This document discusses modern multiscale simulation methods and provides several examples. It introduces crystal plasticity finite element (CPFE) modeling that incorporates dislocations. It also discusses using density functional theory calculations to inform polycrystal modeling of titanium alloys for biomedical implants. Finally, it examines the hierarchical structure and mechanics of lobster exoskeletons using a multiscale modeling approach ranging from atomic to macroscopic scales.

1. Moderne Methoden der Multiskalensimulation: Das Liebesleben der Hummer im Lichte von Quantenmechanik und Kontinuumstheorie M. Friak,S. Nikolov, D. Ma, F. Roters, J. Neugebauer, D. Raabe Hier: Mechanik der Kristalle 19. Juni 2009, Kolloquium, TU Darmstadt

2. performance large products Motivation: Basics of crystal mechanics processes Understand macromechanics in terms of micromechanics Micromechanics for products

6. [111] [-110] [11-2] Motivation: Basics of crystal mechanics Small scale experiments Complex microstructures

7. 6 Scales: exampleofmechanicalproperties Length [m] Top down 100 10-3 Mean field and boundary conditions (FE, FD, FFT) Bottom up Crystals (CPFEM, YS, HT) 10-6 Dislocations (DD, CA, KMC) 10-9 Structure of defects (DFT, MD) Structure of matter (DFT) Time [s] 10-9 103 10-15 10-3

9. Indentierung

10. Ab initio und Kristallmechanik

11. KRZ Ti für Implantate

13. Indentierung

14. Ab initio und Kristallmechanik

15. KRZ Ti für Implantate

17. 10 [11-2] rotations experiment 3D EBSD dislocation-based CPFEM - - + + - - + + + + - - experiment simulation [111] [-110] [11-2] [111] [-110] [11-2] Nanoindentation (smaller is stronger) [111] [-110] [11-2] Cu, 60° conical, tip radius 1μm, loading rate 1.82mN/s, loads: 4000μN, 6000μN, 8000μN, 10000μN Hardness and GND* in one experiment Higher GND density at smaller scales responsible ? Zaafarani, Raabe, Singh, Roters, Zaefferer: Acta Mater. 54 (2006) 1707; Zaafarani, Raabe, Roters, Zaefferer: Acta Mater. 56 (2008) 31 * GND: geometrically necessary dislocations (accomodate curvature)

18. 11 [11-2] rotations experiment 3D EBSD dislocation-based CPFEM - - + + - - + + + + - - 20° experiment simulation [111] [-110] 0° [11-2] Misorientation angle Nanoindentation (smaller is stronger) [111] [-110] [11-2] Cu, 60° conical, tip radius 1μm, loading rate 1.82mN/s, loads: 4000μN, 6000μN, 8000μN, 10000μN Hardness and GND* in one experiment Higher GND density at smaller scales responsible ? Affectedvolume not homogeneous Explained (FEM, analytical) Patterns similarfor different indents Howabout GNDs ? Zaafarani, Raabe, Singh, Roters, Zaefferer: Acta Mater. 54 (2006) 1707; Zaafarani, Raabe, Roters, Zaefferer: Acta Mater. 56 (2008) 31 * GND: geometrically necessary dislocations (accomodate curvature)

19. 12 [11-2] rotations experiment 3D EBSD dislocation-based CPFEM - - + + - - + + + + - - 20° experiment simulation [111] [-110] 0° [11-2] Misorientation angle Nanoindentation (smaller is stronger) [111] [-110] [11-2] Cu, 60° conical, tip radius 1μm, loading rate 1.82mN/s, loads: 4000μN, 6000μN, 8000μN, 10000μN Hardness and GND* in one experiment Higher GND density at smaller scales responsible ? Zaafarani, Raabe, Singh, Roters, Zaefferer: Acta Mater. 54 (2006) 1707; Zaafarani, Raabe, Roters, Zaefferer: Acta Mater. 56 (2008) 31 * GND: geometrically necessary dislocations (accomodate curvature)

20. 13 Extract geometrically necessary dislocations E. Demir, D. Raabe, N. Zaafarani, S. Zaefferer: Acta Mater. 57 (2009) 559

21. 14 Extract geometrically necessary dislocations E. Demir, D. Raabe, N. Zaafarani, S. Zaefferer: Acta Mater. 57 (2009) 559

