The Young’s modulus of silica beads/epoxy composites: Experiments and simulations

Abstract

The effect of particulate volume fraction vp and diameter dp on the composite Young’s modulus Ec is studied both experimentally, using a silica bead/epoxy system, as well as with the help of computer simulations. The experimental and simulation results show that for a given particulate size, the overall Ec vs vp curve displays a concave upward shape and not a linear shape. This superlinear trend of the data implies that the average strain normalized to the applied strain λ=ε̄p/εc transferred to the particulates increases with volume fraction. The above finding is explained in terms of a mean-field picture, where a single particle interacts with an effective medium consisting of the remaining particles embedded in the matrix. As the modulus of the effective medium surrounding a reference particle increases with vp, the modulus mismatch between the reference particulate and the medium is consequently reduced. This leads to an overall increase in the normalized average strain λ transferred to each particulate as vp is increased. The experimental results using silica particulates with various sizes dp, as well as the simulation results, show that smaller particulates provide an increased composite modulus as compared to larger particulates, at constant vp. General equations are developed, which relate the composite modulus to the average particle stress or strain, given only information about the volume fraction and the Young’s modulus of each of the phases present. Through the application of these relations, it is found that smaller particulates display a greater amount of normalized average strain λ transferred than larger particulates. The effect of particulate Young’s modulus Ep in combination with particulate size on the resulting Ec is also studied using simulations only. It is found that for a low particulate to matrix modulus ratio Ep/Em, the particulate size has very little influence on Ec. Moreover, the shape of the Ec vs vp curve can be well approximated by a straight line up to large values of vp. On the other hand, as the ratio Ep/Em is increased, the superlinear trend of the composite modulus Ec vs vp data is more apparent. This results in a smaller range of the Ec vs vp curve, which can be approximated by a linear function. It is also found that the extent of this linear region also decreases with particle size.