Recent experiments have shown that grain size of metals in graphene/metal nanocomposites has a significant effect on their strength and ductility. As the grain size decreases, the strength tends to increase while the ductility tends to decrease. But quantitative assessment of these observations remains a challenge. In this paper, we establish a hierarchical scheme from nano to macro scale to evaluate the dependance of these properties on the grain size and graphene volume concentration. In the nano scale, the elastic properties of graphene nanofiller and metal matrix are evaluated via the density functional theory (DFT). In the micro scale, the plasticity of the ductile metal is described by a dislocation density-based constitutive equation, and its degradation process is accounted for by the generation of micro voids. In the macro scale we consider the system of randomly distributed graphene nanosheets in the degraded metal matrix. The grain-size dependent stress-strain relation of the overall graphene/metal nanocomposites are calculated by a two-scale homogenization method with the assistance of the field-fluctuation approach. In this process, the grain-size dependent thermodynamic driving force for the progressive generation of micro voids and the influence of an ultrathin imperfect interphase surrounding the graphene nanofiller are also considered. It is demonstrated that the predicted results from the developed hierarchical scheme agree well with the experimental data of graphene/aluminum nanocomposites. The developed multiscale theory can provide a useful guideline for the design and applications of graphene/metal nanocomposites through the grain-size controlled process.

最近的实验表明，石墨烯/金属纳米复合材料中金属的晶粒尺寸对其强度和延展性具有重大影响。随着晶粒尺寸的减小，强度趋于增加，而延展性趋于降低。但是，对这些观察结果进行定量评估仍然是一个挑战。在本文中，我们建立了从纳米级到宏观级的分级方案，以评估这些性质对晶粒尺寸和石墨烯体积浓度的依赖性。在纳米尺度上，通过密度泛函理论（DFT）评估了石墨烯纳米填料和金属基体的弹性性能。在微观尺度上，韧性金属的可塑性由基于位错密度的本构方程描述，而其降解过程则由微空隙的产生来解释。在宏观尺度上，我们考虑降解金属基质中随机分布的石墨烯纳米片的系统。借助于场波动方法，通过两尺度均化方法来计算整个石墨烯/金属纳米复合材料的晶粒尺寸依赖性应力-应变关系。在此过程中，还考虑了逐步生成微孔的晶粒尺寸相关的热力学驱动力，以及围绕石墨烯纳米填料的超薄不完美界面的影响。结果表明，所开发的分层方案的预测结果与石墨烯/铝纳米复合材料的实验数据吻合良好。