MULTISCALE SIMULATION TO DETERMINE BRITTLE AND DUCTILE FRACTURE IN GRAPHENE SHEET

1. MULTISCALE SIMULATION TO DETERMINE BRITTLE AND DUCTILE FRACTURE IN GRAPHENE SHEET DEREK S. MOSHER Dept. of Mechanical Engineering Arkansas Tech University Russellville, AR 72801 dmosher@atu.edu 1

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3. Objectives To understand the energetics of the brittle and ductile fracture in carbon nanotubes. To incorporate nudged elastic band method to calculate minimum energy path for crack propagation (brittle), bond rotation, and Stone-Wales defect (ductile). To determine the variation of activation energy barrier for crack propagation and Stone-Wales defect formation with increasing load. 3

4. Introduction Structures (left) Graphene Sheet (right) 4

5. Introduction(Brittle Fracture) Slow Stone-Wales Defect. Bond Separation Crack Propagation 5

6. Introduction (Ductile Fracture) Fast Stone-Wales Defect. Plastic Deformation & Necking Down. Bond Rotation. 6

7. Methods Atomistic Simulations: Atoms/molecules are considered as lumped mass under the action of inter-atomic potential. Molecular Dynamics: Positions of atoms at each time step are determined by simply solving, F = ma. Molecular Mechanics: Local energy minima of the given configuration is found out using conjugate gradient method. 7

8. Macro Crack In Graphene Sheet (a) Infinite Crack Domain (b) Semi-infinite Edge Crack Domain 8

9. Micro Crack In Graphene Sheet Atomistic Model 9

10. Molecular Mechanics Analytical Bond-Order Potential U = Urep + Uprom + Ubond Nudged Elastic Band Method 10

11. Brittle Fracture Graph 11

12. Ductile Fracture Graph 12

13. Activation Energy Barrier Curves 13

14. Conclusions Calculated activation energy barrier for crack propagation in brittle failure. Calculated activation energy barrier for bond rotations in ductile failure. (new contribution) Calculated activation energy barrier for varying loads in brittle and ductile fractures. (new contribution) 14

15. Future Work Try different bonds for rotation in ductile failure. Couple quantum mechanics with molecular mechanics to increase accuracy at atomic crack tip. 15

16. Major References [1] Terdalkar S. S., Zhang S. L., Rencis J. J., Brittle to Ductile Transition in Carbon Nanotubes using Nudged Elastic Band Method. Arkansas Academy of Mechanical Engineering Graduate Research Symposium, University of Arkansas, Fayetteville, Arkansas, April 11, 2007. [2] Pettifor, D.G. and Oleinik, I.I., 1999, �Analytic Bond-Order Potentials Beyond Tersoff-Brenner. I. Theory,� Physical Review B, 59, pp. 8487-8499. [3] Troiani, H.E., Miki-Yoshida, M., Camacho-Bragado, G.A., Marques, M.A.L., Rubio, A. Ascencio, J.A. and Jose-Yacaman, M., 2003, �Direct Observation of the Mechanical Properties of Single-Walled Carbon Nanotubes and Their Junctions at the Atomic Level,� NANO LETTERS, 3, pp. 751-755. [4] Lu, G. and Kaxiras, E., Overview of Multiscale Simulations of Material, in Handbook of Theoretical and Computational Nanotechnology, Rieth, M. and Schommers, W., Editor. 2006, American Scientific Publisher: Stevenson Ranch, CA. pp. 1-33. 16

17. Questions? 17