Dierk Raabe Darmstadt T U Celebration Colloquium Mechanics Of Crystals

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Dierk Raabe Darmstadt T U Celebration Colloquium Mechanics Of Crystals

  1. 1. Moderne Methoden der Multiskalensimulation: Das Liebesleben der Hummer im Lichte von Quantenmechanik und Kontinuumstheorie<br />M. Friak,S. Nikolov, D. Ma, F. Roters, J. Neugebauer, D. Raabe<br />Hier: Mechanik der Kristalle<br />19. Juni 2009, Kolloquium, TU Darmstadt<br />
  2. 2. performance<br />large products<br />Motivation: Basics of crystal mechanics<br />processes<br />Understand macromechanics in terms of micromechanics<br />Micromechanics for products<br />
  3. 3.
  4. 4.
  5. 5.
  6. 6. [111]<br />[-110]<br />[11-2]<br />Motivation: Basics of crystal mechanics<br />Small scale experiments<br />Complex microstructures<br />
  7. 7. 6<br />Scales: exampleofmechanicalproperties<br />Length [m]<br />Top down<br />100<br />10-3<br />Mean field and boundary conditions (FE, FD, FFT)<br />Bottom up<br />Crystals (CPFEM, YS, HT)<br />10-6<br />Dislocations (DD, CA, KMC)<br />10-9<br />Structure of defects (DFT, MD)<br />Structure of matter (DFT)<br />Time [s]<br />10-9<br />103<br />10-15<br />10-3<br />
  8. 8. 7<br />Overview<br /><ul><li>Versetzungsbasierte Kristall-FEM (CPFEM)
  9. 9. Indentierung
  10. 10. Ab initio und Kristallmechanik
  11. 11. KRZ Ti für Implantate
  12. 12. Kristallmechanik von Chitin</li></li></ul><li>8<br />Overview<br /><ul><li>Versetzungsbasierte Kristall-FEM (CPFEM)
  13. 13. Indentierung
  14. 14. Ab initio und Kristallmechanik
  15. 15. KRZ Ti für Implantate
  16. 16. Kristallmechanik von Chitin</li></li></ul><li>9<br />Multiscalecrystalplasticity FEM<br />
  17. 17. 10<br />[11-2] rotations<br />experiment<br />3D EBSD<br />dislocation-based<br />CPFEM<br />-<br />-<br />+<br />+<br />-<br />-<br />+<br />+<br />+<br />+<br />-<br />-<br />experiment<br />simulation<br />[111]<br />[-110]<br />[11-2]<br />[111]<br />[-110]<br />[11-2]<br />Nanoindentation (smaller is stronger)<br />[111]<br />[-110]<br />[11-2]<br />Cu, 60° conical, tip radius 1μm, loading rate 1.82mN/s, loads: 4000μN, 6000μN, 8000μN, 10000μN<br />Hardness and GND* in one experiment<br />Higher GND density at smaller scales responsible ?<br />Zaafarani, Raabe, Singh, Roters, Zaefferer: Acta Mater. 54 (2006) 1707; <br />Zaafarani, Raabe, Roters, Zaefferer: Acta Mater. 56 (2008) 31<br />* GND: geometrically necessary dislocations (accomodate curvature)<br />
  18. 18. 11<br />[11-2] rotations<br />experiment<br />3D EBSD<br />dislocation-based<br />CPFEM<br />-<br />-<br />+<br />+<br />-<br />-<br />+<br />+<br />+<br />+<br />-<br />-<br />20°<br />experiment<br />simulation<br />[111]<br />[-110]<br />0°<br />[11-2]<br />Misorientation angle<br />Nanoindentation (smaller is stronger)<br />[111]<br />[-110]<br />[11-2]<br />Cu, 60° conical, tip radius 1μm, loading rate 1.82mN/s, loads: 4000μN, 6000μN, 8000μN, 10000μN<br />Hardness and GND* in one experiment<br />Higher GND density at smaller scales responsible ?<br />Affectedvolume not homogeneous<br />Explained (FEM, analytical)<br />Patterns similarfor different indents<br />Howabout GNDs ?<br />Zaafarani, Raabe, Singh, Roters, Zaefferer: Acta Mater. 54 (2006) 1707; <br />Zaafarani, Raabe, Roters, Zaefferer: Acta Mater. 56 (2008) 31<br />* GND: geometrically necessary dislocations (accomodate curvature)<br />
  19. 19. 12<br />[11-2] rotations<br />experiment<br />3D EBSD<br />dislocation-based<br />CPFEM<br />-<br />-<br />+<br />+<br />-<br />-<br />+<br />+<br />+<br />+<br />-<br />-<br />20°<br />experiment<br />simulation<br />[111]<br />[-110]<br />0°<br />[11-2]<br />Misorientation angle<br />Nanoindentation (smaller is stronger)<br />[111]<br />[-110]<br />[11-2]<br />Cu, 60° conical, tip radius 1μm, loading rate 1.82mN/s, loads: 4000μN, 6000μN, 8000μN, 10000μN<br />Hardness and GND* in one experiment<br />Higher GND density at smaller scales responsible ?<br />Zaafarani, Raabe, Singh, Roters, Zaefferer: Acta Mater. 54 (2006) 1707; <br />Zaafarani, Raabe, Roters, Zaefferer: Acta Mater. 56 (2008) 31<br />* GND: geometrically necessary dislocations (accomodate curvature)<br />
