On the development of small-scale plastic strips from the point of intersection of microplastic deformation lines

TitleOn the development of small-scale plastic strips from the point of intersection of microplastic deformation lines
Publication TypeJournal Article
Year of Publication2019
AuthorsKaminsky, AA, Kipnis, LA, Polischuk, TV
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
DOI10.15407/dopovidi2019.01.033
Issue1
SectionMechanics
Pagination33-39
Date Published01/2019
LanguageUkrainian
Abstract

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.

Keywordsintersection of microplastic deformation lines, small-scale plastic prefracture zone, tangential displacement rupture lines, Wiener—Hopf method
References: 

1. 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
2. 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
3. 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
4. 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
5. 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
6. Panasyuk, V. V., Andreykiv, A. E. & Parton, V. Z. (1988). Fundamentals of fracture mechanics. Kiev: Naukova Dumka (in Russian).
7. Parton, V. Z. & Perlin, P. I. (1981). Methods of the mathematical theory of elasticity. Moscow: Nauka (in Russian).
8. 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
9. Noble, B. (1962). Using of the Wiener—Hopf method for the solve the partial derivative equations. Moscow: Izda-vo Inostr. lit. (in Russian).