Abstract
Continuum dislocation dynamics (CDD) is a single crystal strain gradient plasticity theory based exclusively on the evolution of the dislocation state. Recently, we derived a constitutive theory for the average dislocation velocity in CDD in a phase field-type description for an infinite domain. In the current work, so-called rational thermodynamics is employed to obtain thermodynamically consistent boundary conditions for the dislocation density variables of CDD. We find that rational thermodynamics reproduces the bulk constitutive equations as obtained from irreversible thermodynamics. The boundary conditions we find display strong parallels to the microscopic traction conditions derived by Gurtin and Needleman (M.E. Gurtin and A. Needleman, J. Mech. Phys. Solids 53 (2005) 1–31) for strain gradient theories based on the Kröner–Nye tensor.
Highlights
Size-effects in small-scale plasticity have received much attention in continuum mechanics and materials science, starting with the work of Fleck and co-workers in the mid 1990s [1,2].The continuum modeling of size-effects has since been divided into strain gradient approaches extending phenomenological laws from macroscopic plasticity to incorporate strain gradient effects on the one hand and approaches from materials science which seek continuum descriptions for the evolution of the dislocation state on the other hand
The current paper tries to build a bridge between both approaches, in that the description of the dislocation state and its kinematic evolution law are taken from continuum dislocation dynamics (CDD) theory [11], while the derivation of the microscopic balance equations and the constitutive law for the average dislocation speed are derived from the virtual work principle and energy imbalance in the spirit of Gurtin [6,7]
We find on the one hand a clarification of the boundary conditions for CDD, which have not yet been achieved without abstract continuum mechanics, while the bulk constitutive laws derived for CDD provide a new perspective for phenomenological strain gradient modeling
Summary
Size-effects in small-scale plasticity have received much attention in continuum mechanics and materials science, starting with the work of Fleck and co-workers in the mid 1990s [1,2]. The current paper tries to build a bridge between both approaches, in that the description of the dislocation state and its kinematic evolution law are taken from continuum dislocation dynamics (CDD) theory [11], while the derivation of the microscopic balance equations and the constitutive law for the average dislocation speed (substituting the flow rule from phenomenological approaches) are derived from the virtual work principle and energy imbalance in the spirit of Gurtin [6,7] Through this combined derivation, we find on the one hand a clarification of the boundary conditions for CDD, which have not yet been achieved without abstract continuum mechanics, while the bulk constitutive laws derived for CDD provide a new perspective for phenomenological strain gradient modeling.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
