Application of J integral to breakdown analysis of a dielectric material

Properties of the J integral for a conductive tubular channel embedded in a dielectric material are examined. It is shown that the J integral can be interpreted as the energy release per unit length of the channel due to the channel growth. In order to investigate the effect of a conductive defect on the dielectric breakdown, the asymptotic problem of a conductive hemispheroid on an electrode sheet is considered. The J integral for the hemispheroidal defect is obtained in the closed form from the electrostatic solution. The J integral for a tubular channel with a hemispheroidal head is calculated numerically through the finite element analysis. It is found that the breakdown strength is sensitive to the length and head shape of the channel. The variation of the apparent breakdown strength for the dielectric material with the conductive hemispheroidal defect is also discussed.