Hardness and Indentation Fracture Toughness of Slip Cast Alumina and Alumina-Zirconia Ceramics

Alumina (Al2O3) and zirconia (ZrO2) have good overall properties and thus are widely used oxide technical ceramics. The biggest drawback of Al2O3 is its low fracture toughness. In contrast, ZrO2 is relatively tough, but is also much more expensive. In order to improve the alumina toughness, composite ceramics are being developed. Slip casting technology has economic advantages over the conventional hot isostatic pressure technology, but problems may arise when preparing stable highly-concentrated suspensions (slip) for filling the mold. The purpose of this study is to prepare aqueous suspensions using 70 wt. % α-Al2O3, with 0, 1, 5 and 10 wt. % of added t-ZrO2. Suspensions were electrosterically stabilized using the ammonium salt of polymethylacrylic acid, an alkali-free anionic polyelectrolyte dispersant. Also, magnesium oxide in form of magnesium aluminate spinel (MgAl2O4) was used to inhibit the abnormal alumina grain growth during the sintering process. Minimum viscosities were used as stability estimators, where an increase in ZrO2 content required adding more dispersant. After sintering, the Vickers indentation test was used to determine the hardness and the indentation fracture toughness from the measurement of the crack length. Also, the brittleness index (Bi, μm−1/2) was calculated from values of Vickers hardness and the Vickers indentation fracture toughness. It was found that with increasing ZrO2 content the fracture toughness increased, while the hardness as well as the brittleness index decreased. Zirconia loading reduces the crystallite sizes of alumina, as confirmed by the X-ray diffraction analysis. SEM/EDS analysis showed that ZrO2 grains are distributed in the Al2O3 matrix, forming some agglomerates of ZrO2 and some pores, with ZrO2 having a smaller grain size than Al2O3.

The stability of the suspension is tested by sedimentation tests, by measuring the zeta potential and the particle size in the suspension and by determining rheological parameters [6,8]. The goal of the presented study was the preparation of stable Al2O3 and Al2O3-ZrO2 suspension by electrosteric stabilization suitable for slip casting. In addition, the main interest of this research is the effect of ZrO2 content (0, 1, 5 and 10 wt. %) on the microstructure and mechanical properties (hardness, fracture toughness and brittleness index) of sintered Al2O3-ZrO2 composite ceramics.

Ceramic Powder and Reagents
Samples of monolithic Al2O3 and composite Al2O3-ZrO2 were prepared by the slip casting technique. For preparation of highly concentrated aqueous suspensions (slips) following components were used:
The stability of the suspension is tested by sedimentation tests, by measuring the zeta potential and the particle size in the suspension and by determining rheological parameters [6,8]. The goal of the presented study was the preparation of stable Al 2 O 3 and Al 2 O 3 -ZrO 2 suspension by electrosteric stabilization suitable for slip casting. In addition, the main interest of this research is the effect of ZrO 2 content (0, 1, 5 and 10 wt. %) on the microstructure and mechanical properties (hardness, fracture toughness and brittleness index) of sintered Al 2 O 3 -ZrO 2 composite ceramics.

Ceramic Powder and Reagents
Samples of monolithic Al 2 O 3 and composite Al 2 O 3 -ZrO 2 were prepared by the slip casting technique. For preparation of highly concentrated aqueous suspensions (slips) following components were used: • In the present study, powder X-ray diffraction (PXRD) analysis was used in order to determine phase compositions of the raw Al 2 O 3 and ZrO 2 powder and heat treated Al 2 O 3 -ZrO 2 composites at 1650 • C. The device used was Shimadzu XRD6000 (Shimadzu Corporation, Kyoto, Japan) X-ray diffractometer with CuKα radiation. The fixed step scans were collected in the 2θ range 20-60 • with steps of 0.02 • 2θ and counting time 0.6 s under accelerating voltage of 40 kV and current of 30 mA.

