Anisotropic size effect in strength in coherent nanowires with tilted twins

When materials are deformed plastically via dislocations, a general finding is that samples with smaller dimensions exhibit higher strengths but with very limited amount of plasticity in tension. Here we report that one-dimensional coherent nanostructures with tilted internal twins exhibit anisotropic size effect: their strengths show no apparent change if only their thicknesses reduce, but become stronger as the sample sizes are reduced proportionally. Large-scale molecular dynamics simulations show that such nanowires deform primarily through twin migration mediated by partial dislocations in one active slip system, and a large amount of plasticity could be achieved in such nanowires via twin migration. The unique structure shown here is suitable to explore strengthening mechanisms in metals when plasticity is controlled by a single dislocation slip system. This study also suggests a novel approach to modulate strength and ductility in one-dimensional coherent nanostructures.

Figure 1

Nanowires with tilted twins in tension. (a) The geometry of a face center cubic nanowire with thickness direction along $\left[\overline{\mathbf{1}}\mathbf{10}\right]$. Shadowed planes in the middle refer to twin boundaries, and twin planes are tilted by an angle θ with respect to the wire/loading axis. Twins are spaced by a uniform distance λ. (b) Average flow stresses versus twin spacings for NWs of $W$ = 30 nm and $h$ = 25.6 nm. For here and in what follows, flow stresses are averaged over engineering strain from 5% to 20% from a stress-strain curve; error bars represent the standard deviation from statistical analyses with 150 sampling points.

Figure 2

Stress-strain behaviors for NWs with $W$ = 30 nm and λ = 20 nm as their thicknesses decrease. (a) Stress-strain curves. (b) Average flow stresses versus sample width. No apparent size effect in strength is observed if we only reduce sample thicknesses.

Figure 3

Strengthening in self-similar wires with sample width from 30 to 6 nm while keeping $W$/$h$ and $W$/λ ratios constant. (a) Stress-strain curves for several wire widths: W/h = 1.2 and $W$/λ = 1.5 (left) and W/h = 5 and W/λ = 5 (right). (b) Average flow stresses versus wire width for W/h = 1.2 and W/λ = 1.5 and W/h = 5 and W/λ = 5. Smaller-being-strong size effect in strength is observed if we reduce all sample dimensions proportionally.

Figure 4

Detwinning in $W$ = 30 nm and λ = 1.88 nm NWs (plane strain deformation). Here color grey, red, and blue are used to identify perfect atoms, atoms in stacking faults, and atoms of other types, respectively. (a) The sample after relaxation; (b) atomic snapshot of the sample deformed by 10% strain; (c) atomic snapshot of the sample deformed by 20% strain.

Figure 5

Dislocation activities in $W$ = 30 nm, $h$ = 25.6 nm, and λ = 1.88 nm NWs at 10% strain. (a) Dislocation pattern (CD: curved dislocation, D-loop: dislocation loop). (b) to (e) Nucleation, extension, bow-out, and absorption of a twinning partial in the twin plane. (b) Formation of the twinning partial from the sample edge. (c) Extension of the twinning partial, with one end moving along $\left[\mathbf{11}\overline{\mathbf{2}}\right]$ direction ($x$ axis) and the other gliding along $\left[\overline{\mathbf{1}}\mathbf{10}\right]$ direction (y axis). (d) One end being pinned by the side wall as the dislocation bows out. (e) Absorption of the twinning partial at the opposite surface.

Figure 6

Finite-element simulations on the deformation in wires with tilted twins. (a) Contour for resolved shear stress in (111) plane along $\left[\mathbf{11}\overline{\mathbf{2}}\right]$ direction before plastic deformation. Only the middle portion of the sample is shown. The stress is normalized by the macroscopic average shear stress in (111) $\left[\mathbf{11}\overline{\mathbf{2}}\right]$ slip system. There is clear stress-concentration at the junctions of a twin plane and sample surfaces. (b) Stress-strain curve from finite element simulation. After the initial yielding, a constant flow stress is shown. (c) Contour for resolved plastic shearing strain in (111) plane along $\left[\mathbf{11}\overline{\mathbf{2}}\right]$ direction at the end (normalized by the applied 5% total strain). It is noted that due to the polar nature of plastic shearing by leading partial dislocations in (111) $\left[\mathbf{11}\overline{\mathbf{2}}\right]$ systems, plastic deformation only occurs in those twinned regimes.

Figure 7

Construction of infinite arrays of image dislocations (in red and green) to ensure traction-free surfaces in the thin film with width $W$ when a dislocation is nucleated (in blue). Those image dislocations in red would result in a net force $F_x$ to the nucleated dislocation; and the green ones would cancel each other and have no contribution to $F_x$.