Multiscale Shear-Lag Analysis of Stiffness Enhancement in Polymer-Graphene Nanocomposites

Graphene and other two-dimensional (2D) materials are of emerging interest as functional fillers in polymer-matrix composites. In this study, we present a multiscale atomistic-to-continuum approach for modeling interfacial stress transfer in graphene-high-density polyethylene (HDPE) nanocomposites. Via detailed characterization of atomic-level stress profiles in submicron graphene fillers, we develop a modified shear-lag model for short fillers. A key feature of our approach lies in the correct accounting of stress concentration at the ends of fillers that exhibits a power-law dependence on filler ("flaw") size, determined explicitly from atomistic simulations, without any ad hoc modeling assumptions. In addition to two parameters that quantify the end stress concentration, only one additional shear-lag parameter is required to quantify the atomic-level stress profiles in graphene fillers. This three-parameter model is found to be reliable for fillers with dimensions as small as ∼10 nm. Our model predicts accurately the elastic response of aligned graphene-HDPE composites and provides appropriate upper bounds for the elastic moduli of nanocomposites with more realistic randomly distributed and oriented fillers. This study provides a systematic approach for developing hierarchical multiscale models of 2D material-based nanocomposites and is of particular relevance for short fillers, which are, currently, typical of solution-processed 2D materials.