On the development of the zone of weakened bonds that precedes the initiation of Cottrell's crack
DOI:
https://doi.org/10.15407/dopovidi2018.05.028Keywords:
Cottrell's mechanism, crack initiation, prefracture zone, Wiener—Hopf methodAbstract
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.
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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).
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