The Effect of Layer Thickness and Nozzle Diameter in Fused Deposition Modelling Printing on the Flexural Strength of Zirconia Ceramic Samples Produced by a Multistage Manufacturing Process

Abstract

The process of creating ceramic items using fused deposition modelling (FDM) enables the creation of intricate shapes for a variety of purposes, including tooling and prototyping. However, due to the numerous variables involved in the process, it is challenging to discern the impact of each parameter on the final characteristics of FDM components, which impedes the advancement of this technology. This paper deals with the application of statistical analysis in the study of the dependence of the flexural strength of sintered zirconia disks on the printing parameters (nozzle diameter, layer thickness, and infill pattern) of the fused deposition method printing of a ceramic–polymer filament containing 80 wt.% zirconia and 20 wt.% polylactide. X-ray-computed tomography and diffraction systems, scanning electron microscopy combined with energy-dispersive spectroscopy, were used for a microstructural analysis of the sintered samples. It was found that the nozzle diameter and infill pattern have no significant influence on the flexural strength values. It was assumed that this is due to the heterogeneous distribution of the ceramic phase in the manufactured filament during extrusion. On the other hand, correlation analysis and analysis of correlation diagrams have shown that the thickness of the filling layer has the greatest effect on flexural strength. The maximum (684 MPa) strength value was found in a sample printed with a layer thickness of 0.2 mm. The minimum layer thickness ensures a more uniform distribution of ceramic particles and minimizes defects in samples that occur during FDM printing. The results obtained make it possible to optimize the considered process of manufacturing ceramic products from ZrO₂ printed using FDM technology from extruded composite filaments.

1. Introduction

Ceramics based on zirconium dioxide (ZrO₂) are versatile structural materials for various applications with such outstanding properties as high bending strength, high fracture toughness, thermal and chemical stability, corrosion resistance, and ionic conductivity. Due to its high biocompatibility and aesthetic properties, zirconium dioxide has gained popularity in biomedicine and dentistry for endoprosthesis of the head of an artificial hip joint, and dental implants (crowns, bridges, and veneers) are made on its basis in dentistry [1,2,3,4,5,6,7].

The manufacturing of products from zirconium dioxide and its derivatives is most often carried out by one of the technologies, namely powder pressing and sintering, injection molding, and additive technologies [8,9]. Depending on the on the chosen method, the formation of the final ceramic product will be realized by subjecting the ZrO₂ precursor to temperature and/or pressure, which will result in the formation of a monolithic product and may lead to changes in the crystallographic structure of the original material. During high-temperature sintering, one of three types of crystalline structures may be formed, that, as a result, will determine the mechanical and physicochemical properties of the final product [9,10] (on a par with the presence of pores and macrodefects). Figure 1 shows the changes in crystallographic structure as a function of temperature: monoclinic (m), tetragonal (t), and cubic (c) [9].

The monoclinic phase (m-ZrO₂) is thermodynamically stable and exists at room temperature. The tetragonal phase (t-ZrO₂) is metastable and exists at temperatures from 1000 to 2285 °C. Under mechanical strains or at lower temperatures, zirconium dioxide’s tetragonal phase can transition to the monoclinic (m) ⇄ (t) phase. The metastable tetragonal phase gives way to the more thermodynamically advantageous monoclinic phase due to tensile stresses near the fracture tip [11]. A 7.7–9% local volume increase occurs during this phase, resulting in a localized compression stress at the fracture tip that opposes the external load. Temperatures greater than 2285 °C are necessary for the cubic phase transition. In the cubic modification, zirconium dioxide exists up to a melting point of 2715 °C. The transition (t) ⇄ (c) occurs without a significant change in the volume of the structure. The change in the crystal structure of zirconium dioxide can occur not only under the influence of temperature, but also under high pressure, which is present during the production of ceramics by powder pressing. At ambient temperature, the pressure range of 4.1 to 4.6 GPa [12,13] is where the transition from monoclinic to tetragonal crystal structure is seen. The tetragonal crystal structure of zirconium dioxide changes to an orthorhombic one as the pressure rises to 15 GPa [14]. There are several methods to control the phase composition of zirconium dioxide-based materials, the main one being the alloying of ZrO₂ with heterovalent metal oxides followed by a heat treatment. The most promising material for use in restorative dentistry is zirconium dioxide stabilized in tetragonal modification. The stabilization of zirconium dioxide is achieved through alloying with magnesium or calcium oxides, but the most common is yttrium oxide. Chemical stability, high hardness and crack resistance, low heat conductivity, and strong light transmission are some of the special qualities of yttrium-stabilized tetragonal zirconia (Y-TZP) ceramic [15,16]. Additionally, it is crucial for aesthetic dentistry because the color properties of these ceramics are like those of genuine tooth tissues [17]. t-ZrO₂-based ceramics do not result in allergies or indications of incompatibility in the oral cavity, according to the research of Filoche et al. [18]. Furthermore, zirconium dioxide is biocompatible with oral cavity tissues and mucosa [19]. The material’s unquestionable benefits include excellent mechanical and aesthetic qualities, as well as high functional and corrosion resistance. Zirconium dioxide does not transmit X-rays and does not take part in galvanic reactions [20]. Because of its poor thermal conductivity and thermal insulation, this material solves the issue of temperature sensitivity [21]. On the other hand, the natural brittleness and high strength characteristics of ceramics cause such limitations related to its processing as long manufacturing time, high labor intensity and increased cost, high tool wear, low machining accuracy, and the impossibility of producing complex shapes, since the material is difficult to be machined even with special diamond tools [22].

