Introduction

Al2O3 ceramics have been widely requested in a variety of applications such as electronic, biomedical, defense, textile and mechanical engineering because of their outstanding properties such as resistance to corrosion and wear, biocompatibility and high mechanical properties [1, 2]. In addition, Al2O3 has low process costs compared with many other advanced ceramic materials [3]. However, when a material is preferred, especially for structural applications, not only material properties and cost are important but also it is necessary to make changes in its design according to new requirements. For instance, emission-reduction and energy saving are critical factors considered in automotive industry due to the global energy crisis [4,5,6]. Weight reduction, especially for electric vehicles whose range is heavily reliant on weight, is a crucial strategy for resolving these problems [4]. In this case, lightweight construction becomes important with high specific strength, energy absorption, and specific stiffness [4, 7, 8].

Sandwich components with two skin panels containing light core filler materials have garnered considerable interest as lightweight structures with excellent capacities for particular bending stiffness, energy absorption, and strength [4, 9]. Honeycomb is a popular alternative among lightweight materials that can be used for sandwich cores [10,11,12,13]. Owing to their combination of lightweight, high energy absorption capacity, low thermal conductivity, and quick manufacture, honeycomb cellular structures are of particular interest and are preferred in a broad range of applications including automotive, railway vehicle, aerospace, satellites, medical implants, and nanofabrication. Honeycombs are explored for different topological positions consisting of square, triangular, circular, and hexagonal units, and different matrix materials such as metals, ceramics, polymers, composites, and papers [13,14,15,16,17]. However, there is little research on the assessment of the use of lightweight advanced ceramic honeycomb structures due to the difficulties of producing these structures that are related to high hardness, brittleness, and complex processing procedures of advanced ceramics. Fortunately, the present developments in additive manufacturing (3D-printing) of advanced ceramics have generated new opportunities to investigate the probable benefits of using advanced ceramic honeycomb sandwich materials [18, 19].

The production of advanced ceramic honeycomb sandwich structures through additive manufacturing techniques and the investigation of their bending properties have been rarely studied. Recently, Gao et al. [13], reported a study about bending behaviour of ZrO2 (3Y-TZP) honeycomb sandwich structures prepared by a digital light processing (DLP) 3D-printing system with a hexagonal square core. The effects of geometric parameters (the height of the cell, the size of the cell etc.) were investigated, and the honeycomb sandwich with a square core showed better performance for their study. In addition, in the manufacturing process, holes were designed consciously in the lower and upper face-sheets of the specimens to allow the uncured ceramic resin to leak. However, in their studies, the position of these holes and their effects on bending strength were not considered. Also, Kafkaslıoğlu Yıldız et al. [19] produced Al2O3 honeycomb sandwich structures with square, triangular, and circular cores using stereolithography (SLA) method but the holes designed for uncured slurry to leak were also positioned in the lower and upper face-sheets of the specimens in their study.

In this research, Al2O3 honeycomb sandwich ceramics with hexagonal core were prepared via the SLA 3D-printing method, and the effects of hole position on the bending strength were explored comprehensively. Due to the exact control of the laser beam, the SLA method can produce ceramic objects with greater degrees of detail and resolution. This can be critical for applications that require precise details or complex geometry [20]. Therefore, this study focused on structures produced with the SLA system, unlike the DLP system. In this research, the changes in bending strength were examined based on the position of the holes designed to allow the removal of uncured slurry, aiming to develop suitable designs for sandwich structures.

