Brittle to Ductile Transitions in Carbon Nanotube Fractures

1
Brittle to Ductile Transitions in Carbon
Nanotube Fractures

• Derek Mosher
• AS Nuclear Technology
• BS Mechanical Engineering

Professor Mentor Dr. Joseph Rencis Graduate
Mentor Sachin Terdalkar
2
Liberty Ships

• Temperature
• Brittle State
• Welded Hulls
• Divided In Half

3
Objectives

• Study the energetics of brittle and ductile
  fractures using molecular mechanics.
• Use Nudged Elastic Band Method to determine
  activation energy barrier.

4
Carbon Nanotubes
(0,10) Zig-Zag
(7,10) Chiral
(10,10) Armchair
5
Properties

• sp2 Configuration of Carbon Bonds
• Radius less than 20 nanometers
• Length 70 nanometers to 5 millimeters
• Stiffness Strength 270 - 950 GPa
• Failure Strength 11 - 63 GPa
• Electric Conductivity greater than copper or
  less than silicon

6
Brittle Fracture

• Low to Standard Temperature (lt 110oC)
• Stone-Wales Defect by 90o Bond Rotation (slow)
• Straight 90o Separation

7
Ductile Fracture

• Elevated Temperature
• (gt 110oC)
• Stone-Wales Defect by 90o Bond Rotation (rapid)
• Necking Down
• Angle 45o Separation

8
Molecular Mechanics

• Conjugate gradient method finds local energy
  minima
• Analytical bond order potential describes the c-c
  interactions
• U Urep Uprom Ubond

9
Nudged Elastic Band Method

• Local Energy Minimum
• (A no defect)
• (B defect)
• Activation Energy Barrier (Eb)
• Saddle Point
• (S)

10
References

• 1 Sachin S. Terdalkar Prof. Sulin L. Zhang
  Prof. Sulin L. Zhang Prof. Joseph J. Rencis,
  Brittle to Ductile Transition in Carbon Nanotubes
  using Nudged Elastic Band Method. University of
  Arkansas, 2007
• 2 Henkelman, G. Jónsson, H., Improved tangent
  estimate in the nudged elastic band method for
  finding minimum energy paths and saddle points.
  J.Chem.Phys., 2000, 113, 9978, AIP
• 3 Pettifor, DG Oleinik, II, Analytic
  bond-order potentials beyond Tersoff-Brenner. I.
  Theory. Physical Review B, 1999, 59, 13,
  8487-8499, APS
• 4 Yu, M.F. Files, B.S. Arepalli, S. Ruoff,
  R.S., Tensile Loading of Ropes of Single Wall
  Carbon Nanotubes and their Mechanical Properties.
  Physical Review Letter, 2000, 84, 24, 5552-5555,
  APS

11
Any Questions?