Cooperative grain boundary sliding and nanograin nucleation process in nanocrystalline, ultrafine-grained, and polycrystalline solids

A special physical mode of plastic deformation in nanocrystalline, ultrafine-grained, and polycrystalline solids is suggested and theoretically described. The mode represents the cooperative grain boundary (GB) sliding and nanoscale grain nucleation (occurring through stress-driven splitting and migration of GBs) process. It is theoretically revealed that, in certain ranges of parameters of the defect structure under consideration, the special deformation mode is more energetically favorable than both “pure” GB sliding and the previously examined [Bobylev et al., Phys. Rev. Lett. 105, 055504 (2010)] cooperative GB sliding and migration process. In addition, the special deformation mode enhances ductility of nanocrystalline and ultrafine-grained solids, and this enhancing effect is more pronounced compared to that of the cooperative GB sliding and migration process.

Figure 1

Grain boundary deformation processes in nanocrystalline specimen. (a) General view. (b) Initial configuration I of grain boundaries is presented. (c) Configuration II results from “pure” grain boundary sliding that produces a dipole of wedge disclinations A and C (small triangles). (d) Crack forms at the disclination dipole AC and grows into the grain interior. (e) Configuration III results from the cooperative grain boundary sliding and nanograin nucleation process. Grain boundary AB splits into immobile grain boundary (also called AB) and mobile grain boundary DE. The mobile boundary DE migrates under the shear stress and carries nanoscale plastic flow. As a result of the grain boundary splitting and migration, new disclinations D, B, and E are formed, and the strength of the disclination A changes. Value of ${\omega }^{\prime }$ is equal to the tilt misorientation angle of the grain boundary DE. (f) When the disclinations D and E converge, the configuration IV forms, which contains the two disclination dipoles. (g) Crack forms at the disclination dipole BE and grows along a grain boundary fragment.

Figure 2

Grain boundary deformation processes in a coarse- or ultrafine-grained specimen. (a) General view. (b) Initial configuration I′ of grain boundaries is presented. (c) Configuration II′ results from “pure” grain boundary sliding. Dipole of wedge disclinations A′ and C′ (small triangles) is generated. (d) Configuration III′ results from the cooperative grain boundary sliding and nanograin nucleation process. Grain boundary A′B′ splits into immobile grain boundary (also called A′B′) and mobile grain boundary D′E′. The grain boundary D′E′ migrates, and this process is accompanied by the formation of the new grain boundary B′E′. Also, new disclinations D′, B′, and E′ are formed, and the strength of the disclination A′ changes due to the cooperative process under consideration. (e) When the disclinations D′ and E′ converge, the configuration IV′ forms, which contains two disclination dipoles.

Figure 3

The defect configuration consisting of five disclinations is equivalent to the configuration consisting of the disclination dipole AC characterized by the strengths $\pm (\omega -{\omega }^{\prime })$, the disclination dipole DC characterized by the strengths $\pm {\omega }^{\prime }$ and the disclination dipole BE characterized by the strengths $\pm {\omega }^{\prime }$.

Figure 4

Map of the energy change $\Delta W(x,y)$, calculated in the intervals of 2 nm $<x\le d$ and 2 nm $<y\le x$, in nanocrystalline Ni, for $R=3d$, $\varphi =2\pi /3$, $\tau =0.05D$, $d=10$ nm, $\omega =0.3$, ${\omega }^{\prime }=\omega /2$. Values of $\Delta W$ are shown in units of ${10}^{-2}D{d}^2$.

Figure 5

Competition between grain boundary sliding and cooperative grain boundary sliding and migration process. (a) Initial configuration of grain boundaries is presented, which enhances cooperative grain boundary sliding and migration process. Grain boundary AB is a low-angle tilt boundary that consists of periodically arranged lattice dislocations whose Burgers vectors are oriented from the left to the right. (b) GB sliding occurs, which produces the dipole of (+ω) disclination A (full triangle), and (−ω) disclination C (open triangle). (c) The shear stress τ drives the dislocations to slip to the right direction, and the low-angle tilt boundary AB migrates cooperatively with GB sliding. (d). Initial configuration of grain boundaries is presented, which enhances pure grain boundary. Grain boundary AB is a low-angle tilt boundary that consists of periodically arranged lattice dislocations whose Burgers vectors are oriented from the right to the left. (e) GB sliding occurs which produces the dipole of (−ω) disclination A (open triangle) and (+ω) disclination C (full triangle). (f) The shear stress τ drives the dislocations to slip to the left direction, but this migration is forbidden because it highly increases both the disclination strain energy as well as the length and thereby energy of the migrating boundary.

Figure 6

The area plot, for nanocrystalline Ni deformed at $\tau =0.05D$, illustrating the ranges of parameters $d$ (grain size) and ω (strength magnitude of disclinations at migrating grain boundary), where either the cooperative grain boundary sliding and nanograin nucleation process or the cooperative grain boundary sliding and migration processes dominates.

Figure 7

Dependences of mean plastic strain, for nanocrystalline Ni on (a) applied stress $\tau$, for $\omega =0.25$; and (b) disclination strength $\omega$ at $\tau =0.8$ GPa. Other parameters are as follows: $R=3d$, $\varphi =2\pi /3$, $d=15$ nm. Solid curves $\langle {\varepsilon }_{\mathrm{CGBSNN}}\rangle$ correspond to the dependences in the case of the cooperative grain boundary sliding and nanograin nucleation process (with ${\omega }^{\prime }=\omega /2$), dotted curves $\langle {\varepsilon }_{\mathrm{CGBSM}}\rangle$ to the cooperative grain boundary sliding and migration process, dashed curves $\langle {\varepsilon }_{\mathrm{GBS}}\rangle$ to pure grain boundary sliding.