ABSTRACT
Three parts of different shape and slope are distinguished in it. The first part, for short times and high stresses, corresponds to strong partial discharges from the beginning of voltage application because the stress is higher than the PD inception stress Ej. This means that during the short life of insulation there is a very quick treeing development up to breakdown. The second part, for stresses lower than Ej (but higher than E^), is practically straight.This is the part where two ageing periods during the lifetime of each specimen take place, as seen above. In the first period (treeing formation) no PDs are detectable but ageing slowly proceeds until treeing starts and grows (second period). The first period is extremely random while the second, which is an increasingly smaller percentage of the first as stress decreases, is in the whole governed by an exponential law. The law governing the times to treeing appearance can then be achieved by means of statistics; since these times, especially at rather low stresses, are much longer than the times of treeing growth, this statistical law may be assumed to govern the times to failure. Therefore, the second part of the life line can be called, for simplicity, the statistical part (even if, of course, the times to failure have, in any case, to be treated statistically). If the material had a very high Ej, the line would proceed straight even for very short times, but the occurrence of strong PDs actually reduces the initial strength, as shown in the figure by comparing with the dotted line. Finally, when stress approaches the electrical threshold, Et, the line becomes curved tending to horizontality (third part). In Fig. 1 the time trend of the PD inception stress can be seen. This is, in fact, a function of time, decreasing down to its minimum value, Et. Below Et partial discharges will never occur and treeing will never start. E^ is the ageing threshold below which electrical ageing ceases. If the pattern illustrated above can be considered of general validity, the length of the various parts into which the life line can be divided is, however, very different from one material to another, besides depending on the environmental conditions, in particular temperature. The tendency of the line towards the threshold is evident for epoxies and, in general, for thermosetting resins after a few thousand hours of testing; even an important material for high-voltage cable insulation, such as cross-linked polyethylene (XLPE), shows this tendency. No tendency, on the contrary, appears until 10,000 hours or more for thermoplastic polyethylene (PE) and ethylene-propylene rubber (EPR), materials of broad application in electric cables. For the latter materials the line has, on the whole, a slight downwards curvature, which is particularly evident for higher-thanroom temperatures. Note that the graph of Fig. 1 is log stress vs log time. If the stress scale is linear, the first two parts of the line come together in one, approximately straight. In a semilog plot, moreover, the tendency towards the threshold is more evident, as the scale at low stresses is reduced.