Additive manufacturing (AM) technologies are an alternative method to produce complex ceramic products with high precision and low cost [23,24,25]. Zirconia ceramics have been made using a variety of AM processes, such as fused deposition modeling (FDM), stereolithography (SLA), inkjet printing (IJP), selective laser sintering (SLS), and selective laser melting (SLM). Each of the above technologies has its own advantages and disadvantages, the main ones being the high cost of the equipment required to produce the final product. In our previous work, we have developed a technology for the fabrication of highly filled ceramic polymer filaments for the subsequent printing of samples by FDM. It has also been shown that the mechanical properties of the fabricated filaments and FDM samples depend on the distribution of ceramic particles [26,27] along both the filament length and the sample volume. In addition, it has been found that the performance of sintered alumina samples in bending tests depends on the thickness of the filler layer and the nozzle diameter of the FDM printer [28].

The authors [29] studied the mechanical properties of composite materials based on polyamide filled with a 30, 35, and 40 wt.% of ZrO₂ ceramics. The samples produced by FDM printing technology were subjected to tensile and bending tests. The results showed that the samples with a 30% filler have enhanced mechanical properties, whereas a further increase in the ZrO₂ filler concentration does not significantly increase the mechanical properties of the samples fabricated by the FDM printing technology of the composite material. In [29], no attempt was made to fabricate a ceramic sample and investigate the resulting ZrO₂-based ceramics. This issue was investigated in [30,31,32,33,34]. It has been shown that the main influence on the strength and density of the ceramic samples obtained after annealing is caused by triangular voids occurring at the intersection of tracks, interlayer defects, and pores. The main cause of pores is the destruction of the binder and the evaporation of moisture arising during extrusion. In [33] it was shown that the shape of defects in ceramic samples caused by excessive extrusion can be different depending on the direction of the tracks during the FDM printing of the workpiece.

In [34,35], the influence of the percentage of filling, thickness, and width of the filling layer on the strength of the samples made by FDM printing technology from polylactide (PLA) and polyvinyl acetate (PVA) plastics was studied. Moradi et al. demonstrated that the width of the filling layer also influences the strength of the samples produced by FDM printing technology by reducing the level of defects. In [36] it is shown that the key trend in the works devoted to ceramic products obtained from blanks produced by FDM printing technology from various composite filaments has been the optimization of printing parameters to improve the quality of ceramic samples. In the same work it is shown that the main direction of work will maintain the identified trend and will be aimed, among other things, at reducing the level of defectiveness.

Investigating the technological aspects of FDM printing that influence the biaxial flexural strength value of sintered zirconia specimens is the aim of this work.

2. Materials and Methods

2.1. Filament Manufacturing, Printing, and Postprocessing

Zirconia (3Y-TZP, 3 mol.% Y₂O₃, Plasmotherm Ltd., Moscow, Russia, d₅₀ = 30 µm) and polylactide (PLA, eSun Ltd., Shenzhen, China, d₅₀ = 45 μm) were mixed in ratios 80-20 3Y-TZP-PLA by weight in a PM 100 (Retsch, Haan, Germany) planetary mill for the subsequent extrusion of the filament. The obtained suspension was dried for 24 h at 90 °C and sieved. A Wellzoom desktop extruder (Wellzoom, Shanghai, China) was used for filament production. This process produced a filament with a composition of 81.7% ZrO₂ and 18.3% PLA. The PrusaSlicer 2.5.2 software was used to print samples from the produced filaments on a Black Widow 3D printer (Tevo 3D, Zhanjiang, China). The extrusion temperature was 220 °C, the table temperature was 70 °C, the feed rate was 20 mm/s, and no forced cooling was used during printing. The following printing settings were used for optimization: filling pattern (zigzag, concentric, and line), nozzle diameter (0.6, 0.8, and 1.0 mm), and layer height (0.2, 0.3, and 0.4 mm). Regardless of the other settings, the filling percentage upon printing was 100%. In the SNOL 1.7/1700 (AB Umega, Utena, Lithuania) air furnace, printed “green” specimens were subjected to thermal debinding (up to 600 °C) and sintering (1550 °C). Figure 2 shows the sintering cycle of the printed samples.

In the first stage, the samples were heated from 20 °C to 600 °C at a rate of 1 °C/min, and in the second step, the heating rate was increased to 2 °C/min and continued as such until a temperature of 1550 °C was reached. In the last stage, the sample was held at 1550 °C for two hours. Then, the oven was turned off and cooling under natural conditions took place. A thorough explanation of these procedures can be found in earlier research [28].

Figure 3 shows an image of the shape and dimensions of a workpiece made by FDM printing technology from a produced filament.

The total number of ZrO₂ ceramic specimens tested in biaxial compression was 165.

2.2. Statistical Analysis Methodology

Descriptive statistical techniques were used to evaluate the structured data, estimating the sample mean, sample mean square deviation, maximum and lowest values, first and third quartiles, and median value [37]. The belonging of the distribution of mechanical properties of zirconium dioxide-based ceramic specimens in three-point bending tests to the normal distribution law was analyzed using two parametric, two non-parametric and two information criteria:

• Shapiro–Wilk criterion [38];
• D’Agostino’s criterion [39];
• Kolmogorov–Smirnov criterion [40];
• Anderson–Darling criterion [41];
• Akaike’s criterion [42];
• Bayes criterion [43].

Based on the Monte Carlo [44] method’s calculation of the criterion’s statistical power based on the number of tested samples (100,000 tests per point), the choice between parametric and non-parametric statistical criteria was made. A level of statistical significance of 0.05 was chosen. The minimum of Akaike’s information criteria and Bayes criterion was used to estimate the simple law of distribution that was closest to the data. Seven simple continuous distributions were taken into consideration as follows:

• Normal;
• Logarithmically Normal;
• Logistic;
• Cauchy;
• Gamma;
• Weibull;
• Exponential;
• Gumbel.

The greatest likelihood approach was used to determine the distributions’ parameters [45]. The selection of the criterion with the highest statistical power for the data under investigation is the outcome of the statistical power assessment of the criterion for determining whether the data conforms to the normal law of distribution, and which is the most similar to the data theoretical distribution. A conclusion regarding the statistically significant difference between the distribution law and the normal law should be drawn based on the outcome of applying the criterion. Based on this finding, a set of criteria was chosen to assess statistically significant differences between the groups of printed samples whose blanks were made using various filling types (Zigzag, Concentric, and Linear), filling thicknesses (0.2 mm, 0.3 mm, and 0.4 mm), and nozzle diameters (0.6 mm, 0.8 mm, and 1 mm).

