On the Minimum Stress Theory of Cable Breakdowns

For the rational and economical design of electric cables, it is important to know the relation be-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 minimumn stresses present a certain degree of constancy, this phenomenon (which remains to be proved) is investigated further.