Stress‐Strain Equation for Rubber in Tension

摘要

A stress‐strain equation is derived for a homogeneous, isotropic material with the assumptions that for any given homogeneous simple tensile strain, the components of the stress tensor are to the first approximation linear, homogeneous functions of the components of the strain tensor and that no volume change occurs during the deformation. Utilizing the dependence of Poisson's ratio upon the extension referred to the initial coordinates, one elastic coefficient, C12, is found to be sufficient to roughly characterize the first stretch stress‐strain curve. Although experimentally this elastic coefficient is found to be essentially constant for extensions greater than 250% its value increases rapidly as zero extension is approached. This behavior agrees qualitatively with data by Blanchard and Parkinson as to the distribution of secondary bond strengths, wherein they found a large number of relatively low‐energy bonds which would be effective only at small extensions in contributing to modulus reinforcement. Various aspects of stress strain and cure behavior are examined with the derived equation as a basis.