Abstract
We present a theoretical model of repeated yielding (ry) which reproduces many experimentally observed features, apart from showing how the temporal behaviour of the phenomenon emerges as a consequence of the cooperative behaviour of defects. We first consider the case of step-like creep curves. Our model leads to a coupled set of nonlinear differential equations which admit limit cycle solutions, and thence jumps on the creep curve. Approximate closed form solutions for the limit cycles and the steps on the creep curve are obtained. The model is then extended to the constant strain rate experiment by including the machine equation. The temporal ordering ofry is shown to follow, as well as several other features characteristic ofry. Chaotic flow is also exhibited: the model has a sequence of period-doubling bifurcations with an exponent equal to that of the quadratic map. Finally, we have analysed the fluctuations during the onset ofry using nonlinear Langevin equations. Fluctuations in the periodic (ry) phase are also investigated. We conclude thatry is another example of a dissipative structure.
Similar content being viewed by others
References
Ananthakrishna G and Sahoo D 1981J. Phys. D14 2081
Ananthakrishna G and Valsakumar M C 1982J. Phys. D15 L171
Ananthakrishna G and Valsakumar M C 1983Phys. Lett. A95 69
Ardley G W and Cottrell A H 1953Proc. R. Soc. A219 328
Bell J F 1973Handbuch der Physik Band VIa/I (Berlin: Springer-Verlag)
Bodner S R and Rosen A 1967J. Mech. Phys. Solids 15 63
Cottrell A H 1953Philos. Mag. 44 829
Da Silveira T L and Monteiro S N 1979Met. Trans. A10 1795
Eckmann J P 1981Rev. Mod. Phys. 53 643
Feigenbaum M J 1978J. Stat. Phys. 19 25
Grossman S and Tnomae S 1977Z. Naturforsch. 32a 1353
Haken H 1978Synergetics (Berlin: Springer-Verlag)
Hall E O 1970Yield point phenomena in metals and alloys (Macmillan: London)
Jefferies D J 1982Phys. Lett. A90 317
Kubin L P, Estrin Y and Spiesser Ph 1984Res. Mechanica 10 25
Lauterborn W and Kramer E 1981Phys. Rev. Lett. 47 1445
Lubahn J D and Felgar R P 1961Plasticity and creep of metals (New York: John Wiley)
McCormic P G 1971Acta Metall. 19 463
McCormic P G 1972Acta Metall. 20 351
Minorsky N 1962Nonlinear oscillations (New Jersey: Van Nostrand)
Navratil V, Hammersky M and Blazkova 1974Czech. J. Phys. B24 907
Neelakantan K and Venkataraman G 1983Acta Met. 31 77
Nicolis G and Prigogine I 1977Self organization in non-equilibrium systems (New York: Wiley)
Ott E 1981Rev. Mod. Phys. 53 643
Penning P 1972Acta Metall. 20 1169
Rosen A and Bodner S R 1969Mater. Sci. Eng. 4 115
Sahoo D and Ananthakrishna G 1982J. Phys. D15 1439
Schultz J 1974Polymer materials science (New Jersey: Princeton-Hall)
Stejskalova V, Hammersky M, Luckac P, Vostry P and Sprusil B 1981Czech J. Phys. B31 195
Takayama 1979Scr. Met. 13 463
Tomita K, Ohta T and Ohta H 1974Prog. Theor. Phys. 52 1744
Tomita K and Tomita H 1974Prog. Theor. Phys. 51 1731
Tyson J J 1977J. Chem. Phys. 66 905
Valsakumar M C and Ananthakrishna G 1983J. Phys. D16 1055
Valsakumar M C, Murthy K P N and Ananthakrishna G 1983J. Stat. Phys. 30 637
van den Beukel A 1975Phys. Status Solidi A30 197
van den Beukel A 1980Acta Metall. 20 965
Wijler A and van Westrum S 1971Scr. Metall. 5 531
Zagarukuyko L N, Ostasky A L and Soldatov V P 1977Phys. Met. Metallogr. 43 156
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ananthakrishna, G. Repeated yield drop phenomena as a cooperative effect. Bull. Mater. Sci. 6, 665–676 (1984). https://doi.org/10.1007/BF02743994
Issue Date:
DOI: https://doi.org/10.1007/BF02743994