Suspension Preparation and Characterization
Four groups of alumina-zirconia aqueous suspensions were prepared. All suspensions contained 70 wt. % of dry ceramic powder and 30 wt. % of deionized water. The dry powder composition was as follows: DOLAPIX CE 64 dispersant was used for the electrosteric stabilization of all ceramic suspensions. The structure of the functional group of the dispersant is shown in Figure 2.  In the present study, powder X-ray diffraction (PXRD) analysis was used in order to determine phase compositions of the raw Al2O3 and ZrO2 powder and heat treated Al2O3-ZrO2 composites at 1650 °C. The device used was Shimadzu XRD6000 (Shimadzu Corporation, Kyoto, Japan) X-ray diffractometer with CuKα radiation. The fixed step scans were collected in the 2θ range 20-60° with steps of 0.02° 2θ and counting time 0.6 s under accelerating voltage of 40 kV and current of 30 mA.

Suspension Preparation and Characterization
Four groups of alumina-zirconia aqueous suspensions were prepared. All suspensions contained 70 wt. % of dry ceramic powder and 30 wt. % of deionized water. The dry powder composition was as follows: DOLAPIX CE 64 dispersant was used for the electrosteric stabilization of all ceramic suspensions. The structure of the functional group of the dispersant is shown in Figure 2. The optimal amount of the dispersant was determined for each suspension separately. The composition of the different suspensions for determining the optimal amount of DOLAPIX CE 64 are given in Table 3. The optimal amount of dispersant was determined by measuring the apparent viscosity as a function of the amount of dispersant added. In previous research, it was found that addition of magnesium aluminate spinel (MgAl2O4) does not affect the apparent viscosity of the high concentrate alumina suspension [22]. The viscosity is at minimum value when the dispersion of ceramic particles is optimal.  The optimal amount of the dispersant was determined for each suspension separately. The composition of the different suspensions for determining the optimal amount of DOLAPIX CE 64 are given in Table 3. The optimal amount of dispersant was determined by measuring the apparent viscosity as a function of the amount of dispersant added. In previous research, it was found that addition of magnesium aluminate spinel (MgAl 2 O 4 ) does not affect the apparent viscosity of the high concentrate alumina suspension [22]. The viscosity is at minimum value when the dispersion of ceramic particles is optimal. For determining the apparent viscosity all suspensions were prepared by adding deionized water containing dissolved DOLAPIX CE 64 into the grinding jar of a planetary ball mill, after which ceramic Materials 2020, 13, 122 5 of 17 powders were added. The grinding jar and ten balls used for homogenization were made of alumina ceramics in order to prevent the contamination of suspensions. Each of the prepared suspensions were homogenized for 90 min at a rate of 300 rpm in the planetary ball mill (PM 100, Retsch, Haan, Germany). After mixing, the ceramic balls were separated from the suspensions. Prior to the apparent viscosity measurement and forming of the green bodies, suspensions were ultrasonically treated in the ultrasonic bath BRANSONIC 220 (Branson Ultrasonics Corp., Danbury, CT, USA) with 50 kHz frequency and power of 120 W to remove trapped air bubbles and agglomerates, as well as tempered at 25 ± 1 • C with the assistance of the thermostatic bath Lauda Eco RE 415 (LAUDA-Brinkmann, Delran, NJ, USA).
The apparent viscosity of each suspension was determined by means of the rotational viscometer DV-III Ultra (Brookfield Engineering Laboratories, Middleboro, MA, USA) with small sample chamber and SC4-18 spindle. Viscosity was determined at the shear rate of 50 s −1 , which is the exact shear rate of gravity slip casting.
After completing the rheological measurements and finding the optimum amount of the dispersant, sedimentation tests were performed. Four groups of suspensions were additionally prepared with the optimum amount of dispersant. The pH-values of these prepared suspensions were determined on the FE20/EL20 pH meter (error range 0.01) manufactured by Mettler Toledo GmbH (Greifensee, Switzerland). In this case the pH value of the samples did not change, it was done only for the confirmation of the stability of the optimized suspensions.

