A constitutive theory of particulate-reinforced viscoelastic materials with partially debonded microvoids

In particulate-reinforced viscoelastic materials, the interfacial debonding between particles and matrix is usually a significant damage mechanism. In this paper, a new theoretical model of constitutive relation for particulate-reinforced viscoelastic materials is proposed. In the new constitutive model, both the reinforced effect of particles and weak effect due to microdamage evolution are taken into account. First, the deformation of a nucleated microvoid due to partially interfacial debonding between a particle and infinite viscoelastic matrix is analyzed in terms of Eshelby’s equivalent inclusion method. Secondly, the porosity of nucleated microvoids is calculated based on the computation of density function of nucleation rate, in which, the size distribution of particles is assumed to be a logarithmic normal function, and the debonding probability of interface between particles and matrix is assumed to obey Weibull’s distribution. Thirdly, a new definition of average stress and average strain for nucleated microvoids is proposed with considering the effect of nucleation time. Based on definition, a new constitutive model is suggested. This new model is consistent with experimental results. Finally, the effects of loading rate, interfacial adhesive energy, geometrical parameters of particles, and relaxation time on the constitutive relation are examined numerically. The simulation results indicate that the increase of loading rate, volume fraction of particles, and relaxation time of matrix not only reinforces the stiffness of composites, but also speeds up the evolution of microdamage. Such a competition mechanism should be taken into account when designing particulate-reinforced composites.