Leaving the Slip System ‐ Cross Slip in Continuum Dislocation Dynamics. Issue 1 (4th September 2019)

• Record Type: Journal Article
• Authors: Weger, Benedikt; Hochrainer, Thomas
• Other Names: Eberhardsteiner J. guestEditor.; Schöberl M. guestEditor.
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 19:Issue 1(2019)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2019-09-04
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201900441
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: Dislocations are the main contributors to plastic deformation of crystalline materials. An important step towards the description of hardening behavior is the consideration of cross slip, as it drives the exchange of dislocations between slip systems, thus playing a major role in dislocation multiplication or annihilation. In density based continuum theories of dislocations, dislocations are usually considered closed curves within their slip planes. Recent discrete dislocation dynamics simulations, however, suggest that only a small fraction of dislocations is actually closed on a single slip system, due to cross slip and dislocation reactions. We therefore investigate how the kinematics of moving open curves can be considered in dislocation density based models. The assumption of open planar curves leads to modified evolution equations for the dislocation state variables. These extended evolution equations are presented for the theory of geometrically necessary dislocations (GND) and for the higher dimensional continuum dislocation dynamics theory (hdCDD). The resulting equations are checked for plausibility by numerical calculations using the finite volume method.