The algorithm used in the presented work was as follows: if the normal distribution law is the closest to the law of data distribution, then ANOVA and Tukey’s test are applied; if not, the Kruskal–Wallis test [46] and Dunn’s criterion [47] are applied, and the Bonferroni correction [48] is used as a multiple comparison correction. Applying these tests results allows us to split the data into groups that differ from one another statistically significantly or do not differ from one another in any way. Hierarchical cluster analysis is based on the conclusion obtained regarding the number of groupings that are statistically substantially different [49]. When data clustering was performed in the study that was given, the distance between the elements that were a part of one cluster was determined by taking the highest difference between any two elements and then averaging the distance in each cluster. The Spearman correlation between the maximum distance and the cofounded distance of hierarchical clustering was used to do the quality testing of the method. Following the division of the data into new groups and the confirmation of the hypothesis that the data’s distribution law deviates from the Gaussian distribution law, the data were analyzed using Spearman correlation [50], with the Evans scale [51] being used to determine the correlation’s strength. The connectedness graph between variables was created using the statistical significance matrix (p-value matrix) and the correlation matrices between variables that were acquired. Variables with a statistically significant correlation were regarded as related variables when the graph was being constructed. Three distinct centrality measures—degree centrality [52,53], proximity centrality [54], and betweenness centrality [55]—were used to rank the variables that were part of the correlation graph. The regression model was constructed using the variable with the highest centrality as the dependent variable as a function of the completion percentage.

Three distinct metrics of centrality were used to rank the variables that were a part of the correlation graph. Degree centrality [55,56]:

$${\mathsf{C}}_D\left(i\right)=\sum _{j=1}^{n}a(i,j)$$

(1)

where C_D—the degree centrality of i-th vertex; n—vertex count; and a(i, j) = 1, if and only if the vertices are connected by an edge.

Closeness centrality [53]:

$$C_c\left(n_i\right)={\left[\sum _{j=1}^{g}d\left(n_i,n_j\right)\right]}^{-1}$$

(2)

where d(n_i, n_j)—the path length between two nodes.

Betweenness centrality [56]:

$$C_B\left(n_i\right)={\displaystyle \frac{\sum _{j<k}{g}_{jk}\left(n_i\right)}{g_{jk}}}$$

(3)

where $g_{jk}\left(n_i\right)$—the number of geodesic distances between nodes j and k that include node i.

The robust regression method [57] was used to construct a model that predicted the centrality variable based on the percentage of occupancy in each of the chosen groups in situations when the data distribution followed a distribution law that was different than normal.

The R programming language and the integrated development environment Rstudio 2023.06.1 Posit Software, PBC, GNU license was used for all of the statistical analysis and model construction in this work.

2.3. Density, X-Ray Diffraction (XRD), Tomography, and Microstructural Analysis

Archimedes’ technique in distilled water was used to determine the density of the sintered samples. The ZrO₂ density of 6.05 g/cm³ was used to compute the theoretical density. The microstructural analysis was performed using an X-Act energy dispersive spectroscopy (EDS) detector (Oxford Instruments, Abingdon, UK) in a scanning electron microscope LYRA3 (SEM, Tescan, Brno, Czech Republic). Using an Empyrean diffractometer (PANalytical, Almelo, the Netherlands) with a radiation source Cu–Kα (λ = 1.54 Å) operating at 30 mA at 40 kV and in the 2θ angle range of 5–70°, the phases of raw powders and sintered samples were determined. A step size of 0.05 and a scanning speed of 0.06/min were used for the study. A Nordson DAGE XD7600NT Ruby FP (Nordson DAGE, Buckinghamshire, UK) was used for the X-ray-computed tomography.

2.4. Mechanical Characterization

In accordance with the ISO 6872:2019 procedure, the flexural strength of the sintered disk-shaped ceramic samples was calculated [58]. The testing equipment INSTRON 5989 (Instron, Norwood, MA, USA) was used to conduct flexural tests at room temperature. The methods used for data collecting and computation are described in detail elsewhere [28]. Figure 4 shows a schematic of the biaxial flexural tests and a testing machine image.

3. Results and Discussion

3.1. Test Results

Figure 5 shows representative optical images of the sintered samples after mechanical testing. The relative density of the sintered composites was calculated as the ratio of the bulk density to the theoretical density of zirconia and was 97–97.5% of the theoretical ZrO₂ value.

Figure 6 shows the stress–strain diagrams for the sintered samples obtained from FDM-printed disks with a fill layer thickness of 0.3, nozzle diameter of 0.6, and zigzag infill pattern.

An analysis of the engineering diagram of the stress–strain state under biaxial loading shows that, for some samples, a stepwise fracture process is observed (Figure 6, sample No. 5). This behavior may be due to the presence of a structural defect in this sample, which leads to a primary fracture, followed by the destruction of the sample at lower stresses and greater strain. As will be shown below, the samples with the lowest strength fell into a separate group, statistically significantly different from the rest of the samples.

3.2. Statistical Analysis

Table A1. The entire data set that was analyzed in the manuscript.

