On the development of small-scale plastic strips from the point of intersection of microplastic deformation lines
DOI:
https://doi.org/10.15407/dopovidi2019.01.033Keywords:
intersection of microplastic deformation lines, small-scale plastic prefracture zone, tangential displacement rupture lines, Wiener—Hopf methodAbstract
The small-scale plastic prefracture zone at the point of intersection of microplastic deformation lines is determined. The problem on the plastic zone is reduced to the symmetric problem of the theory of elasticity for a plane with four straight tangential displacement rupture lines emerging from its point. Two of them are semiinfinite, and two have a finite length. The exact solution of the problem is constructed by the Wiener—Hopf method.
Downloads
References
Panasyuk, V. V. & Savruk, M. P. (1992). Model for plasticity bands in elastoplastic failure mechanics. Mater. Sci., 28, No. 1, pp. 41-57. doi: https://doi.org/10.1007/BF00723631
Berezhnitskii, L. T. & Kundrat, N. M. (1982). Plastic bands at the tip of a linear rigid inclusion. Strength of Materials, Nо. 11, pp. 1502-1505. doi: https://doi.org/10.1007/BF00768948
Berezhnitskii, L. T. & Kundrat, N. M. (1984). Origin and development of plastic strains in the neighborhood of an acute-angled rigid inclusion. Mater. Sci., 19, No. 6, pp. 538-546. doi: https://doi.org/10.1007/BF00722124
Kaminskii, A. A., Kipnis, L. A. & Khazin, G. A. (2001). Study of the Stress State Near a Corner Point in Simulating the Initial Plastic Zone by Slipbands. Int. Appl. Mech., 37, No. 5, pp. 647-653. doi: https://doi.org/10.1023/A:1012312513881
Kaminskii, A. A., Kipnis, L. A. & Khazin, G. A. (2002). Analysis of Plastic Zone at a Corner Point by the Trident Model. Int. Appl. Mech., 38, No. 5, pp. 611-616. doi: https://doi.org/10.1023/A:1019766106040
Panasyuk, V. V., Andreykiv, A. E. & Parton, V. Z. (1988). Fundamentals of fracture mechanics. Kiev: Naukova Dumka (in Russian).
Parton, V. Z. & Perlin, P. I. (1981). Methods of the mathematical theory of elasticity. Moscow: Nauka (in Russian).
Vitvitskii, P. M., Panasyuk, V. V. & Yarema, S. Ya. (1973). Plastic deformation in the vicinity of a crack and the criteria of fracture (Review). Strength of Materials, Nо. 2, pp. 135-151. doi: https://doi.org/10.1007/BF00770282
Noble, B. (1962). Using of the Wiener—Hopf method for the solve the partial derivative equations. Moscow: Izda-vo Inostr. lit. (in Russian).
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2023 Reports of the National Academy of Sciences of Ukraine
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.