Sintering of Monolithic Alumina and Composite Alumina-Zirconia Ceramics
Monolithic Al 2 O 3 and composite Al 2 O 3 -ZrO 2 ceramics were prepared by conventional sintering of green bodies formed by slip casting forming method. Therefore, after the apparent viscosity measurement the suspensions were poured into previously prepared gypsum molds and air-dried. The gypsum mold draws water from the poured slip and gives a form to the green body.
Afterwards, dried samples were removed from molds. The green bodies were sintered in the high-temperature furnace P 310 (Nabertherm, Lilienthal, Germany) by the following regime: initial heating at a rate of 3 • C/min up to the temperature of 500 • C, holding at 500 • C for 1 h, followed by heating at a rate of 5 • C/min up to the temperature of 1650 • C, holding at 1650 • C for 2 h and finally slow cooling in the furnace to room temperature ( Figure 3). After sintering, the Archimedes density was measured for all samples. For determining the apparent viscosity all suspensions were prepared by adding deionized water containing dissolved DOLAPIX CE 64 into the grinding jar of a planetary ball mill, after which ceramic powders were added. The grinding jar and ten balls used for homogenization were made of alumina ceramics in order to prevent the contamination of suspensions. Each of the prepared suspensions were homogenized for 90 min at a rate of 300 rpm in the planetary ball mill (PM 100, Retsch, Haan, Germany). After mixing, the ceramic balls were separated from the suspensions. Prior to the apparent viscosity measurement and forming of the green bodies, suspensions were ultrasonically treated in the ultrasonic bath BRANSONIC 220 (Branson Ultrasonics Corp., Danbury, CT, USA) with 50 kHz frequency and power of 120 W to remove trapped air bubbles and agglomerates, as well as tempered at 25 ± 1 °C with the assistance of the thermostatic bath Lauda Eco RE 415 (LAUDA-Brinkmann, Delran, NJ, USA).
The apparent viscosity of each suspension was determined by means of the rotational viscometer DV-III Ultra (Brookfield Engineering Laboratories, Middleboro, MA, USA) with small sample chamber and SC4-18 spindle. Viscosity was determined at the shear rate of 50 s −1 , which is the exact shear rate of gravity slip casting.
After completing the rheological measurements and finding the optimum amount of the dispersant, sedimentation tests were performed. Four groups of suspensions were additionally prepared with the optimum amount of dispersant. The pH-values of these prepared suspensions were determined on the FE20/EL20 pH meter (error range 0.01) manufactured by Mettler Toledo GmbH (Greifensee, Switzerland). In this case the pH value of the samples did not change, it was done only for the confirmation of the stability of the optimized suspensions.

Sintering of Monolithic Alumina and Composite Alumina-Zirconia Ceramics
Monolithic Al2O3 and composite Al2O3-ZrO2 ceramics were prepared by conventional sintering of green bodies formed by slip casting forming method. Therefore, after the apparent viscosity measurement the suspensions were poured into previously prepared gypsum molds and air-dried. The gypsum mold draws water from the poured slip and gives a form to the green body.
Afterwards, dried samples were removed from molds. The green bodies were sintered in the high-temperature furnace P 310 (Nabertherm, Lilienthal, Germany) by the following regime: initial heating at a rate of 3 °C/min up to the temperature of 500 °C, holding at 500 °C for 1 h, followed by heating at a rate of 5 °C/min up to the temperature of 1650 °C, holding at 1650 °C for 2 h and finally slow cooling in the furnace to room temperature ( Figure 3). After sintering, the Archimedes density was measured for all samples.

Characterisation of Monolithic Alumina and Composite Alumina-Zirconia Ceramics
Sintered samples were prepared for the following tests according to the standard ceramographic technique [28]. Surface morphology of the sintered ceramic samples was determined by the scanning electron microscope (SEM), Tescan Vega Easy Probe 3, Brno-Kohoutovice, Czech Republic operating at 10 kV, additionally equipped with energy dispersive spectrometer (EDS), Oxford Instruments, Abingdon, UK. Distribution of the elements aluminum (Al), zirconium (Zr) oxygen (O) and yttrium (Y) on fracture surface of sintered samples was determined by EDS mapping.
Vickers hardness (HV30) of sintered ceramic samples was measured under 294 N indentation load by means of hardness tester 5030 TKV (Indentec Hardness Testing Machines Ltd., West Midlands, UK). The "Vickers indentation fracture, (VIF)" or "Vickers indentation crack length" method was used for fracture toughness determination of all ceramic samples. This method uses a Vickers indenter to make a hardness indentation on a polished ceramic sample surface. The indenter creates a plastically-deformed region underneath the indenter as well as cracks that emanate radially outward and downward from the vertices of the Vickers indentation. Besides radial-median cracks, Palmqvist cracks can also occur ( Figure 4). A simple way to differentiate between the two types is to polish the surface layers away: the median crack system will always remain connected to the inverted pyramid of the indentation, while the Palmqvist cracks will become detached, as shown in Figure 4.