Materials and methods

Sample preparation

To fabricate the ceramic specimens, Al2O3 ceramic feedstock (3DMIX AL-E03) and a C100 Easy Lab stereolithographic 3D printer provided by 3DCeram (Limoges, France) were used. The ceramic specimens had the geometry of a rectangular bar with a length of 45 mm, height of 3 mm, and width of 4 mm. The dimensions of the bars were consistent with the ASTM 1161 standard for the three-point bending test. SolidWorks software was used to create the specimens’ geometrical model, which was then converted into STL format and transferred to the 3D printer software. Dimensional correctness after sintering was guaranteed by considering the scale factor values (X:1.175, Y:1.190, Z:1.223) provided by the supplier. The 3D model of the parts was divided into thin portions, which were then printed on the printing platform layer by layer. The honeycomb sandwich structures with hexagonal cores (h: 2.4 mm) were composed of upper and lower face-sheets (h:0.3 mm) and several holes (Ø=0.5 mm) were placed specifically on the specimens in the design, as shown in Fig. 1. In Fig. 1, the final dimensions of the holes before printing were also given after transferring the design to the 3D-printer software and entering the scale factor values. In the first design, the holes were open to the upper and lower face-sheets of the honeycomb sandwich structure. In the second design, the holes were placed in the lateral walls (in the direction of sample thickness) on the neutral axis. While there are 220 holes in total for the honeycomb structure with holes on the upper and lower face-sheets, there are 152 holes in total for the sample with lateral holes. In this way, the effect of different hole positions on the bending strength was examined.

Fig. 1
figure 1

Geometrical models of Al2O3 sandwich specimens with two different hole positions; (a) the holes on the upper and lower face-sheets, (b) the holes in the lateral walls

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3D printing was conducted at ambient temperature and, the thickness of each slice layer was set as 50 μm. Also, the laser power was set at 50 mW. In the SLA printing of ceramics, a scraper is initially used to equally distribute the flowing ceramic slurry from the cartridge to the building platform. The laser head then scans linearly to cure the slurry consistent with the cross-sectional shape of the current layer. The building platform goes down to create another layer after the first layer has been formed. Until the entire ceramic component is created, this process continues [21]. Fifteen specimens were printed for each of the two different hole positions. Bulk Al2O3 specimens were also produced under the same conditions.

Following the printing process, a CeraKleaner cleaning station and a solvent provided by 3DCeram were used to clean all the printed specimens to discard any extra unpolymerized ceramic slurry. It is necessary to eliminate the organic components through a debinding process at a lower temperature. Subsequently, a sintering procedure at an elevated temperature is employed to provide the densification. To minimize defects in the printed Al2O3 parts, the debinding procedure was conducted within an electrical tube furnace (Protherm PZF 12/50/750-3Z, Türkiye) under a nitrogen atmosphere in several stages up to 615 °C in accordance with the thermal regime provided by the supplier. Later, the brown bodies were then sintered at 1720 °C for 90 min in air in a box furnace (Protherm MOS-B 180/4, Türkiye). Figure 2 shows the photographs of Al2O3 test samples for each hole position after sintering.

Fig. 2
figure 2

Photographs of the Al2O3 test samples after sintering; (a) the sample with the holes on the upper and lower face-sheets, (b) top view of the sample with the holes in the lateral walls, (c) side view of the sample with the holes in the lateral walls

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Characterization

The bulk density of the 3D printed specimens was measured by the volumetric method from mass and dimensions. Using the ratio of the bulk density to the theoretical density of Al2O3 (d = 3.98 g/cm3), the relative density values were calculated for both groups of specimens. The surface microstructure and hole sizes of the sintered specimens were examined using a scanning electronic microscope (SEM, TESCAN Mira3 XMU, Czechia). The elastic modulus of the ceramic bars after sintering was evaluated by employing an impulse excitation of vibration method via a GrindoSonic® Mk5 device in accordance with ASTM C 1259 standard. A mathematical relationship can be established as given in Eq. 1 between elastic modulus (E), the beam dimensions (length: L, width: b, height: h), mass “m”, and natural resonance frequencies “fi”. In Eq. 1, “αi” are coefficients belonging to the beam’s support condition and the mode numbers and “I” is moment of inertia [22].

$$ E=\frac{m{L}^{3}}{I}{\left(\frac{2\pi {f}_{i}}{{{\alpha }_{i}}^{2}}\right)}^{2}$$
(1)

The moment of inertia can be calculated from “I = (b·h3)/12” and it can be considered as the apparent moment of inertia determined based on the sample’s dimensions. A non-contact transducer was used to pick up the required vibrations while striking the center of the sample with an impulser lightly and elastically. The resultant frequencies were noted after repeating the test until five readings were obtained both in flexural and torsional mode. The elastic modulus values of the samples (Ea, actually apparent elastic modulus) were found by inputting the experimentally measured frequencies, sample dimensions, and mass into the software of the GrindoSonic® device.

