Orientation-dependent Pattern Formation in a 1.5D Continuum Model of Curved Dislocations
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Orientation-dependent Pattern Formation in a 1.5D Continuum Model of Curved Dislocations
Stefan Sandfeld1 , Vanessa Verbeke2 , Benoit Devincre2 1
Institute for Materials Simulation (WW8), Friedrich-Alexander-University Erlangen-N¨urnberg, Dr.-Mack-Str. 77, 90762 F¨urth, Germany 2 Laboratoire d’Etude des Microstructures, UMR 104 CNRS-ONERA, Chatillon, France
ABSTRACT Dislocation pattern formation is a phenomenon where during significant plastic deformation dislocations organize themselves into (meta)stable structures. Modeling such systems is a non-trivial task, because the number of interacting dislocations is high, bringing discrete simulation models to their computational limits. Continuum models, although more efficient, generally do not contain sufficient information for a physically detailed representation of such systems. In this paper we show how a continuum dislocation dynamics theory can be used to model idealized pattern formation. Furthermore, we show how discrete dislocation dynamics (DD) simulations can be used to provide physical input for our continuum model. INTRODUCTION When metals undergo significant plastic deformation the dislocation microstructure changes fundamentally. After an initial ’easy glide’ regime, dislocations tend to collectively and spontaneously form structures which alternate between regions of low dislocation densities and clusters of high dislocation density. These – often metastable – structures are denoted as ’dislocation patterns’ and are responsible for an increased hardening effect on the specimen level [13, 16]. Modeling approaches to predict and understand (evolving) systems of dislocations and patterning have been indispensable already for more than half a century (see e.g. [10]). Early continuum models were often based on analogies with other physical problems but did not consider the linelike nature of dislocations. Discrete dislocation dynamics (DD) simulations - as e.g. by [11, 5], have proven to successfully reproduce dislocation patterning. However, an important drawback of such simulations is the rapid increase of their computational cost with plastic deformation since the number of segments involved in the line discretization is increasing with increasing dislocation density. Continuum dislocation dynamics (CDD) models, on the other hand, are dislocation density based and do not suffer from this computational restriction. However, they are up to date not able to represent dislocation microstructure and their interactions at the same level of details as DD. Nonetheless, simplified CDD models have been applied successfully, e.g. [6, 2]. In this paper we use Hochrainer’s higher-dimensional CDD model which is able to predict fluxes of curved dislocations in a continuum [8, 14]. We start by briefly introducing our model system and the governing equations together with a minimal set of interaction stresses. We then introduce the DD model setup and show how a microstructure-sensitive forest strengthening parameter can be
obtained. Finally, we use the continuum model
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