Crystal Plasticity Analysis of Non-uniform Deformation in Symmetric Type Bicrystals under Tensile Load and Formation of Geometrically Necessary Dislocation Bands

Abstract

Slip deformation in symmetric type bicrystal models subjected to tensile load is analyzed by a finite element crystal plasticity analysis code and accumulation of geometrically necessary dislocations (GNDs) is studied in detail. Uniform deformation was expected to take place because mutual constraint of crystal grains through the grain boundary plane does not occur in symmetric type bicrystals, but, some results of the analysis show non-uniform deformation and the high density of GNDs accumulated in the form of band. Such kind of non-uniform deformation is observed regardless of the model size and the strain-hardening characteristics. Mechanism of non-uniform deformation and accumulation of GNDs in the form of band in the symmetric type bicrystals is discussed from the viewpoint of the boundary condition and shape change of grains after slip deformation

Grain Boundary Accumulation of Geometrically Necessary Dislocations and Asymmetric Deformations in Compatible Bicrystals with Tilted Angle Grain Boundary under Tensile Loading

“…In the previous study, we observed that nonuniform deformation took place with the accumulation of highdensity GN dislocations in the form of bands in symmetric bicrystal models depending on boundary conditions and the combination of the crystal orientation (5), (6) , and that the GN dislocation structure exhibited nonuniform deformation behavior. In this study, we discuss the effect of asymmetric GN dislocation structure formation in bicrystal models with a tilted angle grain boundary on subsequent deformation behavior.…”

“…Grain boundary planes are perpendicular to the x -y planes of the model, which uniformly divide the model into 3 200 finite elements. The continuity requirements of strain components across the grain boundary plane between grains 1 and 2 are given by the following relationships (5), (6) :…”

“…Accordingly, it is considered that the accumulation of geometrically necessary (GN) dislocations with nonuniform deformation is caused by the restraint interaction of deformation through the grain boundary plane. However, under some conditions, nonuniform deformation with a GN dislocation structure occurs in the crystal grain, even if bicrystal models satisfy the requirement (3), (4) in which the mutual constraint of crystal grains through the grain boundary plane does not occur (5), (6) . In our previous study, we concluded that the accumulation of GN dislocations is caused by the incompatibility of shape change (5), (6) , and that the GN dislocation structure that grows inside the crystal grain expands nonuniformly to form macroscopic deformation (6) .…”

“…However, under some conditions, nonuniform deformation with a GN dislocation structure occurs in the crystal grain, even if bicrystal models satisfy the requirement (3), (4) in which the mutual constraint of crystal grains through the grain boundary plane does not occur (5), (6) . In our previous study, we concluded that the accumulation of GN dislocations is caused by the incompatibility of shape change (5), (6) , and that the GN dislocation structure that grows inside the crystal grain expands nonuniformly to form macroscopic deformation (6) . In this way, the investigation of bicrystal models is effective for understanding the pair interaction of crystal grains and the effect of crystal grain boundary in which the mutual constraint of crystal grains occur through the grain boundary plane.…”

Multi-Body Interaction of Crystal Grains in Compatible-Type Tricrystals under Tensile Loading and Formation of Disclination-Type Displacement Field

“…We have performed crystal plasticity analysis of tensile deformation in compatible-type bicrystals satisfy the requirement in which the effects of the elastic incompatibility stress and the plastic stain incompatibility does not work (1) (5) , and stated in a previous study that non-uniform deformation with GN dislocation structure correspond to the kink bands and secondary slip bands (6) were formed in the crystal grains depended on the boundary condition of external loading (7) and the initial crystal orientation (8) , even if the grain boundary effect, in which had been thought to be the main cause of the non-uniform deformation, was removed from analysis model. It was described to cause these phenomena by mutually constrained the shape change of the crystal grain due to the slip deformation in the active slip systems by the boundary condition of external load and the grain boundary (6)(7)(8) .…”