A new unified asymptotic stress field solution for blunt and sharp notches subjected to mixed mode loading

• Published in: International journal of mechanical sciences 2021-03, Vol.193, p.106176, Article 106176
• Main Authors: Mirzaei, A.M., Ayatollahi, M.R., Bahrami, B., Berto, F.
• Format: Article
• Language: English
• Subjects: Asymptotic stress field; Blunt notches; Mixed mode loading; Muskhelishvili's method
• ISSN: 0020-7403; 1879-2162
• DOI: 10.1016/j.ijmecsci.2020.106176

•A new analytical solution was developed for stress field around blunt V-notches.•The proposed asymptotic solution has higher accuracy than previous solutions.•No conformal mapping was used for describing the notch geometry.•The solution is capable of specifying stress distribution around some other types of notches with proper accuracy.•Effect of higher order terms in the proposed stress field is less than that of previous solutions. 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. [Display omitted]