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TECHNICAL PAPERS

On the Propagation of Lüders Bands in Steel Strips

[+] Author and Article Information
S. Kyriakides, J. E. Miller

Research Center for Mechanics of Solids, Structures & Mechanics, WRW 110, The University of Texas at Austin, Austin, TX 78712

J. Appl. Mech 67(4), 645-654 (Apr 18, 2000) (10 pages) doi:10.1115/1.1328348 History: Received April 18, 2000
Copyright © 2000 by ASME
Topics: Deformation , Steel , Stress , Strips
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References

Hall, E. O., 1970, Yield Point Phenomena in Metals and Alloys, Plenum Press, New York.
Cottrell,  A. H., and Bilby,  B. A., 1948, “Dislocation Theory of Yielding and Strain Ageing of Iron,” Proc. Physical Society, 62/I-A, pp. 49–62.
Johnston,  W. G., and Gilman,  J. J., 1959, “Dislocation Velocities, Dislocation Densities, and Plastic Flow in Lithium Fluoride Crystals,” J. Appl. Phys., 30, pp. 129–144.
Hahn,  G. T., 1962, “A Model for Yielding With Special Reference to the Yield-Point Phenomena of Iron and Related BCC Metals,” Acta Metall., 10, pp. 727–738.
Shaw,  J. A., and Kyriakides,  S., 1997, “On the Nucleation and Propagation of Phase Transformation Fronts in a NiTi Alloy,” Acta Mater., 45, pp. 683–700.
Shaw,  J. A., and Kyriakides,  S., 1998, “Initiation and Propagation of Localized Deformation in Elasto-Plastic Strips Under Uniaxial Tension,” Int. J. Plast., 13, pp. 837–871.
Shaw,  J. A., and Kyriakides,  S., 1995, “Thermomechanical Aspects of NiTi,” J. Mech. Phys. Solids, 43, pp. 1243–1281.
Lomer,  W. M., 1952, “The Yield Phenomenon in Polycrystalline Mild Steel,” J. Mech. Phys. Solids, 1, pp. 64–73.
Butler,  J. F., 1962, “Lüders Front Propagation in Low Carbon Steels,” J. Mech. Phys. Solids, 10, pp. 313–334.
Abeyaratne,  R., and Knowles,  J. K., 1993, “A Continuum Model of a Thermoelastic Solid Capable of Undergoing Phase Transitions,” J. Mech. Phys. Solids, 41, pp. 541–571.
Morrison,  W. B., and Glenn,  R. C., 1968, “Examination of the Lüders Front in a Low-Carbon Steel by Transmission Electron Microscopy,” J. Iron Steel Inst., 206, pp. 611–612.
Hill,  R., 1952, “On Discontinuous Plastic States, With Special Reference to Localized Necking in Thin Sheets,” J. Mech. Phys. Solids, 1, pp. 19–30.
Bijlaard,  P. P., 1940, “Theory of Local Plastic Deformations,” Publication of the International Association of Bridge and Structural Engineers, 6, pp. 27–44.
Kyriakides, S., 1993, “Propagating Instabilities in Structures,” Advances in Applied Mechanics, Vol. 30, J. W. Hutchinson and T. Y. Wu, eds., Academic Press, San Diego, pp. 67–189.

Figures

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Typical force-elongation response of mild steel exhibiting Lüders-type deformation
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Results from uniaxial test on steel strip; (a) stress and strain histories recorded, (b) x-t diagram of evolution of deformation front
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Photographic sequence of the evolution of Lüders strain (shown at 14 s intervals)
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Definition of geometric variables of inclined Lüders band
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Photograph of two coexisting Lüders fronts propagating towards each other
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Geometry and mesh of model strips for (a) single Lüders front propagation and (b) two-band propagation
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Simulation of single Lüders front propagation; (a) stress-displacement response and (b) moment-displacement response
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Sequence of black-white deformed configurations corresponding to responses in Fig. 7. White depicts zones with axial strain higher than 1.2 percent and black depicts zones lower than 1.2 percent.
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Lateral displacement of axis of strip as a function of δ for simulation in Figs. 7 and 8
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Expanded deformed configurations in gray scale showing one of the transient events
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Gray scale plot of configuration 21○ showing islands of uneven deformation left by five transient events
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Simulation of propagation of two Lüders fronts; (a) stress-displacement response and (b) moment-displacement response
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Sequence of black-white deformed configurations corresponding to responses in Fig. 12. White depicts zones with axial strain higher than 1.2 percent and black depicts zones lower than 1.2 percent.
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Lateral displacement of axis of strip as a function of δ for simulation in Figs. 12 and 13

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