Possible degradation of cable insulations exposed to radiation and heat is a safety and operational concern for nuclear power plants, particularly in the context of a license extension for the operation beyond original 40-year design life. Ethylene propylene rubber and silicone rubber are two major materials for the cable insulation. Degradation decreases the elongation at break of the insulation, which may lead to the exposure of the metal core in the cable, causing potential safety issues. This article proposes a mechanistic predictive model for the elongation at break as a function of time, temperature, and radiation dose rate. In the proposed model, the elongation at break curve is divided into an incubation section and a drop-off section with two parameters. In contrast to traditional deterministic approaches, this model projects the expected lifespan of cable insulation in the form of a probability distribution. The article also provides a validation of the model behavior using published experimental data.

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Cables transmit signals and power in nuclear power plants. The primary material for the cable insulation is cross-linked polyethylene, which inevitably degrades due to thermal stress. The degradation can become a safety issue, since the brittleness of degraded cross-linked polyethylene may render the exposure of the metal core in a cable. Elongation at break is a widely accepted measurement, evaluating the degree of the brittleness of the insulation. Reaction- and diffusion-controlled kinetics are proposed in this article to quantitatively predict the decrease of the elongation at break as a function of time and temperature. The proposed approaches are based on dichotomy model and Fick’s Law to respectively define the degree of reaction- and diffusion-controlled degradation. Probabilistic techniques are developed by Bayesian parameter estimation to determine the reliability of the cable insulation. These approaches are validated by experimental data.

Cross-linked polyethylene (XLPE or PEX) is a major material for cable insulation. Antioxidant is usually used as a dopant added in XLPE to prevent the insulation from oxidation. However, the antioxidant diffuses out of an XLPE matrix during thermal ageing, which accelerates oxidation, causing the degradation of the insulation. Few models have been developed to represent the diffusion behavior of the antioxidant. One paper has reported that the antioxidant in XLPE migrates from low to high concentration but no explanation has been given. Starting with the theories of uphill diffusion and reaction-diffusion, this paper has developed a physics-based model explicating why the antioxidant migrates against the concentration gradient. In addition to the concentration, the activity coefficient (γ) of the antioxidant is also considered. With physical significance, this study mathematically proves the inhomogeneous distribution of the diffusing oxygen in XLPE makes γ a function of oxygen concentration. γ determines the driving force rendering the uphill diffusion of the antioxidant. Besides the γ function, the decomposition rate of the antioxidant has been modeled.

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