1) The document describes multiscale models of crystals developed by the Department of Microstructure Physics and Metal Forming. 2) These models use physics-based constitutive laws and mean field theory to model phenomena from the atomic to component scale, including dislocation dynamics, grain boundaries, orientation gradients, size effects, and texture evolution. 3) The models are implemented in crystal plasticity finite element methods to simulate the microstructure mechanics of materials undergoing deformation across multiple scales.

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