1. Multiscale Models of Crystals D. Raabe, F. Roters, S. Zaefferer, P. Eisenlohr Department ofMicrostructurePhysicsandMetalForming WWW.MPIE.DE D.RAABE@MPIE.DE 02. May 2010

2. 1 MPIE Departments Shareholder:Max-Planck-Society, German Steel Institute Scientific Board Trustees Board Strategy Board MPIE ScientificBoard JörgNeugebauer HerbertWilk MartinStratmann DierkRaabe Computational Materials Design Administration Microstructure Physics and Metal Forming Interface Chemistry andSurface Engineering

4. 3 Multiscale crystalplasticity FEM Raabe, Zhao, Park, Roters: Acta Mater. 50 (2002) 421

5. 4 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, Ashby, 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)

6. 5 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

7. 6 From local misorientations to GNDs distortion (sym, a-sym) 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

8. 7 Frank loop through area r DDT in terms of 18 b,t combinations DDT in terms of 9 b,t combinations From local misorientations to GNDs Demir, Raabe, Zaafarani, Zaefferer: Acta Mater. 57 (2009) 559

9. 8 Extract geometrically necessary dislocations Demir, Raabe, Zaafarani, Zaefferer: Acta Mater. 57 (2009) 559

10. 9 Size effect sas a mean-field break down phenomenon

11. 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

12. 11 Homogeneityandboundaryconditionsatgrainscale 8% 3% 15% Raabe et al. Acta Mater. 49 (2001) 3433 Sachtleber, Zhao, Raabe: Mater. Sc. Engin. A 336 (2002) 81

13. 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)

14. T T Texturecomponentcrystalplasticity FEM for large scaleforming 13 Zhao, Mao, Roters, Raabe: Acta Mater. 52 (2004) 1003

15. Texturecomponentcrystalplasticity FEM for large scaleforming 14 D. Raabe and F. Roters: Intern. J. Plast. 20 (2004) 339

16. Multiscale crystalplasticity FEM for large scaleforming NumericalLaboratory: From CPFEM toyieldsurface (engineering) DC04 studywith Mercedes, Volkswagen, Audi, Inpro 15 Kraska, Doig, Tikhomirov, Raabe, Roters, Comp. Mater. Sc. 46 (2009) 383