Kinematic assumptions and their consequences on the structure of field equations in continuum dislocation theory

18th Chemnitz Seminar on Materials Engineering – 18. Werkstofftechnisches Kolloquium

Silbermann, C.B.^1 ; Ihlemann, J.^1

Prof. of Solid Mechanics, Technische Universität Chemnitz, Reichenhainer Straße 70, Chemnitz

09126, Germany^1

关键词: Dislocation ensembles;    Dislocation kinematics;    Dislocation networks;    Geometrically necessary dislocations;    Kinematic assumptions;    Macroscopic deformations;    Numerical implementation;    Thermodynamic state variables;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/118/1/012034/pdf
DOI  :  10.1088/1757-899X/118/1/012034

来源: IOP

【 摘 要 】

Continuum Dislocation Theory (CDT) relates gradients of plastic deformation in crystals with the presence of geometrically necessary dislocations. Therefore, the dislocation tensor is introduced as an additional thermodynamic state variable which reflects tensorial properties of dislocation ensembles. Moreover, the CDT captures both the strain energy from the macroscopic deformation of the crystal and the elastic energy of the dislocation network, as well as the dissipation of energy due to dislocation motion. The present contribution deals with the geometrically linear CDT. More precise, the focus is on the role of dislocation kinematics for single and multi-slip and its consequences on the field equations. Thereby, the number of active slip systems plays a crucial role since it restricts the degrees of freedom of plastic deformation. Special attention is put on the definition of proper, well-defined invariants of the dislocation tensor in order to avoid any spurious dependence of the resulting field equations on the coordinate system. It is shown how a slip system based approach can be in accordance with the tensor nature of the involved quantities. At first, only dislocation glide in one active slip system of the crystal is allowed. Then, the special case of two orthogonal (interacting) slip systems is considered and the governing field equations are presented. In addition, the structure and symmetry of the backstress tensor is investigated from the viewpoint of thermodynamical consistency. The results will again be used in order to facilitate the set of field equations and to prepare for a robust numerical implementation.