Mechanism for unconventional nonlinear elasticity

Materials either have a high hardness or excellent ductility, but rarely both at the same time. ${\mathrm{Mo}}_2\mathrm{BC}$ is one of the only crystalline materials that simultaneously has a high Vickers hardness and is also moderately ductile. The origin of this unique balance is revealed here using stress-strain calculations. The results show an anisotropic nonlinear elastic response including an intermediate tensile strain-stiffening behavior and a two-step sequential failure under shear strain that resembles the behavior of soft materials such as biological systems or polymer networks rather than hard, refractory metals. The mechanism of the unusual nonlinear elasticity is established by analyzing changes in the electronic structure and the chemical bonding environments under mechanical perturbation. The optimized structure under extreme strain shows the formation of a pseudogap in DOS and dimerization of the structure's boron-boron zigzag chain. These mechanisms delay the ultimate failure, establishing a pathway for developing the next generation of structural materials with high hardness and ductility.

Figure 1

(a) Crystal structure of ${\mathrm{Mo}}_2\mathrm{BC}$. (b) Calculated stress-strain curves for various crystallographic directions during applied tension. (c) Stress-strain curve for various shear systems.

Figure 2

The stress-strain curve for [001] in ${\mathrm{Mo}}_2\mathrm{BC}$ is segmented into three interdependent stages. (a) Stage 1 of the stress-strain curve is plotted with the highlighted strain steps corresponding to (b) the density of states (DOS) of stage 1. (c) shows stage 2 with the color-coded points corresponding to (d) the DOS of stage 2. (e) Stage 3 shows the final stage of the stress-strain curve and the colors correspond to (f) different strain steps in the DOS of stage 3.

Figure 3

(a) Stacked snapshots of the crystal structure of ${\mathrm{Mo}}_2\mathrm{BC}$ during $\left(111\right)\left[\overline{1}\overline{1}2\right]$ deformation at shear strain steps of 0, 0.05, 0.13, 0.18, 0.22, and 0.26. (b) Stress-strain behavior of ${\mathrm{Mo}}_2\mathrm{BC}$ under $\left(111\right)\left[\overline{1}\overline{1}2\right]$ shear deformation and (c) $-\mathrm{ICOHP}$ values as a function of strain during $\left(111\right)\left[\overline{1}\overline{1}2\right]$ shear for various interactions.