Plastic Flow Macrolocalization: Autowave and Quasi-Particle

Lev B. Zuev, Svetlana A. Barannikova

.

DOI: 10.4236/jmp.2010.11001                

Abstract

A new approach is proposed to describe the autowave processes responsible for plastic deformation localiza-tion in metals and alloys. The existence of a quasi-particle, which corresponds to a localized plastic flow autowave, is postulated and its characteristics are determined. The above postulate leads to a number of cor-ollaries and quantitative assessments that are considered herein. The deformation processes occurring on the macro- and micro-scale levels are found to be directly related.

Keywords

Localization, Plastic Deformation, Autowave, Quasi-Particle

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	L. B. Zuev, “Wave Phenomena in Low-Rate Plastic Flow of Solids,” Annals of Physics, Vol. 10, 2001, pp. 965-984.
[2]	L. B. Zuev, “On the Waves of Plastic Flow Localization in Pure Metals and Alloys,” Annals of Physics, Vol. 16, 2007, pp. 286-310.
[3]	R. J. McDonald, C. Efstathiou and P. Curath, “The Wave-Like Plastic Deformation of Single Crystals Cop-per,” Journal of Engineering Materials and Technology, Vol. 131, 2009, pp. 692-703.
[4]	A. Asharia, A. Beaudoin and R. Miller, “New Perspec-tives in Plasticity Theory: Dislocation Nucleation, Waves and Partial Continuity of Plastic Strain Rate,” Mathemat-ics and Mechanics of Solids, Vol. 13, 2008, pp. 292-315.
[5]	C. Fressengeas, A. Beaudoin and D. Entemeyer, “Dislo-cation Transport and Intermittency in the Plasticity of Crystalline Solids,” Physical Review B, Vol. 79, 2009, pp. 014108-1-014108-9.
[6]	L. B. Zuev, V. V. Gorbatenko and S. N. Polyakov, “In-strumentation for Speckle Interferometry and Techniques for Investigating Deformation and Fracture,” Proceedings of SPIE, Vol. 4900, Part 2, 2002, pp. 1197-1208.
[7]	H. Haken, “Information and Self-Organization,” A Mac-roscopic Approach to Complex Systems, Springer Verlag, Berlin, 1989.
[8]	H. Kolsky, “Stress Waves in Solid,” Phoenix Education, Dover, 2003
[9]	F. R. N. Nabarro, Z. S. Basinski and D. B. Holt, “The Plasticity of Single Crystals,” Tailor and Francis Ltd, London, 1964.
[10]	R. Hill, “The Mathematical Theory of Plasticity,” Uni-versity Press, Oxford, 1998.
[11]	V. A. Davydov, V. S. Zykov and A. S. Michailov, “Kinematics of Autowave Structures in the Excited Me-dia,” Physics-Uspekhi, Vol. 161, 1999, pp. 45-85.
[12]	B. B. Kadomtsev, “Dynamics and Information,” Physics- Uspekhi, Vol. 164, 1994, pp. 449-530.
[13]	A. Seeger and W. Frank, “Structure Formation by Dissi-pative Processes in Crystals with High Defect Densities,” In L. P. Kubin and G. Martin Eds., “Non-Linear Phe-nomena in Material Science,” Trans Tech Publications, New York, 1987, pp. 125-137.
[14]	L. Pauling, “The Nature of the Chemical Bond,” Cornell University Press, Ithaca, 1960.
[15]	S. A. Barannikova, “Dispersion of the Plastic Strain Lo-calization Waves,” Technical Physics Letters, Vol. 30, 2004, pp. 338-340.
[16]	A. Scott, “Nonlinear Science,” Emergence and Dynamics of Coherent Structures, University Press, Oxford, 2003.
[17]	L. D. Landau and E. M. Lifschitz, “Quantum Mechanics: Non-Relativistic Theory,” Course of Theoretical Physics, Pergamon, London, 1977.
[18]	J. M. Ziman, “Electrons and Phonons,” University Press, Oxford, 2001.
[19]	J. P. Billingsley, “The Possible Influence of the De Broglie Momentum-Wavelength Relation on Plastic Strain ‘Autowave’ Phenomena in ‘Active Materials’,” International Journal of Solids and Structures, Vol. 38, 2001, pp. 4221-4234.
[20]	L. B. Zuev, “The Linear Work Hardening Stage and De Broglie Equation for Autowaves of Localized Plasticity,” International Journal of Solids and Structures, Vol. 42, 2005, pp. 943-949.
[21]	A. P. Cracknell and K. C. Wong, “The Fermi Surface. Its Concept, Determination and Use in the Physics of Met-als,” Clarendon Press, Oxford, 1973.
[22]	V. I. Al’shits and V. L. Indenbom, “Mechanisms of Dis-locations Drag,” In F. R. N. Nabarro Ed., Dislocations in Solids, Amsterdam, 1986, pp. 43-111.
[23]	L. D. Landau and E. M. Lifshits, “Hydrodynamics,” Nauka Publications, Moscow, 1988.
[24]	V. V. Pustovalov, “Serrated Deformation of Metals and Alloys at Low Temperatures,” Low Temperature Physics, Vol. 34, 2008, pp. 683-723.
[25]	B. Steverding, “Quantization of stress waves and Frac-ture,” Materials Science and Engineering, Vol. 9, 1972, pp. 185-189.
[26]	E. M. Morozov, L. S. Polack and Ya. B. Fridman, “On Variation Principles of Crack Development in Solids,” Soviet Physics-Doklady, Vol. 156, 1964, pp. 537-540.
[27]	T. Oku and J. M. Galligan, “Quantum Mechanical Tun-neling of Dislocations,” Physical Review Letters, Vol. 22, 1969, pp. 596-597.
[28]	B. V. Petukhov and V. L. Pokrovsky, “Quantum and Classic Motion of Dislocations in the Potential Peierls Relief,” Journal of Experimental and Theoretical Physics, Vol. 63, 1972, pp. 634-647.
[29]	E.C. Aifantis, “Nonlinearity, Periodicity and Patterning in Plasticity and Fracture,” International Journal of Non- Linear Mechanics, Vol. 31, 1996, pp. 797-809.
[30]	E.C. Aifantis, “Gradient Plasticity,” In J. Lemaître, Ed., Handbook of Materials Behavior Models, Academic Press, New York, 2001, pp. 291-307.
[31]	Y. Imry, “Introduction to Mesoscopic Physics,” Univer-sity Press, Oxford, 2002.
[32]	L. P. Dzyaloshinski, “Macroscopic Quantum Phenom-ena,” Soviet Physics-Uspekhi, Vol. 90, 1966, pp. 623- 629.