ISSN 0430-6252. Physicochemical Mechanics of Materials. 2022.
Volume 58, Issue 2
Microcrack at the extension of dislocation core
Keywords
fracture mechanics, microcrack, internal pressure, deformation energy, surface energy, stress intensity factor.
Cite as
Stashchuk M. H. Microcrack at the extension of dislocation core. Physicochemical Mechanics of Materials. 2022. 58(2), 095-102.
Abstract
The stress-strain state in a solid crystalline body is determined by solving the problem of the theory of elasticity for an edge dislocation with a cavity on its extension. The cavity is modeled by a microcrack. The relation for the calculation of the energy of a body with such a microcrack under pressure is obtained. The geometrical parameters of the crack-like dislocation cavity and the values of the equilibrium and nonequilibrium crack lengths are given. The critical pressure at which the crack starts at the continuation of the dislocation defect is indicated. Stress intensity coefficients are also calculated for such a crack.
References
- K. Teodosiu, Elastic Models of Defects in Crystals[in Russian], Mir, Moscow (1985).
- Ya L. Ivanyts’kyi, O. V. Hembara, O. D. Smiyan, and M. Kowalik, “Evaluation of the concentration of hydrogen in the process zone near the crack tip,” Sci.,46, No. 6, 769–774 (2011).
- B. Mytsyk, Ya. Ivanytsky, O. Hembara, Ya. Kost, S. Shtayura, and O. Sakharuk, “Effects of hydrogen influence on strained steel 1020,” Int. J. Hydrogen Energy,45, No. 16, 10199–10208 (2020).
- L. M. Ivas’kevych, “Influence of temperature and cyclic loading on hydrogen embrittlement of nickel refractory alloys,” Mater. Sci.,47, No. 1, 76–81 (2011).
- M. Fan, D. K Yi, and Z. M. Xiao, “Fracture analysis for a sub-interface Zener–Stroh crack in a bi-material plate under small-scale yielding condition,” Theor. Appl. Fract. Mech.,76, 60–66 (2015).
- N. G. Staschuk, Problems of Mechanics of Elastic Bodies with Crack-Llike Defects[in Ukrainian], Naukova Dumka, Kyiv (1993).
- J. Zhuang and Z. Xiao, “Generalized Irwin plastic zone correction of a sub-interface Zener–Stroh crack in a coating-substrate system,” Int. J. Mech. Sci.,94–95, 123–130 (2015).
- A. N. Stroh, “The formulation of cracks as a result of plastic flow,” Proc. Roy. Soc. London,A223, 404–414 (1954).
- O. Ye. Andreikiv and N. T. Hembara, “Modeling of the influence of hydrogen on the deformation of metals,” Fiz.-Khim. Mekh. Mater.,57, No. 6, 23–29 (2021); English translation: Mater. Sci., 57, No. 6, 774–781 (2021).
- I. M. Dmytrakh, R. L. Leshchak, A. M. Syrotyuk, and R. A. Barna, “Effect of hydrogen concentration on fatigue crack growth behaviour in pipeline steel,” Int. J. Hydrogen Energy,42, No. 9, 6401–6408 (2017).
- M. H. Stashchuk and М. І. Dorosh, “Energy of deformation of an elastic body containing a microcrack under pressure,” Mater. Sci.,52, No. 3, 339–348 (2016).
- Zh. Fridel, Dislocations[in Russian], Nauka, Moscow (1964).
- H. Fan, “Interfacial Zener–Stroh crack,” J. Appl. Mech.,61, 829–834 (1994).
- H. Fan and Z. M. Xiao, “A Zener–Stroh crack near an interface,” Int. J. Solids Struct.,34, 2829–2842 (1997).
- Y. Z. Chen, “Multiple Zener–Stroh crack problem in an infinite plate,” Acta Mech.,170, 11–23 (2004).
- H. J. Hoh, Z. M. Xiao, and J. Luo, “On the fracture behavior of a Zener–Stroh crack with plastic zone correction in three-phase cylindrical composite material,” Mech. Mater.,45, 1–9 (2012).
- J. D. Eshelby, F. Seitz, and D. Turnbull, The Continuum Theory of Lattice Defects, Solid State Physics,3, Academic Press, New York (1954), pp. 79–144.
- A. Kottrell, Dislocation Theory[in Russian], Mir, Moscow (1964).
- J. Khirt, I. Lote, Dislocation Theory[in Russian], Atomizdat, Moscow (1972).
- M. H. Stashchuk and M. I. Dorosh, “Evaluation of the potential energy and geometric sizes of a dislocation crack,” Mater. Sci.,51, No. 1, 88–95 (2015).
- N. I. Muskhelishvili, Some Basic Problems of the Mathematical Theory of Elasticity[in Russian], Nauka, Moscow (1966).
- A. A. Griffith, “The phenomenon of rupture and flow in solids,” Phil. Trans. Roy. Soc.,A221, 163–198 (1920).
- A. A. Griffith, “The theory of rupture,” in: Proc. First Int. Congr. Appl. Mech., Delft.(1924), pp. 55–63.
- S. P. Timoshenko and J. Goodier, Theory of Elasticity[in Russian], Nauka, Moscow (1979).
- A. H. Cottrell, “Theory of brittle fracture in steel and similar metals,” Trans. Metal. Soc. AIME,212, 192–203 (1958).
- G. D. Gupta and F. Erdogan, “The problem of edge cracks in an infinite strip,” Trans. ASME,E41, 1001–1006 (1974).
- M. P. Savruk, Two-Dimensional Problems of Elasticity for Bodies with Cracks[in Ukrainian], Naukova Dumka, Kiev (1981).
- V. I. Vladimirov, Physical Nature of the Fracture of Metals[in Russian], Metallurgiya, Moscow (1984).
- J. R. Weertman, “Zener–Stroh crack, Zener–Hollomon parameter, and other topics,” J. Appl. Phys., 60, 1877–1887 (1986).