d. raabe , j. neugebauer, m. friak , f. roters , a. counts, p. eisenlohr, d. ma
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
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