Evolution of dislocation structures and deformation behavior of iron at different temperatures: Part I. strain hardening
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INTRODUCTION
IN order to describe the deformation behavior of crystalline materials, it is necessary to have some knowledge of their dislocation structure evolution, which depends on many variables, such as plastic strain rate, deformation temperature, etc. Recently, Kocks and Mecking t~-4] pursued a phenomenological approach to macroscopic plasticity of metals that appears very useful in describing the work-hardening behavior at the early stages of deformation. This approach is based on the assumption that the kinetics of plastic flow are determined by a single structure parameter (average dislocation density) representing the current structure. The dependence of the flow stress or on the plastic strain rate ~ and the absolute temperature T at a given structure of the material is given by the kinetic equation or -- or(p, ~, T)
[1]
For a complete description of plastic behavior, the kinetic equation is complemented with an evolution equation which describes the variation of the structure parameter with strain e at given strain rate and temperature:
dp/de = f ( p , ~, T)
[2]
According to the Kocks and Mecking approach, the structure parameter evolves toward a saturation value as the deformation progresses, and the flow stress tends to a saturation or steady-state value ors. At constant strain rate g and deformation temperature, the strain-hardening
Y. LAN, Research Assistant, Central Labor for Electron Microscopy, H.J. KLAAR, Doctor, Central Labor for Electron Microscopy, and W. DAHL, Professor and Department Head, Department of Metallurgy, are with the University of Aachen, 5100 Aachen, Federal Republic of Germany. Manuscript submitted February 4, 1991. METALLURGICAL TRANSACTIONS A
rate O, do'/de, is found to decrease linearly with flow stress; this behavior can be simply expressed as O = Oo(1 - or/or,)
[3]
Though the main characteristics of the large-strain behavior are doubtless suitably described by the conclusions of Kocks and Mecking, actual flow curves could be more complex at large strains. For most of the published large-strain flow curves, t51 the strain-hardening rate does not lead directly to a saturation stress or~. Instead, the decrease in the strain-hardening rate slows down rather abruptly at the medium stages of deformation in different modes. The reason for this transition was discussed in terms of the T E M observation with a l u m i n u m f i and it was found that it is correlated with the substructure transition from a stage of cell multiplication to another in which the cell multiplication rate seems equal to the cell annihilation rate. It is obvious that the deformation structure in bodycentered cubic (bcc) metals at low temperature differs from that in face-centered cubic (fcc) metals, - m since the mobility of screws in bcc metals is much smaller than that of nonscrews due to the higher Peierls stress, tS] which decreases rapidly with increasing temperature. However, the question of whether there exists a fundamental difference in work-hardening behavior between bcc and fcc metals,
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