Characterisation of Monolithic Alumina and Composite Alumina-Zirconia Ceramics
Sintered samples were prepared for the following tests according to the standard ceramographic technique [28]. Surface morphology of the sintered ceramic samples was determined by the scanning electron microscope (SEM), Tescan Vega Easy Probe 3, Brno-Kohoutovice, Czech Republic operating at 10 kV, additionally equipped with energy dispersive spectrometer (EDS), Oxford Instruments, Abingdon, UK. Distribution of the elements aluminum (Al), zirconium (Zr) oxygen (O) and yttrium (Y) on fracture surface of sintered samples was determined by EDS mapping.
Vickers hardness (HV30) of sintered ceramic samples was measured under 294 N indentation load by means of hardness tester 5030 TKV (Indentec Hardness Testing Machines Ltd., West Midlands, UK). The "Vickers indentation fracture, (VIF)" or "Vickers indentation crack length" method was used for fracture toughness determination of all ceramic samples. This method uses a Vickers indenter to make a hardness indentation on a polished ceramic sample surface. The indenter creates a plastically-deformed region underneath the indenter as well as cracks that emanate radially outward and downward from the vertices of the Vickers indentation. Besides radial-median cracks, Palmqvist cracks can also occur ( Figure 4). A simple way to differentiate between the two types is to polish the surface layers away: the median crack system will always remain connected to the inverted pyramid of the indentation, while the Palmqvist cracks will become detached, as shown in Figure 4. In the order to calculate Vickers indentation fracture toughness, the lengths of these cracks were measured. Fracture toughness is calculated on the basis of the crack lengths, the indentation load, the hardness, the elastic modulus, the indentation diagonal size, and an empirical fitting constant. Nine equations based on the Palmqvist, radial-median cracks and both were found to be applicable for the fracture toughness determination of the ceramics ( Table 4). The brittleness index (Bi, m −1/2 ) was calculated from the ratio of Vickers hardness and Vickers indentation fracture toughness. In the order to calculate Vickers indentation fracture toughness, the lengths of these cracks were measured. Fracture toughness is calculated on the basis of the crack lengths, the indentation load, the hardness, the elastic modulus, the indentation diagonal size, and an empirical fitting constant. Nine equations based on the Palmqvist, radial-median cracks and both were found to be applicable for the fracture toughness determination of the ceramics ( Table 4). The brittleness index (B i , µm −1/2 ) was calculated from the ratio of Vickers hardness and Vickers indentation fracture toughness.  [29].

