Analysis of Randomness in Mechanical Properties of Carbon Nanotubes Through Atomistic Simulation

Lü, Qiang; Bhattacharya, Baidurya

doi:10.2514/6.2005-1920

Cited by 3 publications

(2 citation statements)

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“…Benchmarking studies investigating the tensile and fracture behaviour of such simulations have already been reported in the literature [16,10,33,34]. It has been found that there is no discernible yield point and fracture of SWNTs is always catastrophic, although a crack-length dependence on fracture resistance has been found.…”

Section: Incorporating Random Stone-wales Defects In Swnt Mechanicsmentioning

confidence: 99%

The asymptotic properties of random strength and compliance of single-walled carbon nanotubes using atomistic simulation

Bhattacharya

Lü

2006

J. Stat. Mech.

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Mechanical response of deformable bodies is often concerned with either the sum or the extreme of an underlying random process. This paper investigates the asymptotic statistical properties of ultimate strength (σu) and compliance (C) of single-walled nanotubes (SWNTs) containing random defects using the technique of atomistic simulation (AS). The defects considered are of the Stone–Wales (SW) kind and a Matern hard-core random field applied on a finite cylindrical surface is used to describe the spatial distribution of the SW defects. A nanotube can be viewed as consisting of nominally identical segments of equal length possessing a stationary distribution of ultimate strength, σu. Under a weak dependence condition among the segment strengths (that decay to zero with increasing distance between the segments), consistent with the non-local nature of atomic interactions, formalized here in the form of strong mixing, the asymptotic properties of σu (as the extreme of the strong mixing sequence) and C (as the sum of a related strong mixing sequence) are studied with increasing tube length, l. The extremal index, measuring the stochastic dependence in the strength field, is estimated. We simulate a set of displacement controlled tensile loading up to fracture of (6, 6) SWNTs with length between 49 and 492 Å. With increasing l, the distribution of σu is found to shift to the left and become narrower and appears to fit the Weibull distribution rather well; the compliance of the tube increases with increasing l and becomes asymptotically normal. The compliance and strength of the tube are found to become asymptotically uncorrelated. These results appear to validate the strong mixing property of the strength field.

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Section: Incorporating Random Stone-wales Defects In Swnt Mechanicsmentioning

confidence: 99%

The asymptotic properties of random strength and compliance of single-walled carbon nanotubes using atomistic simulation

Bhattacharya

Lü

2006

J. Stat. Mech.

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“…Defects can also be introduced by mechanical loading [31] and electron irradiation [37]. These defects have been found to have significant influence on CNT mechanical properties [42,43]. It is reasonable to assume that such defects could initiate brittle fracture in CNTs under appropriate conditions.…”

Section: Introductionmentioning

confidence: 99%

Fracture resistance of zigzag single walled carbon nanotubes

Lü

Bhattacharya

2006

Nanotechnology

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Carbon nanotubes (CNTs) are known to possess extraordinary strength, stiffness and ductility properties. Their fracture resistance is an important issue from the perspective of durability and reliability of CNT-based materials and devices. According to existing studies, brittle fracture is one of the important failure modes of Single-Walled Carbon Nanotube (SWNT) failure due to mechanical loading. However, based on the authors' knowledge, the fracture resistance of CNTs has not been quantified so far. In this paper, the fracture resistance of zigzag SWNTs with preexisting defects is calculated using fracture mechanics concepts based on atomistic simulations. The interatomic forces are modeled with a modified Morse potential; the Anderson Thermostat is used for temperature control. The problem of unstable crack growth at finite temperature, presumably caused by lattice trapping effect, is circumvented by computing the strain energy release rate through a series of displacement-controlled tensile loading of SWNTs (applied through moving the outermost layer of atoms at one end at constant strain rate of 9.4x10 -4 /ps) with pre-existing crack-like defects of various lengths. The strain energy release rate, G, is computed for (17,0), (28,0) and (35,0) SWNTs (each with aspect ratio 4) with pre-existing cracks up to 29.5Å long. The fracture resistance, G c , is determined as a function of crack length for each tube at three different temperatures (1K, 300K and 500K). A significant dependence of G c on crack length is observed reminiscent of the rising R curve behavior of metals at the macroscale: for the zigzag nanotubes G c increases with crack length at small length, and tends to reach a constant value if the tube diameter is large enough. We suspect that the lattice trapping effect plays the role of crack tip plasticity at the atomic scale. For example, at 300 Kelvin, G c for the (35,0) tube with aspect ratio 4 converges to 6 Joule/m 2 as the crack length exceeds 20 Angstrom. This value is comparable with the fracture toughness of graphite and Silicon. The fracture resistance of the tubes is found to decrease significantly as the temperature increases. To study the length effects, the computations are repeated for zigzag nanotubes with the same three chiralities but with aspect ratio 8 at 1K. The fracture resistance of the longer nanotubes are found to be comparable to those of the shorter nanotubes.

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