October  2011, 4(5): 1079-1094. doi: 10.3934/dcdss.2011.4.1079

Dynamics of edge dislocation clusters interacting with running acoustic waves

1. 

Institute for Metals Superplasticity Problems RAS, Ufa 450001, Khalturin St. 39, Russian Federation, Russian Federation, Russian Federation, Russian Federation

Received  September 2009 Revised  February 2010 Published  December 2010

Interaction of straight edge dislocation clusters with monochromatic sound wave having nonzero wavevector is investigated taking into account the dislocation mass. We report on a significant increase of drift velocities of clusters when the sound wave frequency approaches a cluster's eigenfrequency. Of practical importance is the increase of the drift velocity observed for clusters with nonzero topological charge interacting with small frequency sound waves. We also demonstrate the possibility to excite a gap discrete breather in a chain of dislocation dipoles.
Citation: Sergey V. Dmitriev, Asiya A. Nazarova, Anatoliy I. Pshenichnyuk, Albert M. Iskandarov. Dynamics of edge dislocation clusters interacting with running acoustic waves. Discrete and Continuous Dynamical Systems - S, 2011, 4 (5) : 1079-1094. doi: 10.3934/dcdss.2011.4.1079
References:
[1]

O. V. Abramov, "High Intensity Ultrasonics. Theory and Industrial Applications," Gordon and Breach, Dodrecht, 1998.

[2]

V. O. Abramov, O. V. Abramov, F. Sommer, O. M. Gradov and O. M. Smirnov, Surface hardening of metals by ultrasonically accelerated small metal balls, Ultrasonics, 36 (1998), 1013-1019. doi: 10.1016/S0041-624X(98)00027-4.

[3]

E. C. Aifantis, The physics of plastic deformation, Int. J. Plasticity, 8 (1987), 211-247. doi: 10.1016/0749-6419(87)90021-0.

[4]

E. C. Aifantis, Update on a class of gradient theories, Mech. Mater., 35 (2003), 259-280. doi: 10.1016/S0167-6636(02)00278-8.

[5]

J. A. Baimova, S. V. Dmitriev, A. A. Nazarov and A. I. Pshenichnyuk, Dynamics of edge dislocations in a two-dimensional crystal at finite temperatures, Physics of the Solid State, 51 (2009), 1809-1813. doi: 10.1134/S106378340909008X.

[6]

B. Bako and I. Groma, Stochastic O(N) algorithm for dislocation dynamics, Modelling Simul. Mater. Sci. Eng, 7 (1999), 181-188. doi: 10.1088/0965-0393/7/2/004.

[7]

B. Bako, I. Groma, G. Gyorgyi and G. Zimanyi, Dislocation patterning: The role of climb in meso-scale simulations, Comput. Mater. Sci, 38 (2006), 22-28. doi: 10.1016/j.commatsci.2005.12.034.

[8]

B. Bako, I. Groma, I. Mastorakos and E. C. Aifantis, Investigation of dislocation patterning by stochastic integration of dislocation trajectories, Modelling Simul. Mater. Sci. Eng, 13 (2005), 671-681. doi: 10.1088/0965-0393/13/5/003.

[9]

D. S. Balint, V. S. Deshpande, A. Needleman and E. Van Der Giessen, Size effects in uniaxial deformation of single and polycrystals: A discrete dislocation plasticity analysis, Modelling Simul. Mater. Sci. Eng, 14 (2006), 409-430. doi: 10.1088/0965-0393/14/3/005.

[10]

A. A. Benzerga, Y. Brechet, A. Needleman and E. Van den Giessen, Incorporating three-dimensional mechanisms into two-dimensional dislocation dynamics, Modelling Simul. Mater. Sci. Eng, 12 (2004), 159-196. doi: 10.1088/0965-0393/12/1/014.

[11]

C. E. Bottani, P. Cavassi and P. Pisani, Non-linear interaction of dislocation pile-ups with ultrasonic stress waves, J. Phys.: Condens. Matter, 3 (1991), 9351-9362. doi: 10.1088/0953-8984/3/47/008.

[12]

G. V. Bushueva, G. M. Zinenkova, N. A. Tyapunina, V. T. Degtyarev, A. Yu. Losev and F. A. Plotnikov, Self-organization of dislocations in an ultrasound field, Crystallography Reports, 53 (2008), 474-479. doi: 10.1134/S1063774508030152.

[13]

V. T. Degtyarev, On possible mechanisms of the acoustoplastic effect, Doklady physics, 52 (2007), 245-246. doi: 10.1134/S1028335807050011.

[14]

O. Dmitrieva, J. V. Svirina, E. Demir and D. Raabe, Investigation of the internal substructure of microbands in a deformed copper single crystal: experiments and dislocation dynamics simulation, Modelling Simul. Mater. Sci. Eng., 18 (2010), 085011 (14pp).

[15]

J. P. Hirth and J. Lothe, "Theory of Dislocations," 2nd edition, Wiley, New York, 1982.

[16]

S. M. Keralavarma and A. A. Benzerga, A discrete dislocation analysis of strengthening in bilayer thin films, Modelling Simul. Mater. Sci. Eng, 15 (2007), S239-S254. doi: 10.1088/0965-0393/15/1/S18.

