Keynote lecture at European Conference for Computational Mechanics

1. Small scale deformation studied via experiments and dislocation-based crystal plasticity FE simulation D. Raabe, F. Roters, P. Eisenlohr, N. Zaafarani, E. Demir Düsseldorf, Germany WWW.MPIE.DE d.raabe@mpie.de large scale pillar small scale pillar 20. May 2010, ECCM,Paris

4. 2 Multiscale crystalplasticity FEM Raabe, Zhao, Park, Roters: Acta Mater. 50 (2002) 421

5. 3 T T T T T T T T Physics-based constitutive laws: mean field theory 1 dyadic flow law based on dislocation rate theory 1. set internal variables Taylor, Kocks, Mecking, Estrin, Kubin,... plastic gradients, size scale and orientation gradients (implicit) 2 2. set internal variables Nye-Kröner,.... 3 grain boundaries 3. set internal variables activation concept: energy of formation upon slip penetration: conservation law Ma, Roters, Raabe: Acta Mater. 54 (2006) 2169; Ma, Roters, Raabe: Acta Mater. 54 (2006) 2181; Ma, Roters, Raabe: Intern. J Sol. Struct. 43 (2006) 7287 Roters et al.: Acta Mater. (2010)

8. 5 [111] [-110] [11-2] [111] [-110] [11-2] Nanoindentation (smallerisstronger): 3D EBSD and CPFEM Cu, 60° conical, tip radius 1μm, loading rate 1.82mN/s, loads: 4000μN, 6000μN, 8000μN, 10000μN Hardnessand GND* in oneexperiment Higher GND densityatsmallerscales? * GND: geometrically necessary dislocations (accomodate curvature) Zaafaraniet al. ActaMat. 54 (2006) 1707; Wang et al. Acta Mat. 52 (2004) 2229

9. 6 20° 0° Misorientation angle [111] [-110] [11-2] Nanoindentation (smallerisstronger): 3D EBSD and CPFEM Cu, 60° conical, tip radius 1μm, loading rate 1.82mN/s, loads: 4000μN, 6000μN, 8000μN, 10000μN * GND: geometrically necessary dislocations (accomodate curvature) Zaafaraniet al. ActaMat. 54 (2006) 1707; Wang et al. Acta Mat. 52 (2004) 2229

10. 7 25° experiment simulation 20° 15° 10° 5° [111] [111] [-110] [-110] 0 [11-2] [11-2] Comparison, crystal rotations (absolute, about [11-2] axis) Absolute rotations experiment CPFEM, viscoplastic CPFEM, dislocation-based <11-2> rotations - + + - + - experiment CPFEM, viscoplastic CPFEM, dislocation-based Zaafarani, Raabe, Roters, Zaefferer: Acta Mater. 56 (2008) 31

11. Simplify, strainpath 8 Zaafarani, Raabe, Roters, Zaefferer: Acta Mater. 56 (2008) 31

14. 10 Al Bicrystals, low angle g.b. [112] 7.4°, v Misesstrain von Mises strain [1] experiment SSD 10% 20% 30% 40% 50% CPFEM: viscoplastic phenomen. model CPFEM: dislocation- based model; g.b. model 10% 20% 30% 40% 50% Ma, Roters, Raabe: Acta Mater. 54 (2006) 2169 and 2181

15. Crystal Mechanics FEM, grain scale mechanics (2D) Experiment (DIC, EBSD) v Mises strain Simulation (CP-FEM) v Mises strain Sachtleber et al. Mater. Sc. Eng. A 336 (2002) 81; Raabe et al. Acta Mat. 49 (2001)

16. 12 5mm equivalent strain 5mm equivalent strain Crystal plasticity FEM, grainscalemechanics (3D Al) exp., grain orientation, side B exp., grain orientation, side A 8mm 21mm 1mm FE mesh Zhao, Rameshwaran, Radovitzky, Cuitino, Roters, Raabe: Intern. J. Plast. 24 (2008)

19. 14 20° 0° misorientationangle orientation gradient (spacing d from EBSD scan) From local misorientations to GNDs misorientation orientation difference Demir, Raabe, Zaafarani, Zaefferer: Acta Mater. 57 (2009) 559

20. 15 From local misorientations to GNDs dislocation tensor (GND) J. F. Nye. Some geometrical relations in dislocated crystals. Acta Metall. 1:153, 1953. E. Kröner. KontinuumstheoriederVersetzungen 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. Demir, Raabe, Zaafarani, Zaefferer: Acta Mater. 57 (2009) 559

21. 16 Frank loop through area r 18 b,t combinations 9 b,t combinations From local misorientations to GNDs T T T Demir, Raabe, Zaafarani, Zaefferer: Acta Mater. 57 (2009) 559

22. 17 Extract geometrically necessary dislocations Demir, Raabe, Zaafarani, Zaefferer: Acta Mater. 57 (2009) 559

23. 18 Size effect as a mean-field break down phenomenon Meanfield break-down: sourcesizedependence 2. Schmid law break down: fromPeierlstosourcemechanism is NOT identical on systemswiththe same index Demir, Raabe, Roters: Acta Mater. 58 (2010) Pages 1876

26. 20 MicroscaleBauschinger* effect in beam bending straightening (backward) Kernal average misorientation bending (forward) orientation map orientation map Kernal average misorientation * Bauschinger effect: flow stress asymmetry upon load path change

29. 22

30. 23 Exampleofpatterningphenomena: plasticlaminates in bicrystals Kuo et al., Adv. Eng. Mater.5 (2003)563 Zaefferer et al. Acta Mater. 51 (2003) 4719

31. Simplify: plasticlaminates in singlecrystals together with O. Dmitrieva, P. Dondl, S. Müller Dmitrieva et al., Acta Mater 57 (2009) 3439

35. Includephenomenologicalordislocation-basedhardeninglaws

36. Goodatpredictingstresses, strains, shapes, contact, texture

37. One-to-onecomparisontoexperiments

38. Limits: constitutiveaspectswhere DDD isbettersuited (limitsofstatisticalandmeanfieldmodels): sizeeffects, sourcelimitations, bursts, localization, Bauschingereffect, patterningandlaminatesRoters et al. Acta Mater.58 (2010)