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

Joint ab -initio and polycrystal homogenization modeling for designing biomaterials (Ti-Nb) and ultra light weight metals (Mg-Li). D. Ma , M. Friak , A. Counts F. Roters , P. Eisenlohr , J. Neugebauer, D. Raabe. 27. October 2009 , MS&T, Pittsburgh. Overview.

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

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  1. Joint ab-initio and polycrystal homogenization modeling for designing biomaterials (Ti-Nb) and ultra light weight metals (Mg-Li) D. Ma , M. Friak, A. Counts F. Roters, P. Eisenlohr, J. Neugebauer,D. Raabe 27. October 2009, MS&T, Pittsburgh

  2. Overview • Ab-initio-basedpolycrystalstiffness • Ti-Nb • Mg-Li Dierk Raabe, MS&T, Pittsburgh, 27. Oct. 2009, MPIE

  3. Scales: example of mechanical properties Length [m] Top down 100 Scale bridging 10-3 Mean field and boundary conditions (FE, FD, FFT) Crystals (CPFEM, YS, HT) 10-6 Bottom up Dislocations (DD, CA, KMC) 10-9 Structure of defects (DFT, MD) Structure of matter (DFT) Time [s] 10-9 103 10-15 10-3 D. Raabe: Advanced Materials 14 (2002) p. 639

  4. From ab-initioto polycrystal elasticity Gb, Gb2 , ... * DFT: density functional theory Raabe, Sander, Friák, Ma, Neugebauer: Acta Mater. 55 (2007) 4475

  5. Crystal elasticity FEM – multiscale integrator Raabe, Zhao, Park, Roters: Acta Mater. 50 (2002) 421

  6. Overview • Ab-initio-basedpolycrystalstiffness • Ti-Nb • Mg-Li Dierk Raabe, MS&T, Pittsburgh, 27. Oct. 2009, MPIE

  7. 20-25 GPa 115 GPa Motivation – BCC Ti alloys as biomaterials (implants) • Strategy for lower elastic stiffness: • -Ti (BCC: Ti-Nb, Ti-Mo, Ti-V,…) • Bio-compatible alloy elements Ti Ti-Nb • Human bone: 20-25 GPa • Current implant alloys (Ti, Ti-6Al-4V): 115 GPa • Stress shielding (elastic mismatch), bone degeneration, interface abrasion

  8. From ab-initioto polycrystal elasticity 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 Hershey homogenization crystal elasticity FEM Approach: • DFT*: design elastically soft BCC Ti; understand ground state; obtain singlecrystalelasticconstants • Polycrystal coarse graining including texture and anisotropy Raabe, Sander, Friák, Ma, Neugebauer: Acta Mater. 55 (2007) 4475

  9. 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 Elasticproperties: Ti-Nb system Hershey FEM Ma, Friák, Neugebauer, Raabe, Roters: phys. stat. sol. B 245 (2008) 2642

  10. Ultra-sonic measurement exp. polycrystals bcc+hcp phases theory: bcc polycrystals • not homogeneous • textures XRD DFT Elasticproperties / 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 Raabe, Sander, Friák, Ma, Neugebauer, ActaMaterialia 55 (2007) 4475

  11. Comparisonofmethods Young`s modulus Ma, Friák, Neugebauer, Raabe, Roters: phys. stat. sol. B 245 (2008) 2642

  12. 323points, 200 grains, FEM (surface), tensile strain distribution stress distribution CEFEM CEFEM • 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

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