Critical particle size for interfacial debonding in polymer/nanoparticle composites

Interfacial debonding in polymer/nanoparticle composites under uniaxial loading is studied using meso-mechanics. By means of Eshelby's equivalent inclusion method, the step differences of stress and strain just before and after the debonding for a single ellipsoidal particle embedded in an infinite matrix are obtained. The debonding criterion is derived from an energetic analysis. Then, the relationships between the interfacial adhesion strength and the work of adhesion of the components, the shape and size of the particle, and the mechanical properties of both constituents are discussed. The critical particle size, defined as that size below which no interface debonding can occur, is calculated for two special cases: spherical and penny-shape particles. It is shown that this critical size depends on the absolute value of the work of adhesion. In the adhesion range of 0.01-0.40J/m2, the critical radius of a sphere particle varies from tens to several hundreds of nanometers. However, for a penny-shape particle with loading parallel to its faces, the critical particle size is at least several micrometers for an aspect ratio of 100.