Probabilistic investigation of the effect of stochastic imperfect interfaces in nanocomposites

Abstract

This paper presents a probabilistic investigation of the elasticity tensor of an imperfect interface between the nanofillers and matrix in particulate composite materials. Moreover, the effect of nanometric scale, which is typically neglected in classical micromechanics theories, is examined in this study from a probabilistic standpoint. To this end, an imperfect interface model was introduced to characterize the jump in mechanical properties at the interface between the matrix and the reinforcement. As the surface elasticity tensor may or may not be positive-definite, thus, probabilistic models were then constructed for both cases of positive-definite and non-positive-definite property. Random fluctuation in surface properties was propagated to macroscopic moduli on the basis of a generalized self-consistent micromechanical scheme. Results showed that the nanoscale effect played a significant role and must be taken into account when predicting the macroscopic properties of materials presenting nanometric inhomogeneities. From a probabilistic point of view, the confidence interval of the macroscopic properties was also established at different levels of fluctuation of the surface properties. Finally, a parametric study as a function of surface strength and volume fraction of fillers is presented and discussed.