Nevertheless, it is important to note that the “I” values that were valid for the GrindoSonic software do not account for the empty sections within the honeycomb sandwich structure. Therefore, Ea values for honeycomb structures need to be adjusted [19]. The same method was used to quantify the elastic modulus values for the bulk specimens produced, and this modulus represents the actual elastic modulus of the material, which is described as Ec. While finding Ec, the frequency values, mass and dimensions of bulk samples determined in flexural and torsional modes again according to the ASTM C 1259 standard were entered into the device’s software and elastic modulus values were obtained non-destructively.

A ceramic material’s densification affects its elastic modulus [23]. The elastic modulus values of the bulk and honeycomb specimens ought to be comparable, presuming equal densification. Thus, for the honeycomb structures in each hole design, the corrected inertia (Ic) can be computed using the following equation:

$$ {I}_{c}=\frac{{E}_{a}I}{{E}_{c}}$$
(2)

Bending strength, a critical parameter in the structural analysis of beams, is characterized by the distribution of stress across the beam’s cross-section during bending. When a beam undergoes bending, the top and bottom surfaces experience maximum stress, whereas the neutral axis, situated at the beam’s centroid, remains stress-free. The bending strength of the 3D-printed specimens was determined by the three-point bending test procedure using a tension/compression testing machine (Instron® 5569, USA), with a load span of 40 mm and a loading rate of 0.5 mm/min in accordance with the ASTM 1161 standard. In a three-point bending test, the bending stress (σ) at a given distance from the neutral axis (y) can be expressed as follows:

$$ \sigma =\frac{FLy}{4I}$$
(3)

where F is the bending force, L is the outer load span, and I is the moment of inertia. Equation 3 illustrates that the bending stress is directly proportional to the distance from the neutral axis, underscoring the critical role of particular beam design in achieving optimal stress distribution and ensuring structural integrity. Inserting y = h/2 in Eq. 3, the nominal bending strength (σNB) of the beam can be obtained as [24]:

$$ {\sigma }_{NB}=\frac{{F}_{max}Lh}{8I}$$
(4)

where Fmax is the bending force at failure.

However, it is more accurate to calculate true bending strength (σTB) using corrected inertia Ic values for the honeycomb structures in this study. Moment of inertia values for the honeycomb structures found from Eq. 2 were used, and the true bending strength (σTB) was determined using the following equation as given in ASTM C 1674 [25]:

$$ {\sigma }_{TB}=\frac{{F}_{max}Lh}{8{I}_{c}}$$
(5)

Equation 4 could not provide the stress operating directly upon the flaw that led to failure in the outer surface of the specimen for cellular structures [25]. Therefore, in this study, the bending strength was calculated and given by both equations for comparison purposes.

The two-parameter Weibull distribution function was also used for the statistical assessment of the bending strength values in accordance with Eq. 6 [26]:

$$ P=1-exp\left\{{\left(-\frac{\sigma }{{\sigma }_{0}}\right)}^{m}\right\}$$
(6)

where P is the failure probability, m expresses the Weibull modulus, σ0 is characteristic strength (or the scaling factor), and σ is bending strength. OriginPro software was used to draw and find the Weibull diagrams and the Weibull parameters of the ceramic specimens after the bending strength tests. In addition to the Weibull analysis, the bending strength/density ratio values of the samples were evaluated to compare the specific strength of honeycomb structures with different hole designs. The difference in bending strength resulting from the hole position of the honeycomb structures was explained by analyzing the stress distributions created by bending loads using the commercial software COMSOL Multiphysics®. To assess the risk of failure of honeycomb structures with different hole positions, the maximum normal stress criterion (Rankine) with a failure index was examined.