№	ND	Lh	Infill Pattern	DFDM	DS	HFDM	HS	WFDM	WS	Fmax	EFmax	FS
1	0.8	0.2	Line	24.895	20.029	2.329	2.031	3.089	2.594	651.168	0.11	283.002
2	0.6	0.3	ZigZag	25.206	19.963	1.245	0.953	1.982	1.316	132.761	0.056	262.600
3	0.6	0.3	ZigZag	25.170	19.865	1.177	0.9	1.857	1.563	142.661	0.083	315.745
4	0.6	0.3	ZigZag	24.957	20.112	1.146	1.088	1.832	1.688	135.63	0.054	300.184
5	0.6	0.3	ZigZag	25.044	19.987	1.278	0.97	1.871	1.595	289.878	0.134	552.317
6	0.6	0.3	ZigZag	25.092	19.873	1.107	0.973	1.541	1.555	108.736	0.049	205.904
7	0.6	0.3	ZigZag	24.863	19.897	1.287	0.926	1.823	1.585	160.788	0.07	336.162
8	0.6	0.4	ZigZag	25.121	19.779	1.218	0.918	1.805	1.496	286.919	0.115	610.367
9	0.6	0.4	ZigZag	25.268	19.897	1.252	0.987	1.892	1.528	163.084	0.083	300.119
10	0.6	0.4	ZigZag	24.850	20.120	1.159	1.067	1.964	1.423	117.155	0.049	184.479
11	0.6	0.4	ZigZag	24.673	19.920	1.195	0.916	1.848	1.577	90.587	0.041	193.549
12	0.6	0.4	ZigZag	25.097	19.794	1.201	1.024	1.698	1.483	195.178	0.092	333.693
13	0.6	0.4	ZigZag	24.567	20.080	1.292	1.010	1.801	1.574	106.433	0.065	187.047
14	1	0.4	Concentric	25.278	19.672	1.103	0.991	1.856	1.594	155.205	0.111	283.318
15	1	0.4	Concentric	25.383	20.301	1.158	0.932	1.864	1.540	55.977	0.031	115.530
16	1	0.4	Concentric	24.960	20.164	1.085	0.971	1.709	1.372	144.486	0.102	274.729
17	1	0.4	Concentric	24.796	19.651	1.122	0.987	1.713	1.585	143.436	0.062	263.961
18	1	0.4	Concentric	24.779	20.205	1.184	0.941	1.603	1.458	163.548	0.067	331.118
19	1	0.4	Concentric	25.090	20.003	1.115	0.984	1.631	1.466	137.428	0.086	254.449
20	1	0.3	ZigZag	25.388	19.803	1.098	1.028	1.750	1.398	139.988	0.082	237.477
21	1	0.3	ZigZag	24.226	19.928	1.099	1.029	1.801	1.495	159.434	0.071	269.94
22	1	0.3	ZigZag	24.860	19.452	1.385	1.113	1.391	1.028	310.52	0.126	448.63
23	1	0.3	ZigZag	24.969	20.075	1.129	1.098	1.506	1.196	160.994	0.086	239.398
24	1	0.3	ZigZag	24.636	19.695	1.111	0.963	1.763	1.484	98.493	0.059	190.4
25	0.8	0.3	Concentric	24.704	19.692	1.300	1.051	1.949	1.571	183.578	0.083	297.893
26	0.8	0.3	Concentric	24.905	19.719	1.254	1.124	1.940	1.484	164.023	0.052	232.749
27	0.8	0.3	Concentric	24.801	19.730	1.167	1.120	1.904	1.567	235.446	0.073	336.49
28	0.8	0.3	Concentric	27.723	19.772	1.133	1.098	1.622	1.550	218.338	0.128	324.669
29	0.8	0.3	Concentric	24.741	19.939	1.124	1.057	1.763	1.443	296.557	0.097	475.855
30	0.8	0.3	Concentric	24.553	19.856	1.279	1.050	1.889	1.582	168.68	0.069	274.285
31	0.8	0.3	Line	24.560	19.961	1.343	1.053	1.836	1.550	71.489	0.069	115.584
32	0.8	0.3	Line	24.343	19.94	1.339	1.038	1.944	1.521	80.726	0.064	134.318
33	0.8	0.3	Line	24.768	19.943	1.345	1.077	1.831	1.546	101.268	0.055	156.515
34	0.8	0.3	Line	24.733	19.987	1.334	1.099	1.912	1.561	116.469	0.047	172.875
35	0.8	0.3	Line	24.470	19.985	1.311	1.096	1.923	1.575	86.264	0.048	128.746
36	0.8	0.3	Line	24.631	19.969	1.335	1.107	1.907	1.529	101.35	0.038	148.267
37	0.8	0.2	Line	24.698	19.897	1.366	0.974	1.889	1.542	182.911	0.064	345.652
38	0.8	0.2	Line	24.445	19.913	1.363	1.079	1.910	1.553	263.379	0.121	405.56
39	0.8	0.2	Line	24.653	19.918	1.372	0.949	1.872	1.535	183.982	0.066	366.235
40	0.8	0.2	Line	24.473	19.903	1.330	0.987	1.915	1.547	183.22	0.075	338.577
41	0.8	0.2	Line	24.761	19.910	1.374	1.006	1.859	1.545	246.785	0.092	437.159
42	0.8	0.2	Line	24.426	19.925	1.320	0.926	1.876	1.540	103.176	0.059	215.711
43	0.8	0.2	Concentric	24.622	19.998	1.275	1.059	1.863	1.538	219.766	0.131	351.306
44	0.8	0.2	Concentric	24.891	19.924	1.253	1.083	1.814	1.510	180.27	0.063	275.539
45	0.8	0.2	Concentric	24.707	19.927	1.256	0.969	1.894	1.497	178.876	0.083	341.524
46	0.8	0.2	Concentric	24.467	19.946	1.201	1.105	1.671	1.301	155.909	0.053	228.909
47	0.8	0.2	Concentric	24.980	19.937	1.252	1.038	1.845	1.509	182.528	0.062	303.705
48	0.8	0.2	Concentric	24.731	19.949	1.191	1.017	1.871	1.554	194,848	0.094	337.731
49	0.6	0.2	Concentric	24.571	19.745	2.109	1.882	2.048	1.752	612.376	0.114	309.953
50	0.6	0.2	Concentric	24.559	19.250	2.049	1.817	2.088	1.790	396.283	0.106	215.185
51	0.6	0.2	Concentric	24.711	19.756	2.003	1.871	2.045	1.715	457.9	0.153	234.498
52	0.6	0.2	Concentric	24.660	19.674	2.062	1.887	2.007	1.773	432.105	0.086	219.876
53	0.6	0.2	Concentric	24.436	19.969	2.108	1.823	2.020	1.724	454.537	0.093	245.195
54	0.6	0.2	Concentric	24.436	19.969	2.108	1.823	2.020	1.724	885.289	0.228	477.561
