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 & 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, (1998).   Google Scholar

[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.  doi: 10.1016/S0041-624X(98)00027-4.  Google Scholar

[3]

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

[4]

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

[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.  doi: 10.1134/S106378340909008X.  Google Scholar

[6]

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

[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.  doi: 10.1016/j.commatsci.2005.12.034.  Google Scholar

[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.  doi: 10.1088/0965-0393/13/5/003.  Google Scholar

[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.  doi: 10.1088/0965-0393/14/3/005.  Google Scholar

[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.  doi: 10.1088/0965-0393/12/1/014.  Google Scholar

[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.  doi: 10.1088/0953-8984/3/47/008.  Google Scholar

[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.  doi: 10.1134/S1063774508030152.  Google Scholar

[13]

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

[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).   Google Scholar

[15]

J. P. Hirth and J. Lothe, "Theory of Dislocations,", 2nd edition, (1982).   Google Scholar

[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).  doi: 10.1088/0965-0393/15/1/S18.  Google Scholar

[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.   Google Scholar

[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.  doi: 10.1023/A:1009479919904.  Google Scholar

[19]

J. J. Kratochvil and F. Kroupa, Internal vibrations of edge dislocation dipoles,, Research Letters in Materials Science, (2008).   Google Scholar

[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.  doi: 10.1016/j.ijplas.2005.07.011.  Google Scholar

[21]

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

[22]

T. Suzuki, S. Takeuchi and H. Yoshinaga, "Dislocation Dynamics and Plasticity,", Springer Veriag, (1989).   Google Scholar

[23]

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

[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.  doi: 10.1134/1.1575327.  Google Scholar

[25]

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

[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.   Google Scholar

[27]

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

[28]

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

show all references

References:
[1]

O. V. Abramov, "High Intensity Ultrasonics. Theory and Industrial Applications,", Gordon and Breach, (1998).   Google Scholar

[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.  doi: 10.1016/S0041-624X(98)00027-4.  Google Scholar

[3]

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

[4]

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

[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.  doi: 10.1134/S106378340909008X.  Google Scholar

[6]

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

[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.  doi: 10.1016/j.commatsci.2005.12.034.  Google Scholar

[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.  doi: 10.1088/0965-0393/13/5/003.  Google Scholar

[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.  doi: 10.1088/0965-0393/14/3/005.  Google Scholar

[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.  doi: 10.1088/0965-0393/12/1/014.  Google Scholar

[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.  doi: 10.1088/0953-8984/3/47/008.  Google Scholar

[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.  doi: 10.1134/S1063774508030152.  Google Scholar

[13]

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

[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).   Google Scholar

[15]

J. P. Hirth and J. Lothe, "Theory of Dislocations,", 2nd edition, (1982).   Google Scholar

[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).  doi: 10.1088/0965-0393/15/1/S18.  Google Scholar

[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.   Google Scholar

[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.  doi: 10.1023/A:1009479919904.  Google Scholar

[19]

J. J. Kratochvil and F. Kroupa, Internal vibrations of edge dislocation dipoles,, Research Letters in Materials Science, (2008).   Google Scholar

[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.  doi: 10.1016/j.ijplas.2005.07.011.  Google Scholar

[21]

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

[22]

T. Suzuki, S. Takeuchi and H. Yoshinaga, "Dislocation Dynamics and Plasticity,", Springer Veriag, (1989).   Google Scholar

[23]

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

[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.  doi: 10.1134/1.1575327.  Google Scholar

[25]

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

[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.   Google Scholar

[27]

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

[28]

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

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