Atomistic–continuum interphase model for effective properties of composite materials containing nano-inhomogeneities

Abstract

Classical micromechanics were revised to study the elastic properties of heterogeneous materials containing nano-inhomogeneities. Contrary to previous studies, this work introduces the concept of an interphase, in contrast to a sharp interface, to account for the interface excess stress effect at the nano-scale. The interphase's constitutive properties are derived from atomistic simulations within the continuum framework. These properties are then incorporated in a micromechanics-based interphase model to compute the effective properties of nano-composites. This scale transition approach bridges the gap between discrete systems (atomic level interactions) and continuum mechanics. An advantage of this approach is that it combines atomistic with continuum models that consider inhomogeneity and interphase morphology. It thereby enables us to account simultaneously for both the shape and the anisotropy of a nano-inhomogeneity and interphase at the continuum level when we compute a material's overall properties. In so doing, it frees us from making any assumptions about the interface characteristics between matrix and the nano-inhomogeneity.

Keywords:

• interphase model
• interface properties
• nano-composite
• atomistic simulation
• micromechanics

Acknowledgements

The authors would like to acknowledge support from the NanoInterface project FP7NMP2007SMALL1, a part of the 7th framework program by the European Commission under the grant agreement No. 214371.

Notes

1. Note that perfect bonding is assumed between matrix and interphase (S₁), and between the interphase and the inhomogeneity (S₂) i.e. and where superscript p = 1, 2 represents interfaces S₁ and S₂, respectively and [···] represents discontinuity of the quantity at those interfaces.

2. Homogeneous surface implies that the surface properties are not a function of position on the surface. The material, however, is not homogeneous and is composed of a transition region (of thickness t) and a bulk region.