Abstract
The development of a dislocation inhomogeneity in the form of regular spatial patterns during cyclic deformation is examined from a dynamical instability point of view. A gradient-dependent dislocation dynamics framework is devised and the competition between mobility, interaction, and generation processes is considered. Within such a framework, it is shown that uniform dislocation distributions may become unstable versus spatial modulations leading to the formation of different types of patterns including cellular, ladderlike, and labyrinth structures. In particular, the spatially periodic wall structure of persistent slip bands (PSBs), along with the theoretical determination of the corresponding wavelength, is discussed on the basis of nonlinear dynamical equations of the reaction-diffusion type. The effect of temperature on the wavelength selection process is predicted in accordance with experimental observations. Moreover, it is shown that the possibility of secondary or multiple slip effects and the associated labyrinth structures can conveniently be described by the dynamical model. Finally, a preliminary discussion on the applicability of gradient-dependent dislocation dynamics and self-organization techniques, in describing the early stages of the deformation with emphasis on the inhomogeneous development of slip during monotonic loading, is given.
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References
Ackermann, F., Kubin, L. P., Lepinoux, J., and Mughrabi, H. (1984), The dependence of dislocation microstructure on plastic strain amplitude in cyclically strained copper single crystals, Acta Metallurgica 32, 715–725.
Aifantis, E. C. (1978), A proposal for continuum with microstructure, Mech. Res. Comm., 5, 139–145.
Aifantis, E. C. (1983), Dislocation kinetics and the formation of deformation bands, in Defects, Fracture and Fatigue, edited by G. C. Sih and J. W. Provan, MartinusNijhoff, The Hague, pp. 75–84.
Aifantis, E. C. (1984a), On the mechanics of modulated structures, in Modulated Structure Materials, NATO ASI Series 83, edited by T. Tsakalakos, MartinusNijhoff, The Hague, pp. 357–385.
Aifantis, E. C. (1984b), On the microstructural origin of certain inelastic models, Transactions of ASME, J. Mat. Engng. Tech., 106, 326–330.
Aifantis, E. C. (1984c) Towards a continuum approach to dislocation patterning, in Dislocations in Solids—Recent Advances, AMD-63, edited by X. Markenscoff, ASME, New York, pp. 23–33.
Aifantis, E. C. (1985a), Continuum models for dislocated states and media with microstructures, in Mechanics of Dislocations, edited by E. C. Aifantis and J. P. Hirth, ASM, Metals Park, New York, pp. 127–146.
Aifantis, E. C. (1985b), On dislocation patterning, in Dislocations in Solids, edited by H. Suzuki, T. Ninomiya, K Sumino, and S. Takeuchi, Tokyo University Press, Tokyo, pp. 41–47.
Aifantis, E. C. (1986a), Mechanics of microstructures—I, II, III, in Mechanical Properties and Behaviour of Solids: Plastic Instabilities, Proceedings ICTP Enrico Fermi School of Theoretical Physics, Trieste, Italy, edited by V. Balakrishnan and C. E. Bottani, World Scientific, Sinpagore, pp. 314–353.
Aifantis, E. C. (1986b), On the dynamical origin of dislocation patterns, Mat. Sci. Engng., 81, 563–574.
Aifantis, E. C. (1987), The physics of plastic deformation, Int. J. Plasticity, 3, 211–247.
Aifantis, E. C. (1988), On the problem of dislocation patterning the persistent slip bands, in Nonlinear Phenomena in Materials Science (Solid State Phenomena, Vols. 3 and 4), edited by L. Kubin and G. Martin, Trans. Tech. Publ., pp. 397–406.
Arnold, V. (1980), Chapitres supplémentaires de la théorie des equations dii ferentielles ordinaires, MIR, Mowcow.
Bammann, D.J. and Aifantis, E.C. (1982), On a proposal for a continuum with microstructure, Acta Mechanica, 45, 91–121.
Basinski, Z. S., Korbel, A. S., and Basinski, S. J. (1980), The temperature dependence of the saturation stress and dislocation substructure in fatigued copper single crystals, Acta Metallurgica, 28, 191–207.
Buchinger, L., Stanzt, S., and Laird, C. (1984), Dislocation structures in copper single crystals fatigued at low amplitudes, Phil. Mag., A50, 275–298.
Coullet, P., Elphick C., and Repaux, D. (1987), Phys. Rev. Lett. 28, 431.
Essmann, U. and Mughrabi, H. (1979), Annihilation of dislocations during tensile and cyclic deformation and limits of dislocation densities, Phil. Mag., A40, 731–756.