Results and discussion

The relative density values of the sintered ceramics were found 53.4% and 52.2% for the honeycomb specimens in which holes were positioned on the upper and lower face-sheets and lateral sides, respectively as given in Table 1. Also, 95.9% relative density was obtained for the bulk samples. Honeycomb sandwich samples could be produced at 45% lower relative density than bulk samples. Because these samples consist of a small cross-sectional area and a large exposed area within the cells. Since the relative densities of the samples were calculated from the ratio of the volumetric density to the theoretical density of Al2O3 (3.98 g/cm3), the densities of the honeycomb sandwich samples were lower than the bulk samples despite the similar volume (∼ 0.53 cm3) due to large exposed areas and lower weight of honeycomb structures. Average weight of samples were 1.10 g for the samples with lateral holes, 1.13 g for the samples with holes on the upper and lower face-sheets, and 2.05 g for the bulk samples.

Table 1 Relative density, elastic modulus, and bending strength values of the sintered specimens
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The difference in the relative density values between the samples with two different hole positions is also related to the difference between the areas of voids and the number of voids in these samples. After the CAD designs were transferred to the device software in STL format and scale factors were entered for printing, the holes differed from the design dimensions (Ø=0.5 mm) because of different shrinkage ratios and hole positions depending on this direction. Since the specimens shrank at different ratios in the X, Y, and Z directions after sintering, the maximum length of the holes changed to ∼ 0.7 mm after sintering in the Z direction for samples with lateral holes. However, the holes in the upper and lower face-sheets decreased to ∼ 0.2 mm after sintering following densification. The difference can be seen from the SEM images of the sintered samples shown in Fig. 3(a) and Fig. 3(b). The thermally etched microstructure of the samples is also presented in Fig. 3(c).The grain sizes are not very homogeneous, and there are very fine grains as well as coarse grains in the microstructure.

Fig. 3
figure 3

Maximum hole sizes (a) on the upper and lower face-sheets, and (b) on the lateral sides, and (c) thermally etched surface image of the samples

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Table 1 also shows the elastic modulus and calculated moment of inertia values. The names of the samples have been abbreviated for ease of explanation. While “bulk” represents solid samples, “SH” refers to samples with surface holes containing these holes on the upper and lower face-sheets, and “LH” refers to samples with lateral holes. The impulse excitation of vibration method was used in the experiments to determine the samples’ elastic modulus as given in the previous section. A mathematical model that connects a material’s density to its elastic modulus in both bulk and porous forms was established by Ashby and Gibson [27]. This model states that the elastic modulus decreases with decreasing relative density, or increasing porosity. This situation is also evident from the difference in the elastic modulus of the bulk and honeycomb structures. However, explaining the difference in the elastic modulus between Al2O3 (LH) and Al2O3 (SH) samples based on densification may not be entirely appropriate. The elastic modulus was impacted by variations in the moment of inertia.

Using a three-point bending test procedure in which the force operates perpendicular to the printing direction, the bending strength of the samples was determined. Following each sample failure, the test was completed, and the failure load (Fmax) was noted. The standard formula for three-point bending beams (Eq. 4) was used to determine the nominal strength in the bending experiments. Nevertheless, the usual method that calculates a moment of inertia from a whole cross-section does not effectively provide the stress acting upon the flaw that produced failure for such honeycomb geometries [25]. However, the bending strength results obtained using this standard equation were still presented to observe and compare the differences, as given in Table 1, as nominal bending strength. The load-bearing cross-section varies with the core geometry; therefore, the corrected moment of inertia along with ASTM C-1674 should be employed. In evaluating the true bending strength based on Eq. 5, the corrected moment of inertia for honeycomb structures that was determined using the data derived from Eq. 2 was used. In Table 1, the corresponding values for the corrected moment of inertia and true bending strength are also provided.

It is seen that the true strength value of Al2O3 (LH) samples is 73% higher than Al2O3 (SH), while the nominal bending strength is 79% higher. In the ASTM C1674 standard, nominal bending strength, wall fracture strength, and/or honeycomb structure strength are mentioned for ceramic honeycomb cellular structures. Using the standard bending strength formula and accounting for specimen size and fracture force, one can find the bending strength of a nominal beam. On the other hand, the real moment of inertia, which accounts for the hollow sections within the several section channels of the test specimen is considered when computing the wall’s fracture strength. When evaluating the honeycomb bending strength, wall fracture strength offers a more accurate measurement than the nominal bending strength that is computed [25]. In addition, in the case of honeycomb sandwich structures, it is mainly the surfaces (face-sheet) that bear the load. For Al2O3 (SH) samples, compared to Al2O3 (LH) samples, the bending strength was weaker due to the presence of holes on the surfaces exposed to tensile stress, and stress concentration effects.