55	0.6	0.2	Concentric	26.624	19.720	2.011	1.932	2.025	1.715	504.597	0.229	242.352
56	0.6	0.3	Line	25.128	19.770	1.146	0.982	1.842	1.547	273.551	0.174	508.548
57	0.6	0.3	Line	24.967	19.747	1.283	0.967	1.847	1.572	177.433	0.126	340.21
58	0.6	0.3	Line	24.910	19.959	1.154	1.041	1.829	1.590	197.263	0.129	326.333
59	0.6	0.3	Line	25.083	19.842	1.199	0.998	1.861	1.568	113.473	0.04	204.243
60	0.6	0.3	Line	25.125	19.896	1.196	1.046	1.819	1.593	139.662	0.068	228.84
61	0.6	0.3	Line	24.946	19.795	1.210	0.992	1.866	1.558	158.69	0.072	289.086
62	0.8	0.2	ZigZag	24.627	19.884	1.282	1.033	1.882	1.510	69.822	0.032	117.302
63	0.8	0.2	ZigZag	24.773	19.987	1.241	1.072	1.765	1.513	179.682	0.108	280.305
64	0.8	0.2	ZigZag	24.748	19.935	1.247	1.072	1.995	1.520	82.72	0.041	129.044
65	0.8	0.2	ZigZag	24.852	19.990	1.272	1.161	1.883	1.551	119.984	0.05	159,579
66	0.8	0.2	ZigZag	24.775	19.881	1.240	1.062	1.799	1.554	66.903	0.07	106.344
67	0.8	0.2	ZigZag	24.440	19.921	1.267	1.032	1.526	1.515	93.85	0.041	157.976
68	0.8	0.4	Concentric	25.182	20.047	1.640	1.248	1.885	1.610	169.789	0.106	195.432
69	0.8	0.4	Concentric	25.101	19.637	1.472	1.237	1.812	1.551	183.504	0.162	214.992
70	0.8	0.4	Concentric	25.490	20.081	1.397	0.926	1.847	1.581	126.802	0.178	265.107
71	0.8	0.4	Concentric	25.308	20.005	1.091	1.146	1.835	1.498	173.26	0.102	236.508
72	0.8	0.4	Concentric	25.072	19.776	1.385	1.045	1.741	1.487	170.028	0.063	279.129
73	0.8	0.4	Concentric	24.982	19.855	1.568	1.096	1.732	1.481	237.281	0.09	354.127
74	0.8	0.4	Concentric	25.993	19.991	1.531	0.992	1.835	1.568	162.575	0.076	296.174
75	0.6	0.4	Line	25.019	19.951	1.305	1.121	1.805	1.501	129.569	0.06	184.844
76	0.6	0.4	Line	25.030	20.022	1.189	1.010	1.829	1.517	157.908	0.06	277.51
77	0.6	0.4	Line	25.088	20.063	1.116	1.003	1.809	1.523	108.723	0.043	193.747
78	0.6	0.4	Line	25.213	20.074	1.189	1.022	1,805	1.504	170.394	0.109	292.462
79	0.6	0.4	Line	25.257	19.989	1.192	1.020	1.873	1.506	151.024	0.057	260.233
80	0.6	0.4	Line	25.142	20.059	1.168	0.996	1.878	1.520	205.697	0.091	371.729
81	0.8	0.4	Line	25.505	20.205	1.096	1.154	1.797	1.537	145.334	0.082	195.646
82	0.8	0.4	Line	25.068	20.062	1.183	1.002	1.863	1.592	115.57	0.056	206.36
83	0.8	0.4	Line	25.251	19.907	1.173	1.025	1.899	1.621	101.868	0.052	173.823
84	0.8	0.4	Line	25.063	19.860	1.195	0.935	1.826	1.560	92.912	0.04	190.531
85	0.8	0.4	Line	25.252	20.052	1.171	0.955	1.847	1.581	143.127	0.069	281.34
86	0.8	0.4	Line	25.284	20.090	1.148	1.014	1.874	1.560	125.61	0.047	219.01
87	0.8	0.3	ZigZag	24.733	19.846	1.060	1.054	1.560	1.334	115.46	0.045	186.323
88	0.8	0.3	ZigZag	24.765	20.129	1.101	0.935	1.844	1.577	56.772	0.029	116.42
89	0.8	0.3	ZigZag	24.775	19.767	1.206	0.975	1.862	1.593	138.701	0.055	261.569
90	0.8	0.3	ZigZag	24.810	19.836	1.037	1.010	1.788	1.527	107.033	0.058	188.101
91	0.8	0.3	ZigZag	24.890	20.097	1.074	0.909	1.762	1.534	206.383	0.093	447.778
92	0.6	0.2	Concentric	25.008	19.703	1.276	1.098	1.768	1.502	186.299	0.067	277.027
93	0.6	0.2	Concentric	25.011	19.550	1.279	1.075	1.846	1.589	181.833	0.075	282.080
94	0.6	0.2	Concentric	25.071	19.553	1.116	0.995	1.804	1.487	112.238	0.045	203.240
95	0.6	0.2	Concentric	24.948	19.571	1.298	1.004	1.775	1.581	182.269	0.085	324.162
96	0.6	0.2	Concentric	24.985	19.545	1.180	0.962	1.722	1.478	150.932	0.055	292.380
97	0.6	0.2	Concentric	25.240	19.707	1.221	0.993	1.796	1.511	182.691	0.07	332.151
98	0.6	0.2	ZigZag	24.890	19.718	1.302	1.177	1.681	1.425	148.314	0.068	191.931
99	0.6	0.2	ZigZag	24.549	20.083	1.119	0.939	1.778	1.498	231.11	0.111	469.899
100	0.6	0.2	ZigZag	24.404	19.608	1.098	0.998	1.782	1.541	239.796	0.107	431.616
101	0.6	0.2	ZigZag	24.824	19.550	1.111	1.013	1.750	1.506	155.273	0.071	271.265
102	0.6	0.2	ZigZag	24.578	19.729	1.208	1.039	1.808	1.531	306.748	0.128	509.410
103	0.6	0.2	ZigZag	25.188	19.447	1.278	1.029			275.121	0.123	465.811
104	1	0.4	ZigZag	25.054	19.267	1.118	0.990	1.759	1.498	235.799	0.099	431.309
105	1	0.4	ZigZag	24.866	20.076	1.175	0.916	1.679	1.401	202.951	0.102	433.628
106	1	0.4	ZigZag	25.069	19.298	1.240	0.976	1.685	1.487	148.669	0.062	279.793
107	1	0.4	ZigZag	24.358	19.919	1.201	0.984	1.825	1.500	157.306	0.069	291.254
108	1	0.4	ZigZag	24.381	19.800	1.144	0.972	1.739	1.437	107.700	0.06	204.362
109	1	0.2	ZigZag	25.034	19.790	1.174	0.990	1.824	1.571	145.846	0.058	266.772
110	1	0.2	ZigZag	24.867	19.963	1.171	1.034	1.883	1.573	157.980	0.108	264.897
