finite element discretization of digital material...
TRANSCRIPT
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Finite element discretization of Digital Material Representation models
Lukasz Madej, Aleksander Fular, Krzysztof Banas, Filip Kruzel, Pawel Cybulka, Konrad Perzynski
AGH University of Science and Technology, Kraków, Poland,
[email protected]/lmadej
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Outline
• Introduction - motivation
• Digital Material Representation in 2D and 3D
• Experimentally/Statistically based DMR
• Material properties
• Incorporation into FEM models
• Heterogeneous FE meshes in 2D and 3D
• Adaptation techniques in 2D and 3D
• Micro and multi scale simulations
• Conclusions and plans for future work
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Conventional modelling methods describe material as a continuum and provide
the general information about e.g. phase distibution within the sample.
Introduction
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Malinowski Z., Głowacki M., Pietrzyk M., Madej W., „Finite Element Model for
Efficient Simulation of Ring Rolling”, Mat Konf. Pt. Materials Science &
Technology 2004 Conference Proceedings, New Orleans, Louisiana USA, 26-
29.09.2004r., s.397-401CAFE
FE
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Fe30Ni
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OFHC Copper 20% CuZn30 30%
DPInclusion in aluminium alloy
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This days new materials are being developed very fast with microstructures composed of
different grain sizes, phases, inclusions, voids, nano particles etc.
To meet elevated expectations the numerical simulations have to take these features explicitly into account.
Jaroni U., Imlaau K.P., Osburg B.: Neue Losungsansatze fur innovative produkte und umformtechnologien im automobilbau, Proc. ASK25, Aachen, 2010, pp. 3-14.
(DP – dual phase, BH – baking hardening, IF – interstitial free, CP – complex phases, MS – martensitic, FB - ferrite-bainite, RA - retained-austenite, TPN - three-phase nano, X-IP – iron-manganese TWIP, L-IP - light induced plasticity)
Numerical models based on the Digital Material
Representation idea
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Optical microscopy Image processing
SEM EBSD
2D microstructure
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Tomography
Serial sectioning
Undergrad studentsPhD studentsPostdocs
3D microstructure
A Borbély - 2004
RoboMet
FIB
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Voronoi
Cellular Automata
Pietrzyk M., Madej L., Rauch L., Szeliga D., Computational Materials Engineering:
achieving high accuracy and efficiency in metals processing simulations, Butterworth-
Heinemann Elsevier, 2015.
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Cellular Automata + Monte Carlo
initial middle final
ji
SSgb jiJE
,
1
0 exp
0 1
EkT
E
E
Ep
Potts Model
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Cellular Automata + Sphere Growth
Sphere generation Spheres CA sphere growth
R expected
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f, q, y K, n, m
vectorscalar
K
nK mnK
0 0.4 0.8 1.2 1.6strain
0
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str
ess,
MP
a
orientation
cube
hard
Goss
shear
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strain
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str
ess, M
Pa
Reference flow curve
Gauss distribution flow curves
Gauss distribution
Properties
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Err=1
n∑i= 1
n
√(σ exp− σ
sim
σexp
)2
Goal function
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Focused Ion Beam
Madej L., Wang J., Perzynski K., Hodgson P.D., Numerical modelling of dual phase
microstructure behavior under deformation conditions on the basis of digital material
representation, Computational Material Science, 95, 2014, 651–662.
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Uniform mesh generation for the DMR
Forge2,3
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1. Import of the grain boundary geometry.
Points located along the grain boundaries are further used during the Delaunay triangulation. This assures generation of the conforming FE mesh.
2. Generation of additional points located inside the grain area.
Non-uniform mesh generation for the DMR
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3. Delaunay triangulation on the basis of the available points.
4. Mesh correction
- the Laplace smoothing algorithm is applied in order to obtain finite elements with regular shapes.
- edge swaping algorithm
Non-uniform mesh generation for the DMR
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5. Assignment of the finite elements to particular grains.
1. 2.
3. 4.
Non-uniform mesh generation for the DMR
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txt vtk
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Local mesh refinement and adaptation
hσ σσ=e **
Ω
σ
T
σ dΩeDe=e 1
*
h
D
recovered stress tensor
standard stress tensor computed using derivatives of shape functions
elasticity matrix with material constants
Zienkiewicz-Zhu error indicator
Refinement with geometrical similarity - Child elements are similar to parent element
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Kruzel F., Madej L., Perzynski K., Banas K., Development of 3D adaptive mesh generation for multi scale applications, International Journal for Multiscale Computational Engineering.
Local mesh refinement and adaptation
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The key aspect in this approach is to
ensure that an accurate partitioning
strategy is used in the global model for
extracting the steady state boundary
conditions to be imposed to the sub-
model
Transfer of the displacement
boundary conditions taken from the
global simulation into the submodel
Heterogeneous FE mesh – multi scale model
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Numerical simulation of drawing process
Muszka K., Madej L., Majta J., The effects of deformation and microstructure inhomogeneities in the Accumulative Angular Drawing (AAD), Materials Science and Engineering A, 574 , 2013, 68–74.
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Hole Expansion Test Brittle-ductile fracture modelling
Brittle fractures
Du
cti
le f
ractu
res
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Microstructure generation
FE mesh generator
CA model:-DRX-Phase transformation-Fracture-Strain localization-etc.
Micro scalemodeling
Multi scalemodeling
+Crystal plasticity
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Finite element discretization of Digital Material Representation models
Lukasz Madej, Aleksander Fular, Krzysztof Banas, Filip Kruzel, Pawel Cybulka, Konrad Perzynski
AGH University of Science and Technology, Kraków, Poland,
[email protected]/lmadej