A new sight on the singularity of crack-tip stress and its zoom-in elimination

• 1、Department of Engineering Mechanics, China University of Mining and Technology, Xu Zhou 221116, Jiangsu Province, China

Abstract：Stress singularity, that the stress at local crack tip has infinitely great mathematical solutions subjected to very small loads at infinity, is studied. According to the analysis of stress fields deduced from either Westergaard function or Williams\'s eigenfunction, it is found that stress singularity at the crack tip is mainly induced by an incomplete definition of mathematical domain with respect to the stress at crack tip and sequentially inappropriate application of stress functions to the crack tip. Crack tip is not included in the regime described by stress functions, but is simply regarded as the reference point relative to the local stress field. Directly applying traditional stress functions to the crack tip will certainly lead to local singularity, and further influence an infinitesimal vicinity. Redefining the scope of infinitesimal vicinity is introduced to eliminate stress singularity, wherein the stress is considered to be constant. Also, the limit of Bareblatt\'s cohesive zone concept is discussed.

keywords： stress singularity incomplete definition stress function

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