The placement of holes at the upper and lower face-sheets, where y attains its maximum value, posed a potential compromise to the overall strength of the beam. However, a more judicious approach was to place these holes on the neutral plane, where bending stresses are null. This refined design not only mitigated the risk of weakening the beam but also held the promise of yielding enhanced strength values. By aligning holes with the neutral axis, the structural integrity of the beam was preserved, leveraging the inherent balance in stress distribution to optimize the overall performance of the 3D-printed Al2O3 samples.

An analysis of stress distributions resulting from bending loading in honeycomb structures was conducted using COMSOL Multiphysics® to enhance the understanding of the variation in bending strength attributed to the hole positions of the samples. The specimen’s density, Poisson ratio, and elastic modulus were 3.81 g/cm³, 0.2, and 390 GPa, respectively. The model implemented in the software utilized a solid mechanics module featuring a linear elastic material. To simulate static bending, a 75 N load was applied to the center axis which was constrained along a defined line due to circular contact. The material’s tensile strength was set to 417 MPa, and the Rankine criterion (maximum normal stress criterion) was used to assess the cross-sectional failure risk of the geometries. According to the Rankine criteria, the first principal stress must be greater than the material’s tensile strength for a crack to propagate in brittle materials (e.g. ceramics) [28]. Finite element analysis utilizes a failure index, derived from the ratio of the computed value to the specified tensile strength. A result less than 1 signifies the satisfaction of the criterion, whereas a result exceeding 1 indicates a violation. In other words, as the failure index approaches 1, the specimen approaches failure, signifying a critical point in its structural integrity. This index serves as a crucial indicator that offers insights into the proximity of the analyzed structure to potential failure, aiding in the assessment of material performance and design robustness.

The cross-sectional distribution of the Rankine failure criterion for both the bulk and honeycomb structures is presented in Fig. 4. The Rankine failure index values were calculated as 0.1560, 0.2944, and 0.8731 for Al2O3 (bulk), Al2O3 (LH) and Al2O3 (SH), respectively. The finite element analysis shows that the Rankine failure index of the bulk specimen is roughly half that of the Al2O3 (LH) specimen, confirming an approximately 1/2 ratio between the nominal bending strengths of Al2O3 (LH) specimens and the bulk specimens presented in Table 1. On the other hand, according to the results of the finite element analysis, the Al2O3 (SH) specimens exhibited a significantly higher failure index compared with both the bulk material and Al2O3 (LH) samples. This is attributed to the fact that the load-bearing regions consist of surfaces, which are inherently weakened by the presence of holes in Al2O3 (SH) samples. These holes not only reduce the cross-sectional area of the surface but also contribute to an increase in stresses due to the stress concentration effect. The findings support that the design of a honeycomb structure with lateral holes for 3D printing production can be highly effective in achieving bending strength values comparable to those of a bulk structure.

Fig. 4
figure 4

Failure index and first principal stress distribution of the honeycomb structures (a) bulk, (b) Al2O3 (LH), and (c) Al2O3 (SH)

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The bending strength of brittle ceramics is fundamentally statistical and depends on the probability that a crack can be a source of fracture under certain external stresses. Different strength values are obtained, leading to scatter, depending on the flaw size and/or specimen size, flaw location within the sample, and orientation with respect to the applied stress. A gauge of material homogeneity (variation in strength) is the Weibull modulus (m). A high m value denotes low strength variation and a high degree of homogeneity [26, 29, 30]. Table 2 shows the statistical properties of the produced bulk and honeycomb structures after the bending tests. Weibull diagrams drawn using Origin software are also shown in Fig. 5. The Weibull modulus typically changes from 3 to 15 implying that a material with m = 15 exhibits less scattering of the bending strength than a material with m = 4 [26]. According to the Weibull analysis, the scaling factor is associated with a particular failure probability, which is typically 63.2%. In engineering applications, a high σ0 indicates a lower probability of failure and offers a safety margin. An increased scaling factor suggests that a considerable percentage of the ceramic specimens have strengths that are on par with or higher than this value [31].