Results and Discussion
From the diffractogram in Figure 5, the qualitative crystalline composition determination was possible for all samples. The diffractogram in Figure 5 indicates that the raw Al 2 O 3 consists of only α-Al 2 O 3 crystalline phase (corundum) (ICDD PDF#46-1212). On the other hand, for raw ZrO 2 powder two phases were assigned to the main phase; zirconia tetragonal phase (t-ZrO 2 ) (ICDD PDF#42-1164) and the minor phase; zirconia monoclinic phase (m-ZrO 2 ) (ICDD PDF#37-1484). Amorphous phase or residuals are not present. Qualitatively, sintered zirconia-toughened alumina composite shows the presence of α-Al 2 O 3 (ICDD PDF#46-1212) as the main phase, t-ZrO 2 (ICDD PDF#42-1164) as the minor phase and m-ZrO 2 (ICDD PDF#37-1484) in traces. With increase of the zirconia content, both t-ZrO 2 and m-ZrO 2 intensity increased (the intensity increase of the t-ZrO 2 phase peak is shown in Inset). Semiquantitatively, the loading of the t-ZrO 2 is also shown in Inset (having in mind Al 2 O 3 and ZrO 2 show different absorption coefficients, the loading should only point out to a trend between different values and not to exact values).
The intensity of the t-ZrO 2 strongest peak and m-ZrO 2 strongest peak were compared to allow an insight in the mutual dependence of the zirconia phases (t-ZrO 2 to m-ZrO 2 ratio) as a function of the zirconia loading. With the introduction of 1 wt. % of zirconia, the relative content of the m-ZrO 2 is about 15 wt. % (85 wt. % t-ZrO 2 ). However, the calculation of the ratio of phases that are present in levels of about 1 % is questionable. Upon an increase in the zirconia loading to 5 wt. %, the relative presence of the m-ZrO 2 is reduced to about 7 % (93 % t-ZrO 2 ), and the similar ratio remains for further increase of the zirconia loading up to 10 wt. %. Basically, the ratio between m-ZrO 2 and t-ZrO 2 zirconia phases remains the same. This actually makes sense as there is no clear reason why the increased zirconia content would affect the ratio between m-ZrO 2 and t-ZrO 2 zirconia. The only reason could be the consequence of the phase transformation from tetragonal into monoclinic phase in the cracking zone (closure of the crack due to the volume changes). However, such microeffects are not statistically observable using a method like XRD. The important issue is that for the healing of the crack there is plenty of the main zirconia phase, the t-ZrO 2 available [36,37]. As the microstructure is considered, the use of raw α-alumina yields crystallites of about 262 nm in size, while raw zirconia yields crystallites of about 32 nm. Crystallite size was calculated by applying the Scherrer equation on the XRD patterns.  Viscosity measurements were used for the suspension stability estimation. Rheological measurements showed that measured apparent viscosity increases with the increasing zirconia content. The optimal amount of Dolapix CE 64 also increases with the increasing zirconia content. The diagram in Figure 6 shows the apparent viscosity at the shear rate of app. 50 s −1 , which is the shear rate of the gravity slip casting.
The obtained minimum viscosity values represent the most stable suspension, which served as the guideline for the preparation of the most suitable ceramic suspensions to be poured into the mold to prepare green bodies and to be sintered, in order to get the samples of monolithic Al2O3 and Al2O3-ZrO2 composite ceramics.
By comparing the results in Figure 6 it is evident that the optimum amount of the dispersant increases with increased ZrO2 content. The reason for this is probably the fact that this component has finer particles. Ceramic particles of smaller dimensions have a larger specific surface. Therefore, the area that the macromolecules of the dispersant must cover to ensure the stability of the system is larger. Hence, a higher amount of the dispersant is needed to stabilize such suspensions [18]. Viscosity measurements were used for the suspension stability estimation. Rheological measurements showed that measured apparent viscosity increases with the increasing zirconia content. The optimal amount of Dolapix CE 64 also increases with the increasing zirconia content. The diagram in Figure 6 shows the apparent viscosity at the shear rate of app. 50 s −1 , which is the shear rate of the gravity slip casting.
The obtained minimum viscosity values represent the most stable suspension, which served as the guideline for the preparation of the most suitable ceramic suspensions to be poured into the mold to prepare green bodies and to be sintered, in order to get the samples of monolithic Al 2 O 3 and Al 2 O 3 -ZrO 2 composite ceramics.
By comparing the results in Figure 6 it is evident that the optimum amount of the dispersant increases with increased ZrO 2 content. The reason for this is probably the fact that this component has finer particles. Ceramic particles of smaller dimensions have a larger specific surface. Therefore, the area that the macromolecules of the dispersant must cover to ensure the stability of the system is larger. Hence, a higher amount of the dispersant is needed to stabilize such suspensions [18]. Materials 2020, 13, x FOR PEER REVIEW 9 of 17  Table 3 shows the composition of the tested suspensions, while the optimal compositions (i.e., optimal dispersant amount) are shown in Table 5. In this study no typical sedimentation tests were performed [14,38], meaning, the sedimentation rate of the suspension was not observed depending on the pH value. Only the sedimentation rates for suspensions with the optimum proportion of the dispersant at their "natural" pH value were measured. The measured pH values of the real samples and their mean values of three measurements are shown in Table 6. The prepared suspensions did not show any indication of phase separation after 3 days and the suspensions were still homogeneous. Full separation of the solid and liquid phase was observed after more than seven days in all four suspension groups. For this reason, the prepared suspensions can be considered stable [14,38], without the need for pH control.
