Introduction to Finite Element Analysis (FEA) or Finite Element
Finite element crystal plasticity analysis and ... · Finite element crystal plasticity analysis...
1
(μm) 2.0 1.4 1.1 0.8 0.5 0 -3.0 -8.0 -13 -18 -23 Motivation: ► Tungsten, as candidate materials for divertor of the ITER ► Localized behavior (eg.blistering) when subjected to high-flux deuterium- tritium plasma and high heat flux during operation ► Mechanical properties of tungsten in local scale ► Microindentation test to obtain local mechanical properties ► Identify the material parameters included in certain constitutive models (eg. crystal plasticity model in this work) based on experiments and extensive finite element analysis. Experiment and simulation ► Indentation tests were conducted on the (100), (110), and (111) oriented single crystal tungsten samples (see Fig.1). A Zwick Z2.5 testing machine was used to obtain load-displacement curves (see Fig.3 and Fig.4.). After indentation tests, the indents were scanned by surface profilometer to acquire the imprint profiles (see Fig.5.). Conclusions [email protected] Finite element crystal plasticity analysis and microindentation tests of single crystal tungsten W. Yao a, *, B. Albinski b , H.-C. Schneider b , J-H. You a a Max-Planck-Institut für Plasmaphysik, EURATOM Association, D-85748 Garching, Germany b Karlsruher Institut für Technologie, Institute for Applied Materials, D-76131 Karlsruhe, Germany Determination of model parameters Inverse fitting Indentation test Parameters identification of crystal plasticity material model Finite-Element-Calculation E… 0 h s τ 0 τ n a ɺ q Inverse fitting Fig.3. Indentation experiment on Zwick 2.5 Fig.4. Experimental load- displacement curve Fig.5. Experimental imprint profile Fig.6. Experimental imprint profile (section) Fig.7. FEM simulation of indentation Fig.8. Numerical load-displacement curve Fig.9. Numerical imprint profile Fig.10. Numerical imprint profile (section) ► The FEM simulations on single crystal tungsten were performed with the commercial finite element code ABAQUS. Details of the model are given as following: Size of the ball indenter: diameter 0.5 mm Size of the cylinder substrate: radius 1 mm; height 1 mm, Direction of indentation: Y-axis, Maximum indentation depth: ca.24 μm. Results and discussion ► The parameters of the crystal plasticity material model were identified by inverse fitting method. After extensive FEM calculations the numerical load- displacement curves and imprint profiles were fitted to the experimental data to obtain material parameters for the crystal plasticity model. See the figures below. Fig.1. Crystallographic planes of tungsten and ABAQUS analysis coordinate systems ► The experimental and numerical load-displacement curves shown in Fig.11 indicate that the indentation forces are very close to each other at the same depth for indentation on all three orientations. ► The simulated load-displacement curves agree well with the experimental data in all three orientations. See Fig.12. ► The experimental and numerical imprint profiles shown in Fig.13 and Fig.14 indicate that the differences are significant in both patterns and magnitude among all three orientations. ► The simulated imprint profiles show agreement with experimental data in both pile-up patterns and maximum pile-up. ► The comparisons of the section profiles shown in Fig.15 Fig.13. Experimental imprint profiles of single crystal samples of different crystallographic orientations. ► 3D crystal plasticity model simulation results consistent with both load- displacement curves and imprint profiles: validation of the current material model. ► Material behavior: the imprint characteristics, the magnitude of the pile-ups, Mises stress distributions, depends strongly on the crystal orientation while the load-displacement curves appear independent. ► Comparison between the experimental and numerical results indicates that the material model and parameters are reasonably appropriate in predicting the local