Aspects of Dynamic Recrystallization in Cobalt at High Temperatures
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DYNAMIC recrystallization (DRX) during the hot deformation of materials has been widely studied and fairly well understood (References 1 and 2 give a good account of the basics of DRX). Materials with moderate to low stacking fault energy (SFE) are expected to favor the process of DRX, e.g., Cu, Cu-Al alloys,[3–5] and stainless steels.[6–10] The typical mechanical response of a material during DRX is a peak in the stress-strain curve followed by either a gradual decrease in the stress to a steady-state value or the occurrence of multiple peaks (oscillations) in stress finally leading to a steady state. It is customary to identify certain parameters during DRX such as peak stress rp, corresponding strain ep, critical strain ec, critical stress rc at the start of DRX, steadystate stress rs, and steady-state grain size ds, and to relate these with the deformation conditions of strain rate e_ and temperature T through the temperature-compensated strain rate, also called the Zener–Hollomon parameter Z e_ expðQ=RTÞ, where Q is the activation energy of the process.[1,2] Although the concept of a critical strain is very often used to characterize the start of DRX, it was argued by Wray[11] that, since the driving force for DRX R. KAPOOR, B. PAUL, and J.K. CHAKRAVARTTY, Scientific Officers, are with the Materials Group, Bhabha Atomic Research Centre, Mumbai-400 085, India. S. RAVEENDRA, Graduate Student, and I. SAMAJDAR, Professor, are with the Department of Metallurgical Engineering and Materials Science, Indian Institute of Technology Bombay, Powai, Mumbai-400 076, India. Contact e-mail: [email protected] Manuscript submitted October 21, 2008. Article published online February 20, 2009 818—VOLUME 40A, APRIL 2009
depends on the stored energy in the material, the criteria for the start of DRX should be the amount of the stored energy (a function of work done on material during deformation) prior to the start of DRX, rather than the strain. Later the concepts of irreversible thermodynamics, again based on the stored energy criteria, were used by Poliak and Jonas[6] to identify the critical condition for the initiation of DRX. Here, for the initiation of DRX, the local stored energy should attain a maximum and the rate of dissipation should reduce to a minimum. Using this and the hardness parameter of Hart,[12] the critical condition for DRX was identified as the point of inflection in the h vs r plot, where h is the workhardening rate @r=@e. This implies a minimum in ð@h=@rÞ. During DRX, inflections in the h-r curve have been observed earlier,[13] but no specific explanation for this was provided. A clearer physical picture was given by Gottstein et al.,[14] in which they used a threeinternal-variable model (dislocation density of three kinds: mobile, stored in cell interiors, and stored in cell walls) and showed the h-r plot to have an inflection. Their interpretation was related to the various stages of hardening: III, IV, and V. During stage III, h decreases with increasing r, but before h reaches zero, stage IV hardening
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