Data-driven exploration and continuum modeling of dislocation networks

Markus Sudmanns,Daniel Weygand,Katrin Schulz,Jakob Bach

doi:10.1088/1361-651x/ab97ef

Abstract

The microstructural origin of strain hardening during plastic deformation in stage II deformation of face-centered cubic (fcc) metals can be attributed to the increase in dislocation density resulting in a formation of dislocation networks. Although this is a well known relation, the complexity of dislocation multiplication processes and details about the formation of dislocation networks have recently been revealed by discrete dislocation dynamics (DDD) simulations. It has been observed that dislocations, after being generated by multiplication mechanisms, show a limited expansion within their slip plane before they get trapped in the network by dislocation reactions. This mechanism involves multiple slip systems and results in a heterogeneous dislocation network, which is not reflected in most dislocation-based continuum models. We approach the continuum modeling of dislocation networks by using data science methods to provide a link between discrete dislocations and the continuum level. For this purpose, we identify relevant correlations that feed into a model for dislocation networks in a dislocation-based continuum theory of plasticity. As a key feature, the model combines the dislocation multiplication with the limitation of the travel distance of dislocations by formation of stable dislocation junctions. The effective mobility of the network is determined by a range of dislocation spacings which reproduces the scattering travel distances of generated dislocation as observed in DDD. The model is applied to a high-symmetry fcc loading case and compared to DDD simulations. The results show a physically meaningful microstructural evolution, where the generation of new dislocations by multiplication mechanisms is counteracted by a formation of a stable dislocation network. In conjunction with DDD, we observe a steady state interplay of the different mechanisms.

Highlights

Dislocation networks interconnecting different slip systems are a key feature of stageII hardening in fcc single crystals which have been observed and described in early experimental works [1, 2, 3]
The results show that this interplay of dislocation reactions is able to reproduce observations in discrete dislocation dynamics (DDD) simulations [4], where it is shown that cascades of multiplication events produces further plasticity, which in turn is limited by other reactions
We introduce a model for the evolution of dislocation networks in a dislocation-based formulation of crystal plasticity, which provides an approach for a homogenization of the interaction between dislocation multiplication and the stabilization of the emerging dislocation network

Summary

Introduction

Dislocation networks interconnecting different slip systems are a key feature of stageII hardening in fcc single crystals which have been observed and described in early experimental works [1, 2, 3]. Dislocation networks interconnecting different slip systems are a key feature of stage. 5 allow for a deeper understanding of the microstructural features which govern the effective mobility of dislocations in networks [4]. It has been shown that dislocation multiplication mechanisms lead to cascades of further reactions and multiplication events, which can span the whole simulation volume even though the multiplication events are local. In the course of this observation, a dislocation may trigger several. 10 other reactions but its own travel distance is limited by the reaction it triggers. A large scatter in dislocation spacings and travel distances of individual dislocations is observed [4, 5]. Dislocation networks are characterized by individual and very heterogeneous dislocation reaction and multiplication events

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