Submicron plasticity: yield stress, dislocation avalanches, and velocity distribution

The existence of a well defined yield stress, where a macroscopic piece of crystal begins to plastically flow, has been one of the basic observations of materials science. In contrast to macroscopic samples, in micro- and nanocrystals the strain accumulates in distinct, unpredictable bursts, which makes controlled plastic forming rather difficult. Here we study by simulation, in two and three dimensions, plastic deformation of submicron objects under increasing stress. We show that, while the stress-strain relation of individual samples exhibits jumps, its average and mean deviation still specify a well-defined critical stress, which we identify with the jamming-flowing transition. The statistical background of this phenomenon is analyzed through the velocity distribution of short dislocation segments, revealing a universal cubic decay and an appearance of a shoulder due to dislocation avalanches. Our results can help to understand the jamming-flowing transition exhibited by a series of various physical systems.Comment: 5 page

A graph database for feature characterization of dislocation networks

Three-dimensional dislocation networks control the mechanical properties such as strain hardening of crystals. Due to the complexity of dislocation networks and their temporal evolution, analysis tools are needed that fully resolve the dynamic processes of the intrinsic dislocation graph structure. We propose the use of a graph database for the analysis of three-dimensional dislocation networks obtained from discrete dislocation dynamics simulations. This makes it possible to extract (sub-)graphs and their features with relative ease. That allows for a more holistic view of the evolution of dislocation networks and for the extraction of homogenized graph features to be incorporated into continuum formulation. As an illustration, we describe the static and dynamic analysis of spatio-temporal dislocation graphs as well as graph feature analysis

Data-driven exploration and continuum modeling of dislocation networks

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

Characterization of Lomer junctions based on the Lomer arm length distribution in dislocation networks

During the plastic deformation of crystalline materials, 3d dislocation networks form based on dislocation junctions. Particularly, immobile Lomer junctions are essential for the stability of dislocation networks. However, the formed Lomer junctions can unzip and dissolve again, if the linked mobile dislocations of the Lomer junction - the Lomer arms - experience sufficiently high resolved shear stresses. To generate a better understanding of the dislocation network stability and to pave the way to a general stability criterion of dislocation networks, we investigate the Lomer arm length distribution in dislocation networks by analyzing discrete dislocation dynamics simulation data of tensile-tested aluminum single crystals. We show that an exponential distribution fits best to the Lomer arm length distribution in the systems considered, which is independent of the crystal orientation. The influence of the slip system activity on the Lomer arm length distribution is discussed

Dislocation multiplication by cross-slip and glissile reaction in a dislocation based continuum formulation of crystal plasticity

Modeling dislocation multiplication due to interaction and reactions on a mesoscopic scale is an important task for the physically meaningful description of stage II hardening in face centered cubic crystalline materials. In recent Discrete Dislocation Dynamics simulations it is observed that dislocation multiplication is exclusively the result of mechanisms, which involve dislocation reactions between different slip systems. These findings contradict multiplication models in dislocation based continuum theories, in which density increase is related to plastic slip on the same slip system. An application of these models for the density evolution on individual slip systems results in self-replication of dislocation density. We introduce a formulation of dislocation multiplication in a dislocation based continuum formulation of plasticity derived from a mechanism-based homogenization of cross-slip and glissile reactions in three-dimensional face-centered cubic systems. As a key feature, the presented model includes the generation of dislocations based on an interplay of dislocation density on different slip systems. This particularly includes slip systems with vanishing shear stress. The results show, that the proposed dislocation multiplication formulation allows for a physically meaningful microstructural evolution without self-replication of dislocations density. The results are discussed in comparison to discrete dislocation dynamics simulations exposing the coupling of different slip systems as the central characteristic for the increase of dislocation density on active and inactive slip systems. (C) 2019 Elsevier Ltd. All rights reserved