Multiscale modelling of aluminium-based metal–matrix composites with oxide nanoinclusions

Abstract

In this work, we study the dependence of Young’s modulus and the strength of aluminium-based metal–matrix composites from the volume fraction of inclusions and the size of oxide inclusions dispersed in the matrix. We consider the metal–matrix composites containing extremely low volume fraction of oxide inclusions (<0.15%) with the inclusion size from 30nm to 600nm. We analyse the non-monotonic experimental dependences of the mechanical properties from the volume fractions of inclusions and the inclusions size, which reflect the scale effects. We study the effective properties and yield strength of the filled aluminium-based metal–matrix composites with spherical inclusions and take into account the possibility of agglomerates formation from the inclusions. To describe the anomalous behaviour of materials with saturated internal structural heterogeneity, the gradient theories are involved. As a result, in this work, on the basis of the gradient elasticity, the self-consistent method of three spherical bodies and the method of radial multipliers, we provide the modelling of experimentally observed effects of scale amplification of the mechanical characteristics of the metal–matrix composites depending on the volume fraction of the particles. The theoretical modelling uses the idea of the interphase layer and demonstrates correspondence to the experimentally observed effects of scale amplification of mechanical characteristics for the aluminium-based metal–matrix composites reinforced by the extremely low volume fraction of oxide inclusions. Based on a comparison with experimental data, the additional parameters of the non-classical models are determined, which helps to explain the impact of scale effects (the size of the inclusions) on the properties of composites.