22. Limits of statistical dislocation laws

24. Indentierung

25. Ab initio und Kristallmechanik

26. KRZ Ti für Implantate

28. Verwendung in Kontinuumstheorie (Elastizität, Defektenergien, Phasendiagramme)

29. Konstitutive Daten ableiten, die experimenell nicht zugänglich sind

31. -Ti (BCC: Ti-Nb, Ti-Mo, Ti-V,…)

33. Current implant alloys (Ti, Ti-6Al-4V): 115 GPa

35. Polycrystal coarse graining including texture and anisotropy* DFT: density functional theory

36. 20 Az= 2 C44/(C11 − C12) Young‘s modulus surface plots Ti-18.75at.%Nb Ti-25at.%Nb Ti-31.25at.%Nb Pure Nb [001] [100] [010] Az=3.210 Az=2.418 Az=1.058 Az=0.5027 Elastic properties: Ti-Nb system Hershey FEM FFT D. Ma, M. Friák, J. Neugebauer, D. Raabe, F. Roters: phys. stat. sol. B 245 (2008) 2642

38. texturesXRD DFT Elastic properties / Hershey homogenization Ti-hcp: 117 GPa polycrystal Young`s modulus (GPa) MECHANICAL INSTABILITY!! D. Raabe, B. Sander, M. Friák, D. Ma, J. Neugebauer, Acta Materialia 55 (2007) 4475

39. 22 Homogeneity and boundary conditions – meso-scale 8% 3% 15% M. Sachtleber, Z. Zhao, D. Raabe: Mater. Sc. Engin. A 336 (2002) 81

40. 23 5mm equivalent strain 5mm equivalent strain Crystal plasticity FEM, grain scale mechanics (3D) exp., grain orientation, side B exp., grain orientation, side A 8mm 21mm 1mm FE mesh Zhao, Rameshwaran, Radovitzky, Cuitino, Roters, Raabe (IJP, 2008)

41. 24 Discrete FFTs, stress and strain; different anisotropy stress strain

42. 25 323 points, 200 grains, FEM (surface), FFT (periodic), tensile strain distribution stress distribution CEFEM CEFEM strain distribution stress distribution FFT FFT

44. Ti-20wt.%Mo-7wt.%Zr-5wt.%Ta: 81.5 GPa

45. Ti-35wt.%Nb-7wt.%Zr-5wt.%Ta: 59.9 GPa (elastic isotropic)323 points, 200 grains, FEM (surface), FFT (periodic), tensile strain distribution stress distribution CEFEM CEFEM strain distribution stress distribution FFT FFT

47. Indentierung

48. Ab initio und Kristallmechanik

49. KRZ Ti für Implantate

51. 29 The materials science of the arthropods

52. 30 Structure hierarchy of arthropods Al-Sawalmih, C. Li, S. Siegel, H. Fabritius, S.B. Yi, D. Raabe, P. Fratzl, O. Paris: Advanced functional materials 18 (2008) 3307 H. Fabritius, C. Sachs, P. Romano, D. Raabe, Advanced materials 21 (2009) 391.

53. 31 Epicuticle Cuticle hardened by mineralization with CaCO3 Exocuticle Exocuticle and endocuticle display different stacking density of twisted plywood layers Endocuticle

54. 32

55. 33 exocuticle endocuticle

56. 34 180° rotation of fiber planes

57. 35

58. 36 Normal direction

59. 37

60. 38

61. 39

62. 40

63. 41

64. 42

65. 43

66. 44

67. 45 Compression tests (macroscopic), lobster

68. 46 350 Endocuticle 300 250 200 Hardness Universal, MPa 150 100 Exocuticle 50 0 0 100 200 300 400 500 600 surface Cut Depth, µm Hardness (mesoscopic)

69. 47 Mechanical properties (micoscopic) nanoindentation

70. 48 What is -chitin?

72. 50 Ab initio prediction of α-chitin elastic properties c b

73. 51 Hierarchical coarse graining 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.

74. 52 Hierarchical stiffness modeling

75. 53 Results and comparison with experiments Young’s modulus as a function of the mineral content for different in-plane area fractions of the pore canals.

77. Examples: dislocations and coarse graining in CPFE

78. Ab initio and polycrystal modeling: Ti, Mg, Al

79. Biological crystal mechanics