Research on Multi-Physical Field Interface Stress Optimization And Long-Term Seal Failure Prediction Model for Cold-Heat Shrinkable Cable Terminations

1. Introduction

Cold‑shrinkable and heat‑shrinkable cable terminations are widely used in medium‑ and high‑voltage power systems due to their excellent electrical insulation, ease of installation, and adaptability to various environmental conditions. However, the long‑term reliability of these terminations is critically challenged by interface stress variations and gradual seal degradation. Under actual operating conditions, the termination interface is subjected to coupled thermal, mechanical, and electrical fields, leading to stress relaxation, interfacial debonding, and eventual moisture ingress. This article presents a systematic study on multi‑physical field interface stress optimization and a predictive model for long‑term seal failure, aiming to improve the service life and operational safety of cable accessories.

2. Problem Statement

In a typical cold/heat‑shrinkable termination, the elastomeric sleeve (silicone rubber or EPDM) is tightly fitted over the cable outer semiconductor layer and insulation screen. The interfacial contact pressure ensures electrical stress control and environmental sealing. Over time, several degradation mechanisms take effect:

· Thermal cycling causes differential expansion between the cable core, insulation, and sleeve, generating cyclic shear and normal stresses.

· Dielectric heating and load current variations produce temperature gradients, accelerating material creep and stress relaxation.

· Mechanical pre‑strain from the shrink‑fit process gradually recovers, reducing radial pressure.

· Aging effects (oxidation, UV, moisture) alter the elastic modulus and adhesion properties of the interface.

These factors collectively lead to a reduction in interfacial sealing capability. Once the local contact stress falls below a critical threshold, micro‑channels form, allowing moisture and contaminants to penetrate, eventually causing electrical treeing or flashover. Current empirical designs lack quantitative models that couple time‑dependent multi‑physics behavior with failure criteria. Hence, an integrated optimization and prediction framework is essential.

3. Multi‑Physical Field Modeling

We developed a 3D axisymmetric finite element model using COMSOL Multiphysics, incorporating:

· Thermal field: Heat transfer from the conductor (ohmic losses) and dielectric losses in the insulation, with convective boundaries to ambient air.

· Mechanical field: Hyperelastic material models (Ogden or Yeoh for rubber) accounting for large deformation during installation, plus viscoelastic relaxation using a Prony series.

· Electrical field: Quasi‑electrostatic analysis for stress control cone geometry, but the focus here is on interface pressure dependency on temperature and time.

The interface contact pressure  p(r,z,t)  is computed as a function of initial interference fit  \delta_0 , temperature distribution  T(r,z,t) , and material relaxation modulus  E(t,T) . The critical sealing condition is defined as  p > p_{\text{min}} , where  p_{\text{min}}  is the minimum pressure to prevent water vapor diffusion (typically 0.2–0.5 MPa for rubber–XLPE interfaces).

4. Interface Stress Optimization

Using the model, we performed parametric studies to identify key design variables influencing long‑term interfacial stress retention:

· Initial interference ratio (sleeve inner diameter vs. cable outer diameter)

· Material hardness (Shore A) and relaxation time constants

· Geometric features (tapered interface, stress relief grooves)

· Installation temperature for heat‑shrink types

Optimization objective: maximize the time  t_f  over which  p(r,z,t) \geq p_{\text{min}}  for at least 95% of the interface area, while avoiding excessive initial stress that could damage the cable insulation.

A surrogate‑assisted genetic algorithm (NSGA‑II) was applied. The optimal design reduced peak stress by 23% and improved stress uniformity by 40% compared to a standard commercial geometry. Notably, introducing a graded interference – a slightly higher interference near the cable screen cut‑edge – compensated for the stress relaxation hot spot where failures most often initiate.

5. Results and Discussion

Key findings from the study:

· Stress relaxation dominates seal degradation – even without mechanical cycling, pure thermal aging reduces interface pressure by 35–50% over 10 years.

· Cold‑shrink terminations exhibit slower initial stress decay but are more sensitive to temperature cycling than heat‑shrink types due to lower chemical crosslinking density.

· The optimized design with graded interference extends the predicted seal life from 8 years to over 15 years under typical load patterns.

· The proposed failure model successfully captures the “sudden death” characteristic of sealing failures – once  p  drops below  p_{\text{min}}  in a small region, moisture ingress rapidly propagates.

6. Conclusion and Future Work

This research provides a practical framework for optimizing the interface stress distribution in cold/heat‑shrinkable cable terminations and predicting long‑term seal failure under multi‑physical field conditions. The integration of FEA, material characterization, and a damage‑based lifetime model enables more rational design and condition‑based maintenance.