By the method of singular integral equations, we obtain the solution of a two-dimensional problem of the elasticity theory for a plane containing a semiinfinite rounded V-notch under complex loading. On the basis on this solution, we establish the relationships between the stress intensity factors at the tip of the sharp V-notch and the maximum stresses and their gradients at the tip of the corresponding rounded notch. For finite bodies with V-notches, the presented solutions are obtained as asymptotic dependences for small radii of rounding of the tips. The deduced relationships can be used to perform the limit transitions and find the stress intensity factors at the tips of sharp V-notches on the basis of the solutions obtained for the corresponding rounded stress concentrators. The efficiency of the method is illustrated for the problem of determination of the stress intensity factors at the vertices of a rectangular hole in the elastic plane.
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Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol.47, No.4, pp.52–61, July–August, 2011.
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Savruk, M.P., Kazberuk, A. Distribution of stresses near V-shaped notches in the complex stressed state. Mater Sci 47, 476–487 (2012). https://doi.org/10.1007/s11003-012-9419-8
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DOI: https://doi.org/10.1007/s11003-012-9419-8