On the minimum stress theory of cable breakdowns

Abstract

For the rational and economical design of electric cables, it is important to know the relation between the dimensions of the cable and its breakdown strength. Many different theories have been proposed, in the past, such as the maximum stress theory, the average stress theory, Russell's theory, and Osborne's theory, all of them conflicting. Recently a new theory has been proposed by Fernie that the minimum stress, namely that at the sheath of a cable is the limit. It is the purpose of this paper to discuss Fernie's theory and data, inasmuch as it is so diametrically opposed to some of the earlier theories. It seems quite plausible that insulating materials have a specific breakdown stress. Fernie having discovered, as he states, that the minimum stresses were constant in his tests, feels forced to abandon this idea and attempts to explain his results in terms of a limiting value of stress at the sheath, namely the minimum value. An analysis of his test results, however, does not seem to justify him inasmuch as, although his minimum stresses were much more constant than the maximum stresses, they were by no means constant, and in fact, it could be claimed with almost equal justice that his test results vindicated the average stress theory. Since, however, Fernie's experimental minimum stresses present a certain degree of constancy, this phenomenon (which remains to be proved) is investigated further. It is shown that if it be assumed (1) that the inner layers of insulation may be overstressed without complete rupture of the cable due to the stable equilibrium of the remainder of the insulation, and (2) that insulating materials have a critical breakdown gradient, a direct result of these two hypotheses is that the minimum stress at breakdown is a constant, though it is not in itself the criterion. It may be concluded therefore, that Fernie's experimental data are not sufficient to justify his claim that the minimum stress is a constant, and that if later tests should prove the constancy of minimum stress, this phenomenon could be explained otherwise than by assuming that the minimum stress itself is the limit.