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A general stress solution in a plastic region near a traction-free boundary of arbitrary shape under plane-strain conditions

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Abstract

The stress field near voids (or holes, or pores) essentially contributes to the fracture process in metallic and nonmetallic materials. In contrast to strains, it is practically impossible to measure stresses experimentally. Therefore, accurate theoretical methods are required to calculate the stress field near a void of arbitrary shape. The present paper develops such a method for the Mohr–Coulomb yield criterion under plane strain conditions. The boundary value problem is a free surface boundary value problem. The boundary conditions on the void contour result in the Cauchy problem for a hyperbolic system of equations. Therefore, the solution in a plastic region adjacent to the void is independent of other boundary conditions. It is required to evaluate one ordinary integral numerically for calculating the stresses at any point of the plastic region. The general solution applies to determining the stress field near two families of void contours. One family consists of contours with the same aspect ratio, including an ellipse as a particular contour. The other family consists of equal-areal voids, including a circle as a particular contour. This choice of the contour families reveals the void shape’s effect on the stress field. The effect of the internal friction angle of the stress field is also discussed.

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Acknowledgements

This work was made possible by the NCKU 90 and AAAA-A20-120011690136-2 programs. It was financially supported by the Ministry of Science and Technology of Taiwan (MOST 106-2923-E-194-002-MY3, 108- 2221-E-006-228-MY3 and 108-2119-M-006-010) and Air Force Office of Science Research (AFOSR) under Contract No. FA4869- 06-1-0056 AOARD 064053. Professor Yeau-Ren Jeng would like to acknowledge Medical Device Innovation Center (MDIC) and Intelligent Manufacturing Research Center (iMRC) from The Featured Areas Research Center Program within the framework of the Higher Education Sprout Project by the Ministry of Education (MOE) in Taiwan and AC2T research GmbH (AC2T) in Austria (COMET InTribology, FFG-No.872176).

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Authors and Affiliations

  1. Laboratory for Technological Processes, Ishlinsky Institute for Problems in Mechanics RAS, 101-1 Prospect Vernadskogo, Moscow, Russia, 119526

    Sergei Alexandrov & Elena Lyamina

  2. Department of Biomedical Engineering, National Cheng Kung University (NCKU), Tainan, 70101, Taiwan

    Yeau-Ren Jeng

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Alexandrov, S., Lyamina, E. & Jeng, YR. A general stress solution in a plastic region near a traction-free boundary of arbitrary shape under plane-strain conditions. Continuum Mech. Thermodyn. 35, 121–139 (2023). https://doi.org/10.1007/s00161-022-01173-w

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