  20. 20. 13<br />Extract geometrically necessary dislocations<br />E. Demir, D. Raabe, N. Zaafarani, S. Zaefferer: Acta Mater. 57 (2009) 559<br />
  21. 21. 14<br />Extract geometrically necessary dislocations<br />E. Demir, D. Raabe, N. Zaafarani, S. Zaefferer: Acta Mater. 57 (2009) 559<br />
  22. 22. Limits of statistical dislocation laws<br />
  23. 23. 16<br />Overview<br /><ul><li>Versetzungsbasierte Kristall-FEM (CPFEM)
  24. 24. Indentierung
  25. 25. Ab initio und Kristallmechanik
  26. 26. KRZ Ti für Implantate
  27. 27. Kristallmechanik von Chitin</li></li></ul><li>17<br />Ab initio und Vielkristall-Modellierung<br /><ul><li>Elektronische Regeln für Legierungsdesign (Struktur, Stabilität, Funktion, thermodynamische Parameter)
  28. 28. Verwendung in Kontinuumstheorie (Elastizität, Defektenergien, Phasendiagramme)
  29. 29. Konstitutive Daten ableiten, die experimenell nicht zugänglich sind
  30. 30. Verknüpfung mit neuen experimentellen Methoden (TEM, Atomsonde, Kombinatorik)</li></li></ul><li>18<br />20-25 GPa<br />115 GPa<br />Motivation – BCC Ti alloys as biomaterials (implants)<br /><ul><li>Strategy for lower elastic stiffness:
  31. 31. -Ti (BCC: Ti-Nb, Ti-Mo, Ti-V,…)
  32. 32. Bio-compatible alloy elements</li></ul>Ti<br />Ti-Nb<br /><ul><li>Human bone: 20-25 GPa
  33. 33. Current implant alloys (Ti, Ti-6Al-4V): 115 GPa
  34. 34. Stress shielding (elastic mismatch), bone degeneration, interface abrasion, allergies, toxic reactions</li></li></ul><li>19<br />Ab initio alloy design: Ti alloys for medical application<br /> plane wave pseudopotential (VASP)<br /> cutoff energy: 170 eV<br /> 8×8×8 Monkhorst<br />supercells of 2×2×2 cubic unit cells<br /> total of 16 atoms<br /> 48 bcc and 28 hcp configurations<br />Hershey homogenization<br />discrete FFT<br />crystal elasticity FEM<br />Approach: <br /><ul><li>DFT*: design elastically soft BCC Ti; understand ground state; obtain single crystal elastic constants
  35. 35. Polycrystal coarse graining including texture and anisotropy</li></ul>* DFT: density functional theory<br />
  36. 36. 20<br />Az= 2 C44/(C11 − C12)<br />Young‘s modulus surface plots<br />Ti-18.75at.%Nb<br />Ti-25at.%Nb<br />Ti-31.25at.%Nb<br />Pure Nb<br />[001]<br />[100]<br />[010]<br />Az=3.210<br />Az=2.418<br />Az=1.058<br />Az=0.5027<br />Elastic properties: Ti-Nb system<br />Hershey<br />FEM<br />FFT<br />D. Ma, M. Friák, J. Neugebauer, D. Raabe, F. Roters: phys. stat. sol. B 245 (2008) 2642 <br />
  37. 37. 21<br />Ultra-sonic measurement<br />exp. polycrystals <br />bcc+hcp phases<br />theory: bcc <br />polycrystals<br /><ul><li> not homogeneous
  38. 38. textures</li></ul>XRD<br />DFT<br />Elastic properties / Hershey homogenization<br />Ti-hcp: 117 GPa<br />polycrystal Young`s modulus (GPa)<br />MECHANICAL<br />INSTABILITY!!<br />D. Raabe, B. Sander, M. Friák, D. Ma, J. Neugebauer, Acta Materialia 55 (2007) 4475<br />
  39. 39. 22<br />Homogeneity and boundary conditions – meso-scale<br />8%<br />3%<br />15%<br />M. Sachtleber, Z. Zhao, D. Raabe: Mater. Sc. Engin. A 336 (2002) 81<br />
  40. 40. 23<br /> 5mm<br />equivalent strain<br /> 5mm<br />equivalent strain<br />Crystal plasticity FEM, grain scale mechanics (3D)<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 (IJP, 2008)<br />
  41. 41. 24<br />Discrete FFTs, stress and strain; different anisotropy<br />stress<br />strain<br />
  42. 42. 25<br />323 points, 200 grains, FEM (surface), FFT (periodic), tensile <br />strain distribution<br />stress distribution<br />CEFEM<br />CEFEM<br />strain distribution<br />stress distribution<br />FFT<br />FFT<br />
