d. raabe , j. neugebauer, m. friak , f. roters , a. counts, p. eisenlohr, d. ma

Joint ab-initio and polycrystal homogenization modeling for designing biomaterials (Ti-Nb) and ultra light weight metals (Mg-Li)

D. Raabe, J. Neugebauer, M. Friak, F. Roters, A. Counts, P. Eisenlohr, D. Ma

27. October 2009, MS&T, Pittsburgh

Overview

Ab-initio Multiscale Polycrystal Mechanics Ti-Nb Mg-Li Conclusions

Dierk Raabe, MS&T, Pittsburgh, 27. Oct. 2009, MPIE

3

Length [m]

10-9

10-6

10-3

100

10-15 10-9 10-3 103 Time [s]

Scales: 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)

Scale brid

ging Top downBotto

m up

D. Raabe: Advanced Materials 14 (2002) p. 639

4* DFT: density functional theory

Raabe, Sander, Friák, Ma, Neugebauer: Acta Mater. 55 (2007) 4475

From ab-initio to polycrystal elasticity

Gb, Gb2 , ...

5Raabe, Zhao, Park, Roters: Acta Mater. 50 (2002) 421

Crystal plasticity FEM – multiscale integrator

Overview

Ab-initio Multiscale Polycrystal Mechanics Ti-Nb Mg-Li Conclusions

Dierk Raabe, MS&T, Pittsburgh, 27. Oct. 2009, MPIE

7

115 GPa

20-25 GPa

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

Strategy for lower elastic stiffness: -Ti (BCC: Ti-Nb, Ti-Mo, Ti-V,…) Bio-compatible alloy elements

Ti-Nb

Ti

8

Hershey homogenization

crystal elasticity FEM

discrete FFT

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

Raabe, Sander, Friák, Ma, Neugebauer: Acta Mater. 55 (2007) 4475

From ab-initio to polycrystal elasticity

Approach: DFT*: design elastically soft BCC Ti; understand ground state; obtain

single crystal elastic constants Polycrystal coarse graining including texture and anisotropy

9

00

0210

0021

)(43)( 1211

2 CCU tetr

)(23

12112

2

CCU tetr

32 1211 CCB

0000000

44

22)( CU tri

442

2

4CU tri

Method of SimulationAb-initio calculation: Equilibrium elastic constants

ε, strain tensorδ, strainU, elastic energy densityB, bulk modulus

10

Elastic 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)

Ma, Friák, Neugebauer, Raabe, Roters: phys. stat. sol. B 245 (2008) 2642

HersheyFEMFFT

11

MECHANICALINSTABILITY!!

Ultra-sonic measurement

exp. polycrystals

bcc+hcp phases

Ti-hcp: 117 GPa

theory: bcc polycrystals

Elastic properties / Hershey homogenization

XRDDFTpo

lycr

ysta

l You

ng`s

mod

ulus

(G

Pa)

D. Raabe, B. Sander, M. Friák, D. Ma, J. Neugebauer, Acta Materialia 55 (2007) 4475

• not homogeneous • textures

Raabe, Sander, Friák, Ma, Neugebauer, Acta Materialia 55 (2007) 4475

12

 Ti-18.75at.%Nb (Az=3.21)

Ti-25at.%Nb (Az=2.418)

Ti-31.25at.%Nb (Az=1.058)

FFT 49.35 GPa 44.11 GPa 53.73 GPaCEFEM 50.55 GPa 45.08 GPa 54.61 GPaHershey's 49.40 GPa 44.20 GPa 54.90 GPa

Comparison of methods

Young`s modulus

Ma, Friák, Neugebauer, Raabe, Roters: phys. stat. sol. B 245 (2008) 2642

13

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 o

f Cou

nts

Ti-18.75at.%NbTi-25at.%NbTi-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 o

f Cou

nts

Ti-18.75at.%NbTi-25at.%NbTi-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 o

f Cou

nts

Ti-18.75at.%NbTi-25at.%NbTi-31.25at.%Nb

FFTFFT

0

200

400

600

800

1000

1200

200 300 400 500 600 700 800Equivalent Stress [MPa]

Num

ber o

f Cou

nts

Ti-18.75at.%NbTi-25at.%NbTi-31.25at.%Nb

CEFEM CEFEMstrain distribution

strain distributionstress distribution

stress distribution

stress prescribedFEM more compliant (BC)

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)

Ma, Friák, Neugebauer, Raabe, Roters: phys. stat. sol. B 245 (2008) 2642

14

Discrete FFTs, stress and strain; different anisotropy

stress

strain

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)

Ma, Friák, Neugebauer, Raabe, Roters: phys. stat. sol. B 245 (2008) 2642

15

Ultralight weight materials derived by DFT

W.A. Counts, M. Friák, D. Raabe, J. Neugebauer: Acta Mater. 57 (2009) 69-76