111	1	0.2	ZigZag	25.254	19.710	1.186	1.013	1.603	1.402	224.800	0.086	392.730
112	1	0.2	ZigZag	24.336	19.986	1.126	1.019	1.756	1.485	266.888	0.136	460.784
113	0.8	0.4	ZigZag	25.033	20.006	1.069	0.954	1.830	1.566	79.710	0.039	156.694
114	0.8	0.4	ZigZag	24.917	19.908	1.063	0.947	1.681	1.436	80.798	0.032	161.189
115	0.8	0.4	ZigZag	24.988	19.817	1.050	0.924	1.735	1.485	75.057	0.027	157.283
116	0.8	0.4	ZigZag	24.787	20.033	1.048	0.936	1.777	1.520	104.467	0.044	213.336
117	0.8	0.4	ZigZag	23.754	19.562	1.219	1.133	1.798	1.539	216.682	0.096	301.995
118	0.8	0.4	ZigZag	24.810	20.130	1.062	0.965	1.817	1.550	84.781	0.035	162.885
119	1	0.3	Concentric	25.088	19.559	1.145	1.017	1.633	1.485	76.566	0.06	132.712
120	1	0.3	Concentric	25.202	19.789	1.160	1.050	1.665	1.489	146.606	0.112	238.391
121	1	0.3	Concentric	25.041	19.685	1.118	0.974	1.723	1.502	208.468	0.101	393.947
122	1	0.3	Concentric	25.096	19.720	1.180	1.042	1.778	1.501	143.341	0.055	236.674
123	1	0.3	Concentric	25.024	19.656	1.147	1.014	1.846	1.480	85.358	0.058	148.828
124	1	0.3	Concentric	24.910	19.989	1.113	0.941	1.783	1.436	196.756	0.092
125	1	0.2	Concentric	24.890	19.709	1.153	0.935	1.845	1.503	171.845	0.085	352.395
126	1	0.2	Concentric	25.069	19.847	1.168	0.908	1.867	1.500	127.343	0.155	276.898
127	1	0.2	Concentric	25.097	19.619	1.125	0.959	1.820	1.502	124.563	0.058	242.811
128	1	0.2	Concentric	25.083	19.858	1.141	0.865	1.742	1.461	107.426	0.067	257.391
129	1	0.2	Concentric	24.941	19.977	1.143	0.986	1.765	1.465	251.357	0.138	463.505
130	1	0.2	Concentric	25.170	20.042	1.156	0.992	1.817	1.498	110.924	0.316	202.078
131	1	0.2	Concentric	25.119	20.011	1.102	0.851	1.780	1.473	136.624	0.164	338.209
132	0.6	0.4	Concentric	24.931	19.596	1.109	0.889	1.716	1.425	122.769	0.081	278.485
133	0.6	0.4	Concentric	25.088	19.573	1.199	0.916	1.728	1.418	126.733	0.079	270.779
134	0.6	0.4	Concentric	24.967	19.760	1.147	0.905	1.833	1.500	172.705	0.099	378.028
135	0.6	0.4	Concentric	25.028	19.890	1.151	0.897	1.785	1.489	117.780	0.072	262.424
136	0.6	0.4	Concentric	25.076	20.077	1.188	0.917	1.802	1.501	66.903	0.041	142.634
137	0.6	0.4	Concentric	25.031	19.558	1.174	0.909	1.787	1.456	140.778	0.072	305.438
138	0.6	0.3	Concentric	24.960	19.606	1.098	0.895	1.775	1.401	145.325	0.091	325.245
139	0.6	0.3	Concentric	24.949	19.571	1.173	0.929	1.845	1.492	194.29	0.105	403.586
140	0.6	0.3	Concentric	24.990	19.735	1.176	0.918	1.885	1.486	125.705	0.078	267.414
141	0.6	0.3	Concentric	25.108	19.895	1.028	0.898	1.851	1.503	116.599	0.049	259.214
142	0.6	0.3	Concentric	25.102	19.969	1.147	0.930	1.781	1.498	195.817	0.089	405.883
143	0.6	0.3	Concentric	25.097	19.894	1.158	0.910	1.792	1.494	273.041	0.116	591.013
144	0.6	0.2	Line	25.159	20.012	1.124	0.980	1.795	1.491	172.009	0.111	321.082
145	0.6	0.2	Line	24.975	20.005	1.137	0.949	1.799	1.516	141.687	0.07	282.042
146	0.6	0.2	Line	25.169	19.369	1.189	1.053	1.782	1.519	312.009	0.115	504.461
147	0.6	0.2	Line	25.114	19.938	1.194	1.043	1.839	1.551	103.959	0.059	171.321
148	1	0.3	Line	25.068	19.804	1.137	1.099	1.797	1.542	247.766	0.14	247.766
149	1	0.3	Line	25.050	19.918	1.171	0.918	1.732	1.588	124.721	0.075	126.696
150	1	0.3	Line	25.042	19.344	1.133	0.935	1.789	1.497	136.188	0.08	279.275
151	1	0.3	Line	24.990	19.612	1.152	0.985	1.787	1.589	96.97	0.047	179.176
152	1	0.3	Line	24.970	19.474	1.183	0.886	1.716	1.500	94.901	0.067	216.73
153	1	0.3	Line	25.003	19.551	1.147	0.992	1.816	1.510	181.783	0.093	331.167
154	1	0.4	Line	25.190	19.417	1.130	1.072	1.831	1.565	131.461	0.062	205.08
155	1	0.4	Line	24.997	19.207	1.192	0.981	1.753	1.514	234.967	0.096	437.709
156	1	0.4	Line	25.074	19.907	1.155	1.003	1.765	1.602	140.227	0.061	249.888
157	1	0.4	Line	26.060	19.859	1.163	1.014	1.859	1.545	141.663	0.057	247.000
158	1	0.4	Line	25.173	19.422	1.089	0.900	1.743	1.489	111.415	0.099	246.590
159	1	0.4	Line	25.207	19.249	1.202	1.048	1.761	1.502	218.982	0.106	357.439
160	1	0.2	Line	25.117	19.740	1.166	0.983	1.793	1.470	223.165	0.09	413.728
161	1	0.2	Line	25.166	20.048	1.124	0.920	1.738	1.480	247.881	0.132	525.030
162	1	0.2	Line	24.952	19.837	1.119	0.946	1.870	1.507	249.353	0.100	499.516
163	1	0.2	Line	25.107	19.875	1.113	0.979	1.854	1.510	365.734	0.136	684.96
164	1	0.2	Line	25.073	19.950	1.198	1.027	1.779	1.482	121.845	0.052	207.101
165	1	0.2	Line	25.024	19.939	1.175	1.020	1.857	1.499	227.871	0.096	392.650

