values. No homogeneous distribution. The total GND density below the indents decreases with decreasingindentation depths. This observation does not conform to strain gradienttheories attributing size-dependent material properties to GNDs. The amount of deformation imposed reduces with decreasingindentation depths. Therefore, SSDs that evolve through strain do notaccount for the increasing hardness values with decreasing indentationdepth. Inhomogeneous distribution of GNDs plays a main role. Explaining size dependent material strengthening effects by usingaverage density measures for both GNDs and SSDs is not sufficient to understand the indentation size effect. More critical experiments on physics of size effects Control and numerical analysis of boundary conditionsConclusions (indents)

http://hdl.handle.net/11858/00-001M-0000-0019-42B8-D

3D EBSD analysis of mechanical size effects during indentation: EBSD tomography and crystal plasticity FEM

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