## 2 Materials and Methods  
The following raw powders were used in the experiments:  
1. a-Al\({}_{2}\)O\({}_{3}\) corundum A16 SG (Alcao, New York, NY, USA), with an average particle diameter of \(d_{50}\) = 0.53 \(\upmu\)m,
2. TiC (Plasmotherm, Moscow, Russia), with 99.5% purity and an average particle diameter of \(d_{50}\) = 0.6 \(\upmu\)m.  
Powder mixtures with different amounts of TiC 30 and 40 vol.% were mixed in a multidirectional Turbula shaker mixer (Eskens B.V., Alphen aan den Rijn, Netherlands) in ethanol in a polyethylene container at 150 rpm for 24 h [17]. Lyophilizer FreeZone2.5 (LabConco, Kansas, MO, USA) was used for the drying of the obtained slurries to avoid agglomerates of TiC phase in the alumina matrix. The collector temperature was set at \(-50\pm 2\ ^{\circ}\)C, while the shell temperature was \(+23\pm 2\ ^{\circ}\)C and the chamber pressure was 0.02 \(\pm\) 0.01 mbar during the entire process. Also, this method allows powders to be sintered without sieving [44]. The powders were sintered with a KCE FCT-H HP D-25 SD spark plasma sintering machine (FCT Systeme GmbH, Rauenstein, Germany) at 1400 \({}^{\circ}\)C with a heating rate of 100 \({}^{\circ}\)C\(\cdot\)min\({}^{-1}\), under a uniaxial pressure of 80 MPa in a vacuum. The final temperature and pressure were maintained for 3 min and 20-mm-diameter, 2-4-mm-thick as-sintered sample disks were labeled depending on their TiC content. XRD measurements were carried out in an Empyrean diffractometer (PANalytical, Almelo, Netherlands) ranging from 25\({}^{\circ}\) to 70\({}^{\circ}\). The step size was 0.05\({}^{\circ}\) with a scan speed of 0.06 \({}^{\circ}\)/min. The diffractometer used Cu K\(\alpha\) radiation (\(\uplambda\)= 1.5405981), working at 60 kV and with an intensity of 30 mA. Density measurements (\(\rho\)) of the sintered specimens were done in distilled water using Archimedes' principle and compared with the theoretical values (3.89 g/cm\({}^{3}\) for Al\({}_{2}\)O\({}_{3}\) and 4.93 g/cm\({}^{3}\) for TiC, respectively) calculated from the rule of mixture. A scanning electron microscope (SEM) VEGA3 (Tescan, Brno, The Czech Republic) was used for characterization of surfaces polished down to 1 \(\upmu\)m. The energy-dispersive X-ray spectroscopy (EDS) spectra were conducted in specific regions at 20 kV voltage and 12 \(\upmu\)A beam current for 5 min to obtain well-resolved Y-K\(\upalpha\) and Zr-K\(\upalpha\) peaks for the chemical microanalysis of sintered samples. Ten Vickers impressions were carried out in the surfaces of each of the tested samples, which had previously been polished down 1 \(\upmu\)m. The 9.8 N load was applied for ten seconds by a Vickers diamond indenter Leco 100-A (Leco Corp., St. Joseph, MI, USA). The HV magnitude was calculated as follows:  
\[HV\ =\ 0.1891\frac{P}{d^{2}}, \tag{2}\]  
where \(P\) is the applied load, N; \(d\) is the average length of the two diagonals, mm. SEM was used for evaluation of the size of the indentations. The values of fracture toughness (K\({}_{1\mathrm{c}}\)) were also estimated by Vickers microindentation. The cracks were observed at 294 N and load holding time was set to 10 s.  
At least 10 indentations tests were performed per specimen. The fracture toughness was calculated using the formula presented in [PERSON] [45]. The flexural strength (\(\sigma_{\mathrm{f}}\)) was evaluated through a biaxial bending test. Each sample was placed onto a device with three balls of 3 mm in diameter that were made of hardened steel and disposed on a holder (10 mm diameter) at 120\({}^{\circ}\) to each other. The load was applied with a 5 kN universal testing machine (Auto Graph AG-X, Shimadzu Corp., Kyoto, Japan) using a plain head of 1.2 mm in diameter at a speed of 1 mm\(\cdot\)min\({}^{-1}\) up to failure. The specimen thickness was measured at the breakage point. 12 specimens were tested to obtain the average strength value. A review of the procedure is reported in Smirnov [46].