A data driven approach for cross-slip modelling in continuum dislocation dynamics. (May 2023)

• Record Type: Journal Article
• Authors: Vivekanandan, Vignesh; Anglin, Benjamin; El-Azab, Anter
• Is Part Of: International journal of plasticity. Volume 164(2023)
• Publication Date: 2023-05
• Subjects: Plasticity -- Periodicals; Plasticité -- Périodiques; Plasticity; Periodicals; 620.11233
• DOI: 10.1016/j.ijplas.2023.103597
• Languages: English
• ISSNs: 0749-6419

Abstract

Highlights: A novel data driven approach to model cross-slip in continuum dislocation dynamics (CDD) was proposed. Statistics of screw segment length and stress fluctuation were found to follow exponential and Lorentzian distribution respectively. Different cross-slip activation energy formulations yielded different cross-slip rates in CDD simulations. However, its impact on stress-strain response and dislocation density evolution in CDD simulations were found to be minimal for the [001] monotonic loading case. Cell-like structure was observed in the dislocation microstructure predicted by CDD after relaxation. Abstract: Cross-slip is a thermally activated process by which screw dislocation changes its glide plane to another slip plane sharing the same Burgers vector. The rate at which this process happens is determined by a Boltzmann type expression that is a function of the screw segment length and the stress acting on the dislocation. In continuum dislocation dynamics (CDD), the information regarding the length of the screw dislocation segment and local stress state on dislocations are lost due to the coarse-grained representation of the density. In this work, a data driven approach to characterize the lost information by analyzing the discrete dislocation configurations is proposed to enable cross-slip modeling in the CDD framework in terms of the coarse-grained dislocation density and stress fields. The analysis showed that the screw segment length follows an exponential distribution, and the stress fluctuations, defined as the difference between the stress on the dislocations and the mean field stress in CDD, follows a Lorentzian distribution. A novel approach for cross slip implementation in CDD employing the screw segment length and stress fluctuation statistics was proposed and rigorously tested by comparing the CDD cross-slip rates with discrete dislocation dynamics (DDD) rates. This approach has been applied in conjunction with three cross-slip models used in DDD simulations differing mainly in the functional form of cross slip activation energy. It was found that different cross-slip activation energy formulations yielded different cross-slip rates, yet the effect on mechanical stress-strain response and dislocation density evolution was minimal for the [001] type loading.