(Appendix A) presents the full dataset used for further analysis.

Table 1. Baseline statistical values of the results of the mechanical tests *.

Statistical Value	ND, mm	DFDM, mm	Ds, mm	HFDM, mm	Hs, mm	WFDM, g	Ws, g	Fmax, N	EFmax, mm	FS, MPa
Mean value	0.6	24.984	19.816	1.292	1.090	1.837	1.542	211.412	0.089	309.625
Standard deviation		0.311	0.198	0.295	0.296	0.0988	0.094	143.202	0.040	108.422
Median		25.015	19.854	1.191	0.996	1.821	1.518	161.936	0.08	285.583
Minimum value		24.404	19.250	1.028	0.889	1.541	1.316	66.903	0.04	142.634
Maximum value		26.624	20.120	2.109	1.932	2.088	1.790	885.289	0.229	610.367
First quartile		24.895	19.704	1.148	0.929	1.786	1.495	130.367	0.061	236.462
Third quartile		25.107	19.969	1.278	1.045	1.865	1.576	224.757	0.109	335.545
Mean value	0.8	24.886	19.927	1.268	1.057	1.852	1.552	155.954	0.071	244.385
Standard deviation		0.517	0.126	0.199	0.155	0.193	0.154	88.700	0.032	92.880
Median		24.775	19.935	1.253	1.045	1.847	1.545	145.334	0.064	228.909
Minimum value		23.754	19.562	1.037	0.909	1.526	1.301	56.772	0.027	106.344
Maximum value		27.723	20.250	2.329	2.031	3.089	2.594	651.168	0.178	475.855
First quartile		24.676	19.871	1.1575	0.975	1.797	1.514	101.309	0.048	162.037
Third quartile		25.011	19.995	1.337	1.096	1.889	1.566	183.362	0.091	302.850
Mean value	1	25.013	19.768	1.152	0.985	1.757	1.484	166.095	0.092	301.299
Standard deviation		0.286	0.258	0.047	0.057	0.095	0.093	62.972	0.044	114.303
Median		25.052	19.802	1.147	0.986	1.765	1.498	146.226	0.086	268.356
Minimum value		24.226	19.207	1.085	0.851	1.391	1.028	55.977	0.031	115.530
Maximum value		26.060	20.301	1.385	1.113	1.883	1.602	365.734	0.316	684.096
First quartile		24.954	19.627	1.123	0.949	1.725	1.475	125.377	0.062	237.706
Third quartile		25.115	19.947	1.173	1.019	1.823	1.510	216.354	0.105	383.847

* The interpretation of the abbreviations is provided in the Abbreviations list.

shows the results of the basic statistical analysis of the sintered specimens after flexural tests. The analysis results are grouped according to the nozzle diameter (D) parameter used in printing the ceramic–polymer filament blank. The complete data set used for the analysis is presented in Appendix A.

Figure 7 shows the scatter analysis of the specimen flexural stress and strain corresponding to the maximum load under flexural loading depending on the nozzle diameter used in the FDM printing of the ceramic–polymer specimens.

After mechanical flexural tests, the specimens were grouped based on the thickness of the filler layer used to print the ceramic–polymer filament blank. The findings of the basic statistical analysis are shown in

Table 2. Baseline statistical values of the results of the flexural tests grouped by the fill layer thickness (H) parameter *.

