Crystalmechanics Introduction

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Crystalmechanics Introduction

  1. 1. Multiscale Models of Crystals<br />D. Raabe, F. Roters, S. Zaefferer, P. Eisenlohr<br />Department ofMicrostructurePhysicsandMetalForming<br />WWW.MPIE.DE<br />D.RAABE@MPIE.DE<br />02. May 2010<br />
  2. 2. 1<br />MPIE Departments<br />Shareholder:Max-Planck-Society, German Steel Institute<br />Scientific Board<br />Trustees Board<br />Strategy Board<br />MPIE<br />ScientificBoard<br />JörgNeugebauer<br />HerbertWilk<br />MartinStratmann<br />DierkRaabe<br />Computational <br />Materials<br />Design<br />Administration<br />Microstructure<br />Physics<br />and Metal <br />Forming<br />Interface <br />Chemistry <br />andSurface<br />Engineering<br />
  3. 3. Overview<br /><ul><li>Multiscale Crystal PlasticityFEM</li></ul>Raabe: Adv. Mater. 14 (2002), Roters et al. Acta Materi.58 (2010)<br />
  4. 4. 3<br />Multiscale crystalplasticity FEM<br />Raabe, Zhao, Park, Roters: Acta Mater. 50 (2002) 421<br />
  5. 5. 4<br />T<br />T<br />T<br />T<br />T<br />T<br />T<br />T<br />Physics-based constitutive laws: mean field theory<br />1<br />dyadic flow law based on dislocation rate theory<br />1. set <br />internal<br />variables<br />Taylor, Kocks, Mecking, Estrin, Kubin,...<br />plastic gradients, <br />size scale and orientation gradients (implicit)<br />2<br />2. set <br />internal<br />variables<br />Nye, Ashby, Kröner,....<br />3<br />grain boundaries<br />3. set <br />internal<br />variables<br />activation concept:<br />energy of formation upon slip penetration: conservation law<br />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<br />Roters et al.: Acta Mater. (2010)<br />
  6. 6. 5<br />20°<br />0°<br />misorientationangle<br />orientation gradient<br />(spacing d from EBSD scan)<br />From local misorientations to GNDs<br />misorientation<br />orientation difference<br />Demir, Raabe, Zaafarani, Zaefferer: Acta Mater. 57 (2009) 559<br />
  7. 7. 6<br />From local misorientations to GNDs<br />distortion<br />(sym, a-sym)<br />dislocation tensor (GND)<br />J. F. Nye. Some geometrical relations in dislocated crystals. Acta Metall. 1:153, 1953.<br />E. Kröner. KontinuumstheoriederVersetzungen und Eigenspannungen (in German). Springer, Berlin, 1958.<br />E. Kröner. Physics of defects, chapter Continuum theory of defects, p.217. North-Holland Publishing, Amsterdam, Netherlands, 1981.<br />Demir, Raabe, Zaafarani, Zaefferer: Acta Mater. 57 (2009) 559<br />
  8. 8. 7<br />Frank loop through area r<br />DDT in terms of 18 b,t combinations<br />DDT in terms of 9 b,t combinations<br />From local misorientations to GNDs<br />Demir, Raabe, Zaafarani, Zaefferer: Acta Mater. 57 (2009) 559<br />
  9. 9. 8<br />Extract geometrically necessary dislocations<br />Demir, Raabe, Zaafarani, Zaefferer: Acta Mater. 57 (2009) 559<br />
  10. 10. 9<br />Size effect sas a mean-field break down phenomenon<br />
  11. 11. 10<br />Al Bicrystals, low angle g.b. [112] 7.4°, v Misesstrain<br />von Mises<br />strain [1]<br />experiment<br />SSD<br /> 10% 20% 30% 40% 50%<br />CPFEM:<br />viscoplastic<br />phenomen.<br />model<br />CPFEM:<br />dislocation-<br />based model;<br />g.b. model <br /> 10% 20% 30% 40% 50%<br />Ma, Roters, Raabe: Acta Mater. 54 (2006) 2169 and 2181<br />
  12. 12. 11<br />Homogeneityandboundaryconditionsatgrainscale<br />8%<br />3%<br />15%<br />Raabe et al. Acta Mater. 49 (2001) 3433<br />Sachtleber, Zhao, Raabe: Mater. Sc. Engin. A 336 (2002) 81<br />
  13. 13. 12<br /> 5mm<br />equivalent strain<br /> 5mm<br />equivalent strain<br />Crystal plasticity FEM, grainscalemechanics (3D Al)<br />exp., grain orientation, side B <br />exp., grain orientation, side A<br />8mm<br />21mm<br />1mm<br />FE mesh<br />Zhao, Rameshwaran, Radovitzky, Cuitino, Roters, Raabe: Intern. J. Plast. 24 (2008)<br />
  14. 14. T<br />T<br />Texturecomponentcrystalplasticity FEM for large scaleforming<br />13<br />Zhao, Mao, Roters, Raabe: Acta Mater. 52 (2004) 1003<br />
  15. 15. Texturecomponentcrystalplasticity FEM for large scaleforming<br />14<br />D. Raabe and F. Roters: Intern. J. Plast. 20 (2004) 339<br />
  16. 16. Multiscale crystalplasticity FEM for large scaleforming<br />NumericalLaboratory: From CPFEM toyieldsurface (engineering)<br />DC04 studywith Mercedes, Volkswagen, Audi, Inpro<br />15<br />Kraska, Doig, Tikhomirov, Raabe, Roters, Comp. Mater. Sc. 46 (2009) 383<br />

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