finite element discretization of digital material...

April, 12-15, 2016, BarcelonaICME2016

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


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


Conventional modelling methods describe material as a continuum and provide

the general information about e.g. phase distibution within the sample.

Introduction

240 260 280 300 320 340

mm

0

20

40

60

80

100

120

140

mm

50

150

250

350

450

550

650

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


Fe30Ni

240 260 280 300 320 340

mm

0

20

40

60

80

100

120

140

mm

50

150

250

350

450

550

650

OFHC Copper 20% CuZn30 30%

DPInclusion in aluminium alloy


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


Optical microscopy Image processing

SEM EBSD

2D microstructure


Tomography

Serial sectioning

Undergrad studentsPhD studentsPostdocs

3D microstructure

A Borbély - 2004

RoboMet

FIB


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.


Cellular Automata + Monte Carlo

initial middle final

ji

SSgb jiJE

,

1

0 exp

0 1

EkT

E

E

Ep

Potts Model


Cellular Automata + Sphere Growth

Sphere generation Spheres CA sphere growth

R expected


f, q, y K, n, m

vectorscalar

K

nK mnK

0 0.4 0.8 1.2 1.6strain

0

200

400

600

str

ess,

MP

a

orientation

cube

hard

Goss

shear

0 0.2 0.4 0.6 0.8

strain

450

500

550

600

650

700

750

str

ess, M

Pa

Reference flow curve

Gauss distribution flow curves

Gauss distribution

Properties


Err=1

n∑i= 1

n

√(σ exp− σ

sim

σexp

)2

Goal function


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.


Uniform mesh generation for the DMR

Forge2,3


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


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



5. Assignment of the finite elements to particular grains.

1. 2.

3. 4.



txt vtk


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


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


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


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.


Hole Expansion Test Brittle-ductile fracture modelling

Brittle fractures

Du

cti

le f

ractu

res


Microstructure generation

FE mesh generator

CA model:-DRX-Phase transformation-Fracture-Strain localization-etc.

Micro scalemodeling

Multi scalemodeling

+Crystal plasticity


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

finite element discretization of digital material...

Documents