A Constitutive Model of a Particle Reinforced Viscoelastic Composite Material with Debonded Microvoids

The statistical behavior of microvoids’ evolution in a linear viscoelastic material which contains well bonded second phase particles is investigated. The particle size distribution is assumed to obey a logarithmic normal distribution. Because of the difference in mechanical properties between the matrix and the second phase particles, the debonding damage of particle-matrix interface may occur under the action of external loads. This kind of damage will lead to microvoids’ nucleation and growth. In this paper, the reinforcing effect due to rigid particles and the weakening effect due to microvoids produced from the debonding on the overall mechanical property of the particle reinforced composite material are studied. By virtue of Eshelby’s equivalent inclusion method and Mori-Tanaka theory, the average normal stress on the particle-matrix interface which governs the void nucleation and the dilational rate of void volume which governs the void growth are calculated. Then, based on the kinetic conditions for the microvoids’ nucleation and growth as well as the balance law of voids’ number, the distribution functions of the number densities both for perfectly bonded particles and for microvoids are obtained. Thus, a macroscopic constitutive relation of the considered composite material is derived. It is shown that the macroscopic strain rate,