[17]

V. M. Klyachin, V. V. Nikolaev, N. I. Noskova and Y. E. G. Ponomareva, Local change in the substructure of aluminium and alloy Al+11wt% Mg exposed to focused ultrasonic waves, Physics of Metals and Metallography, 71 (1991), 188-198.

[18]

Yu. R. Kolobov, O. A. Kashin, E. F. Dudarev, G. P. Grabovetskaya, G. P. Pochivalova, V. A. Klimenov, N. V. Girsova and E. E. Sagymbaev, Effects of ultrasonic surface treatment on the structure and properties of polycrystalline and nanostructured titanium, Russian Physics Journal, 43 (2000), 754-758. doi: 10.1023/A:1009479919904.

[19]

J. J. Kratochvil and F. Kroupa, Internal vibrations of edge dislocation dipoles, Research Letters in Materials Science, (2008), Article ID 907895 (3 pages).

[20]

J. Pontes, D. Walgraef and E. C. Aifantis, On dislocation patterning: Multiple slip effects in the rate equation approach, Int. J. Plasticity, 22 (2006), 1486-1505. doi: 10.1016/j.ijplas.2005.07.011.

[21]

E. Sh. Statnikov, O. V. Korolkov and V. N. Vityazev, Physics and mechanism of ultrasonic impact, Ultrasonics, 44 (2006), 533-538. doi: 10.1016/j.ultras.2006.05.119.

[22]

T. Suzuki, S. Takeuchi and H. Yoshinaga, "Dislocation Dynamics and Plasticity," Springer Veriag, Berlin, 1989.

[23]

N. A. Tyapunina and E. P. Belozerova, Charged dislocations and properties of alkali halide crystals, Sov. Phys. Usp, 31 (1988), 1060-1084. doi: 10.1070/PU1988v031n12ABEH005660.

[24]

N. A. Tyapunina, G. V. Bushueva, M. I. Silis, D. S. Podsoblyaev, Yu. B. Likhushin and V. Yu. Bogunenko, The cross slip of a dislocation in an ultrasound field and its dependence on the ultrasound amplitude and frequency, sample orientation, and dynamic viscosity, Phys. Solid State, 45 (2003), 880-885. doi: 10.1134/1.1575327.

[25]

N. A. Tyapunina, E. K. Naimi and G. M. Zinenkova, "Ultrasound Action on Crystals with Defects" (in Russian), Mosk. Gos. Univ., Moscow, 1999.

[26]

J. Vollmann, D. M. Profunser and J. Dual, Sensitivity improvement of a pump-probe set-up for thin film and microstructure metrology, Ultrasonics, 40 (2002), 757-763.

[27]

D. Walgraef and E. C. Aifantis, Dislocation patterning in fatigued metals as a result of dynamical instabilities, J. Appl. Phys., 58 (1985), 688-691. doi: 10.1063/1.336183.

[28]

R. Walker and C. T. Walker, Hardening of immersed metals by ultrasound, Nature, 250 (1974), 410-411. doi: 10.1038/250410a0.

show all references

References:
[1]

O. V. Abramov, "High Intensity Ultrasonics. Theory and Industrial Applications," Gordon and Breach, Dodrecht, 1998.

[2]

V. O. Abramov, O. V. Abramov, F. Sommer, O. M. Gradov and O. M. Smirnov, Surface hardening of metals by ultrasonically accelerated small metal balls, Ultrasonics, 36 (1998), 1013-1019. doi: 10.1016/S0041-624X(98)00027-4.

[3]

E. C. Aifantis, The physics of plastic deformation, Int. J. Plasticity, 8 (1987), 211-247. doi: 10.1016/0749-6419(87)90021-0.

[4]

E. C. Aifantis, Update on a class of gradient theories, Mech. Mater., 35 (2003), 259-280. doi: 10.1016/S0167-6636(02)00278-8.

[5]

J. A. Baimova, S. V. Dmitriev, A. A. Nazarov and A. I. Pshenichnyuk, Dynamics of edge dislocations in a two-dimensional crystal at finite temperatures, Physics of the Solid State, 51 (2009), 1809-1813. doi: 10.1134/S106378340909008X.

[6]

B. Bako and I. Groma, Stochastic O(N) algorithm for dislocation dynamics, Modelling Simul. Mater. Sci. Eng, 7 (1999), 181-188. doi: 10.1088/0965-0393/7/2/004.

[7]

B. Bako, I. Groma, G. Gyorgyi and G. Zimanyi, Dislocation patterning: The role of climb in meso-scale simulations, Comput. Mater. Sci, 38 (2006), 22-28. doi: 10.1016/j.commatsci.2005.12.034.

[8]

B. Bako, I. Groma, I. Mastorakos and E. C. Aifantis, Investigation of dislocation patterning by stochastic integration of dislocation trajectories, Modelling Simul. Mater. Sci. Eng, 13 (2005), 671-681. doi: 10.1088/0965-0393/13/5/003.

