Establishment of Constitutive Model of Silicone Rubber Foams Based on Statistical Theory of Rubber Elasticity

Abstract

In this study, a constitutive model based on microscopic physical mechanism of silicone rubber foams was established. A theoretical statistical model of rubber elasticity considering the effect of dangling chains was modified to build this model. When a strain amplification factor (X) was introduced, the theoretical model could fit the tensile stress-strain data of mono- and bi-modal foam matrix well (Adj. R-Square = 0.9989, 0.9983). Parameters related to the polymer network, namely, average molecular weight (M_c) and volume fraction (ϕ) of chain segments between adjacent cross-linking points (network strands), were calculated by probabilistic method from the number-average molecular weight (M_n), vinyl content (w_Vi) of the primary polysiloxanes and percent conversion (q) of vinyl groups. The primary and infinite strain amplification factors (X₀, X_∞) and decay exponent (z), introduced by X and related to the nanoparticles, were obtained by fitting. Inspired by the fact that the actual strain of matrix was lower than that of the foams’, we introduced another item, strain hysteresis item (H, related with the foam porosity and cell structure), into the statistical model as well. With the same above values of M_c, ϕ, X₀ and X_∞, the model could also fit the compressive stress-strain data of mono- and bi-modal foams well (Adj. R-Square = 0.9948, 0.9985). Interestingly, the strain hysteresis items of the mono- and bi-modal foams almost completely coincided under all experimental strains, which may be attributed to the almost equal porosity and similar cell structure of the two foams. This constitutive model may connect the macroscopic stress-strain behaviour to the parameters of microscopic molecular structures, promisingly providing a basis for the performance improvement and optimization of silicone rubber foams.