Modeling and simulation of buckling of embedded carbon nanotubes

Abstract

Carbon nanotube (CNT) has been identified as a good reinforcing fiber in composites. Several studies have proven buckling of CNT as a common mode of failure of CNT composites. Hence the knowledge on buckling properties of embedded CNTs is essential in designing nanocomposites and nanodevices. However, Molecular Dynamics Simulations (MDS) based studies on buckling of embedded CNTs are found to be lacking in the literature. As a result, the accuracy of the continuum mechanics models employed in analyzing buckling of embedded CNTs is not sufficiently verified. Therefore, in this study we employ MDS to study buckling of single-walled CNTs (SWNTs) embedded in polyethylene matrix. Moreover, the accuracy of the continuum mechanics based analytical models in predicting buckling properties of embedded CNTs is discussed. The analytical models employed in this study are well-known equations for beam or shell on an elastic foundation in which the elastic foundation is modeled as a Winkler foundation. In addition to these well-known formulae, a formula proposed by the authors is also included in the discussion. Derivation and application of this first-order shell theory based formula to freestanding CNTs have been discussed in authors’ previous paper.Our MDS results reveal that the volume fraction of CNT in composite have a considerable effect on buckling stress of embedded CNT. As expected, the embedded CNT is found to have higher buckling stress compared to freestanding CNT. This stress increment in embedded CNTs compared to freestanding CNTs is higher in CNTs with smaller diameter and larger lengths. Of the three formulae considered in this study, the formula proposed by the authors is found to produce the most accurate results. However, the results obtained from this formula are also found to deviate considerably from the MDS results.