For instance: The Scientific Opinion
About consortium subscription Contacts
(812) 4095364 Non-commercial partnership
St. Petersburg


"Humanities and Science University Journal" №17 (Physical and mathematical, biological and technical science), 2016

Models for Plastic Deformation Research

I. G. Panin, V. V. Blagoveshchenskii, Y. L. Lustgarten
Price: 50 руб.
 This paper gives a brief description of several models of the motion of dislocation lines in the simulation region: the principal model of dislocation multiplication of the Frank — Read type and models developed on its basis. The latter include models of a single dislocation motion, multiplication and motion of an ensemble of dislocations, formation of a dislocation pile-up. The paper presents the main results obtained on the basis of these models: the curve of deformation under constant uniaxial loading; the curve of deformation at a constant rate of deformation; the curve of dependence of the number of dislocations in a pile-up on the value of the external applied stress.
Keywords: crystal, defect, dislocation, deformation, ultrasound, differential equation,
1. Friedel, J. Dislocations. 1972, Moscow: Mir.
2. Hirth, J.P., & Lothe, J. Theory of Dislocations. 1972, Moscow: Atomizdat.
3. Belan, V.I., & Landau, A.I. Net-Statistical Model of Dislocational Amplitude
Dependent Internal Friction [Сеточно-статистическая модель дислокационного
амплитудно-зависимого внутреннего трения]. FMM, 1988, 65(2), 259–267.
4. Dubnova, G.N., Idenbom, V.L., & Shtolberg, A.A. On the bowing-out of a dislocation segment and a Frank–Read source [О прогибании дислокационного сегмента
и источника Франка–Рида]. FTT, 1968, 10, 1760–1768.
5. Stratan, N.V., & Predvoditelev, A.A. Simulation of the dislocation motion process in a dislocation ensemble [Моделирование процесса движения дислокаций в
трехмерном дислокационном ансамбле]. FTT, 1970, 12(7), 1729–1733.
6. Popov, L.E., Slobodskoi, M.I., & Kolupaeva, S.N. Simulation of single slip in
FCC metals. Russian Physics Journal, 2006, 49(1), 62–73.
7. Natsik, V.D., & Chishko, K.A. Dynamics and sound radiation of dislocation FrankRead source. I. The initial stage of work of a source [Динамика и звуковое излучение
дислокационного источника Франка–Рида. I. Начальная стадия работы источника].
Physics of the condensed state, 1974, FTINT, Kharkov, Iss. 33, pp. 44–57.
8. Benzerga, A.A., Brechet, Y., Needleman, A., & Van der Giessen, E. Incorporating
three-dimensional mechanisms into two-dimensional dislocation dynamics. Modelling
Simul. Mater. Sci. Eng., 2004, 12(1), 159–196.
9. Akarapu, S., & Hirth, J.P. Dislocation pile-ups in stress gradients revisited. Acta
Materialia, 2013, 61(10), 3621–3629.
10. Blagoveshchenskii, V.V. Evolution of the dislocation structure under the influence
of ultrasound and the inelasticity of crystals [Эволюция дислокационной структуры
под действием ультразвука и неупругость кристаллов] (Doctoral thesis, Kostroma
State Technological University, Kostroma). 2001.
11. Blagoveshchenskii, V.V, & Panin, I.G. Construction of a Dynamic Model of the
Frank–Read Dislocation Source [Построение динамической модели дислокационного
источника Франка–Рида]. Vychislitelnye tekhnologii, 2008, 13(5), 5–10.
12. Blagoveshchenskii, V. V., & Panin, I.G. Elastic and plastic properties of crystalline materials: An analysis based on a mathematical model of motion of a dislocation
line. The Physics of Metals and Metallography, 2009, 108(2), 212–215.
13. Blagoveshchenskii, V. V., & Panin, I.G. On the problem of a yield tooth. The
Physics of Metals and Metallography, 2010, 109(3), 286–288.
14. Polukhin, P.I., Gun, G.Ya., & Galkin, A.M. Resistance of metals and alloys to
plastic deformation (2nd ed.) [Сопротивление пластической деформации металлов
и сплавов]. 1983, Moscow: Metallurgiya.
15. Petukhov, B.V. A Theory of Sharp Yield Point in Low Dislocation Crystals
[Теория зуба текучести в малодислокационных кристаллах]. ZTF, 2001, 71(11),
Price: 50 рублей
To order