On the contribution of discontinuities in a near-tip stress field to the J-integral

The path-independence of the J-integral considering discontinuities (e.g. microcracks) in a near-tip stress field is studied in detail. The well-known integral defined by Rice and the related J(k)-vector discussed by Bergez, Cherepanov, and Herrmann and Herrmann are evaluated, respectively, along three different closed contours. The first of them is surrounding the tip of a semi-infinite crack only, the second encloses the discontinuities completely, while the third encloses both the tip and the discontinuities. It is found that there is a simple, but universal relation among three values of the J-integral corresponding to the contributions induced from the semi-infinite crack tip, the discontinuities and the remote stress field, respectively. This means that the interaction effect between a macrocrack and discontinuities can be considered as the redistribution of the J-integral arising from the existence of the discontinuities. Copyright (C) 1996 Elsevier Science Ltd