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a new sight on the singularity of crack-tip stress and its zoom-in elimination
首发时间：2017-12-18
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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一种关于裂纹尖端应力奇异性及其消除的新视角
摘要：应力奇异性，即当无穷远处承受非常小的载荷时，裂纹尖端处的应力具有无限大的数学解。本文根据westergaard函数和williams特征函数推导的应力场解析解，分析发现裂纹尖端的应力奇异性主要是由于裂纹尖端处应力的定义域不完整，以及应力函数在裂缝尖端的不合理应用。裂纹尖端不包括在由应力函数描述的区域内，而仅仅被视为局部应力场的相对参考点。直接将传统的应力函数应用于裂纹尖端必然会导致局部应力奇异性，并进一步影响到裂纹尖端的无穷小邻域。为了消除应力奇异性，重新定义裂纹尖端无穷小领域的范围是必要的，且在该范围内应力可以认为是恒定的。此外，笨重还讨论了bareblatt的内聚力概念的局限性。
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