1. KIT – University of the State of Baden-Wuerttemberg and National Research Center of the Helmholtz Association Institute for Applied Materials (IAM-WBM) www.kit.edu Crushing Analysis of Pebbles in a Pebble Assembly using DEM Ratna Kumar Annabattula, Shuo Zhao, Yixiang Gan and Marc Kamlah

2. CBBI-16 Meeting, Portland, OR, USA 8-10 September 2011. 209/09/11 Ratna Kumar Annabattula, Karlsruhe Institute of Technology Outline Introduction Model Results Summary Outlook

3. CBBI-16 Meeting, Portland, OR, USA 8-10 September 2011. 309/09/11 Ratna Kumar Annabattula, Karlsruhe Institute of Technology Introduction Pebble Assembly and Pebble-Pebble Interactions Assumptions: Pebble shape: spherical Pebble size: uniform, r s = r g = 0.25 mm Y. Gan et. Al, JMPS 2010 Idealizations: A unit cell of interest from a large assembly Periodic boundary conditions

4. CBBI-16 Meeting, Portland, OR, USA 8-10 September 2011. 409/09/11 Ratna Kumar Annabattula, Karlsruhe Institute of Technology Introduction Crush tests on single Li 2 SiO 4 pebbles F c – Crush load F u - 3.03 F 0 - 3.18 Fitting Parameters m - 2.50 The fit parameters depend on plate material Phd Thesis, ShuoZhao, 2010 and FML at KIT Different contact states

5. CBBI-16 Meeting, Portland, OR, USA 8-10 September 2011. 509/09/11 Ratna Kumar Annabattula, Karlsruhe Institute of Technology Introduction Failure criterion for Osi Pebbles Failure criterion based on maximum stress in the pebble. Failure criterion based on the energy absorbed by the pebble. Failure criterion based on maximum stress in the pebble. Failure criterion based on the energy absorbed by the pebble. Phd Thesis, ShuoZhao, 2010 These parameters depend on the plate material

6. CBBI-16 Meeting, Portland, OR, USA 8-10 September 2011. 609/09/11 Ratna Kumar Annabattula, Karlsruhe Institute of Technology Model Macroscopic Average Stress Average normal contact force ( f ave ) and hydrostatic pressure ( p ) An assembly of 5000 pebbles in a box with periodic boundary conditions. Uni-axial compression to 3% strain and then unloading to stress-free state.

7. CBBI-16 Meeting, Portland, OR, USA 8-10 September 2011. 709/09/11 Ratna Kumar Annabattula, Karlsruhe Institute of Technology Model Damage Criterion and simulation flow chart Φ: Stored elastic energy Φ cr : Critical failure energy D: Damage variable E = (1-D)*E 0, if E >= 1 kPa E = 1 kPa if E < 1 kPa

8. CBBI-16 Meeting, Portland, OR, USA 8-10 September 2011. 809/09/11 Ratna Kumar Annabattula, Karlsruhe Institute of Technology Results Damaged Pebbles ε 33 = 0% ε 33 = 1.65 % ε 33 = 3 % No Damage Localization

9. CBBI-16 Meeting, Portland, OR, USA 8-10 September 2011. 909/09/11 Ratna Kumar Annabattula, Karlsruhe Institute of Technology Results Stress-Strain Response Effect of packing factorEffect of damage criterion

10. CBBI-16 Meeting, Portland, OR, USA 8-10 September 2011. 1009/09/11 Ratna Kumar Annabattula, Karlsruhe Institute of Technology Results Damaged Pebbles Effect of random energy distribution Effect of packing factorEffect of damage criterion

11. CBBI-16 Meeting, Portland, OR, USA 8-10 September 2011. 1109/09/11 Ratna Kumar Annabattula, Karlsruhe Institute of Technology Results Damaged Pebles: Effect of damage law

12. CBBI-16 Meeting, Portland, OR, USA 8-10 September 2011. 1209/09/11 Ratna Kumar Annabattula, Karlsruhe Institute of Technology Results Damage Histograms: Effect of packing factor 350 230

13. CBBI-16 Meeting, Portland, OR, USA 8-10 September 2011. 1309/09/11 Ratna Kumar Annabattula, Karlsruhe Institute of Technology Summary Crushing analysis of pebbles in the frame work of damage mechanics A mere 0.2% of failed pebbles in the assembly ceases the further load carrying capacity of the assembly. An assembly with high packing factor is prone to more total damage. A sudden damage law exhibits a higher flow stress than gradual damage. The fraction of critical pebbles to failure is independent of damage accumulation law. The stress plateau after the critical number of failed pebbles indicate a creep like behavior.

14. CBBI-16 Meeting, Portland, OR, USA 8-10 September 2011. 1409/09/11 Ratna Kumar Annabattula, Karlsruhe Institute of Technology Outlook Implementation of pebble failure into small particles. The present damage law is heuristic and a damage law with a physical basis based on experiments to be developed. Extend the analysis to polydisperse pebble assembly.

15. CBBI-16 Meeting, Portland, OR, USA 8-10 September 2011. 1509/09/11 Acknowledgments Regina Knitter for Pebbles and Crush load data. European Fusion Development Agreement (EFDA) for funding. Ratna Kumar Annabattula, Karlsruhe Institute of Technology

16. CBBI-16 Meeting, Portland, OR, USA 8-10 September 2011. 1609/09/11 Ratna Kumar Annabattula, Karlsruhe Institute of Technology Thank you for your attention! Questions?

17. CBBI-16 Meeting, Portland, OR, USA 8-10 September 2011. 1709/09/11 Backup slides Ratna Kumar Annabattula, Karlsruhe Institute of Technology

18. CBBI-16 Meeting, Portland, OR, USA 8-10 September 2011. 1809/09/11 Backup Slides Ratna Kumar Annabattula, Karlsruhe Institute of Technology