A theory of subgrain dislocation structures
The authors construct a micromechanical theory of dislocations and finite-deformation single-crystal plasticity on the basis of a direct generalization of deformation microstructures and the computation of the attendant effective behavior. The final purpose is the description of lamellar dislocation structures that develop at large strains under monotonic loading. The authors use a constructive approach in that they exploit an explicit construction of microstructures by recursive lamination and their subsequent equilibration in order to relax the incremental constitutive description of the material. Dislocation structures are related to the plastic deformation gradient via the Nye-Kroener's formula for dislocation density tensor. Nonlocality is introduced by accounting for the self-energy of dislocations. Applications of the theory are given to the generation of complex microstructures. Among the predictions obtained is the effective behavior of crystal to stiffen with decreasing sample size in accordance with experimental observations. The present theory differs from the fashionable strain-gradient theories of plasticity in that the said size effect occurs for nominally uniform macroscopic deformations, and the dimension of microstructures depend sensitively on the loading geometry, the extent of macroscopic deformation, and the size of the sample. An interesting remark concerns the obtained expression for the configurational force which relates it to the orientation of dislocation walls. Also, recursive algorithms are given explicitly.
finite-deformation single-crystal plasticity
scientific article; zbMATH DE number 1513352
scientific article