Dislocation multiplication by cross-slip and glissile reaction in a dislocation based continuum formulation of crystal plasticity. (November 2019)

• Record Type: Journal Article
• Authors: Sudmanns, Markus; Stricker, Markus; Weygand, Daniel; Hochrainer, Thomas; Schulz, Katrin
• Is Part Of: Journal of the mechanics and physics of solids. Volume 132(2019)
• Publication Date: 2019-11
• Subjects: Crystal plasticity -- Continuum dislocation dynamics -- Dislocation multiplication -- Dislocation interaction; Mechanics, Applied -- Periodicals; Solids -- Periodicals; Mechanics -- Periodicals; Mécanique appliquée -- Périodiques; Solides -- Périodiques; Mechanics, Applied; Solids; Periodicals; 531.05
• DOI: 10.1016/j.jmps.2019.103695
• Languages: English
• ISSNs: 0022-5096

Abstract

Highlights: The presented model is a homogenization of discrete multiplication mechanisms (instead of a slip-system-wise application of phenomenological formulations as done in various existing models.). As observed in the underlying discrete dislocation dynamics simulations, only dislocation multiplication by glissile and cross-slip is considered, avoiding dislocation multiplication based on the picture of Frank-Read sources. The model is able to link the dislocation density activity on different slip systems by the homogenized multiplication mechanisms. This also includes "inactive" slip systems with a zero shear stress, leading to a dislocation density increase by deposition of the products of glissile reactions. It is shown that the increasing dislocation density on the inactive slip systems may affect the evolution of the active slip systems by contributing to further glissile reactions and strain hardening in the continuum model. The results for the dislocation density increase are therefore close to discrete dislocation dynamics results and thus mechanisms-based in contrast to models based on a slip-system-wise adoption of the Kocks-Mecking theory. Abstract: 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.