3.8 POISSON'S RATIO

Poisson's ratio ( ?) is the absolute value of the ratio of transverse strain to the corresponding axial strain resulting from uniformly distributed axial stress below the proportional limit of the material [80]. This ASTM standard recommends an axial tensile test rather than a compressive load, because it is easier to obtain a uniform stress distribution. This ratio is named after S.D. Poisson, the French mathematician who determined the ratio analytically by using the molecular theory of the structure of matter. It is unique to a material only if it is isotropic. For isotropic materials, the ratio lies between ?1 and 0.5 and for most metals 0.25 < ? < 0.35. Rubbery materials have values approaching 0.5 as they readily undergo shear deformations but resist volumetric or bulk deformations. The theoretical value for an isotropic elastomer is 0.5, implying also no plastic compressibility. With anisotropic materials, Poisson's ratio can vary over a much wider range. Poisson's ratios of composite constituents are not well known. Matrices such as polymers are generally assumed to be isotropic, and thus volumetric methods may be adopted for their measurement [81]. Epoxy resin matrices (e.g., 5208) may exhibit values of about 0.44 at low strains to nearly 0.5 at high strains [82]. Fillers or processing parameters may lead to anisotropy, and this value could be exceeded. Measurements on polymer (polyethylene and polypropylene) fibers suggest values of about 0.4 [83]. A laser diffractographic technique indicated the axial Poisson's ratio for carbon...