Fig. 1. Simulation samples. (a)-(j) Nanocrystalline Cu (NC Cu) and graphene-boundary embedded nanocrystalline Cu (GrB/Cu) samples with grain size from 15.96, 12.50, 8.33, 6.53 to 5.39 nm. (a1)-(j1) The equilibrium structures of (a)-(e) NC Cu and (f)-(j) GrB/Cu samples with grain size from 15.96, 12.50, 8.33, 6.53 to 5.39 nm. Grain growth process gradually enhanced with reducing grain size in NC Cu marked by black arrows, while no grain growth was observed in GrB/Cu samples. Atoms are colored by CNA, and green, red and gray atoms indicate fcc, hcp and other structures, respectively. Graphene atoms are rendered purple for convenient observation.

Fig. 2. Equilibrium microstructures. (a) The volume fractions of atoms with tensile and compressive stress in NC Cu and GrB/Cu samples with various grain sizes. (b) The stress distribution of the two samples with grain size of 5.39 nm as an example. The atoms are colored by normal stress in x direction and the color maps in (b) are in unit of GPa; and the change from blue to red corresponds to the transition from compressive stress to tension stress. Only atoms whose stress value larger than 10 GPa (-10 GPa) are shown.

Fig. 3. Mechanical properties. (a) The stress-strain curves of different grain size samples with increasing strain. (b) The relationship between tensile strength and failure strain varying with different grain sizes.

Fig. 4. HP relation. (a) The relation curve between strength and grain diameter. NC Cu samples exhibit HP relation when reduce to 10 nm, then show inverse HP relation. However, GrB/Cu samples always exhibit enhanced HP relation even until very small grain diameter. Black and blue curve represent linear and exponential fitting, respectively. (b)-(c) The HP slope k as a function of grain diameter d and graphene fraction Vf. The dash line represents exponential fitting relation.

Fig. 5. Successive snapshots illustrating the atomic scale tensile deformation mechanism in GrB/Cu samples. Here, atoms are colored based on the CNA, green, red and gray atoms indicate fcc, hcp and other structures, respectively. Graphene atoms are colored by purple for easy observation.

Fig. 6. Dislocation blockage and load bearing behavior in GrB/Cu samples with the grain size of 15.96 nm. (a)-(c) Showing dislocation interaction with interface as strain increases; and (d) load bearing behavior illustrated by graphene layer without Cu atoms. Atoms are colored by normal stress in x direction, color map is in unit of GPa and blue to red means compressive stress to tension stress. Atoms zoom in or out for better observation, large atoms indicating graphene layer, smaller atoms indicating Cu atoms. The dark kinked line where the arrow pointed represents a dislocation.

Fig. 7. Average stress statistically distribution of the interfacial Cu with interior Cu atoms in NC Cu and GrB/Cu samples from the view of x-z plane divided by 100 bins, colored by normal stress in x direction and color map is in unit of GPa, blue to red meaning compressive stress to tension stress. Each picture corresponds to certain grain size with whose grain size gradually reduces from top to bottom. Delete graphene atoms in GrB/Cu samples only to observe the influence on Cu atoms.

Fig. 8. Section-view of microstructures of (a) NC Cu and (b) GrB/Cu at strain of 10 % that atoms colored by CNA, green, red and gray atoms indicating fcc, hcp and other structures, respectively. Graphene atoms are colored by purple for recognition. (c) and (d) are section-view colored based on shear strain corresponding to (a) and (b). The brighter the color, the greater the strain.

Fig. 9. Dislocation density as a function of strain in GrB/Cu samples.

Fig. 10. Grain size dependent Hall-Petch strengthening mechanism in NC Cu and GrB/Cu samples. Purple and dark hexagons indicate GrB/Cu and NC Cu grains, respectively. Different shades of blue represent the magnitude of interfacial stress, the darker the color, the greater the negative stress. CG and UFG represent coarse-grained and ultrafine-grained regimes, respectively.