Deformation bands, the LEDS theory, and their importance in texture development: Part I. Previous evidence and new obser
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INTRODUCTION—PRIOR EVIDENCE ON DEFORMATION BANDS A. The Four Most Important Models of Polycrystal Deformation
THE geometry and mechanics of single crystal deformation in terms of glide on close-packed lattice planes in closepacked lattice directions, with the different possible slip systems selected in accordance with the highest resolved shear stress, was well established even before dislocations were discovered, as documented in the foundational book by Schmid and Boas.[1] We now know, of course, that the carriers of this kind of deformation are glide dislocations. We also know that in glide they respond virtually instantaneously to resolved shear stresses above the level of the “friction stress,” t0, but respond very sluggishly, if at all, to normal stresses, namely, via climb, which is negligible below about one-half of the absolute melting temperature, TM /2. Initially, it seemed to be an easy matter to account for polycrystalline deformation as the collective effect of the individual grains, each behaving much like a single crystal under the same imposed stress, as done in the Sachs model of texture formation.[2] Correspondingly, from the outset, most of the relevant experimental and theoretical work was devoted to the simplest case, i.e., axisymmetric flow under uniaxial stress such as is approximated in tensile testing, small-strain compression, wire drawing, or extrusion. However, single- or double-glide deformation, as expected under tensile stress, cannot account for the shape changes that are obviously necessary to maintain cohesion among the grains. Besides, attainment of the same critical resolved shear stress on the most highly stressed slip system(s) would require D. KUHLMANN- WILSDORF, University Professor of Applied Science, Department of Physics, J.T. MOORE, Research Scientist, Department of Materials Science and Engineering, and E.A. STARKE, Jr., University Professor of Materials Science and Oglesby Professor of Materials Science and Engineering, Department of Materials Science and Engineering, are with the University of Virginia, Charlottesville, VA 22903. S.S. KULKARNI, formerly Graduate Student with the Department of Materials Science and Engineering, University of Virginia, is Research Scientist, Advanced Materials Division, Materials Research Corporation, Orangeburg, NY 10962. Manuscript submitted July 6, 1998. METALLURGICAL AND MATERIALS TRANSACTIONS A
different tensile stresses from grain to grain. Hence, the Sachs model implies both strain and stress incompatibility at grain boundaries. Chronologically, the next important model was due to Boas and Schmid,[3] who proposed that always the three most highly stressed slip systems act simultaneously and produce that lattice orientation in the grains which is stable under such triple slip. The stable orientations would correspond to the ^112& axis orientation produced by ^110& {111} double-glide in cubic crystals under tension. Yet, this model still does not solve the stress incompatibility nor the coherency problem at grain boundaries, the l
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