For the treatment of strongly correlated electrons, the corresponding Hartree-Fock exchange energy is used instead of the local density approximation (LDA) or generalized gradient approximation (GGA) functional, as suggested recently [P. Novák et al., Phys. Status Solidi B 243, 563 (2006)]. If this is done only inside the atomic spheres, using an augmented plane wave scheme, a significant simplification and reduction of computational cost is achieved with respect to the usual but costly implementation of the Hartree-Fock formalism in solids. Starting from this, we construct exchange-correlation energy functionals of the hybrid form like B3PW91, PBE0, etc. These functionals are tested on the transition-metal monoxides MnO, FeO, CoO, and NiO, and the results are compared with the LDA, GGA, $\mathrm{LDA}+U$, and experimental ones. The results show that the proposed method, which does not contain any system-dependent input parameter, gives results comparable or superior to the ones obtained with $\mathrm{LDA}+U$ which is designed to improve significantly over the LDA and GGA results for systems containing strongly correlated electrons. The computational efficiency, similar to the $\mathrm{LDA}+U$ one, and accuracy of the proposed method show that it represents a very good alternative to $\mathrm{LDA}+U$.

A variety of cutting tool materials are used for the contact mode mechanical machining of components under extreme conditions of stress, temperature and/or corrosion, including operations such as drilling, milling turning and so on. These demanding conditions impose a seriously high strain rate (an order of magnitude higher than forming), and this limits the useful life of cutting tools, especially single-point cutting tools. Tungsten carbide is the most popularly used cutting tool material, and unfortunately its main ingredients of W and Co are at high risk in terms of material supply and are listed among critical raw materials (CRMs) for EU, for which sustainable use should be addressed. This paper highlights the evolution and the trend of use of CRMs) in cutting tools for mechanical machining through a timely review. The focus of this review and its motivation was driven by the four following themes: (i) the discussion of newly emerging hybrid machining processes offering performance enhancements and longevity in terms of tool life (laser and cryogenic incorporation); (ii) the development and synthesis of new CRM substitutes to minimise the use of tungsten; (iii) the improvement of the recycling of worn tools; and (iv) the accelerated use of modelling and simulation to design long-lasting tools in the Industry-4.0 framework, circular economy and cyber secure manufacturing. It may be noted that the scope of this paper is not to represent a completely exhaustive document concerning cutting tools for mechanical processing, but to raise awareness and pave the way for innovative thinking on the use of critical materials in mechanical processing tools with the aim of developing smart, timely control strategies and mitigation measures to suppress the use of CRMs.