Deformation bands, the LEDS theory, and their importance in texture development: Part II. Theoretical conclusions
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THE plastic deformation of solids is arguably among the most important phenomena in our lives, let alone in engineering, yet it is among the least understood. This is highly regrettable, especially in regard to technological metals whose deformation is mediated through glide dislocations, because it stymies the development of effective constitutive equations. These must inevitably be based on a thorough understanding of the correlations between straining conditions, resulting deformation structures, and the mechanical properties derived therefrom. This state of affairs is due to the lack of a unified approach. The foundational, basically irreconcilable publications are due to Taylor[1] and Becker,[2–6] respectively. Taylor proposed the first dislocation-based work-hardening theory simultaneously with his introduction of the dislocation concept into materials science. According to it, on stress application, dislocations virtually instantaneously multiply and move via glide into configurations that are in mechanical equilibrium with the applied tractions. The resulting dislocation density is proportional to the square of the resolved shear stress, in agreement with firmly established empirical
D. KUHLMANN-WILSDORF, University Professor of Applied Science, is with the Department of Materials Science and Engineering and the Department of Physics, University of Virginia, Charlottesville, VA 22903. Manuscript submitted July 6, 1998. METALLURGICAL AND MATERIALS TRANSACTIONS A
observation. As Taylor assumed a constant mean free-glide path, he obtained a parabolic stress-strain curve. Becker’s 1925 theory,[2,3,4] by contrast, predates the dislocation concept. He proposed that crystals deform, much like fluids and amorphous materials, via thermally activated events. While in noncrystalline materials, these events are place changes of individual atoms, Becker envisaged that in crystals, discrete volume elements would shear by elementary glide steps. These glide events would be triggered whenever statistical thermal activation momentarily and locally generated a critical resolved shear stress. In this view, the apparent one-to-one correlation between applied stress and resulting strain, so familiar from work-hardening curves, results (a) from the extremely steep stress dependence of the activated glide event frequency in the vicinity of the critical stress; and (b) because the flow would soon cease through work-hardening, the nature of which Becker did not attempt to elucidate. Rather, Becker had his theory tested by his pupils Boas[5] and Orowan[6] via low-strain creep tests of thin metal wires near room temperature. Becker’s theory is no longer under active consideration, but its successor theory, of self-organizing dislocation structures (SODS), has for the past several years received the lion’s share of attention. It is an adaptation of a model by Holt[7] and Staker and Holt[8] to Prigogine’s thermodynamics of energy-flow-through systems. SODS modeling has been pioneered by Aifantis and Walgraef[9–13] and is current
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