Time-dependent deformation of metals
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I.
INTRODUCTION
I T is fitting that a report on time-dependent deformation of metals should be included in a symposium to celebrate the 50th anniversary of the introduction of dislocations. A reading of the classic 1934 papers of Taylor 1 and Orowan 2 indicates that these pioneers had strong interests in the effects of strain rate and temperature on plastic flow and in the shape of the stress-strain curve. We now know that the shape of the stress-strain curve is the result of a competition between strain hardening and recovery processes, and thus depends on both strain rate and temperature. This relationship was specifically discussed by Orowan and was implicit in Taylor's attempt to derive a relation for the shape of the stress-strain curve. These remarkable papers not only set forth the properties of dislocations and their interactions, but also correctly described the hardening produced by their presence and the strain produced by their movement. Taylor went even further to derive an expression for the shape of an ordinary stress-strain curve. By assuming that dislocations move a fixed distance when they are formed, he derived a parabolic stress-strain law that compared favorably with the stressstrain curves then available for pure aluminum single crystals. This result reduces to the widely accepted linear strain hardening law for stage II deformation if the more natural assumption that the distance moved scales with the average dislocation spacing is made. Taylor's attempt to derive the shape of the stress-strain curve represented a giant step forward in the understanding of time-dependent plastic deformation. Plastic flow of metals and the shape of the stress-strain curve are now believed to be dominated by the competition
W. D. NIX, Professor, and D. A. HUGHES, Sandia Fellow, are with the Department of Materials Science and Engineering, Stanford University, Stanford, CA 94305. J. C. GIBELING is Assistant Professor, Department of Mechanical Engineering, University of California, Davis, CA. This paper is based on a presentation made at the symposium "50th Anniversary of the Introduction of Dislocations" held at the fall meeting of the TMS-AIME in Detroit, Michigan in October 1984 under the TMSAIME Mechanical Metallurgy and Physical Metallurgy Committees. METALLURGICAL TRANSACTIONS A
between strain hardening and recovery. In the present paper we adopt the view that strain hardening occurs by the storage of dislocations, which is statistical in nature, and that recovery involves the rearrangement and annihilation of dislocations. These recovery processes occur when dislocations move out of their slip planes, either by cross-slip of screw dislocations, which dominates at low temperatures, or by the climb of edge dislocations, which occurs at high temperatures. In general, climb of edge dislocations is assumed to be more sluggish than cross-slip of screw dislocations, because the climb motion must be accompanied by vacancy diffusion. It should be noted, however, that when dislocations are widely extended, the c
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