Abstract This paper presents a new relation for the stress field around blunt and sharp notches in a linear elastic body. The stress components are determined by using Kolosov-Muskhelishvili's approach and considering proper complex potential functions. Then, to reduce the number of free parameters in the stress components, the boundary conditions of blunt V-notches are satisfied without applying a conformal mapping method. After replacing the free parameters, the stress components are calculated in the form of two series expansions related to mode I and mode II loading. In the case of sharp V-notches, it is demonstrated that the eigenvalues of the problem are the same as those of the well-known Williams’ solution. Afterwards, the stress intensity factors of blunt V-notches are presented by utilizing two different approaches. In order to evaluate the accuracy of the proposed relation, finite element analysis is conducted on a number of different types of notches and the results are compared with those of the presented and classical solutions. It is shown that the proposed relation is more accurate than the best available solutions for blunt V-notches. Furthermore, the proposed stress field solution is capable of specifying the stress distribution around some other types of notches with proper accuracy. Finally, some advantages of the proposed stress relations in comparison with other stress field solutions are presented and discussed.

中文翻译：

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一种新的统一渐近应力场解，用于受混合模式加载的钝和尖锐的缺口

摘要 本文提出了一种新的线性弹性体中钝和尖锐缺口周围应力场的关系。应力分量是通过使用 Kolosov-Muskhelishvili 的方法并考虑适当的复势函数来确定的。然后，为了减少应力分量中自由参数的数量，不应用保角映射方法而满足钝 V 型缺口的边界条件。替换自由参数后，应力分量以与模式 I 和模式 II 加载相关的两个系列扩展的形式计算。在尖锐的 V 形缺口的情况下，证明问题的特征值与著名的威廉姆斯解的特征值相同。然后，利用两种不同的方法给出了钝 V 形缺口的应力强度因子。为了评估所提出的关系的准确性，对许多不同类型的缺口进行了有限元分析，并将结果与​​提出的和经典解决方案的结果进行了比较。结果表明，所提出的关系比钝 V 形凹口的最佳可用解决方案更准确。此外，所提出的应力场解决方案能够以适当的精度指定一些其他类型的凹口周围的应力分布。最后，提出并讨论了所提出的应力关系与其他应力场解决方案相比的一些优点。结果表明，所提出的关系比钝 V 形凹口的最佳可用解决方案更准确。此外，所提出的应力场解决方案能够以适当的精度指定一些其他类型的凹口周围的应力分布。最后，提出并讨论了所提出的应力关系与其他应力场解决方案相比的一些优点。结果表明，所提出的关系比钝 V 形凹口的最佳可用解决方案更准确。此外，所提出的应力场解决方案能够以适当的精度指定一些其他类型的凹口周围的应力分布。最后，提出并讨论了所提出的应力关系与其他应力场解决方案相比的一些优点。