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An efficient strategy that can guide the synthesis of materials with superior mechanical properties is important for advanced material/device design. Here, we report a feasible way to enhance hardness in transition-metal monocarbides (TMCs) by optimally filling the bonding orbitals of valence electrons. We demonstrate that the intrinsic hardness of the NaCl- and WC-type TMCs maximizes at valence electron concentrations of about 9 and 10.25 electrons per cell, respectively; any deviation from such optimal values will reduce the hardness. Using the spark plasma sintering technique, a number of W1–x Re x C (x = 0–0.5) have been successfully synthesized, and powder X-ray diffractions show that they adopt the hexagonal WC-type structure. Subsequent nanoindentation and Vickers hardness measurements corroborate that the newly developed W1–x Re x C samples (x = 0.1–0.3) are much harder than their parent phase (i.e., WC), marking them as the hardest TMCs for practical applications. Furthermore, the hardness enhancement can be well rationalized by the balanced occupancy of bonding and antibonding states. Our findings not only elucidate the unique hardening mechanism in a large class of TMCs but also offer a guide for the design of other hard and superhard compounds such as borides and nitrides.

A new numerical method for calculating the singularity orders of V‐notches in Reissner's plate is proposed in this paper. By introducing the asymptotic expansion of the generalised displacement field at the notch tip into the equilibrium equations of a plate, a set of characteristic ordinary differential equations with respect to the singularity order are established. In addition, by adopting the variable substitution technique, the obtained non‐linear characteristic equations are transformed into linear ones, which are solved by the interpolating matrix method. The singularity orders of moments and shear forces can be obtained simultaneously and can be distinguished from the corresponding characteristic angular functions conveniently. Four types of boundary conditions are proposed to investigate the influence of boundary conditions on the singularity order values. The effect of the Poisson's ratio on the singularity orders of the V‐notch in Reissner's plate is discussed. The present method is versatile for the singularity analysis of single material V‐notches and bi‐material V‐notches, and can be easily extended to multi‐material V‐notches.