THE YOUNGS MODULUS OF SILICA BEADS EPOXY COMPOSITES - EXPERIMENTS AND SIMULATIONS

The effect of particulate volume fraction v(p) and diameter d(p) on the composite Young's modulus E(c) 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 E(c) vs v(p) 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 lambda=($) over bar epsilon(p)/epsilon(c) 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 v(p), the modulus mismatch between the reference particulate and the medium is consequently reduced. This leads to an overall increase in the normalized average strain lambda transferred to each particulate as v(p) is increased. The experimental results using silica particulates with various sizes d(p), as well as the simulation results, show that smaller particulates provide an increased composite modulus as compared to larger particulates, at constant v(p). 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 lambda transferred than larger particulates. The effect of particulate Young's modulus E(p) in combination with particulate size on the resulting E(c) is also studied using simulations only. It is found that for a low particulate to matrix modulus ratio E(p)/E(m), the particulate size has very little influence on E(c). Moreover, the shape of the E(c) vs v(p) curve can be well approximated by a straight line up to large values of v(p). On the other hand, as the ratio E(p)/E(m) is increased, the superlinear trend of the composite modulus E(c) vs v(p) data is mote apparent. This results in a smaller range of the E(c) vs v(p) 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.