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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
19. Juni 2009, Kolloquium, TU Darmstadt
Hier: Mechanik der Kristalle
Dierk Raabe, TU Darmstadt, 19. Juni 2009, MPIE
Understand macromechanics in terms of micromechanics
Motivation: Basics of crystal mechanicsMotivation: Basics of crystal mechanics
processes performancelarge products
Micromechanics for products
Dierk Raabe, TU Darmstadt, 19. Juni 2009, MPIE
Dierk Raabe, TU Darmstadt, 19. Juni 2009, MPIE
Dierk Raabe, TU Darmstadt, 19. Juni 2009, MPIE
Dierk Raabe, TU Darmstadt, 19. Juni 2009, MPIE
Motivation: Basics of crystal mechanicsMotivation: Basics of crystal mechanics
[-110][1
1-2]
[111]
Complex microstructures
Small scale experiments
Dierk Raabe, TU Darmstadt, 19. Juni 2009, MPIE
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Length [m]
10-9
10-6
10-3
100
10-15 10-9 10-3 103 Time [s]
Top downBot
tom
up
Scales: example of mechanical propertiesScales: example of mechanical properties
Structure of defects (DFT, MD)
Dislocations (DD, CA, KMC)
Crystals (CPFEM, YS, HT)
Mean field and boundary conditions (FE, FD, FFT)
Structure of matter (DFT)
Dierk Raabe, TU Darmstadt, 19. Juni 2009, MPIE
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OverviewOverview
Versetzungsbasierte Kristall-FEM (CPFEM) Indentierung
Ab initio und Kristallmechanik KRZ Ti für Implantate Kristallmechanik von Chitin
Dierk Raabe, TU Darmstadt, 19. Juni 2009, MPIE
9
OverviewOverview
Versetzungsbasierte Kristall-FEM (CPFEM) Indentierung
Ab initio und Kristallmechanik KRZ Ti für Implantate Kristallmechanik von Chitin
Dierk Raabe, TU Darmstadt, 19. Juni 2009, MPIE
10
Multiscale crystal plasticity FEMMultiscale crystal plasticity FEM
Dierk Raabe, TU Darmstadt, 19. Juni 2009, MPIE
11* GND: geometrically necessary dislocations (accomodate curvature)
[-110][111
]
[11-2]
Zaafarani, Raabe, Singh, Roters, Zaefferer: Acta Mater. 54 (2006) 1707; Zaafarani, Raabe, Roters, Zaefferer: Acta Mater. 56 (2008) 31
[11-2] rotations experiment3D EBSD
dislocation-basedCPFEM
expe
rim
ent
sim
ulat
ion
[-110][111
]
[11-2]
-+ -
+-+-
+ -+
-+
Nanoindentation (smaller is stronger)Nanoindentation (smaller is stronger)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 ?
[-110]
[11-
2]
[111]
Dierk Raabe, TU Darmstadt, 19. Juni 2009, MPIE
12* GND: geometrically necessary dislocations (accomodate curvature)
[-110][111
]
[11-2]
Misorientation angle
0°
20°
Zaafarani, Raabe, Singh, Roters, Zaefferer: Acta Mater. 54 (2006) 1707; Zaafarani, Raabe, Roters, Zaefferer: Acta Mater. 56 (2008) 31
[11-2] rotations experiment3D EBSD
dislocation-basedCPFEM
expe
rim
ent
sim
ulat
ion
[-110][111
]
[11-2]
-+ -
+-+-
+ -+
-+
Affected volume not homogeneousExplained (FEM, analytical)Patterns similar for different indentsHow about GNDs ?
Affected volume not homogeneousExplained (FEM, analytical)Patterns similar for different indentsHow about GNDs ?
Nanoindentation (smaller is stronger)Nanoindentation (smaller is stronger)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 ?
Dierk Raabe, TU Darmstadt, 19. Juni 2009, MPIE
13* GND: geometrically necessary dislocations (accomodate curvature)
[-110][111
]
[11-2]
Misorientation angle
0°
20°
Zaafarani, Raabe, Singh, Roters, Zaefferer: Acta Mater. 54 (2006) 1707; Zaafarani, Raabe, Roters, Zaefferer: Acta Mater. 56 (2008) 31
[11-2] rotations experiment3D EBSD
dislocation-basedCPFEM
expe
rim
ent
sim
ulat
ion
[-110][111
]
[11-2]
-+ -
+-+-
+ -+
-+
Nanoindentation (smaller is stronger)Nanoindentation (smaller is stronger)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 ?
