Extreme Mechanics of Probing the Ultimate Strength of Nanotwinned Diamond

Recently synthesized nanotwinned diamond (NTD) exhibits unprecedented Vickers hardness exceeding 200 GPa [Q. Huang et al., Nature (London) 510, 250 (2014)]. This extraordinary finding challenges the prevailing understanding of material deformation and stress response under extreme loading conditions. Here we unveil by first-principles calculations a novel indenter-deformation generated stress confinement mechanism that suppresses the graphitization or bond collapse failure modes commonly known in strong covalent solids, leading to greatly enhanced peak stress and strain range in the indented diamond lattice. Moreover, the twin boundaries in NTD promote a strong stress concentration that drives preferential bond realignments, producing a giant indentation strain stiffening. These results explain the exceptional indentation strength of NTD and offer insights into the extreme mechanics of the intricate interplay of the indenter and indented crystal in probing ultrahard materials.

Figure 1

Calculated stress-strain relations of cubic diamond compressed along various directions.

Figure 2

(a) A sketch of indentation stress conditions and the relation between the shear stress ${\sigma }_{zx}$ and normal stress ${\sigma }_{zz}$ beneath the indenter. (b) Calculated stress-strain relations of cubic diamond in the easy $\mathbf{(}(111)[11\overline{2}]\mathbf{)}$ and hard $\mathbf{(}(111)[\overline{11}2]\mathbf{)}$ directions under pure shear (${\sigma }_{zz}^{\max }=0$), constrained shear (${\sigma }_{zz}^{\max }=200\mathrm{GPa}$), and Vickers shear. Also shown are the snapshots of cubic diamond deformed in the hard $\mathbf{(}(111)[\overline{11}2]\mathbf{)}$ direction right before and after (c) graphitization under pure shear, (d) bond collapse under Vickers shear, and (e) a new bond breaking mode under the constrained (V200 GPa) shear.

Figure 3

(a) The top and front view of the NTD-9 unit cell at equilibrium ($\epsilon =0$). The red and black arrows indicate various crystalline directions in NTD-9, while the green arrows show the equivalent directions in cubic diamond. (b),(c) Calculated stress-strain curves of NTD-9 under various tensile directions and the indentation shear deformation in the (001)[110] direction with ${\sigma }_{zz}^{\max }=0$ (pure shear), ${\sigma }_{zz}^{\max }=200\mathrm{GPa}$ (compressible Vickers indentation), and ${\sigma }_{zz}^{\max }\to \infty$ (incompressible Vickers indentation). (d),(e),(f) Structural snapshots of NTD-9 under compressible Vickers indentation in the (001)[110] shear direction at $\epsilon =0.23$ and 0.235 right before and after the initial twin boundary movement by one atomic layer and at $\epsilon =0.515$ when all the C-C bonds are aligned in the hard shear direction.