Peierls-nabarro plastic deformation in the presence of solute clusters
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I.
INTRODUCTION
MANY bcc
alloys display a n o m o l o u s mechanical properties.~'2'3 In particular, it is possible for the yield stress of the alloy to be lower than that of the pure metal at low temperatures (solid solution weakening). A model which may provide an explanation for this p h o n o m e n o n - - at least for certain m e t a l s - - i s concerned with dislocation double kink formation and lateral motion of single kinks 4-1~in the presence of solute atoms. These atoms occupy substitutional positions in a bcc lattice with a given Peierls stress. The deformation is assumed to be controlled by the motion of screw dislocations. The solute atoms are assumed to interact with the dislocation via a classical size" or modulufl 2 effect interaction. Hence, this semicontinuum model neglects such important effects as dislocation core structure, the influence of solute atoms on the core structure and the associated Peierls barrier, and the modification of the defect-dislocation interaction at short range. We will consider very specific defect cluster geometries (as opposed to a random dispersal) to gain insight into critical cluster sizes/shapes as well as the general applicability of the simple semicontinuum model. In our model, the internal stress fields due to the solute atoms were taken as a superposition of either individual size or modulus impurity-dislocation interactions. These effects are based on a continuum model, but will be assumed to be valid even to nearest-neighbor distances. The interaction stress between the dislocation and solute atom, either for size or modulus effect, decays rapidly with distance (effectively as 1/r3). The very short range interactions were retained in order to obtain an upper bound on these effects, as well as to maintain consistency in the strain fields. Neglect of nearest and next-nearest neighbor interactions in our model will be shown to impact the results significantly. Substitutional atoms can influence both the formation of a double kink (DK) and the lateral propagation of a single kink. In a random alloy, the internal stresses due to the impurities can either aid or oppose both processes. An initially straight dislocation (parallel to a Peierls valley) will
D. M. ESTERLING is Professor of Engineering, George Washington University, NASA-Langley Research Center, Hampton, VA 23665. R. J. ARSENAULT is Professor of Engineering Materials, University of Maryland, College Park, MD 20742. Manuscript submitted October 22, 1981. METALLURGICALTRANSACTIONS A
form a DK in the region where the impurities provide the greatest "assist." Hence, the critical nucleation stress is lowered by the presence of solute atoms, which can lead to weakening. For the dislocation to move, each kink must propagate laterally (either to the assumed pinning points or to be annihilated by an opposite kink). In a pure metal there is only a small barrier to lateral motion. In an alloy the lateral motion will be controlled by the maximum opposing stress arising from the solute atoms. This leads to a har
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