mechanical properties of single crystal tungsten. Fig. 2. FEM model: partial FEM domain (left) and details of the mesh at the region of contact (right). ► The Mises stress distributions (Fig.16. simulations) of the indented planes show significant dependence on crystallographic planes. (μm) 2.0 1.4 1.1 0.8 0.5 0 -3.0 -8.0 -13 -18 -23 0 200 400 600 800 1000 1000 800 600 400 200 μm 0 100 200 300 400 500 Distance along path (μm) 5.0 0 -5.0 -10 -15 -20 -25 Displacement in Y direction (μm) 0 100 200 300 400 500 Distance along path (μm) 5.0 0 -5.0 -10 -15 -20 -25 Displacement in Y direction (μm) (100) (110) (111) (μm) 2.0 1.4 1.1 0.8 0.5 0 -3.0 -8.0 -13 -18 -23 0 200 400 600 800 1000 1000 800 600 400 200 μm (μm) 2.0 1.4 1.1 0.8 0.5 0 -3.0 -8.0 -13 -18 -23 0 200 400 600 800 1000 1000 800 600 400 200 μm (μm) 2.0 1.4 1.1 0.8 0.5 0 -3.0 -8.0 -13 -18 -23 0 200 400 600 800 1000 1000 800 600 400 200 μm Fig.11. Experimental and numerical load-displacement curves on single crystal samples of different crystallographic orientations. Fig.12. Comparisons between experimental and numerical load-displacement curves on single crystal samples of different crystallographic orientations. Fig.15. Comparisons of the section profiles of imprints on all three orientations Fig.16. Mises stress distributions on the indented planes of different orientations. (100) (110) (111) Fig.14. Numerical imprint profiles of single crystal samples of different crystallographic orientations. (100) (μm) 2.0 1.4 1.1 0.8 0.5 0 -3.0 -8.0 -13 -18 -23 Acknowledgements The activities leading to these results has received funding from the European Atomic Energy Community’s Seventh Framework Programme (FP7 / 2007-2011) under Grant Agreement 224752 (μm) 2.0 1.4 1.1 0.8 0.5 0 -3.0 -8.0 -13 -18 -23 (111) (μm) 2.0 1.4 1.1 0.8 0.5 0 -3.0 -8.0 -13 -18 -23 (110) P96A 96A 96A 96A
Transcript of Finite element crystal plasticity analysis and ... · Finite element crystal plasticity analysis...
(μm)2.01.41.10.80.50-3.0-8.0-13-18-23
Motivation: ► Tungsten, as candidate materials for divertor of the ITER► Localized behavior (eg.blistering) when subjected to high-flux deuterium-tritium plasma and high heat flux during operation► Mechanical properties of tungsten in local scale► Microindentation test to obtain local mechanical properties ► Identify the material parameters included in certain constitutive models (eg. crystal plasticity model in this work) based on experiments and extensive finite element analysis.
Experiment and simulation► Indentation tests were conducted on the (100), (110), and (111) oriented single crystal tungsten samples (see Fig.1). A Zwick Z2.5 testing machine was used to obtain load-displacement curves (see Fig.3 and Fig.4.). After indentation tests, the indents were scanned by surface profilometer to acquire the imprint profiles (see Fig.5.).
Conclusions
Finite element crystal plasticity analysis and microindentation tests of single crystal tungsten
W. Yaoa,*, B. Albinskib, H.-C. Schneiderb, J-H. Youa
aMax-Planck-Institut für Plasmaphysik, EURATOM Association, D-85748 Garching, GermanybKarlsruher Institut für Technologie, Institute for Applied Materials, D-76131 Karlsruhe, Germany
Determination of model parameters
Inverse fitting
Indentation test Parameters identification of crystal plasticitymaterial model
Finite-Element-Calculation
E…
0h
sτ 0τn aɺq
Inverse fitting
Fig.3. Indentation experiment on Zwick 2.5
Fig.4. Experimental load-displacement curve
Fig.5. Experimental imprint profile
Fig.6. Experimental imprint profile (section)
Fig.7. FEM simulation of indentation
Fig.8. Numerical load-displacement curve
Fig.9. Numerical imprint profile
Fig.10. Numerical imprint profile (section)
► The FEM simulations on single crystal tungsten were performed with the commercial finite element code ABAQUS. Details of the model are given as following:Size of the ball indenter: diameter 0.5 mm Size of the cylinder substrate: radius 1 mm; height 1 mm,Direction of indentation: Y-axis,Maximum indentation depth: ca.24 µm.
