Interaction mechanism between edge dislocations and asymmetrical tilt grain boundaries investigated via quasicontinuum simulations

The interactions between edge dislocations and grain boundaries—dislocation pileup, dislocation absorption, and dislocation transmission—are studied by performing quasicontinuum simulations. The $⟨112⟩$ asymmetrical tilt grain boundaries with different misorientation angles are used. The atomic configurations and stress fields of equilibrium and nonequilibrium asymmetrical grain boundaries are investigated in detail by comparison with analytical models. The influence of the grain boundary structure on the stress concentration due to dislocation pileup and the accommodation of extrinsic dislocations in the grain boundaries are also examined by using low- and high-angle grain boundaries. The critical forces on the dislocation in small-angle tilt grain boundaries for it to eject from the boundaries are evaluated by atomic simulations, and the results are compared with dislocation theory. It is also found that the rearrangement of the grain boundary dislocations with local grain boundary sliding in the local region, where the extrinsic dislocation is absorbed, is the characteristic accommodation mechanism of low-angle asymmetrical grain boundaries. The effects of the interaction between dislocations and grain boundaries on the mechanical properties of coarse-grained metals with dislocation sources in their grain and on those of nanocrystalline metals without sources in their grain are also discussed.

Figure 1

Atomic configuration of the analysis model comprising two grains—$A$ and $B$. The misorientation angle $\theta$ is set to $13.0°$. Magnified images in the vicinity of the (a) crack tip and (b) grain boundary. Light, medium, and dark gray atoms represent “nonlocal,” “local,” and “quasinonlocal” atoms, respectively. Dimensions along the $X,$ $Y,$ and $Z$ directions are approximately 24, 55, and $200\mathrm{nm}$, respectively.

Figure 2

(Color online) Distributions of the shear stress ${\tau }_{ZY}$ in the vicinity of the grain boundary expressed by the full atomistic resolution and the quasicontinuum methods in model 1. (a) Atomic configurations in the full atomistic model, and (b) shear stress in the square region shown in Fig. 2a.

Figure 3

(Color online) Asymmetrical tilt grain boundary structures of two (112) atomic planes in different analysis models. (a) Model 1, $\theta =13.0°$; (b) model 2, $\theta =29.5°$; (c) model 3, $\theta =63.0°$; and (d) model 4, $\theta =89.3°$. Open, red (dark gray), and blue (black) circles represent atoms in the local fcc, hcp, and defect environments, respectively. Two sets of grain boundary dislocations shown in green (dark gray) and magenta (light gray) can be observed in the low-angle tilt grain boundaries. Solid lines represent the actual asymmetrical grain boundary planes, and red (dark gray) broken lines represent the symmetrical grain boundary planes. Black thin broken lines in atomic configurations indicate the slip planes of the incoming dislocations from the crack tip. (d) Schematic of the tilt grain boundary composed of two sets of uniformly spaced edge dislocations $D_1$ and $D_2$.

Figure 4

(Color online) Distributions of shear stress ${\tau }_{ZY}$ around the tilt grain boundary in model 2 under no external applied stress. (a) The tilt grain boundary is composed of only IGBDs, as shown in Fig. 3b—equilibrium grain boundary. (b) Tilt grain boundary with the same misorientation angle of model 2 but containing an EGBD—nonequilibrium grain boundary. The detailed atomic configuration of the grain boundary with one EGBD is almost the same as that shown in Fig. 9b.

Figure 5

(Color online) Interactions between lattice edge dislocations from the crack tip and asymmetrical tilt grain boundaries under shear deformation. (a) Model 1, $\theta =13.0°$, ${\gamma }_{ZY}=0.024$; (b) model 2, $\theta =29.5°$, ${\gamma }_{ZY}=0.034$; (c) model 3, $\theta =63.0°$, ${\gamma }_{ZY}=0.034$; and (d) model 4, $\theta =89.3°$, ${\gamma }_{ZY}=0.036$. (e)–(h) Model 2, ${\gamma }_{ZY}=0.010$, 0.012, 0.020, and 0.028, respectively. Atoms in the local hcp and defect environments are shown in brown (dark gray) and gray (light gray), respectively. Defect atoms in the grain boundary regions are shown as transparent atoms.

Figure 6

(Color online) Relationship between shear stress and shear strain ${\gamma }_{ZY}$. (a) Macroscopic shear stress is estimated by using the average shear stress ${\tau }_{ZY}$ in regions including the grain boundary: $-30\le Y\le 50\mathrm{nm}$. (b) Local shear stress is estimated by using ${\tau }_{ZY}$ in the stress concentration region produced by the dislocation pileup: $0\le Y\le 5\mathrm{nm}$ and $-2.5\le Z\le 2.5\mathrm{nm}$. “$+$” represents the local shear stress ${\tau }_{z^B{y}^B}$ in the region of the five Burgers vectors in front of the extrinsic grain boundary dislocation in model 1.

Figure 7

Force on the middle edge dislocation in a finite array of edge dislocations. Thick lines represent the force in the finite array and the thin lines represent the interaction force between the parallel dislocations with parallel Burgers vectors.

Figure 8

(Color online) Atomic configurations of the tilt grain boundary in model 1 under shear deformation: ${\gamma }_{ZY}=$ (a) 0.002, (b) 0.012, and (c) 0.024.

Figure 9

(Color online) Atomic configurations of the tilt grain boundary in model 2 under shear deformation: ${\gamma }_{ZY}=$ (a) 0.002, (b) 0.012, and (c) 0.028. The distributions of ${\tau }_{ZY}$ in the vicinity of the grain boundaries of (a) and (b) after the removal of ${\gamma }_{ZY}$ are shown in Fig. 4.

Figure 10

(Color online) Atomic configurations of the tilt grain boundary in model 3 under shear deformation: ${\gamma }_{ZY}=$ (a) 0.002, (b) 0.012, and (c) 0.026.

Figure 11

(Color online) Atomic configurations of the tilt grain boundary in model 4 under shear deformation: ${\gamma }_{ZY}=$ (a) 0.002, (b) 0.012, and (c) 0.028.