Interaction of a dislocation pileup with {332} tilt grain boundary in bcc metals studied by MD simulations

The sustainability and capacity of macroscopic deformation by polycrystalline metals and metallic alloys is controlled by the propagation of dislocation-mediated slip through grains. In this paper, the interaction of a pileup of $1/2\langle 111\rangle$ dislocations with the $\left\{332\right\}$ tilt grain boundary (GB) is studied as a function of temperature in three bcc metals: iron (Fe), chromium (Cr), and tungsten (W). The interaction results in the transformation of the crystal dislocation into GB dislocations. The $\left\{332\right\}$ tilt GB absorbs the crystal dislocations of the pileup, neither the transmission nor reflection of dislocations was observed. The reaction product at the GB is determined by the crystallography of the GB and the features of the crystal dislocations involved, specifically, the orientation of the Burgers vector and the glide plane of the dislocation. In general, the decomposition results in the formation of a sessile GB dislocation with a riser that facets the GB and several elementary disconnections that glide away. In some cases, the riser increases its length with the number of dislocations absorbed and a new asymmetrical grain boundary of $\left\{112\right\}/\left\{110\right\}$ type is created. For a given external shear stress, the number of dislocations absorbed depends on the orientation of the Burgers vector, glide plane of the pileup, and material.

Figure 1

Schematics of the dislocation reactions at the GB: (a, b) Absorption of the pileup dislocation (black) and split into sessile GBD (red) and several elementary disconnections (green) that step the interface several planes in both grains. (c) Transmission and (d) reflection with emission of elementary disconnections. The arrows indicate the sense of motion.

Figure 2

Snapshot of MD simulation of a GB with marked selected groups of atoms. Each group is a pair of regions lying below and above glide planes. See text for details. The insert shows an example of reaction with group no. 2 around it.

Figure 3

Dichromatic pattern of (332) GB. Black sites (upper grain), white sites (lower grain). Bv of crystal dislocations: Edge =1, 2, 5, and 6; Mixed = 7, 8, 9, and 10. Disconnections: $3={\mathbf{b}}_{2/2}$ and $4={\mathbf{b}}_{-2/-2}$ stepping the interface up and down, respectively. Red and blue vectors are translation vectors of $\lambda$ and $\mu$ crystals: their difference is ${\mathbf{b}}_{-2/-2}$. The unit cells of both crystals are included.

Figure 4

Snapshots of the interaction of the DPU with the $\left\{332\right\}$ GB in Fe at $T=300$ K. (a) After the absorption of the first dislocation of the pileup. (b) After the absorption of the second dislocation. (c) Before the absorption of the third dislocation. (d) After the absorption of the third dislocation.

Figure 5

Dichromatic pattern with possible Bv's of GBDs with core riser for a different number of absorbed dislocations (a) ${\mathbf{b}}_{2/0}$ and (b) ${\mathbf{b}}_{-2/0}$. Black horizontal lines indicate the GB. Black arrows are Bv's of pileup dislocations. Arrows from black to white sites are Bv's of GB defects. Examples of reactions (green circles) are shown for (a) no. 2 and (b) no. 12.

Figure 6

Shear stress, measured in the interaction region no. 2, for the absorption of the pileup dislocations ${\mathbf{b}}_{2/0}$ and ${\mathbf{b}}_{-2/0}$ vs temperature for (a) Fe and (b) Cr.

Figure 7

(a) First dislocation of pileup after relaxation (no absorption). (b) First dislocation is absorbed under the stress of the second dislocation. (c) Second dislocation absorbed under the stress of the third dislocation.

Figure 8

Dichromatic pattern with possible Bv's of GBDs with core riser for a different number of absorbed mixed dislocations. (a) ${\mathbf{b}}_{1/0}$ dislocation and the GBD associated (from no. $22$ to no. 25). In the top ina green circle it includes the dislocations ${\mathbf{b}}_{4/0}$ and ${\mathbf{b}}_{-4/0}$ with the only GBD associated (no. 19). (b) ${\mathbf{b}}_{-1/0}$ dislocation and the GBD associated (no. $20$ and no. 21). Black horizontal lines indicate the GB. Arrows from white to black sites are Bv's of GB defects. An example of reaction is shown on (a): $2{\mathbf{b}}_{1/0}=\frac{1}{11}\left[3\overline{3}\overline{2}\right]+\left[110\right]+6\frac{1}{22}\left[\overline{1}1\overline{3}\right]$.

Figure 9

Snapshots of the interaction of the mixed dislocation DPU with the GB. ${\mathbf{b}}_{-1/0}$: before (i) during (ii) and after (iii) interaction. ${\mathbf{b}}_{1/0}$: first dislocation is absorbed (i) before absorption of second dislocation (ii) and after absorption of second dislocation (iii): notice the riser is parallel to the glide plane.

Figure 10

(a) Local shear stress along the glide plane for the absorption of the first mixed dislocation as a function of the temperature and the orientation of the Bv. (b) Shear stress for absorption of first and second ${\mathbf{b}}_{1/0}$ dislocations.

Figure 11

Shear stress (normalized with the shear modulus) necessary for the absorption of a pileup with glide plane at 29.5 degrees of the GB.