Three-dimensional investigation of long-range internal stresses in a single crystal deforming by nonsymmetrical slip
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I. INTRODUCTION
THE discovery of the asymmetric character of X-ray diffraction profiles[1] was the most “surprising” experimental result revealed by the high resolution diffractometer,[2,3] developed in the beginning of the 1980s. Theoretical investigations[4,5] pointed out that the asymmetric character results from the polarization of dislocation structures. However, the present experimental techniques do not allow large spatial investigations of dislocation dipoles and, thus, do not enable a straightforward application of these theories. Concurrently, a phenomenological approach was proposed by Mughrabi,[3] relating asymmetric character to the prevailing of long-range internal stresses (LRIS). According to this model, a deformed microstructure can be divided into “hard” and “soft” materials, associated to regions of high and low dislocation density, i.e., cell walls and cell interiors, respectively. The LRIS are thought to be generated by interface dislocations, necessary to enable the homogeneous shear of heterogeneous dislocation structures. The investigation of the dynamic stability of this composite material was carried out by Nabarro.[6] He has shown that, if plausible assumptions are made on the creation and annihilation of dislocations, the composite model of Mughrabi may account for kinetic properties of plastic deformation. It predicts a relationship between flow stress and strain that is in good agreement with experimental results. Here, we note that Argon and Haasen[7] suggested an alternative interpretation of asymmetric peak profiles based on a new work-hardening description in stage IV. Investigations over a large range of deformation have shown, however, that this model applies, with some modifications, only to stage IV.[8] The LRIS have also been observed by non X-ray macroscopic methods (for G. MONNET, formerly with LPMTM, is Postdoctoral Fellow, LEM, CNRS-ONERA, 92322 Chaˆtillon, Cedex, France. B. BACROIX, Director of Research, is with CNRS, LPMTM, Universite´ Paris Nord, 93430 Villetaneuse, France. J.-L. LEBRUN, Associate Professor, is with ENSAM Angers, France. T. UNGAR, Professor, is with the Department of General Physics, Eo¨tvo¨s University Budapest, Budapest VIII, P.O.B. 323, Hungary. Manuscript submitted November 21, 2000. METALLURGICAL AND MATERIALS TRANSACTIONS A
a review see References 9 and 10). A two-phase description of the dislocation cell structure was also developed by Pedersen et al.,[11] assuming that the cell walls can be seen as hard inclusions put under the stress of interface dislocations as in the precipitation hardening model of Ashby.[12] Among these different models, the composite model of Mughrabi seems to provide the most simple and straightforward interpretation of the asymmetry of diffraction profiles. The main experimental evidence is that most of the measured asymmetric profiles can be resolved into two symmetrical subprofiles.[13] The results obtained in various experimental conditions reveal good agreement with Mughrabi’s model, i.e., LRIS in dislocation walls a
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