Constitutive relation of particulate-reinforced viscoelastic composite materials with debonded microvoids

In this paper, the constitutive relation of particulate-reinforced viscoelastic composite materials is studied by considering the evolution of microvoids. Owing to the difference in mechanical properties between matrix and second phase particles, debonding of particle-matrix interface may occur under the condition of high stress triaxiality. This kind of damage will lead to the nucleation and growth of microvoids. The reinforcing effect due to rigid particles and the weakening effect due to microvoids caused by debonding on the overall mechanical properties of particulate-reinforced composites are investigated. Using the energy criterion of interfacial debonding, an expression for the nucleation rate of microvoids is suggested. Then, the growth of these voids is studied by means of Eshelby's equivalent inclusion method. It is shown that the strain of the microvoids depends not only on the remote strain history but also on their nucleation time. By considering the effect of nucleation time, a new definition of an average strain of microvoids is given. According to the Mori-Tanaka scheme, a macroscopic constitutive relation of the composite material is finally derived. The results show that macroscopic strain rate, particle-size dispersity, relaxation time of matrix, and interface adhesive strength all play key roles in the overall mechanical properties of particulate-reinforced composites.