Results and discussion
► The parameters of the crystal plasticity material model were identified by inverse fitting method. After extensive FEM calculations the numerical load-displacement curves and imprint profiles were fitted to the experimental data to obtain material parameters for the crystal plasticity model. See the figures below.
Fig.1. Crystallographic planes of tungsten and ABAQUS analysis coordinate systems
► The experimental and numerical load-displacement curves shown in Fig.11 indicate that the indentation forces are very close to each other at the same depth for indentation on all three orientations.
► The simulated load-displacement curves agree well with the experimental data in all three orientations. See Fig.12.
► The experimental and numerical imprint profiles shown in Fig.13 and Fig.14 indicate that the differences are significant in both patterns and magnitude among all three orientations.
► The simulated imprint profiles show agreement with experimental data in both pile-up patterns and maximum pile-up.
► The comparisons of the section profiles shown in Fig.15
Fig.13. Experimental imprint profiles of single crystal samples of different crystallographic orientations.
► 3D crystal plasticity model simulation results consistent with both load-displacement curves and imprint profiles: validation of the current material model.
► Material behavior: the imprint characteristics, the magnitude of the pile-ups, Mises stress distributions, depends strongly on the crystal orientation while the load-displacement curves appear independent.
► Comparison between the experimental and numerical results indicates that the material model and parameters are reasonably appropriate in predicting the local mechanical properties of single crystal tungsten.
Fig. 2. FEM model: partial FEM domain (left) and details of the mesh at the region of contact (right).
► The Mises stress distributions (Fig.16. simulations) of the indented planes show significant dependence on crystallographic planes.
(μm)2.01.41.10.80.50-3.0-8.0-13-18-23
0 200 400 600 800 1000
1000
800
600
400
200
μm
0 100 200 300 400 500Distance along path (μm )
5.0
0
-5.0
-10
-15
-20
-25Dis
plac
emen
t in
Y d
irect
ion
(μm
)
0 100 200 300 400 500Distance along path (μm )
5.0
0
-5.0
-10
-15
-20
-25Dis
plac
emen
t in
Y d
irect
ion
(μm
)
(100) (110) (111)(μm)2.01.41.10.80.50-3.0-8.0-13-18-23
0 200 400 600 800 1000
1000
800
600
400
200
μm
(μm)2.01.41.10.80.50-3.0-8.0-13-18-23
0 200 400 600 800 1000
1000
800
600
400
200
μm
(μm)2.01.41.10.80.50-3.0-8.0-13-18-23
0 200 400 600 800 1000
1000
800
600
400
200
μm
Fig.11. Experimental and numerical load-displacement curves on single crystal samples of different
crystallographic orientations.
Fig.12. Comparisons between experimental and numerical load-displacement curves on single crystal samples of
different crystallographic orientations.
Fig.15. Comparisons of the section profiles of imprints on all three orientations
Fig.16. Mises stress distributions on the indented planes of different orientations.
(100) (110) (111)
Fig.14. Numerical imprint profiles of single crystal samples of different crystallographic orientations.
(100)
(μm)2.01.41.10.80.50-3.0-8.0-13-18-23
AcknowledgementsThe activities leading to these results has received funding from the European Atomic Energy Community’s Seventh Framework Programme (FP7 / 2007-2011) under Grant Agreement 224752
(μm)2.01.41.10.80.50-3.0-8.0-13-18-23
(111)
(μm)2.01.41.10.80.50-3.0-8.0-13-18-23
(110)
PPPP96A96A96A96A
