Elastic Distortion of Dislocations in Deforming FCC Crystals
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Elastic Distortion of Dislocations in Deforming FCC Crystals Mamdouh Mohamed1, Anter El-Azab1* and B. C. Larson2 1
Department of Scientific Computing, Florida State University, Tallahassee, FL, USA Materials Sciences and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN, USA * Corresponding author. E-mail address: [email protected] 2
ABSTRACT A computational technique is developed to predict the statistics of internal elastic fields of threedimensional dislocation systems in deforming crystals. The internal elastic fields are computed based on 3D dislocation realizations generated by the method of dislocation dynamics simulation. Preliminary results are presented for the statistical characteristics of the elastic strain, lattice rotation and dislocation density tensor fields. The importance of the current analysis is discussed in the context of direct comparison of simulations with spatially resolved 3D X-ray microscopy measurements of lattice rotation and the dislocation density tensor. INTRODUCTION During plastic deformation of metallic crystals, the dislocation density evolves with the level of deformation, which in turn determines the hardening behavior of the crystal during the course of deformation. The dislocation population induces elastic distortions in the crystal that can be probed experimentally. The geometrical fields, namely the lattice rotation and elastic strain, are particularly important since they contain important information about the underlying dislocation system itself. For example, these fields can be used to compute the dislocation density tensor, a key geometric measure for the dislocation system in distorted crystals [1]. X-ray microscopy currently provides spatially resolved measurements of local lattice orientation and dislocation density tensor in 3D with micron or sub-micron scale resolution [2-4]. The ability to reveal such detailed microstructure information provides a previously missing link between mesoscale deformation experiments and computer simulations results. This short communication highlights the procedure to calculate the elastic strain and lattice rotation fields (and dislocation density tensor) in highly dislocated crystals, starting with dislocation configurations extracted from dislocation dynamics simulations [5]. The statistical behavior of these fields, described in terms of probability density and pair correlation functions, is investigated, as a step towards comparison between mesoscale simulations and experiments. Preliminary results from simulations are presented and discussed in this communication. THEORETICAL FORMALISM Dislocations disturb the perfect arrangement of crystal atoms resulting in elastic distortions in the lattice, which can be described in terms of an elastic displacement field u(x). Within the linear theory of elasticity, the gradient of this displacement field can be decomposed into symmetric and antisymmetric parts, giving the elastic strain and elastic lattice rotation, respectively. In mathematical terms, this (additive) deco
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