[9]

D. S. Balint, V. S. Deshpande, A. Needleman and E. Van Der Giessen, Size effects in uniaxial deformation of single and polycrystals: A discrete dislocation plasticity analysis, Modelling Simul. Mater. Sci. Eng, 14 (2006), 409-430. doi: 10.1088/0965-0393/14/3/005.

[10]

A. A. Benzerga, Y. Brechet, A. Needleman and E. Van den Giessen, Incorporating three-dimensional mechanisms into two-dimensional dislocation dynamics, Modelling Simul. Mater. Sci. Eng, 12 (2004), 159-196. doi: 10.1088/0965-0393/12/1/014.

[11]

C. E. Bottani, P. Cavassi and P. Pisani, Non-linear interaction of dislocation pile-ups with ultrasonic stress waves, J. Phys.: Condens. Matter, 3 (1991), 9351-9362. doi: 10.1088/0953-8984/3/47/008.

[12]

G. V. Bushueva, G. M. Zinenkova, N. A. Tyapunina, V. T. Degtyarev, A. Yu. Losev and F. A. Plotnikov, Self-organization of dislocations in an ultrasound field, Crystallography Reports, 53 (2008), 474-479. doi: 10.1134/S1063774508030152.

[13]

V. T. Degtyarev, On possible mechanisms of the acoustoplastic effect, Doklady physics, 52 (2007), 245-246. doi: 10.1134/S1028335807050011.

[14]

O. Dmitrieva, J. V. Svirina, E. Demir and D. Raabe, Investigation of the internal substructure of microbands in a deformed copper single crystal: experiments and dislocation dynamics simulation, Modelling Simul. Mater. Sci. Eng., 18 (2010), 085011 (14pp).

[15]

J. P. Hirth and J. Lothe, "Theory of Dislocations," 2nd edition, Wiley, New York, 1982.

[16]

S. M. Keralavarma and A. A. Benzerga, A discrete dislocation analysis of strengthening in bilayer thin films, Modelling Simul. Mater. Sci. Eng, 15 (2007), S239-S254. doi: 10.1088/0965-0393/15/1/S18.

[17]

V. M. Klyachin, V. V. Nikolaev, N. I. Noskova and Y. E. G. Ponomareva, Local change in the substructure of aluminium and alloy Al+11wt% Mg exposed to focused ultrasonic waves, Physics of Metals and Metallography, 71 (1991), 188-198.

[18]

Yu. R. Kolobov, O. A. Kashin, E. F. Dudarev, G. P. Grabovetskaya, G. P. Pochivalova, V. A. Klimenov, N. V. Girsova and E. E. Sagymbaev, Effects of ultrasonic surface treatment on the structure and properties of polycrystalline and nanostructured titanium, Russian Physics Journal, 43 (2000), 754-758. doi: 10.1023/A:1009479919904.

[19]

J. J. Kratochvil and F. Kroupa, Internal vibrations of edge dislocation dipoles, Research Letters in Materials Science, (2008), Article ID 907895 (3 pages).

[20]

J. Pontes, D. Walgraef and E. C. Aifantis, On dislocation patterning: Multiple slip effects in the rate equation approach, Int. J. Plasticity, 22 (2006), 1486-1505. doi: 10.1016/j.ijplas.2005.07.011.

[21]

E. Sh. Statnikov, O. V. Korolkov and V. N. Vityazev, Physics and mechanism of ultrasonic impact, Ultrasonics, 44 (2006), 533-538. doi: 10.1016/j.ultras.2006.05.119.

[22]

T. Suzuki, S. Takeuchi and H. Yoshinaga, "Dislocation Dynamics and Plasticity," Springer Veriag, Berlin, 1989.

[23]

N. A. Tyapunina and E. P. Belozerova, Charged dislocations and properties of alkali halide crystals, Sov. Phys. Usp, 31 (1988), 1060-1084. doi: 10.1070/PU1988v031n12ABEH005660.

[24]

N. A. Tyapunina, G. V. Bushueva, M. I. Silis, D. S. Podsoblyaev, Yu. B. Likhushin and V. Yu. Bogunenko, The cross slip of a dislocation in an ultrasound field and its dependence on the ultrasound amplitude and frequency, sample orientation, and dynamic viscosity, Phys. Solid State, 45 (2003), 880-885. doi: 10.1134/1.1575327.

[25]

N. A. Tyapunina, E. K. Naimi and G. M. Zinenkova, "Ultrasound Action on Crystals with Defects" (in Russian), Mosk. Gos. Univ., Moscow, 1999.

[26]

J. Vollmann, D. M. Profunser and J. Dual, Sensitivity improvement of a pump-probe set-up for thin film and microstructure metrology, Ultrasonics, 40 (2002), 757-763.

[27]

D. Walgraef and E. C. Aifantis, Dislocation patterning in fatigued metals as a result of dynamical instabilities, J. Appl. Phys., 58 (1985), 688-691. doi: 10.1063/1.336183.

[28]

R. Walker and C. T. Walker, Hardening of immersed metals by ultrasound, Nature, 250 (1974), 410-411. doi: 10.1038/250410a0.

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