SEVERAL VARIATIONS OF THE GENERALIZED SELF-CONSISTENT METHOD FOR HYBRID COMPOSITES

Several models are proposed to extend the generalized self-consistent method to hybrid composites, ie. composites with three or more phases. These models degrade to the eigensolution approach in the generalized self-consistent method for two-phased composites. It is established t hat the difference in elastic moduli predicted by these models, the Mo ri-Tanaka method and the decoupled model, are small; and all are in re asonable agreement with available experimental data. A solid containin g two extreme types of inclusions, voids and rigid particles, is also studied. For the same volume fraction of spherical voids and rigid par ticles, all models reveal that the weakening effect of voids and the s trengthening effect of rigid particles cancel each other out so that t he effective Young's modulus of the composite is almost identical to t hat of the matrix. Among these models, Mori-Tanaka's method and the de coupled model provide closed-form solutions. For a solid with two type s of reinforcements, Mori-Tanaka's method gives the lower bounds, and the decoupled method the average estimate for the moduli.