Polycrystal theory and simulation Small scale crystal plasticity
27
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
-
Upload
vincent-watson -
Category
Documents
-
view
234 -
download
0
description
Motivation Overview Products Boundary conditions Complex engineering materials Performance in service Consider microstructure and texture Multiscale models
Transcript of Polycrystal theory and simulation Small scale crystal plasticity
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
Dierk Raabe, lecture MFPT 2009, Dortmund, www.mpie.de
Overview
Motivation Polycrystal theory and simulation Small scale crystal plasticity Large scale polycrystal mechanics Quantum mechanics and crystal mechanics
Dierk Raabe, lecture MFPT 2009, Dortmund, www.mpie.de
Motivation
Overview
Products Boundary conditions Complex engineering materials Performance in service
Consider microstructure and texture
Multiscale models
Dierk Raabe, lecture MFPT 2009, Dortmund, www.mpie.de
Overview
Motivation Polycrystal theory and simulation Small scale crystal plasticity Large scale polycrystal mechanics Quantum mechanics and crystal mechanics
Dierk Raabe, lecture MFPT 2009, Dortmund, www.mpie.de
Al Bicrystals, low angle g.b. [112] 7.4°, v Mises strain
SSD
10% 20% 30% 40% 50%
experiment
viscoplasticphenomen.model
dislocation-based model;g.b. model
von Misesstrain [1]
Dierk Raabe, lecture MFPT 2009, Dortmund, www.mpie.de
Polycrystal mechanics: homogenization
?
stress / strain in grain1 grain2 grain3 grain4…. ?
Dierk Raabe, lecture MFPT 2009, Dortmund, www.mpie.de
activecrit
33
11.
T
T
T
T
differentstresses
same strain
Single crystal yield surface, Taylor Bishop-Hill
critijljlkik bana
1 crystal, 1 slip system:33
11
active)(1crits
...
.
slip system 2
slip system 1
active)(2crits
imposed stress
internal stress
tota
l stre
sscrit
ijsljl
skik bana
1 crystal, 2 slip systems:
Dierk Raabe, lecture MFPT 2009, Dortmund, www.mpie.de
....
..
.
.11
33
imposed strain
grain 1
grain 2
grain 3
grain 4
stre
ss in
gra
in 1
stres
s in
grain
2
stress
in grain 3
stress in grain 4
Single crystal yield surface, Taylor Bishop-Hill
Many crystals, many slip systems:
Dierk Raabe, lecture MFPT 2009, Dortmund, www.mpie.de
3% 8%
15%
Homogeneity and boundary conditions – meso-scale
M. Sachtleber, Z. Zhao, D. Raabe: Mater. Sc. Engin. A 336 (2002) 81
Dierk Raabe, lecture MFPT 2009, Dortmund, www.mpie.de
Crystal Mechanics FEM (General): full field; direct CPFEM
D. Raabe: Adv. Mater. 14 (2002) 639; Acta Mater. 49 (2001) 3433
Dierk Raabe, lecture MFPT 2009, Dortmund, www.mpie.deD. Raabe: Adv. Mater. 14 (2002) 639; Acta Mater. 49 (2001) 3433
Crystal mechanics FEM (General): CPFEM & homogenization
Dierk Raabe, lecture MFPT 2009, Dortmund, www.mpie.de
Overview
Motivation Polycrystal theory and simulation Small scale crystal plasticity Large scale polycrystal mechanics Quantum mechanics and crystal mechanics
Dierk Raabe, lecture MFPT 2009, Dortmund, www.mpie.de* GND: geometrically necessary dislocations (accomodate curvature)
[-110][111
]
[11-2]
Misorientation angle
0°
20°
Zaafarani, Raabe, Singh, Roters, Zaefferer: Acta Mater. 54 (2006) 1707; Zaafarani, Raabe, Roters, Zaefferer: Acta Mater. 56 (2008) 31
[11-2] rotations experimentexperiment3D EBSD3D EBSD
dislocation-baseddislocation-basedCPFEMCPFEM
expe
rimen
t
sim
ulat
ion
[-110][111
]
[11-2]
-+ -
+-+-+ -
+-+
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]
Dierk Raabe, lecture MFPT 2009, Dortmund, www.mpie.de
Example: Micro-bending
Dierk Raabe, lecture MFPT 2009, Dortmund, www.mpie.de
Crystal Mechanics FEM, grain scale mechanics (2D)
Experiment (DIC, EBSD)v Mises strain
Simulation (CP-FEM)v Mises strain
Dierk Raabe, lecture MFPT 2009, Dortmund, www.mpie.de
1mm
21mm
8mm
5mm
5mm
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
Dierk Raabe, lecture MFPT 2009, Dortmund, www.mpie.de
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) 021012-1 - 021012-12andIJP 2009 in press
Dierk Raabe, lecture MFPT 2009, Dortmund, www.mpie.de
Overview
Motivation Polycrystal theory and simulation Small scale crystal plasticity Large scale polycrystal mechanics Quantum mechanics and crystal mechanics
Dierk Raabe, lecture MFPT 2009, Dortmund, www.mpie.de
10 billion grains in an auto part
too manycrystals
Dierk Raabe, lecture MFPT 2009, Dortmund, www.mpie.de
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
Dierk Raabe, lecture MFPT 2009, Dortmund, www.mpie.de
Crystal Plasticity FEM: large scale
Dierk Raabe, lecture MFPT 2009, Dortmund, www.mpie.de
Example: crystal plasticity FEM for automotiveNumerical Laboratory
Dierk Raabe, lecture MFPT 2009, Dortmund, www.mpie.de
Overview
Motivation Polycrystal theory and simulation Small scale crystal plasticity Large scale polycrystal mechanics Quantum mechanics and crystal mechanics
Dierk Raabe, lecture MFPT 2009, Dortmund, www.mpie.de
Ab 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
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
Dierk Raabe, lecture MFPT 2009, Dortmund, www.mpie.de
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)
D. Ma, M. Friák, J. Neugebauer, D. Raabe, F. Roters: phys. stat. sol. B 245 (2008) 2642
HersheyFFTFEM
Dierk Raabe, lecture MFPT 2009, Dortmund, www.mpie.de
Discrete FFTs, stress and strain; different anisotropy
stress
strain
Hershey, FEM, FFT similar for random texture
Ti-35wt.%Nb-7wt.%Zr-5wt.%Ta: 59.9 GPa (elastic isotropic)
Dierk Raabe, lecture MFPT 2009, Dortmund, www.mpie.de
Simulation of complex materials, products, and processes (boundary condtions) requires
a) Advanced characteriation of microstructureb) Multiscale modelsc) Advanced mechanical testingd) Quantum mechanics for engineering
applications
Summary
