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

Abstract

Mechanical response of deformable bodies is often concerned with eitherthe sum or the extreme of an underlying random process. This paperinvestigates the asymptotic statistical properties of ultimate strength(σu) andcompliance (C) of single-walled nanotubes (SWNTs) containing random defects using the technique ofatomistic simulation (AS). The defects considered are of the Stone–Wales (SW) kind and aMatern hard-core random field applied on a finite cylindrical surface is used to describe thespatial distribution of the SW defects. A nanotube can be viewed as consisting of nominallyidentical 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 withincreasing distance between the segments), consistent with the non-local nature of atomicinteractions, formalized here in the form of strong mixing, the asymptotic properties ofσu (as the extreme of the strong mixing sequence) andC (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 upto fracture of (6, 6) SWNTs with length between 49 and 492 Å. With increasingl, thedistribution of σu is found to shift to the left and become narrower and appears to fit the Weibulldistribution rather well; the compliance of the tube increases with increasingl and becomes asymptotically normal. The compliance and strength of the tube are found tobecome asymptotically uncorrelated. These results appear to validate the strong mixingproperty of the strength field.