An improved definition for mode I and mode II crack problems

In this research, the common definitions for mode I and mode II are evaluated and improved. For this purpose, the in-plane linear elastic stress field around the crack tip is written as a set of infinite series expansions. Mode I and mode II fields are classically defined as symmetric and anti-symmetric parts of these expansions, respectively. There is also a constant term called “T-stress” in these expansions; parallel to the crack line and independent of the distance from the crack tip. Previous definitions assume that T-stress exists only in pure mode I or combined mode I and mode II conditions. Based on these definitions, T-stress always vanishes in pure mode II. However, the published results of several analytical and experimental researches indicate that the constant stress term can exist in mode II stress field, as well. In this paper, some examples are presented which indicate the presence and importance of T-stress in pure mode II conditions. Then, the classical definition for mode I and mode II is modified to make it consistent with the results presented in the literature.