The results of SEM-EDS analysis of surface fracture of sintered monolithic Al2O3 and Al2O3-ZrO2 composite ceramics are shown in Figures 7-11. It can be seen (Figures 7b-d, 9, 10 and 11) that the ZrO2 particles (the brighter phase) are distributed in Al2O3 matrix, with some agglomerates of ZrO2 and some pores. These observations were additionally confirmed by the SEM-EDS mapping of the surface fracture of sintered samples (Figures 9-11).  Table 3 shows the composition of the tested suspensions, while the optimal compositions (i.e., optimal dispersant amount) are shown in Table 5. In this study no typical sedimentation tests were performed [14,38], meaning, the sedimentation rate of the suspension was not observed depending on the pH value. Only the sedimentation rates for suspensions with the optimum proportion of the dispersant at their "natural" pH value were measured. The measured pH values of the real samples and their mean values of three measurements are shown in Table 6. The prepared suspensions did not show any indication of phase separation after 3 days and the suspensions were still homogeneous. Full separation of the solid and liquid phase was observed after more than seven days in all four suspension groups. For this reason, the prepared suspensions can be considered stable [14,38], without the need for pH control.
The results of SEM-EDS analysis of surface fracture of sintered monolithic Al 2 O 3 and Al 2 O 3 -ZrO 2 composite ceramics are shown in Figures 7-11. It can be seen (Figure 7b-d, Figures 9-11) that the ZrO 2 particles (the brighter phase) are distributed in Al 2 O 3 matrix, with some agglomerates of ZrO 2 and some pores. These observations were additionally confirmed by the SEM-EDS mapping of the surface fracture of sintered samples (Figures 9-11).
The composites with 5 and 10 wt. % ZrO 2 have shown larger agglomerates of ZrO 2 in Al 2 O 3 matrix compared to 1 wt. % ZrO 2 (Figure 7b-d)). The pores are mostly distributed around ZrO 2 agglomerates. Also, the increasing of ZrO 2 content has resulted in a reduction of Al 2 O 3 grain size. All these microstructural characteristics typically affect the mechanical properties, such as hardness and fracture toughness. The composites with 5 and 10 wt. % ZrO2 have shown larger agglomerates of ZrO2 in Al2O3 matrix compared to 1 wt. % ZrO2 (Figure 7b-d)). The pores are mostly distributed around ZrO2 agglomerates. Also, the increasing of ZrO2 content has resulted in a reduction of Al2O3 grain size. All these microstructural characteristics typically affect the mechanical properties, such as hardness and fracture toughness.    The composites with 5 and 10 wt. % ZrO2 have shown larger agglomerates of ZrO2 in Al2O3 matrix compared to 1 wt. % ZrO2 (Figure 7b-d)). The pores are mostly distributed around ZrO2 agglomerates. Also, the increasing of ZrO2 content has resulted in a reduction of Al2O3 grain size. All these microstructural characteristics typically affect the mechanical properties, such as hardness and fracture toughness.    The composites with 5 and 10 wt. % ZrO2 have shown larger agglomerates of ZrO2 in Al2O3 matrix compared to 1 wt. % ZrO2 (Figure 7b-d)). The pores are mostly distributed around ZrO2 agglomerates. Also, the increasing of ZrO2 content has resulted in a reduction of Al2O3 grain size. All these microstructural characteristics typically affect the mechanical properties, such as hardness and fracture toughness.       The results of measuring the density of sintered samples (Al2O3 and Al2O3-ZrO2 composite) confirm that the density increases with increasing the ZrO2 content ( Table 7). The theoretical density of pure Al2O3 is 3.97 g/cm 3 and of pure ZrO2 6.10 g/cm 3 . From these theoretical densities of pure ceramics, weight content of components, and from the measured bulk densities, the relative densities of each sample were calculated ( Table 7). The highest relative densities were recorded for pure Al2O3 and for the composite with 1 wt. % ZrO2. When ZrO2 content was increased to 5 and 10 wt. %, the relative density decreased and consequently the porosity has increased. Similar results were published previously [39].
The Vickers indentation method was used for the determination of hardness (HV30), fracture toughness (KIC) and brittleness index (Bi) of sintered samples of monolithic Al2O3 and Al2O3-ZrO2 composite ceramics. The results (Table 7) showed that the hardness of the prepared samples decreased with the increased ZrO2 content. There are several reasons for this phenomenon. One of them is the fact that zirconia has lower hardness than Al2O3. Also, as previously described, the microstructure analysis of composites has shown the coarsening of ZrO2 grains and consequently the formation of porosity. These findings are in correlation with other publications [2,40,41]. Higher relative density, hence higher hardness, may be achieved when, for example, hot-pressing (HP) is used to prepare Al2O3-ZrO2 composites [42], hot isostatic pressing [43] or by spark plasma sintering (SPS) [44].
