Constitutive Model of Radiation Aging Effects in Filled Silicone Elastomers under Strain

Filled silicone elastomers, an essential component in many technological applications, are often subjected to controlled or unintended radiation for a variety of reasons. Radiation exposure can lead to permanent mechanical and structural changes in the material, which is manifested as altered mechanical response, and in some cases, a permanent set. For unfilled elastomers, network theories developed and refined over decades can explain these effects in terms of chain-scission and cross-link formation and a hypothesis involving independent networks formed at different strain levels of the material. Here, we expose a filled silicone rubber to gamma radiation while being under finite elongational strain and show that the observed mechanical and structural changes can be quantitatively modeled within the same theoretical framework developed for unfilled elastomers as long as nuances associated with the Mullins effect are accounted for in a consistent manner. In this work, we employ Ogden's incompressible hyperelastic model within the framework of Tobolsky's two-network scheme to describe the observed permanent set and mechanical modulus changes as a function of radiation dosage. In the process, we conclude that gamma radiation induces both direct cross-linking at chain crossings (H-links) and main-chain-scission followed by cross-linking (Y-links). We provide an estimate of the ratio of chain-scission to cross-linking rates, which is in reasonable agreement with previous experimental estimate from Charlesby-Pinner analysis. We use density functional theory (DFT)-based quantum mechanical calculations to explore the stability of -Si and -SiO radicals that form upon a radiation-induced chain-scission event, which sheds light on the relative rates of Y-linking and H-linking processes.