Finite element discretization of Digital Material Representation models

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1 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, home.agh.edu.pl/lmadej

Outline Introduction - motivation Digital Material

Heterogeneous FE meshes in 2D and 3D Adaptation

2 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

mm Introduction Conventional modelling methods describe material as a continuum

140 120 650 100 550 80 60 450 350 250 40 150 20 FE 50 CAFE 0 240 260 280 300 320

, Finite Element Model for Efficient Simulation of Ring Rolling, Mat Konf. Pt.

3 mm Introduction Conventional modelling methods describe material as a continuum and provide the general information about e.g. phase distibution within the sample FE 50 CAFE mm 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, r., s

4 mm Inclusion in aluminium alloy DP OFHC Copper 20% CuZn30 30% mm Fe30Ni

3-14. Numerical models based on the Digital Material Representation idea (DP dual phase, BH baking hardening, IF

nano, X-IP iron-manganese TWIP, L-IP - light induced plasticity) This days new materials are being developed very fast

5 Jaroni U., Imlaau K.P., Osburg B.: Neue Losungsansatze fur innovative produkte und umformtechnologien im automobilbau, Proc. ASK25, Aachen, 2010, pp Numerical models based on the Digital Material Representation idea (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) 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.

6 2D microstructure Optical microscopy Image processing SEM EBSD

7 Serial sectioning 3D microstructure RoboMet Undergrad students PhD students Postdocs FIB Tomography A Borbély

8 Pietrzyk M., Madej L., Rauch L., Szeliga D., Computational Materials Engineering: achieving high accuracy and efficiency in metals processing simulations, Butterworth- Heinemann Elsevier, Cellular Automata Voronoi

9 Cellular Automata + Monte Carlo initial middle final j i S S gb j i J E, 1 0 exp 0 1 E kt E E E p Potts Model

10 Cellular Automata + Sphere Growth Sphere generation Spheres CA sphere growth R expected

stress, MPa stress, MPa Properties n K scalar K vector f, q, y K, n, m n K m 750 600 Gauss distribution 700 650 400 600 550 500 450

11 stress, MPa stress, MPa Properties n K scalar K vector f, q, y K, n, m n K m Gauss distribution Reference flow curve Gauss distribution flow curves strain orientation cube hard Goss shear strain

12 Err= 1 n i= 1 Goal function n ( σ exp σ sim σ exp )2

13 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,

14 Uniform mesh generation for the DMR Forge2,3

Points located along the grain boundaries are further used during the

16 Non-uniform mesh generation for the DMR 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.

17 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

18 Non-uniform mesh generation for the DMR Assignment of the finite elements to particular grains.

19 txt vtk

20 Local mesh refinement and adaptation Zienkiewicz-Zhu error indicator e = σ * * σ σ h e = Ω e T σ D 1 e σ dω * h D recovered stress tensor standard stress tensor computed using derivatives of shape functions elasticity matrix with material constants Refinement with geometrical similarity - Child elements are similar to parent element

21 Local mesh refinement and adaptation Kruzel F., Madej L., Perzynski K., Banas K., Development of 3D adaptive mesh generation for multi scale applications, International Journal for Multiscale Computational Engineering.

extracting the steady state boundary conditions to be imposed to the submodel

23 Heterogeneous FE mesh multi scale model 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 submodel Transfer of the displacement boundary conditions taken from the global simulation into the submodel

24 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,

$fractures$ Hole

25 Ductile fractures Hole Expansion Test Brittle-ductile fracture modelling Brittle fractures

26 Microstructure generation FE mesh generator + CA model: -DRX -Phase transformation -Fracture -Strain localization -etc. Crystal plasticity Micro scale modeling Multi scale modeling

27 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, home.agh.edu.pl/lmadej

Modeling Discontinuities and their Evolution within Finite Elements: Application to Material Interfaces, 3-D Cracks, and Microstructures

University of California, Davis Modeling Discontinuities and their Evolution within Finite Elements: Application to Material Interfaces, 3-D Cracks, and Microstructures N. Sukumar UC Davis Rutgers University,