Folie 1 - UCLA

Folie 1 - UCLA

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

2 09/09/11 Ratna Kumar Annabattula, Karlsruhe Institute of Technology CBBI-16 Meeting, Portland, OR, USA 8-10 September 2011. Introduction Pebble Assembly and Pebble-Pebble Interactions Idealizations: Assumptions: A unit cell of interest from a large assembly Pebble shape: spherical Periodic boundary conditions Pebble size: uniform, rs = rg= 0.25 m

Y. Gan et. Al, JMPS 2010 3 09/09/11 Ratna Kumar Annabattula, Karlsruhe Institute of Technology CBBI-16 Meeting, Portland, OR, USA 8-10 September 2011. Introduction Crush tests on single Li2SiO4 pebbles Different contact states Fc Crush load Fu - 3.03

F0 - 3.18 Fitting Parameters m - 2.50 The fit parameters depend on plate materialPhd Thesis, ShuoZhao, 2010 and FML at KIT 4 09/09/11 Ratna Kumar Annabattula, Karlsruhe Institute of Technology CBBI-16 Meeting, Portland, OR, USA 8-10 September 2011. Introduction Failure criterion for Osi Pebbles Failure criterion based on

maximum stress in the pebble. Failure criterion based on maximum stress in the pebble. Failure criterion based on the energy absorbed by the pebble. Failure criterion based on the energy absorbed by the pebble. These parameters depend on the plate material Phd Thesis, ShuoZhao, 2010 5 09/09/11

Ratna Kumar Annabattula, Karlsruhe Institute of Technology CBBI-16 Meeting, Portland, OR, USA 8-10 September 2011. Model Macroscopic Average Stress Average normal contact force (fave) 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. 6 09/09/11

Ratna Kumar Annabattula, Karlsruhe Institute of Technology CBBI-16 Meeting, Portland, OR, USA 8-10 September 2011. Model Damage Criterion and simulation flow chart : Stored elastic energy cr: Critical failure energy D: Damage variable 7 09/09/11 E = (1-D)*E0, if E >= 1 kPa E = 1 kPa if E < 1 kPa

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

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

8-10 September 2011. Results Damaged Pebbles Effect of random energy distribution 10 09/09/11 Effect of packing factor Ratna Kumar Annabattula, Karlsruhe Institute of Technology Effect of damage criterion

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

230 12 09/09/11 Ratna Kumar Annabattula, Karlsruhe Institute of Technology 350 CBBI-16 Meeting, Portland, OR, USA 8-10 September 2011. Summary

13 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. 09/09/11 Ratna Kumar Annabattula, Karlsruhe Institute of Technology CBBI-16 Meeting, Portland, OR, USA 8-10 September 2011. Outlook 14 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. 09/09/11 Ratna Kumar Annabattula, Karlsruhe Institute of Technology CBBI-16 Meeting, Portland, OR, USA 8-10 September 2011. Acknowledgments Regina Knitter for Pebbles and Crush load data. European Fusion Development Agreement (EFDA) for funding. 15 09/09/11

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

Backup slides 17 09/09/11 Ratna Kumar Annabattula, Karlsruhe Institute of Technology CBBI-16 Meeting, Portland, OR, USA 8-10 September 2011. Backup Slides 18 09/09/11 Ratna Kumar Annabattula, Karlsruhe Institute of Technology

CBBI-16 Meeting, Portland, OR, USA 8-10 September 2011.

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