Dierk Raabe, TU Darmstadt, 19. Juni 2009, MPIE
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Extract geometrically necessary dislocationsExtract geometrically necessary dislocations
E. Demir, D. Raabe, N. Zaafarani, S. Zaefferer: Acta Mater. 57 (2009) 559
Dierk Raabe, TU Darmstadt, 19. Juni 2009, MPIE
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Extract geometrically necessary dislocationsExtract geometrically necessary dislocations
E. Demir, D. Raabe, N. Zaafarani, S. Zaefferer: Acta Mater. 57 (2009) 559
Dierk Raabe, TU Darmstadt, 19. Juni 2009, MPIE
Limits of statistical dislocation lawsLimits of statistical dislocation laws
Dierk Raabe, TU Darmstadt, 19. Juni 2009, MPIE
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OverviewOverview
Versetzungsbasierte Kristall-FEM (CPFEM) Indentierung
Ab initio und Kristallmechanik KRZ Ti für Implantate Kristallmechanik von Chitin
Dierk Raabe, TU Darmstadt, 19. Juni 2009, MPIE
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Ab initio und Vielkristall-ModellierungAb initio und Vielkristall-Modellierung
Elektronische Regeln für Legierungsdesign (Struktur, Stabilität, Funktion, thermodynamische Parameter)
Verwendung in Kontinuumstheorie (Elastizität, Defektenergien, Phasendiagramme)
Konstitutive Daten ableiten, die experimenell nicht zugänglich sind
Verknüpfung mit neuen experimentellen Methoden (TEM, Atomsonde, Kombinatorik)
Dierk Raabe, TU Darmstadt, 19. Juni 2009, MPIE
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115 GPa115 GPa
20-25 GPa20-25 GPa
Motivation – BCC Ti alloys as biomaterials (implants)Motivation – BCC Ti alloys as biomaterials (implants)
Human bone: 20-25 GPa Current implant alloys (Ti, Ti-6Al-4V): 115 GPa Stress shielding (elastic mismatch), bone
degeneration, interface abrasion, allergies, toxic reactions
Strategy for lower elastic stiffness: -Ti (BCC: Ti-Nb, Ti-Mo, Ti-V,…) Bio-compatible alloy elements
Ti-Nb
Ti
Dierk Raabe, TU Darmstadt, 19. Juni 2009, MPIE
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Ab initio alloy design: Ti alloys for medical applicationAb initio alloy design: Ti alloys for medical application
Approach: DFT*: design elastically soft BCC Ti; understand ground state;
obtain single crystal elastic constants Polycrystal coarse graining including texture and anisotropy
Hershey homogenization
discrete FFT
crystal elasticity FEM
Hershey homogenization
discrete FFT
crystal elasticity FEM
plane wave pseudopotential (VASP)
cutoff energy: 170 eV
8×8×8 Monkhorst
supercells of 2×2×2 cubic unit cells
total of 16 atoms
48 bcc and 28 hcp configurations
plane wave pseudopotential (VASP)
cutoff energy: 170 eV
8×8×8 Monkhorst
supercells of 2×2×2 cubic unit cells
total of 16 atoms
48 bcc and 28 hcp configurations
* DFT: density functional theory
Dierk Raabe, TU Darmstadt, 19. Juni 2009, MPIE
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Elastic properties: Ti-Nb systemElastic properties: Ti-Nb system
Ti-18.75at.%Nb Ti-25at.%Nb Ti-31.25at.%Nb
Az=3.210 Az=2.418 Az=1.058
[001]
[100] [010]
Young‘s modulus surface plots
Pure Nb
Az=0.5027
Az= 2 C44/(C11 − C12)
D. Ma, M. Friák, J. Neugebauer, D. Raabe, F. Roters: phys. stat. sol. B 245 (2008) 2642
HersheyFEMFFT
HersheyFEMFFT
Dierk Raabe, TU Darmstadt, 19. Juni 2009, MPIE
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MECHANICALINSTABILITY!!
