On the kinetics of the spreading of extrinsic grain boundary dislocations
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I.
INTRODUCTION
THEproblem of the spreading of extrinsic grain boundary dislocations (EGBDs), brought to the attention for the first time by Ishida et al. ~and then investigated by Pumphrey and Gleiter 2"3-4 and Varin, 5-8 appears to be one of the most important problems in physical metallurgy in recent years as it can in many ways, both directly and indirectly, affect plastic deformation at ambient and elevated temperatures of polycrystalline metals and alloys. As pointed out by Varin, 9 EGBDs existing at random grain boundaries in most commercially important metals are in a matter of seconds annihilated at temperatures higher than about 0.4Tin (where Tm is the melting point). It means that any lattice dislocation entering a random grain boundary during plastic deformation at elevated temperature loses its "lattice" identity, being quickly incorporated into a grain boundary structure. However, many processes occur in polycrystals at temperatures much lower than -0.4T,, where it is reasonable to expect that the EGBD's spreading time would be significantly prolonged. As usual, the dependence between time and temperature of any thermally activated process gives the kinetics of the process under consideration and it is usually expressed by an equation of the Arrhenius type. So far, a few models of the spreading of EGBDs have been proposed resulting in the equations describing the kinetics of this process. 2'~~ Unfortunately, none of the proposed kinetic equations has been tested in a relatively wide temperature interval. The aim of the present work is to investigate which of hitherto developed models of the spreading of EGBDs describes most adequately the kinetics of this process. R.A. VARIN is an Assistant Professor of Materials Science in the Department of Mechanical Engineering, University of Waterloo, Waterloo, ON, Canada, N2L 3GI. E. ROMANOWSKA-HAFTEK is a Senior Researcher with Institut of the Electronics Technology, Electron Microscopy Laboratory, AI. Lotnikow 32/46, 02-668 Warsaw, Poland. Manuscript submitted December 3, 1985. METALLURGICAL TRANSACTIONS A
II. MODELS OF THE SPREADING OF EXTRINSIC GRAIN BOUNDARY DISLOCATIONS
Johannesson and Th/~len~~developed the first model to describe the spreading of EGBDs. These authors considered dislocations with the Burgers vectors both parallel and perpendicular to the boundary plane. In the case of parallel Burgers vectors they assumed that an impinging lattice dislocation (forming an EGBD) dissociates immediately into a "train" of dislocations with very small Burgers vectors and the process is virtually temperature-independent. However, a dislocation with the Burgers vector perpendicular to the boundary plane dissociates also into dislocations with smaller Burgers vectors but at least partially by climb which involves diffusion and hence the process is strongly temperature-dependent. A schematic model of this process is shown in Figure 1. The rate of separation of dissociated dislocations in the boundary plane is given by: ~~ dS dt
DbGbbUt 27r(1 - v)kTS 1
[1]
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