Essmann, U., Gösele, U., and Mughrabi, H. (1981), A model of extrusions and intrusions in fatigued metals, I. Point-defect production and the growth of extrusions“, Phil. Mag., A44, 406–426.
Franek, A., Kalus, R., and Kratochvil, J. (1989), On stability of dislocation structure in cyclically deformed metal crystals and formation of persistent slip bands, preprint.
Haken, H. (1978), Synergetics—An Introduction, 2nd ed., Springer-Verlag, BerlinHeidelberg–New York.
Holt, L. (1970), Dislocation cell formation in metals, J. Appl. Phys., 41, 3197–3201.
Jin, N. Y. and Winter, A. T. (1984), Dislocation structures in cyclically deformed [001] copper crystals, Acta Metallurgica, 32, 1173–1176. (See also: Cyclic deformation of copper single crystals oriented for double slip, Acta Metallurgica, 32, 989–995.)
Kuhlmann-Wilsdorf, D. (1982), Theory of dislocation cell sizes in deformed metals, Mat. Sci. Engng., 55, 79–83.
Kwadjo, R. and Brown, L. M. (1978), Cyclic hardening of magnesuim single crystals, Acta Metallurgica, 26, 1117–1132.
Mughrabi, H. (1981), Cyclic plasticity of matrix and persistent slip bands in fatigued metals, in Continuum Models for Discrete Systems, Vol. 4, edited by O. Bruhn and R. K. T. Hsieh, North-Holland, pp. 241–257.
Mughrabi, H., Ackermann, F., and Herz, K. (1979), Persistent slipbands in fatigued face-centered and body-centered cubic metals, in Fatigue Mechanisms, edited by J. T. Fong, ASTM-STP 675, ASTM, New York, pp. 69–105.
Mura, T. (1982), Micromechanics of Defects in Solids, Martinus-Nijhoff, The Hague.
Neuhauser, H. (1986), Physical manifestations of instabilities in plastic flow, in Mechanical Behaviour of Solids: Plastic Instabilities, Proceedings ICTP Enrico Fermi School of Theoretical Physics Trieste, Italy, edited by V. Balakrishnan and C. Bottani, World Scientific, Singapore, pp. 209–252.
Newell, A. C. (1974), Envelope equations, in Nonlinear Wave Motion, Lectures in Applied Mathematics, Vol. 15, edited by A. C. Newell, AMS, Providence, pp. 157–163.
Schiller, C. and Walgraef, D. (1988), Numerical simulation of persistent slip band formation, Acta Metallurgica, A36, 563–574.
Tabata, T., Fujita, H., Hiraoka, M., and Onishi, K. (1983), Dislocation behavior and the formation of persistent slip bands in fatigued copper single crystals observed by high-voltage electron microscopy. Phil. Mag., A47, 841–857.
Walgraef, D. and Aifantis, E. C. (1985a), On the formation and stability of dislocation patterns I, II, III, Int. J. Engng. Sci., 23, 1351–1358, 1359–1364, 1365–1372.
Walgraef, D. and Aifantis, E. C. (1985b), Dislocation patterning in fatigued metals as a result of dynamical instabilities, J. Appl. Phys., 58, 688–691.
Walgraef, D. and Aifantis, E. C. (1986), Dislocation patterning in fatigued metals: Labyrinth structures and rotational effects, Int. J. Engng. Sci., 1789–1798.
Walgraef, D., Schiller, C., and Aifantis, E. C. (1987), Reaction—diffusion approach for dislocation patterns, in Patterns, Defects, and Microstructures in Nonequilibrium Systems, edited by D. Walgraef, Martinus-Nijhoff, The Hague, pp. 257–269.
Walgraef, D. and Aifantis, E. C. (1988), Plastic instabilities, dislocation patterns and nonequilibrium phenomena, Res. Mechanica, 23, 161–195.
Winter, A. T. (1974), A model for the fatigue of copper at low plastic strain amplitudes, Phil. Mag., 30, 719–738.
Winter, A. T., Pedersen, O. B., and Rasmussen, K. V. (1981), Dislocation microstructures in fatigued copper polycrystals, Acta Metallurgica, 29, 735–748.
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Walgraef, D., Aifantis, E.C. (1990). Dislocation Inhomogeneity in Cyclic Deformation. In: Weng, G.J., Taya, M., Abé, H. (eds) Micromechanics and Inhomogeneity. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8919-4_32
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DOI: https://doi.org/10.1007/978-1-4613-8919-4_32
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