Ultra-sonic measurement
exp. polycrystals
bcc+hcp phases
Ti-hcp: 117 GPa
theory: bcc polycrystals
Elastic properties / Hershey homogenizationElastic properties / Hershey homogenization
XRDDFT
po
lycr
ysta
l Yo
un
g`s
mo
du
lus
(G
Pa)
D. Raabe, B. Sander, M. Friák, D. Ma, J. Neugebauer, Acta Materialia 55 (2007) 4475
• not homogeneous • textures
• not homogeneous • textures
Dierk Raabe, TU Darmstadt, 19. Juni 2009, MPIE
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3% 8%
15%
Homogeneity and boundary conditions – meso-scaleHomogeneity and boundary conditions – meso-scale
M. Sachtleber, Z. Zhao, D. Raabe: Mater. Sc. Engin. A 336 (2002) 81
Dierk Raabe, TU Darmstadt, 19. Juni 2009, MPIE
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1mm
21mm
8mm
5mm
5mm
Crystal plasticity FEM, grain scale mechanics (3D)Crystal plasticity FEM, grain scale mechanics (3D)
Zhao, Rameshwaran, Radovitzky, Cuitino, Roters, Raabe (IJP, 2008)
FE mesh
exp., grain orientation, side A exp., grain orientation, side B
equivalent strain
equivalent strain
Dierk Raabe, TU Darmstadt, 19. Juni 2009, MPIE
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Discrete FFTs, stress and strain; different anisotropyDiscrete FFTs, stress and strain; different anisotropy
stress
strain
Dierk Raabe, TU Darmstadt, 19. Juni 2009, MPIE
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323 points, 200 grains, FEM (surface), FFT (periodic), tensile 323 points, 200 grains, FEM (surface), FFT (periodic), tensile
0
200
400
600
800
1000
1200
200 300 400 500 600 700 800Equivalent Stress [MPa]
Num
ber
of C
ount
s
Ti-18.75at.%Nb
Ti-25at.%Nb
Ti-31.25at.%Nb
0
200
400
600
800
1000
1200
1400
0.007 0.009 0.011 0.013 0.015 0.017 0.019 0.021 0.023Equivalent Strain
Num
ber
of C
ount
s
Ti-18.75at.%Nb
Ti-25at.%Nb
Ti-31.25at.%Nb
0
200
400
600
800
1000
1200
0.007 0.009 0.011 0.013 0.015 0.017 0.019 0.021 0.023Equivalent Strain
Num
ber
of C
ount
s
Ti-18.75at.%Nb
Ti-25at.%Nb
Ti-31.25at.%Nb
FFTFFT
0
200
400
600
800
1000
1200
200 300 400 500 600 700 800Equivalent Stress [MPa]
Num
ber
of C
ount
s
Ti-18.75at.%Nb
Ti-25at.%Nb
Ti-31.25at.%Nb
CEFEM CEFEMstrain distribution
strain distributionstress distribution
stress distribution
Dierk Raabe, TU Darmstadt, 19. Juni 2009, MPIE
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323 points, 200 grains, FEM (surface), FFT (periodic), tensile 323 points, 200 grains, FEM (surface), FFT (periodic), tensile
0
200
400
600
800
1000
1200
200 300 400 500 600 700 800Equivalent Stress [MPa]
Num
ber
of C
ount
s
Ti-18.75at.%Nb
Ti-25at.%Nb
Ti-31.25at.%Nb
0
200
400
600
800
1000
1200
1400
0.007 0.009 0.011 0.013 0.015 0.017 0.019 0.021 0.023Equivalent Strain
Num
ber
of C
ount
s
Ti-18.75at.%Nb
Ti-25at.%Nb
Ti-31.25at.%Nb
0
200
400
600
800
1000
1200
0.007 0.009 0.011 0.013 0.015 0.017 0.019 0.021 0.023Equivalent Strain
Num
ber
of C
ount
s
Ti-18.75at.%Nb
Ti-25at.%Nb
Ti-31.25at.%Nb
FFTFFT
0
200
400
600
800
1000
1200
200 300 400 500 600 700 800Equivalent Stress [MPa]
Num
ber
of C
ount
s
Ti-18.75at.%Nb
Ti-25at.%Nb
Ti-31.25at.%Nb
CEFEM CEFEMstrain distribution
strain distributionstress distribution
stress distribution
Ti: 115 GPa
Ti-20wt.%Mo-7wt.%Zr-5wt.%Ta: 81.5 GPa
Ti-35wt.%Nb-7wt.%Zr-5wt.%Ta: 59.9 GPa (elastic isotropic)
Dierk Raabe, TU Darmstadt, 19. Juni 2009, MPIE
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OverviewOverview
Versetzungsbasierte Kristall-FEM (CPFEM) Indentierung
Ab initio und Kristallmechanik KRZ Ti für Implantate Kristallmechanik von Chitin
Dierk Raabe, TU Darmstadt, 19. Juni 2009, MPIE
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Chitin is main exoskeleton component of more than 90% of all animal species
adaptive material candidate for bio-inspired material
Introduction - Arthropod cuticle Introduction - Arthropod cuticle
Dierk Raabe, TU Darmstadt, 19. Juni 2009, MPIE
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The materials science of the arthropodsThe materials science of the arthropods
Dierk Raabe, TU Darmstadt, 19. Juni 2009, MPIE
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Structure hierarchy of arthropodsStructure 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.
