Computer Modelling of Dynamically-Induced Dislocation Patterning
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COMPUTER MODELLING OF DYNAMICALLY-JINDUCED DISLOCATION PATTERNING BENOIT DEVINCRE AND VASSILIS PONTIKIS Section d'Etude des Solides Irradi6s, CEA-CEREM, 91128 Palaiseau Cedex, France
Ecole
Polytechnique,
ABSTRACT The evolution of a random and initially homogeneous distribution of parallel and infinitely extended edge dislocations is studied by using elastic energy minimization without and in presence of a periodic external stress, ta. During the energy minimization without external stress (relaxation), randomly distributed dislocation dipoles are formed whereas, when the external stress is acting, the dislocations condense in walls. We investigated the spatial periodicity of this microstructure, X, as a function of, Ta, and of the total dislocation density. The elastic energy of the stress-induced microstructure is found to be comparable to the value obtained by relaxation. Thereby, emphasis is given to the dynamical character of patterning. A phenomenological model has been developed, explaining the correlation between X and ca found in the simulations and comparing favorably with existing experimental data. INTRODUCTION The formation of dislocation cells is a common feature of deformed materials that despite extensive experimental and theoretical investigations is still not well understood. Among the aspects of deformation induced microstructures one of the most fascinating is the empirically established law according to which the cell diameter, X, is inversely proportional to the applied stress, Xo-l/ta [1,2]. This relation rises indeed the questions of how the mechanical response of a deformed material is related to a given microstructure and of the importance of interactions between dislocations in the process of deformation-induced dislocation patterning. These are of two types: long-range stress and strain fields and interactions related to short-range effects such as annihilation or reactions leading to the formation of sessile junctions [1]. Due to complexity of the phenomena involved during the plastic deformation of materials, only a computer assisted approach can help in clarifying the mechanisms of the cell formation' Several such approaches exist, based on 2D [3,6] and more recently on 3D [7,8] computer models. The former have been extensively used in the past years whereas the latter are still now under development. Dislocation patterns in 2D simulations have been shown to form when an initially random distribution of dislocations relaxes under the influence of their mutual interactions. However, the microstructures thereby produced are mainly composed by dislocation dipoles and loosely shaped walls having only a vague resemblance to their experimental counterparts [5]. Are these features related to the dimensionality or to the absence of an essential ingredient, namely the absence of an external stress, is the question that we try to address in present work. In the following, we first give the computational details concerning our 2D model we used and the algorithm simulating dislocation motion by
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