Dierk Raabe Darmstadt T U Celebration Colloquium Mechanics Of Crystals

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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

Transcript of Dierk Raabe Darmstadt T U Celebration Colloquium Mechanics Of Crystals

Page 1: Dierk  Raabe  Darmstadt  T U  Celebration  Colloquium  Mechanics Of  Crystals

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

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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

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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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Motivation: Basics of crystal mechanicsMotivation: Basics of crystal mechanics

[-110][1

1-2]

[111]

Complex microstructures

Small scale experiments

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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)

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OverviewOverview

Versetzungsbasierte Kristall-FEM (CPFEM) Indentierung

Ab initio und Kristallmechanik KRZ Ti für Implantate Kristallmechanik von Chitin

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OverviewOverview

Versetzungsbasierte Kristall-FEM (CPFEM) Indentierung

Ab initio und Kristallmechanik KRZ Ti für Implantate Kristallmechanik von Chitin

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Multiscale crystal plasticity FEMMultiscale crystal plasticity FEM

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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]

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12* GND: geometrically necessary dislocations (accomodate curvature)

[-110][111

]

[11-2]

Misorientation angle

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 ?

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13* GND: geometrically necessary dislocations (accomodate curvature)

[-110][111

]

[11-2]

Misorientation angle

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 ?

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Extract geometrically necessary dislocationsExtract geometrically necessary dislocations

E. Demir, D. Raabe, N. Zaafarani, S. Zaefferer: Acta Mater. 57 (2009) 559

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Extract geometrically necessary dislocationsExtract geometrically necessary dislocations

E. Demir, D. Raabe, N. Zaafarani, S. Zaefferer: Acta Mater. 57 (2009) 559

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Limits of statistical dislocation lawsLimits of statistical dislocation laws

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OverviewOverview

Versetzungsbasierte Kristall-FEM (CPFEM) Indentierung

Ab initio und Kristallmechanik KRZ Ti für Implantate Kristallmechanik von Chitin

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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)

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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

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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

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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

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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

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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

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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

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Discrete FFTs, stress and strain; different anisotropyDiscrete FFTs, stress and strain; different anisotropy

stress

strain

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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

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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)

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OverviewOverview

Versetzungsbasierte Kristall-FEM (CPFEM) Indentierung

Ab initio und Kristallmechanik KRZ Ti für Implantate Kristallmechanik von Chitin

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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

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The materials science of the arthropodsThe materials science of the arthropods

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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.

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Exocuticle

Endocuticle

Epicuticle

Exocuticle and endocuticle display different stacking density of twisted plywood layers

Cuticle hardened by mineralization with CaCO3

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exocuticleexocuticle

endocuticleendocuticle

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180° rotation of fiber planes180° rotation of fiber planes

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Normal direction

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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

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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)

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Mechanical properties (micoscopic)Mechanical properties (micoscopic)

nanoindentation

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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.

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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)

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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

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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.

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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