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Research Paper

Analysis of Crack Propagation in Fixed-Free Single-Walled Carbon Nanotube Under Tensile Loading Using XFEM

[+] Author and Article Information
Anand Y. Joshi

Department of Mechanical and Industrial Engineering, Vibration and Noise Control Laboratory, Indian Institute of Technology, Roorkee, Roorkee 247667, Uttarakhand, Indiaanandyjoshi@gmail.com

Satish C. Sharma

Department of Mechanical and Industrial Engineering, Vibration and Noise Control Laboratory, Indian Institute of Technology, Roorkee, Roorkee 247667, Uttarakhand, Indiasshmefme@iitr.ernet.in

S. P. Harsha

Department of Mechanical and Industrial Engineering, Vibration and Noise Control Laboratory, Indian Institute of Technology, Roorkee, Roorkee 247667, Uttarakhand, Indiasurajfme@iitr.ernet.in

J. Nanotechnol. Eng. Med 1(4), 041008 (Oct 22, 2010) (7 pages) doi:10.1115/1.4002417 History: Received June 11, 2010; Revised August 18, 2010; Published October 22, 2010; Online October 22, 2010

Fracture mechanics at the nanoscale level is a very complex phenomenon, whereas the macroscale fracture mechanics approach can be employed for nanoscale to simulate the effect of fracture in single-walled carbon nanotubes (SWCNTs). In this study, an extended finite element method is used to simulate crack propagation in carbon nanotubes. The concept of the model is based on the assumption that carbon nanotubes, when loaded, behave like space frame structures. The nanostructure is analyzed using the finite element method, and the modified Morse interatomic potential is used to simulate the nonlinear force field of the C–C bonds. The model has been applied to single-walled zigzag, armchair, and chiral nanotubes subjected to axial tension. The contour integral method is used for the calculation of the J-integral and stress intensity factors (SIFs) at various crack locations and dimensions of nanotubes under tensile loading. A comparative study of results shows the behavior of cracks in carbon nanotubes. It is observed that for the smaller length of nanotube, as the diameter increased, the stress intensity factor is linearly varied while for the longer nanotube, the variation in stress intensity factor is nonlinear. It is also observed that as the crack is oriented closer to the loading end, the stress intensity factor shows higher sensitivity to smaller lengths, which indicates more chances for crack propagation and carbon nanotube breakage. The SIF is found to vary nonlinearly with the diameter of the SWCNT. Also, it is found that the predicted crack evolution, failure stresses, and failure strains of the nanotubes correlate very well with molecular mechanics simulations from literature.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

J-integral in two dimensions

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Figure 2

J-integral in three dimensions

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Figure 3

(a) Stone–Wales defect can be seen as a pair of dislocations, where each 5–7 pair represents a dislocation and (b) 5–7 pairs are gliding away from each other due to bond reconstructions (29)

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Figure 4

Climb motion of dislocation due to sequential removal of two atom pairs (circled atoms) (29)

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Figure 5

Space frame model of a fixed-free carbon nanotube subjected to axial tension

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Figure 6

Comparison of stress-strain curves predicted for the (20,0) tube with the corresponding theoretical (12) and experimental (33) curves from literature

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Figure 7

Half CNT crack model with a/L=0.5 indicating crack propagation in atomic structure (12)

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Figure 8

((a)–(e)) Progressive fracture models of SWCNT using XFEM

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Figure 9

Variations in stress intensity factor with the changes in length and diameter for (a) a/L=0.1, (b) a/L=0.5, and (c) a/L=0.9

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Figure 10

SIF for different crack positions along the length of SWCNT

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