synopsisWe consider two approaches to strain magnification in a composite material, point out that they apply to different situations, and caution against misapplication of the equations derived.Strain magnification occurs when a sample of a deformable matrix containing essentially nondeformable particles is subjected to an elongation or compression. Barring the formation of voids, the total sample deformation has to be accommodated by the matrix; hence the strain in the matrix is larger than the measured overall strain.I n general, it is necessary to distinguish between the maximum strain, which would prevail between the closest points of approach of two neighboring particles, and the mean strain, which is obtained by averaging the strains over the entire range of particle separation distances. The former value would probably be relevant to failure properties of a composite; the latter would be the appropriate quantity to use for modulus, energy storage and dissipation.Even though the particles in a composite are most likely randomly distributed, a number of authors have found it convenient to assume a particular spatial arrangement. Smith,' using a model of spheres in a closepacked array, predicts a strain magnification E ' / C given by:where e is the measured overall strain (ALILO), AL is the change in length, Lo is the initial specimen length, e' is the magnified strain in the matrix, and p~ is the volume fraction of filler particles. This result gives the strain in the matrix along the line between centers of adjacent spheres, i.e., the maximum rather than the mean strain. A similar result is obtained by F. Bueche2 using a model of cubical particles apparently in a cubic array. He gives the line fraction of polymer between two reference points in a filled system as 1 -(PF"'; hence the line fraction of filler, Lp/L0, is pF1/'. This led Bueche to the conclusion that the magnified extension ratio a' is 867

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