The aging of extruded insulation is not as simple as with oil/paper insulation. I don't think you can come up with a mathematical expression like an Arrehenius curve. Accelerated life cable tests generally will use heat cycling and overvoltage stress, with the cables submerged in water. See:
Accelerated aging of extruded dielectric power cables. II. Life testing of 15 kV XLPE-insulated cables; Bernstein, B.S.; Thue, W.A.; Walton, M.D.; Smith, J.T., III;
Electr. Power Res. Inst., Washington, DC;
This paper appears in: IEEE Transactions on Power Delivery
Publication Date: Apr 1992
On page(s): 603-608
Volume: 7, Issue: 2
ISSN: 0885-8977
References Cited: 7
CODEN: ITPDE5
INSPEC Accession Number: 4171888
Abstract:
For pt.I see ibid., vol.7, no.2, p.596-602 (1992). Preliminary results are described in which 15 kV XLPE cables were subjected to accelerated aging tests under a variety of controlled voltage stress and thermal load cycle conditions, with loss of life being calculated for each set of conditions in terms of the geometric mean time to failure (GMTF). The relative influence of voltage stress and load cycle temperature are discussed. Accelerated aging results show a reduction in GMTF for 15 kV XLPE-insulated cables as the voltage stress or conductor load cycle temperature is increased in a controlled manner. The relative influence of voltage stress versus load cycle temperature can be compared. The GMTF increases more in going from 90°C to 60°C at constant applied voltage stress than in going from 4X to 2X rated voltage at constant load cycle temperature condition.