A theoretical modelling of strengthening mechanism in graphene-metal nanolayered composites

Graphene-metal nanolayered composites (GMNCs) are a new generation of nano-structural composites characterized by a very high density of graphene reinforced interfaces (GRI) between metal nanolayers. Compared to traditional graphene flake reinforced composites, GMNCs have much higher strength, toughness and ductility due to the excellent ability of GRI on constraining dislocation motion and crack propagation. Despite numerous experimental and numerical studies on the mechanical behavior of GMNCs, the underlying strengthening mechanism is still not fully understood due to the absence of appropriate theoretical model. This paper proposes a continuum mechanics based theoretical model to explain the strengthening mechanism in GMNCs. In this model, the metal matrix and the GRI are simulated as homogenous elastic medium of infinite extend and inextensible thin membrane of zero thickness, respectively. Using the theoretical model, two boundary value problems namely (i) A circular prismatic dislocation loop approaching to the GRI and (ii) A mixed mode I/II penny-shaped crack near the GRI are formulated to reveal the two key strengthening mechanism: dislocation blocking and crack shielding, respectively. The two problems are solved analytically by the Generalized Kelvin's Solution (GKS) based method for 3D elasticity and Fredholm integral integration technique. Exact closed form solution for the Peach-Koehler (P-K) force on the dislocation loop is obtained. An efficient numerical scheme is developed to solve the Fredholm integral integration for the crack problem with very high accuracy. It is shown that our theoretical model can well capture and explain the strengthening mechanism observed in experiments. Moreover, the dominant role of Poisson's ratio on the strengthening efficiency is also revealed by our model. This finding implies the exciting possibility that the strength of GMNCs can be tailored by controlling the Poisson's ratio of the metal matrix. The present theoretical modeling can provide valuable insights into the mechanics-based design of GMNCs.