Determination of the effective moduli of composite reinforced by hollowcoating spheres based on the five phase spherical model

The theoretical formulas are worked out to predict the effective bulk moduli , shear moduli and Young’smoduli of the composite reinforced by hollow coating spheres using the developed five phase spherical model. Therelations of the effective moduli of the composite , the thickness of the hollow sphere wall , volume f raction of thefiller , and thickness of the coating were investigated. In order to illust rate the validity of the present result s , thefive phase model can be reduced to the case of hollow noncoating spheres filled into the mat rix , and the reducedresult s were compared with the experimental data. The calculating example shows that the greater filler volumef raction and relatively thicker wall lead to the bigger elastic moduli , and the smallest elastic moduli appear in the caseof the greatest filler volume f raction and the relative thinnest wall when the thickness of the coating is very thin.