Dierk Raabe, TU Darmstadt, 19. Juni 2009, MPIE
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Exocuticle
Endocuticle
Epicuticle
Exocuticle and endocuticle display different stacking density of twisted plywood layers
Cuticle hardened by mineralization with CaCO3
Dierk Raabe, TU Darmstadt, 19. Juni 2009, MPIE
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Dierk Raabe, TU Darmstadt, 19. Juni 2009, MPIE
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exocuticleexocuticle
endocuticleendocuticle
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180° rotation of fiber planes180° rotation of fiber planes
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Dierk Raabe, TU Darmstadt, 19. Juni 2009, MPIE
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Normal direction
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Dierk Raabe, TU Darmstadt, 19. Juni 2009, MPIE
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Dierk Raabe, TU Darmstadt, 19. Juni 2009, MPIE
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Dierk Raabe, TU Darmstadt, 19. Juni 2009, MPIE
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Dierk Raabe, TU Darmstadt, 19. Juni 2009, MPIE
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Dierk Raabe, TU Darmstadt, 19. Juni 2009, MPIE
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Dierk Raabe, TU Darmstadt, 19. Juni 2009, MPIE
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Dierk Raabe, TU Darmstadt, 19. Juni 2009, MPIE
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0 5 10 15 20 25 30 35 400
25
50
75
100
125
150
175
glo
ba
l str
ess
[M
Pa
]
global strain [%]
normal dry
transverse wet
transverse dry
normal wet
0 5 10 15 20 25 30 35 400
25
50
75
100
125
150
175
glo
ba
l str
ess
[M
Pa
]
global strain [%]
normal drynormal dry
transverse wettransverse wet
transverse drytransverse dry
normal wetnormal wet
Compression tests (macroscopic), lobsterCompression tests (macroscopic), lobster
Dierk Raabe, TU Darmstadt, 19. Juni 2009, MPIE
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Endocuticle
Exocuticle
0 100 200 300 400 500 6000
50
100
150
200
250
300
350H
ardn
ess
Uni
vers
al,
MP
a
Cut Depth, µmsurfa
ce
Hardness (mesoscopic)Hardness (mesoscopic)
Dierk Raabe, TU Darmstadt, 19. Juni 2009, MPIE
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Mechanical properties (micoscopic)Mechanical properties (micoscopic)
nanoindentation
Dierk Raabe, TU Darmstadt, 19. Juni 2009, MPIE
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What is -chitin?What is -chitin?
P218.96 35.64 19.50 90˚α-Chitin
Space groupUnit cell dimensions (Bohrradius)
a b c γPolymer
Carlstrom, D.
The crystal structure of α -chitin
J. Biochem Biophys. Cytol., 1957, 3, 669 - 683.
P218.96 35.64 19.50 90˚α-Chitin
Space groupUnit cell dimensions (Bohrradius)
a b c γPolymer
Carlstrom, D.
The crystal structure of α -chitin
J. Biochem Biophys. Cytol., 1957, 3, 669 - 683.
Dierk Raabe, TU Darmstadt, 19. Juni 2009, MPIE
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Methodological hierarchyMethodological hierarchy
CPU time Accuracy
• Empirical Potentials Geometry optimization Molecular Dynamics (universal force field)
~10 min
High
Low
~10000 min
~500 min Medium
Resulting structures
~103
~102
~101
• Tight Binding (SCC-DFTB)
Geometry optimization (SPHIngX)
• DFT (PWs, PBE-GGA) Geometry Optimization (SPHIngX)
Dierk Raabe, TU Darmstadt, 19. Juni 2009, MPIE
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0.00
0.20
0.40
0.60
0.80
1.00
1.20
-0.015 -0.01 -0.005 0 0.005 0.01 0.015 0.02
Lattice elongation [%]
En
erg
y E
- E
0 [k
ca
l/mo
l]
a_Lattice
b_Lattice
c_Lattice
GPa.
.
..
CCH
200000
080000
005000
00024211
00022810
0001110119
Ab initio prediction of α-chitin elastic propertiesAb initio prediction of α-chitin elastic properties
c
b
Dierk Raabe, TU Darmstadt, 19. Juni 2009, MPIE
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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.
Hierarchical coarse grainingHierarchical coarse graining
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Hierarchical stiffness modelingHierarchical stiffness modeling
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Results and comparison with experimentsResults and comparison with experiments
Young’s modulus as a function of the mineral content for different in-plane area fractions of the pore canals.
Dierk Raabe, TU Darmstadt, 19. Juni 2009, MPIE
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Mutiscale modeling in crystal plasticity
Examples: dislocations and coarse graining in CPFE
Ab initio and polycrystal modeling: Ti, Mg, Al
Biological crystal mechanics
OverviewOverview
Recommended