Representative Volume Element Size of Elastoplastic and Elastoviscoplastic Particle-Reinforced Composites with Random Microstructure

With the progress of miniaturization, in many modern applications the characteristic dimensions of the physical volume occupied by particle-reinforced composites are getting comparable with the reinforcement size and many of those composite materials undergo plastic deformations. In both experimental and modelling contexts, it is therefore very important to know whether, and up to which characteristic size, the description of the composites in terms of effective, homogenized properties is sufficiently accurate to represent their response in the actual geometry. Herein, the case of particle-reinforced composites with elastoviscoplastic matrix materials and polyhedral randomly arranged linear elastic reinforcement is considered since it is representative of many metal matrix composites of technical interests. A large parametric study based on 3D finite element microstructural models is carried out to study the dependence of the Representative Volume Element (RVE) size on the mechanical properties of the constituents, the reinforcement volume fraction and the average strain level. The results show that RVE size mainly depends on the reinforcement volume fraction and on the macroscopic strain level. The estimated RVE size for elastoplastic composites with 5% to 10% volume fraction of reinforcements is found in the range of 5-6 times the average size of reinforcement particles, while for higher volume fraction, e.g. 15% to 25%vol., the RVE size increases rapidly to 10 to 20 times the reinforcement size. Moreover insights on the influence of mesh refinement and boundary conditions on finite element homogenization analysis are obtained.