Abstract
The paper deals with the dislocation dynamics of coherently propagating modes of plastic shear (Lüders bands) in single crystals oriented for single slip, in terms of a generalized Fisher-Kolmogorov equation. The role of (1) cross-slip and (2) non-axial stresses as propagation mechnisms is investigated, and the problem of propagation velocity selection is addressed. The phenomenon of slip band clustering which was observed in sufficiently thick tensile specimens is traced back to a propagative instability owing to non-axial stresses.
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References
P. Hähner: Theory of Solitary Plastic Waves: I. Lüders Bands in Polycrystals. Appl. Phys. A 58, 41 (1994)
Y. Estrin, L.P. Kubin: Res Mech 23, 197 (1988)
H. Neuhäuser: In Dislocations in Solids, ed. by F.R.N. Nabarro (North Holland, Amsterdam 1983) Vol. 6, p. 319
H. Alexander: In Dislocations in Solids, ed. by F.R.N. Nabarro (North Holland, Amsterdam, 1986) Vol. 7, p. 113
H. Neuhäuser: Solid State Phenom. 3 & 4, 407 (1988)
H. Neuhäuser: Res Mechanica 23, 113 (1988)
H. Godon, H.-H. Potthoff, N. Neuhäuser: Cryst. Res. Technol. 19, 373 (1984)
H. Alexander, P. Haasen: Solid State Phys. 22, 27 (1968)
H. Steinhardt, P. Haasen: Phys. Status Solidi (a) 49, 93 (1978)
H.-H. Potthoff: Phys. Status Solidi (a) 77, 215 (1983)
H. Wiedersich: J. Appl. Phys. 33, 854 (1962)
U. Essmann, K. Differt: Scr. Metall. 22, 1337 (1988)
V.I. Vladimirov, A.A. Kusov: Sov. Phys.-Solid State 18, 886 (1976)
Y. Bréchet, F. Louchet: Solid State Phenom. 3 & 4, 347 (1988)
L.P. Kubin, J.-P. Poirier: Solid State Phenom. 3 & 4, 473 (1988)
Y. Estrin: Solid State Phenom. 3 & 4, 417 (1988)
R.A. Fisher: Ann. Eugenics 7, 355 (1937)
A. Kolmogorov, I. Petrovskii, N. Piskunov: Bull. Univ. Moscow, Ser. Internat., Sect. A 1, 1 (1937)
H.P. McKean: Comm. Pure Appl. Math. 28, 323 (1975)
D.G. Aronson, H.F. Weinberger: Adv. Math. 30, 33 (1978)
W. van Saarloos: Phys. Rev. A 37, 211 (1988)
G.B. Whitham: Linear and Nonlinear Waves (Wiley, New York 1974)
G. Dee, J.S. Langer: Phys. Rev. Lett. 50, 383 (1983)
P. Hähner: Versetzungsdynamik propagierender plastischer Verformungsmoden. Dissertation, Universität Stuttgart (1992)
N.I. Muschelischwili: Einige Grundaufgaben zur mathematischen Elastizitätstheorie (Hanser, München 1971) p. 264