The fracture toughness of the tested samples (Table 8) also increases with the increase of the ZrO2 amount for all applied mathematical models. These results may be assigned to possible phase transformations, formation of microcracks or crack branching [2]. Composite ceramics with ZrO2 grains, exhibit the martensitic phase transformation: when the stress is applied, tetragonal ZrO2 grains transform into monoclinic ZrO2 at the crack tip ( Figure 12). The results of measuring the density of sintered samples (Al 2 O 3 and Al 2 O 3 -ZrO 2 composite) confirm that the density increases with increasing the ZrO 2 content ( Table 7). The theoretical density of pure Al 2 O 3 is 3.97 g/cm 3 and of pure ZrO 2 6.10 g/cm 3 . From these theoretical densities of pure ceramics, weight content of components, and from the measured bulk densities, the relative densities of each sample were calculated ( Table 7). The highest relative densities were recorded for pure Al 2 O 3 and for the composite with 1 wt. % ZrO 2 . When ZrO 2 content was increased to 5 and 10 wt. %, the relative density decreased and consequently the porosity has increased. Similar results were published previously [39].
The Vickers indentation method was used for the determination of hardness (HV30), fracture toughness (K IC ) and brittleness index (B i ) of sintered samples of monolithic Al 2 O 3 and Al 2 O 3 -ZrO 2 composite ceramics. The results (Table 7) showed that the hardness of the prepared samples decreased with the increased ZrO 2 content. There are several reasons for this phenomenon. One of them is the fact that zirconia has lower hardness than Al 2 O 3 . Also, as previously described, the microstructure analysis of composites has shown the coarsening of ZrO 2 grains and consequently the formation of porosity. These findings are in correlation with other publications [2,40,41]. Higher relative density, hence higher hardness, may be achieved when, for example, hot-pressing (HP) is used to prepare Al 2 O 3 -ZrO 2 composites [42], hot isostatic pressing [43] or by spark plasma sintering (SPS) [44].
The fracture toughness of the tested samples (Table 8) also increases with the increase of the ZrO 2 amount for all applied mathematical models. These results may be assigned to possible phase transformations, formation of microcracks or crack branching [2]. Composite ceramics with ZrO 2 grains, exhibit the martensitic phase transformation: when the stress is applied, tetragonal ZrO 2 grains transform into monoclinic ZrO 2 at the crack tip ( Figure 12).
The fracture toughness of the tested samples (Table 8) also increases with the increase of the ZrO2 amount for all applied mathematical models. These results may be assigned to possible phase transformations, formation of microcracks or crack branching [2]. Composite ceramics with ZrO2 grains, exhibit the martensitic phase transformation: when the stress is applied, tetragonal ZrO2 grains transform into monoclinic ZrO2 at the crack tip ( Figure 12).  [29]. Figure 12. Transformation toughening mechanism in zirconia [29].
This transformation induces a volume expansion from 3-5 %, which prevents the crack propagation due to induced compressive stress. This phenomenon is known as the transformation toughening. The larger the ZrO 2 content in the composite ceramics, the higher the possibility of crack closure [29]. Besides the zirconia phase transformation, it was found that the alumina grain bridging is also a toughening mechanism which contributes to an increase in toughness of similar alumina zirconia composites [30].
The ratio of the Vickers crack length and half of the Vickers indentation diagonal (c/a, Table 7) indicates the crack type and the crack depth. The crack type is an indirect indicator of material toughness [1,29,35,45]. According to the obtained results (Table 7) and interpretation from literature sources [1,29,35,45], median cracks occurred in the first three groups of samples, while shallow, Palmqvist cracks appeared in the fourth group (90 wt. % Al 2 O 3 + 10 wt. % ZrO 2 ). It should be emphasized that the c/a ratio for the first three groups of samples is slightly above the limit value of 2.5, so it can be concluded that even low ZrO 2 content reduces the crack depth, i.e., increases the toughness. According to Tang et al. [45], samples with a c/a ratio between 2.5 and 3.5 indicate the presence of both types of cracks (both Palmqvist and median), therefore represent the transition between the two types of cracks. According to this interpretation, it is possible to determine the presence of the transitional crack shape (between median and Palmqvist type) in the first three groups of samples, while in the fourth sample group only the Palmqvist cracks occur. According to the obtained c/a values, from 2.3 to 3.9, the most adequate model for the indentation fracture toughness is the Langford model, since it is applicable to both crack types (median and Palmquist). Since not all groups of samples developed the same crack type, not all selected models were applicable to all four sample groups [32]. Nevertheless, all models showed the same trend, i.e., an increase in fracture toughness with increasing ZrO 2 content (Table 8 and Figure 13). The obtained results show that the toughness of monolithic Al 2 O 3 ceramics can be improved by the addition of ZrO 2 nanoparticles.  For each sample, the brittleness index (Bi, m −1/2 ) was calculated from the ratio of values of Vickers hardness (HV30, GPa) and the Vickers indentation fracture toughness (KIC, MPa m 1/2 ) using Equation (1) [46]: Calculated values of the brittleness index for all sintered samples are shown in Figure 14. All models showed that the brittleness index decreases with increasing ZrO2 content.  For each sample, the brittleness index (B i , µm −1/2 ) was calculated from the ratio of values of Vickers hardness (HV30, GPa) and the Vickers indentation fracture toughness (K IC , MPa m 1/2 ) using Equation (1) [46]: Calculated values of the brittleness index for all sintered samples are shown in Figure 14. All models showed that the brittleness index decreases with increasing ZrO 2 content. Materials 2020, 13, x FOR PEER REVIEW 14 of 17

