Title | On the development of the zone of weakened bonds that precedes the initiation of Cottrell's crack |
Publication Type | Journal Article |
Year of Publication | 2018 |
Authors | Kaminsky, AA, Kipnis, LA, Polischuk, TV |
Abbreviated Key Title | Dopov. Nac. akad. nauk Ukr. |
DOI | 10.15407/dopovidi2018.05.028 |
Issue | 5 |
Section | Mechanics |
Pagination | 28-35 |
Date Published | 5/2018 |
Language | Ukrainian |
Abstract | The length of the small-scale narrow zone of weakened bonds (prefracture zone) at the point of intersection of the lines of microplastic deformation (slip lines) in the elastic body is found. The prefracture zone is modeled by the line of rupture of a normal displacement. The development of this zone precedes the crack initiation by Cottrell's mechanism. The exact solution of the corresponding problem of the linear theory of elasticity is constructed by the Wiener—Hopf method. |
Keywords | Cottrell's mechanism, crack initiation, prefracture zone, Wiener—Hopf method |
References:
- 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, No. 2, pp. 135-151. doi: https://doi.org/10.1007/BF00770282
- Leonov, M. Ya., Vitvitskii, P. M. & Yarema, S. Ya. (1963). Plasticity bands when tension plates with a cracked concentrator. Doklady Akademii Nauk SSSR, 148, No. 3, pp. 541-544. (in Russian).
- Panasyuk, V. V. (1968). Limit equilibrium of brittle bodies with cracks. Kiev: Naukova Dumka (in Russian).
- Dugdale, D. S. (1960). Yielding of steel sheets containing slits. J. Mech. and Phys. Solids, 8, No. 2, pp. 100-104. doi: https://doi.org/10.1016/0022-5096(60)90013-2
- 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
- Sherepanov, G. P. (1976). Plastic rupture lines at the tip of a crack. J. Appl. Math. and Mech., 40, No. 4, pp. 666-674. doi: https://doi.org/10.1016/0021-8928(76)90177-5
- Berezhnitskii, L. T. & Kundrat, N. M. (1982). Plastic bands at the tip of a linear rigid inclusion. Strength of Materials, No. 11, pp. 1502-1505. doi: https://doi.org/10.1007/BF00768948
- 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
- Panasyuk, V. V., Andreykiv, A. E. & Parton, V. Z. (1988). Fundamentals of fracture mechanics. Kiev: Naukova Dumka (in Russian).
- Van Byuren. (1962). Defects in crystals. Moscow: Izda-vo Inostr. Lit. (in Russian).
- Parton, V. Z. & Perlin, P. I. (1981). Methods of the mathematical theory of elasticity. Moscow: Nauka (in Russian).
- Yarema, S. Ya. & Ivanitskaya, G. S. (1986). Limiting equilibrium and the development of angled cracks. Review of criteria. Mater. Sci., 22, No. 1, pp. 40-51. doi: https://doi.org/10.1007/BF00720865
- Noble, B. (1962). Using of the Wiener—Hopf method for the solution of the partial differential equations. Moscow: Izda-vo Inostr. Lit. (in Russian).
- Uflyand, Ya. S. (1967). Integral transformations in problems of the theory of elasticity. Leningrad: Nauka (in Russian).