Table 2 Statistical properties of bulk and honeycomb structures
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The Al2O3 (SH) samples exhibited the highest Weibull modulus value, whereas the bulk and Al2O3 (LH) samples showed similar values. Despite the presence of surface holes lessening the strength of Al2O3 (SH) specimens, it also reduced defect variability among the samples, contributing to a relatively high m value. Conversely, the difference between the bulk and Al2O3 (LH) in σ0 values was only 10% for the true strength values. This variation is thought to be due to differences in flaws that may occur during the sintering of face-sheets lying on a hollow structure, namely honeycomb. For Al2O3 (SH), σ0 value found using true bending strength values is around half of the bulk, which is compatible with the stress concentration caused by the holes on the face-sheet. Considering all these results, it is evident that Al2O3 (LH) samples exhibited relatively high strength, minimizing the risk of unexpected failures and optimizing material usage in various structural applications.

Fig. 5
figure 5

Weibull diagrams for bulk and honeycomb structures obtained from (a) nominal bending strength and, (b) true bending strength values, ■: bulk, □: Al2O3 (SH), ○: Al2O3 (LH)

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Cellular materials have the advantage of exhibiting high specific physical properties [32]. In applications requiring light load-bearing, materials with high specific strength are crucial. Figure 6 illustrates the specific strength values of 3D-printed Al2O3 samples, considering both nominal bending strength and true bending strength. Analyzing the specific strength for nominal bending strength values reveals that, while bulk samples have an average value of 110 kNm/kg, Al2O3 (LH) samples achieve values close to bulk samples because of their low density, whereas Al2O3(SH) remains low. However, when the low densities of Al2O3 (LH) samples and the true strength values were combined, Al2O3 (LH) samples provided a significant advantage not only over Al2O3 (SH) but also over bulk Al2O3. Their specific strength reached an average value of 180 kNm/kg, representing a 65% increase compared with the specific strength of bulk samples. These results indicate that the lightweight Al2O3 sandwich honeycomb structures, produced with a lateral hole design, serve as a viable alternative to the bulk Al2O3 structures in applications that prioritize lightness. Lightness of honeycomb sandwich structures makes suitable these materials for the applications where weight and strength are important. Al2O3 honeycomb sandwich structures can be used in aerospace applications, such as in the construction of aircraft components and satellite systems. The combination of high strength and the lightweight honeycomb structure contributes to overall weight reduction in aerospace structures. This kind of materials can also be preferred in lightweight vehicle structures or components. This study establishes ultimately that the optimal hole position for honeycomb sandwich structures to be used in lightweight designs, produced using slurry-based 3D printing techniques such as SLA or DLP, is lateral holes.

Fig. 6
figure 6

Specific strength values of Al2O3 samples for (a) nominal bending strength, and (b) true bending strength

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Conclusions

In this study, Al2O3 ceramic honeycomb sandwich samples with a hexagonal core were prepared using SLA 3D-printing in order to examine the effect of the position of the holes made to remove uncured slurry on the bending strength of the samples. The following were the main conclusions reached:

  • The relative density values were 53.4% and 52.2% for Al2O3(SH) and Al2O3(LH) samples, respectively, due to the difference between the area of voids and the number of voids in these samples.

  • The true bending strength value of Al2O3 (LH) samples calculated using the corrected moment of inertia was 73% higher than Al2O3(SH), while the nominal bending strength was 79% higher due to the presence of holes on the surfaces exposed to tensile stress, and stress concentration effects for Al2O3(SH) samples.

  • The Rankine failure index of the Al2O3 (SH) samples was noticeably higher than that of the bulk material and the Al2O3 (LH) samples because the holes not only reduced the cross-sectional area of the tensile surface but also contributed to an increase in stresses due to the stress concentration effect.

  • Al2O3(LH) samples gave a significant advantage over both bulk Al2O3 and Al2O3(SH) when their low densities and true bending strengths were combined. Their specific strength averaged 180 kNm/kg, which is 65% more than that of the bulk samples.

These findings indicate that for applications where weight is a critical factor, Al2O3 sandwich honeycomb structures with a lateral hole design are a viable substitute for bulk Al2O3.