Conclusions
In this paper, monolithic Al2O3 and composite Al2O3-ZrO2 ceramics samples were formed by slip casting stable suspensions in gypsum molds. The following conclusions can be drawn as a result of the research:  XRD analysis confirmed that alumina powder consists of α-phase alumina (corundum). The XRD results confirm the changing levels of alumina and zirconia in the composites, and point out to the stable ratio between main tetragonal phase and monoclinic zirconia phase in traces. In addition, the change of the crystallite sizes because of the zirconia loading was quantified.

Conclusions
In this paper, monolithic Al 2 O 3 and composite Al 2 O 3 -ZrO 2 ceramics samples were formed by slip casting stable suspensions in gypsum molds. The following conclusions can be drawn as a result of the research: • XRD analysis confirmed that alumina powder consists of α-phase alumina (corundum). The XRD results confirm the changing levels of alumina and zirconia in the composites, and point out to the stable ratio between main tetragonal phase and monoclinic zirconia phase in traces. In addition, the change of the crystallite sizes because of the zirconia loading was quantified. • Green bodies of monolithic Al 2 O 3 and composite Al 2 O 3 -ZrO 2 ceramics were formed by slip casting process in plaster molds. After drying, the green bodies were sintered at a temperature of 1650 • C. • SEM-EDS analysis of prepared composite ceramics showed that ZrO 2 particles are dispersed in Al 2 O 3 matrix with some agglomerates of ZrO 2 , and pores.

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The obtained c/a values ranging from 2.3 to 3.9 indicate that the Langford model is the most appropriate model for the indentation fracture toughness, because this model can be applied to both median and Palmquist crack types.

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By adding ZrO 2 nanoparticles in alumina matrix, the hardness has decreased because the hardness of tetragonal zirconia is lower than alumina. Also, the addition of ZrO 2 nanoparticles has caused an increase in total porosity, hence lowering the hardness.

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On the other hand, the fracture toughness of alumina matrix has increased by adding ZrO 2 nanoparticles as a result of the synergistic effect of transformation toughening and the microstructural changes.