  43. 43. 26<br /><ul><li>Ti: 115 GPa
  44. 44. Ti-20wt.%Mo-7wt.%Zr-5wt.%Ta: 81.5 GPa
  45. 45. Ti-35wt.%Nb-7wt.%Zr-5wt.%Ta: 59.9 GPa (elastic isotropic)</li></ul>323 points, 200 grains, FEM (surface), FFT (periodic), tensile <br />strain distribution<br />stress distribution<br />CEFEM<br />CEFEM<br />strain distribution<br />stress distribution<br />FFT<br />FFT<br />
  46. 46. 27<br />Overview<br /><ul><li>Versetzungsbasierte Kristall-FEM (CPFEM)
  47. 47. Indentierung
  48. 48. Ab initio und Kristallmechanik
  49. 49. KRZ Ti für Implantate
  50. 50. Kristallmechanik von Chitin</li></li></ul><li>28<br />Introduction - Arthropod cuticle <br />Chitin is main exoskeleton component of more than 90% of all animal species<br /> adaptive material  candidate for bio-inspired material<br />
  51. 51. 29<br />The materials science of the arthropods<br />
  52. 52. 30<br />Structure hierarchy of arthropods<br />Al-Sawalmih, C. Li, S. Siegel, H. Fabritius, S.B. Yi, D. Raabe, P. Fratzl, O. Paris: Advanced functional materials 18 (2008) 3307<br />H. Fabritius, C. Sachs, P. Romano, D. Raabe, Advanced materials 21 (2009) 391.<br />
  53. 53. 31<br />Epicuticle<br />Cuticle hardened by mineralization with CaCO3<br />Exocuticle<br />Exocuticle and endocuticle display different stacking density of twisted plywood layers<br />Endocuticle<br />
  54. 54. 32<br />
  55. 55. 33<br />exocuticle<br />endocuticle<br />
  56. 56. 34<br />180° rotation of fiber planes<br />
  57. 57. 35<br />
  58. 58. 36<br />Normal direction<br />
  59. 59. 37<br />
  60. 60. 38<br />
  61. 61. 39<br />
  62. 62. 40<br />
  63. 63. 41<br />
  64. 64. 42<br />
  65. 65. 43<br />
  66. 66. 44<br />
  67. 67. 45<br />Compression tests (macroscopic), lobster<br />
  68. 68. 46<br />350<br />Endocuticle<br />300<br />250<br />200<br />Hardness Universal, MPa<br />150<br />100<br />Exocuticle<br />50<br />0<br />0<br />100<br />200<br />300<br />400<br />500<br />600<br />surface<br />Cut Depth, µm<br />Hardness (mesoscopic)<br />
  69. 69. 47<br />Mechanical properties (micoscopic)<br />nanoindentation<br />
  70. 70. 48<br />What is -chitin?<br />
  71. 71. 49<br />Methodological hierarchy<br />CPU time<br />Accuracy<br />Resulting <br />structures<br /><ul><li>Empirical Potentials</li></ul>Geometry optimization<br /> Molecular Dynamics<br /> (universal force field)<br />Low<br />~103<br />~10 min<br /><ul><li>Tight Binding</li></ul>(SCC-DFTB)<br />Geometry optimization<br />(SPHIngX)<br />~500 min<br />Medium<br />~102<br /><ul><li>DFT </li></ul> (PWs, PBE-GGA) <br /> Geometry Optimization <br /> (SPHIngX)<br />~10000 min<br />High<br />~101<br />
  72. 72. 50<br />Ab initio prediction of α-chitin elastic properties<br />c<br />b<br />
  73. 73. 51<br />Hierarchical coarse graining<br />Hierarchical modelling of the lobster cuticle: (I), (II) -chitin properties via ab initio calculations; (III) representative volume element (RVE) for a single chitin-protein fibre; (IV a) RVE for chitin-protein fibres arranged in twisted plywood and embedded in mineral-protein matrix; (IV b) RVE for the mineral-protein matrix. Level (V): homogenized twisted plywood without canals; (VI) homogenized plywood pierced with hexagonal array of canals; (VII) 3-layer cuticle.<br />
  74. 74. 52<br />Hierarchical stiffness modeling<br />
  75. 75. 53<br />Results and comparison with experiments<br />Young’s modulus as a function of the mineral content for different in-plane area fractions of the pore canals.<br />
  76. 76. 54<br />Overview<br /><ul><li>Mutiscale modeling in crystal plasticity
  77. 77. Examples: dislocations and coarse graining in CPFE
  78. 78. Ab initio and polycrystal modeling: Ti, Mg, Al
  79. 79. Biological crystal mechanics</li>

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