0. F. Roters, M. Friák, J. Neugebauer, D. Raabe
Multiscale modeling of metal forming considering microstructure and texture: micro to macro
F. Roters, M. Friák, J. Neugebauer, D. Raabe
Department of Microstructure Physics and Metal Forming
06. April 2009

1. Polycrystal theory and simulation Small scale crystal plasticity
Overview
Motivation
Polycrystal theory and simulation
Small scale crystal plasticity
Large scale polycrystal mechanics
Quantum mechanics and crystal mechanics

2. Motivation Overview Products Boundary conditions
Complex engineering materials
Performance in service
Consider microstructure and texture
Multiscale models

3. Polycrystal theory and simulation Small scale crystal plasticity
Overview
Motivation
Polycrystal theory and simulation
Small scale crystal plasticity
Large scale polycrystal mechanics
Quantum mechanics and crystal mechanics

4. Al Bicrystals, low angle g.b. [112] 7.4°, v Mises strain
experiment
von Mises
strain [1]
SSD
viscoplastic
phenomen.
model
dislocation-
based model;
g.b. model
10% % % % %

5. grain1 grain2 grain3 grain4…. ?
Polycrystal mechanics: homogenization
stress / strain in
grain1 grain2 grain3 grain4…. ? ?

6. . . Single crystal yield surface, Taylor Bishop-Hill
slip system 2
slip system 1
imposed stress
internal stress
total stress
1 crystal, 2 slip systems:
1 crystal, 1 slip system: . T
different
stresses
same strain

7. . Single crystal yield surface, Taylor Bishop-Hill
Many crystals, many slip systems: .
imposed strain
grain 1
grain 2
grain 3
grain 4
stress in grain 1
stress in grain 2
stress in grain 3
stress in grain 4

8. Homogeneity and boundary conditions – meso-scale3% 8%
15%
M. Sachtleber, Z. Zhao, D. Raabe: Mater. Sc. Engin. A 336 (2002) 81

9. Crystal Mechanics FEM (General): full field; direct CPFEM
D. Raabe: Adv. Mater. 14 (2002) 639; Acta Mater. 49 (2001) 3433

10. Crystal mechanics FEM (General): CPFEM & homogenization
D. Raabe: Adv. Mater. 14 (2002) 639; Acta Mater. 49 (2001) 3433

11. Polycrystal theory and simulation Small scale crystal plasticity
Overview
Motivation
Polycrystal theory and simulation
Small scale crystal plasticity
Large scale polycrystal mechanics
Quantum mechanics and crystal mechanics

12. Nanoindentation (smaller is stronger)
Cu, 60° conical, tip radius 1μm, loading rate 1.82mN/s, loads: 4000μN, 6000μN, 8000μN, 10000μN
[-110]
[11-2]
[111]
Misorientation angle 0°
20°
Hardness and GND* in one experiment
Higher GND density at smaller scales responsible ?
[11-2] rotations
experiment
3D EBSD
dislocation-based
CPFEM
simulation
[-110]
[111]
[11-2] - +
[-110]
[111]
[11-2]
* GND: geometrically necessary dislocations (accomodate curvature)
Zaafarani, Raabe, Singh, Roters, Zaefferer: Acta Mater. 54 (2006) 1707;
Zaafarani, Raabe, Roters, Zaefferer: Acta Mater. 56 (2008) 31

13. Example: Micro-bending

14. Crystal Mechanics FEM, grain scale mechanics (2D)
Experiment
(DIC, EBSD)
v Mises strain
Simulation
(CP-FEM)
v Mises strain

15. exp., grain orientation, side A exp., grain orientation, side B
Crystal plasticity FEM, grain scale mechanics (3D)
5mm
5mm
exp., grain orientation, side A
exp., grain orientation, side B
equivalent strain
8mm
21mm
1mm
FE mesh
Zhao, Rameshwaran, Radovitzky, Cuitino, Roters, Raabe (IJP, 2008)

16. Crystal plasticity FEM, grain scale mechanics (3D)
D. Kumar, T.R. Bieler, P. Eisenlohr, D.E. Mason, M.A. Crimp, F. Roters, D. Raabe: Journal of Engineering and Materials Technology (Transactions of ASME) 130 (2008)
and
IJP 2009 in press

17. Polycrystal theory and simulation Small scale crystal plasticity
Overview
Motivation
Polycrystal theory and simulation
Small scale crystal plasticity
Large scale polycrystal mechanics
Quantum mechanics and crystal mechanics

18. 10 billion grains in an auto part
too many
crystals

19. Homogenization and cluster models in CPFEM
Raabe, Roters: Intern. J. Plast. 20 (2004) 339; Raabe et al.: Adv. Eng. Mater. 4 (2002) 169; Zhao, Mao, Roters, Raabe: Acta Mater. 52 (2004) 1003

20. Crystal Plasticity FEM: large scale

21. Example: crystal plasticity FEM for automotive
Numerical Laboratory

22. Polycrystal theory and simulation Small scale crystal plasticity
Overview
Motivation
Polycrystal theory and simulation
Small scale crystal plasticity
Large scale polycrystal mechanics
Quantum mechanics and crystal mechanics

23. Ab initio alloy design: Ti alloys for medical application
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
discrete FFT
crystal elasticity FEM
Approach:
DFT*: design elastically soft BCC Ti; understand ground state; obtain single crystal elastic constants
Polycrystal coarse graining including texture and anisotropy
* DFT: density functional theory

24. 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)
Hershey
FFT
FEM
D. Ma, M. Friák, J. Neugebauer, D. Raabe, F. Roters: phys. stat. sol. B 245 (2008) 2642

25. stress strain Discrete FFTs, stress and strain; different anisotropy
Hershey, FEM, FFT similar for random texture
Ti-35wt.%Nb-7wt.%Zr-5wt.%Ta: 59.9 GPa (elastic isotropic)
strain

26. a) Advanced characteriation of microstructure b) Multiscale models
Summary
Simulation of complex materials, products, and processes (boundary condtions) requires
a) Advanced characteriation of microstructure
b) Multiscale models
c) Advanced mechanical testing
d) Quantum mechanics for engineering applications