Shear response of $\Sigma 3\{112\}$ twin boundaries in face-centered-cubic metals

Molecular statics and dynamics simulations were used to study the mechanisms of sliding and migration of Σ3{112} incoherent twin boundaries (ITBs) under applied shear acting in the boundary in the face-centered-cubic (fcc) metals, Ag, Cu, Pd, and Al, of varying stacking fault energies. These studies revealed that (i) ITBs can dissociate into two phase boundaries (PBs), bounding the hexagonal 9$R$ phase, that contain different arrays of partial dislocations; (ii) the separation distance between the two PBs scales inversely with increasing stacking fault energy; (iii) for fcc metals with low stacking fault energy, one of the two PBs migrates through the collective glide of partials, referred to as the phase-boundary-migration (PBM) mechanism; (iv) for metals with high stacking energy, ITBs experience a coupled motion (migration and sliding) through the glide of interface disconnections, referred to as the interface-disconnection-glide (IDG) mechanism.

Figure 1

Dichromatic pattern of a [110]Σ3{112}∥{112} twin boundary showing the atomic structure of the boundary: (a) Dichromatic pattern of an ITB containing a set of partial dislocations on every (111) plane with a repetitive sequence $b_2:b_1:b_3$, and (b) the equivalent bicrystal structure of an ITB. The dashed lines outline the boundary atoms belonging to two grains. (c) Plan view of (111) plane stacking and three partials. $b_1$ is a pure edge dislocation, $b_2$ and $b_3$ are mixed partial dislocations with opposite sign screw components. (d) Schematic illustration of the glide of the three partials to create a twin. The length units are $|\frac{a}{2}[112]|$ for the $x$ axis and $|\frac{a}{3}[111]|$ for the $y$ axis. The solid symbols represent atoms in grain $\alpha$ and the empty symbols represent atoms in grain $\beta$. The repeatable pattern with a unit involving three {111} planes is delineated by solid lines. The sense vector $\mathit{\xi }$ points out of the figure in this and the following figures. The black symbols in (d) represent the initial (111) plane stacking in a perfect crystal and the red symbols represent the final (111) plane stacking in the twinned crystal.

Figure 2

Simulation setup for MD: (a) initial ITB created through the glide of partials on every (111) plane, and (b) schematic illustration of the dissociation of partials in the initial ITB, resulting in two phase boundaries comprising different arrays of partials.

Figure 3

Relaxed atomic structures of Σ3{112} IGBs under zero applied stress, showing (a) atomic structure in Cu, and (b) atomic structure in Al. Different atom colors represent different excess potential energies.

Figure 4

Disregistry plots of the three partial dislocations in an ITB:(a) in Cu and (b) in Al. From this plot, the size of the dissociation region can be determined as half of the magnitude of the $x$ component of Burgers vector of partial b${}_1$. The results are summarized in Table .

Figure 5

Interface disconnection glide mechanism of ITBs. Dichromatic pattern of a [110]Σ3{112}∥{112} twin boundary showing the atomic structure after the lower part of grain $\beta$ (symbolized with empty circles and triangles) shifts upward with a magnitude of $\frac{2}{3}[111]$. The black dashed line indicates the location of the initial ITB and the red dashed line indicates the final location of the ITB. The solid symbols represent atoms in grain $\alpha$ and the empty symbols represent atoms in grain $\beta$. The length units are $|\frac{a}{2}[112]|$ for the $x$ axis and $|\frac{a}{3}[111]|$ for the $y$ axis.

Figure 6

Possible kinetics processes involved in the glide of interface disconnection. (a) Red solid spheres move upward ($\frac{2}{3}[111]$) to red empty circles; (b) red solid spheres move to blue triangles, and blue triangles move to red empty circles, corresponding to a synchroshear shuffle mechanism. The length units are $|\frac{a}{2}[112]|$ for the $x$ axis and $|\frac{a}{3}[111]|$ for the $y$ axis.

Figure 7

Mechanical response of ITBs in Ag, Cu, Pd, and Al when the bicrystal model is subjected to shear stresses acting in the ITB plane, revealing two typical stress-strain behaviors that correspond to the two different motion mechanisms.

Figure 8

Phase-boundary-migration (PBM) mechanism verified in Cu by MD simulation. (a) Atomic structure of the dissociated Σ3{112} ITBs in Cu under applied shear stress, showing the migration of PB${}_2$ through a collective glide of partials ${\mathit{b}}_1$, and (b) shear stress and dissociation distance of the emitted partial dislocation from the initial boundary as a function of applied displacement gradients. Atoms are colored by their excess potential energies. The 9$R$ phase is the region between the two PBs. The angle θ is 13.0°.

Figure 9

Interface disconnection glide mechanism verified in Al by MD simulation. (a) Atomic structure of an ITB before the glide of one disconnection, and (b) atomic structure of the ITB after the glide of one disconnection. Atoms are colored by their excess potential energies.

Figure 10

Vector plot shows atom displacements in association with the glide of one disconnection. The length units are $|\frac{a}{2}[112]|$ for the $x$ axis and $|\frac{a}{3}[111]|$ for the $y$ axis.