A triple-scale crystal plasticity modeling and simulation on size effect due to fine-graining

In this paper, a triple-scale crystal plasticity model bridging three hierarchical material structures, i. e., dislocation structure, grain aggregate and practical macroscopic structure is developed. Geometrically necessary (GN) dislocation density and GN incompatibility are employed so as to describe isolated dislocations and dislocation pairs in a grain, respectively. Then the homogenization method is introduced into the GN dislocation-crystal plasticity model for derivation of the governing equation of macroscopic structure with the mathematical and physical consistencies. Using the present model, a triple-scale FE simulation bridging the above three hierarchical structures is carried out for f. c. c. polycrystals with different mean grain size. It is shown that the present model can qualitatively reproduce size effects of macroscopic specimen with ultrafine-grain, i. e., the increase of initial yield stress, the decrease of hardening ratio after reaching tensile strength and the reduction of tensile ductility with decrease of its grain size. Moreover, the relationship between macroscopic yielding of specimen and microscopic grain yielding is discussed and the mechanism of the poor tensile ductility due to fine-graining is clarified.