The properties of the Poisson's ratio of microcellular foams with low porosity: non-stationary, negative value, and singularity

摘要

The properties of the Poisson's ratio of microcellular foams with an internal pressure in the voids and low porosity are investigated. Of prime interest is the effect of the matrix creep on the deformation of the foam and how this effect influences the later deformation characteristics of the material in terms of a Poisson description. First, the definitions of Poisson's ratio for the microcellular foams under uniaxial stress are reviewed. Second, the deformation of the microvoids under the influence of the internal pressure is analyzed by means of Eshelby's equivalent inclusion method. Next, the formula of the macroscopic strain of the microcellular foams is derived by using Mori-Tanaka's scheme, and based on this formula, the expression of the Poisson's ratio of the material is obtained. Further, the calculation of the Poisson's ratio of the material is then carried out. Numerical results show that the Poisson's ratio of the microcellular foams is a time-dependent parameter. It is also discussed that because of the effect of the internal pressure in the voids, the global Poisson's ratio may be negative. Under the action of remote comprcssive load, the Poisson's ratio of the microcellular foams may be unbounded. Finally, the effects of the loading rate, the Poisson's ratio and the relaxation time of the polymeric matrix material, the porosity, and the pressure in the microvoids on the Poisson's ratio are discussed with the aid of numerical estimates. These analytical results indicate that the Poisson's ratio under uniaxial tension is different from that under uniaxial compression.