Scaling of maximum strength with grain size in nanotwinned fcc metals

Engineers usually face the difficulty of making careful choices between one good and another in terms of strength, ductility, and electrical conductance in nanostructured metals. The emergence of polycrystalline Cu with ultrafine grains and the included nanotwins supplies an ideal solution because such materials owe high strength, high electrical conductance, and intermediate ductility. We answer in this Brief Report where the strength of such materials maximizes and how it depends on grain size. Based on the competitive plastic deformation mechanisms—the strengthening mechanism by inclined dislocations (with respect to twin planes) and detwinning-induced softening—we find that the critical twin thickness where the strength maximizes is proportional to $d^{1/2}$ and the maximum strength is proportional to $d^{-1/2}$.

Figure 1

Planar view of typical nucleated partial dislocations in nanotwinned fcc metals from molecular dynamics simulations (gray: atoms in fcc lattice; orange: atoms of other type). Snapshots are abstracted from MD simulations on polycrystalline nanotwinned Cu reported in Ref. 22, where details about those simulations could be found. (a) A twinning partial (indicated by the arrow in the cycle) residing in twin planes and moving parallel to the twin planes in a sample with narrow twins; (b) inclined partial dislocations (with respect to twin planes) in a sample with wide twins.

Figure 2

Yield strength (experiments and modeling) versus twin thickness for nt-Cu. Experimental data replotted from Ref. 12, theoretical data from Eqs. (1) and (2b), where one parameter has been fitted ($\alpha$ and n, respectively). The critical shear strengths are multiplied by the Taylor factor of 3 to convert them to tensile strengths.

Figure 3

Predicted grain size versus the transitional twin thickness where the strength nt-Cu maximizes. The prediction by Eq. (6) that matches well with the experimental data comes from Ref. 12 and those from MD simulations Ref. 22.

Figure 4

Predicted grain size versus the maximum strength in nt-Cu using Eq. (7) that matches well with the experimental data comes from Ref. 12 and those from MD simulations Ref. 22.