Graphene/polymer nanocomposites: The active role of the matrix in stiffening mechanics

Abstract

In this study we investigate the efficiency of graphene in stiffening polymer matrix nanocomposites. The analysis focuses primarily on the effect of the matrix modulus Em on the strain fields, whilst assuming perfect graphene and interface conditions with no agglomeration. The matrix was found to have an active role in stiffening due to the regions with large strain levels. The upper and lower bounds were discussed from the perspective of strain distribution. The effective modulus of graphene nanocomposite E¯ was relatively closer to the lower bound, while it showed a transitional behavior towards the upper bound with increasing Em and the volume fraction. The matrix contribution to stiffening surpasses the graphene in terms of the strain energy due to the graphene’s low strain levels resulting from the large modulus-mismatch. A novel measure to the internal state of strain that could represent the strain variation between the graphene and the matrix was derived. Lower modulus-mismatch show lower strain variation and a better stiffening efficiency of graphene. These measures could also interpret the effect of interphase on stiffening. This study provides new insights to the analysis and design of graphene/polymer nanocomposites.