Statistical Value	Lh, mm	DFDM, mm	Ds, mm	HFDM, mm	Hs, mm	WFDM, g	Ws, g	Fmax, N	EFmax, mm	FS, MPa
Mean value	0.2	24.865	19.834	1.332	1.128	1.858	1.556	230.198	0.097	314.318
Standard deviation		0.346	0.178	0.319	0.312	0.195	0.165	152.946	0.050	115.904
Median		24.890	19.907	1.215	1.018	1.832	1.514	182.610	0.086	287.691
Minimum value		24.336	19.25	1.098	0.851	1.526	1.301	66.903	0.032	106.344
Maximum value		26.624	20.083	2.329	2.031	3.089	2.594	885.289	0.316	684.096
First quartile		24.634	19.719	1.154	0.979	1.779	1.498	142.727	0.064	236.461
Third quartile		25.071	19.960	1.301	1.074	1.883	1.552	248.985	0.113	386.046
Mean value	0.3	24.966	19.816	1.185	1.006	1.797	1.508	155.724	0.078	275.248
Standard deviation		0.454	0.173	0.088	0.070	0.117	0.106	61.812	0.031	114.126
Median		24.967	19.842	1.160	1.010	1.823	1.529	142.661	0.071	261.569
Minimum value		24.226	19.344	1.028	0.886	1.3913	1.028	56.772	0.029	115.584
Maximum value		27.723	20.129	1.385	1.124	1.982	1.688	310.520	0.174	591.013
First quartile		24.772	19.720	1.131	0.944	1.763	1.491	111.105	0.055	189.251
Third quartile		25.086	19.942	1.250	1.054	1.861	1.569	188.934	0.093	328.750
Mean value	0.4	25.056	19.865	1.196	0.997	1.794	1.516	145.384	0.075	262.894
Standard deviation		0.344	0.264	0.125	0.081	0.072	0.057	47.865	0.030	88.724
Median		25.071	19.914	1.174	0.987	1.805	1.510	142.395	0.069	261.329
Minimum value		23.754	19.207	1.048	0.889	1.603	1.372	55.977	0.027	115.53
Maximum value		26.060	20.301	1.640	1.248	1.964	1.621	286.919	0.178	610.367
First quartile		24.962	19.764	1.119	0.935	1.741	1.487	112.454	0.056	195.486
Third quartile		25.203	20.061	1.201	1.022	1.844	1.564	169.968	0.096	295.246

* The interpretation of the abbreviations is provided in the Abbreviations list.

.

Figure 8 shows the scatter analysis of the specimen flexural stress and strain corresponding to the maximum load under mechanical loading as a function of the layer thickness used in the FDM printing of ceramic–polymer specimens.

The mechanical test results of the specimens grouped by the parameter and infill pattern in the FDM printing of the ceramic–polymer filament blank are displayed in

Table 3. Baseline statistical values of the results of the mechanical test results, grouped by the infill pattern *.

Statistical Value	Infill Pattern	DFDM, mm	Ds, mm	HFDM, mm	Hs, mm	WFDM, g	Ws, g	Fmax, N	EFmax, mm	FS, MPa
Mean value	ZigZag	24.811	19.864	1.173	1.004	1.770	1.493	154.317	0.0724	278.568
Standard deviation		0.304	0.201	0.083	0.067	0.121	0.107	67.127	0.030	124.144
Median		24.851	19.897	1.175	0.994	1.793	1.514	144.254	0.069	263.479
Minimum value		23.754	19.267	1.037	0.900	1.391	1.028	56.772	0.027	106.344
Maximum value		25.388	20.130	1.385	1.177	1.995	1.688	310.520	0.136	610.367
First quartile		24.664	19.787	1.106	0.954	1.738	1.484	105.942	0.049	186.866
Third quartile		25.033	19.988	1.2403	1.035	1.835	1.554	197.121	0.094	334.310
Mean value	Concentric	25.043	19.808	1.304	1.096	1.821	1.528	203.715	0.096	289.917
Standard deviation		0.481	0.197	0.297	0.288	0.108	0.094	137.845	0.049	84.372
Median		25.0095	19.774	1.178	0.994	1.816	1.50105	169.909	0.085	276.963
Minimum value		24.436	19.250	1.028	0.851	1.603	1.301	55.977	0.031	115.530
Maximum value		27.723	20.301	2.109	1.932	2.088	1.79	885.289	0.316	591.013
First quartile		24.823	19.673	1.144	0.931	1.764	1.484	136.825	0.067	239.381
Third quartile		25.097	19.964	1.279	1.093	1.866	1.568	195.574	0.106	331.893
Mean value	Linear	24.997	19.852	1.230	1.027	1.856	1.558	171.822	0.080	285.250
Standard deviation		0.291	0.229	0.175	0.152	0.180	0.149	92.593	0.031	120.352
Median		25.050	19.918	1.189	1.003	1.836	1.542	143.127	0.069	260.233
Minimum value		24.343	19.207	1.089	0.886	1.716	1.470	71.489	0.038	115.584
Maximum value		26.060	20.250	2.329	2.031	3.089	2.594	651.168	0.174	684.096
First quartile		24.910	19.804	1.148	0.979	1.797	1.510	113.473	0.057	195.646
Third quartile		25.142	19.987	1.305	1.046	1.872	1.565	205.697	0.099	345.652

* The interpretation of the abbreviations is provided in the Abbreviations list.

together with the findings of the basic statistical analysis.

Figure 9 shows an analysis of the variation of the flexural stress of the specimens and the strain corresponding to the maximum load biaxial loading depending on the infill pattern used in the FDM printing of ceramic–polymer discs.

The results of the basic statistical analysis show the presence of samples with abnormally high values of mechanical properties among the samples fabricated by multistage technology, as well as noticeable differences in the change of the medians of the mechanical properties of the samples depending on the layer thickness and nozzle diameter used in the FDM printing of the sample.

The results of the estimation of the closest to the distribution of the flexural stress of the theoretical distribution law by the Akaike and Bayesian information criteria are presented in

Table 4. The evaluation of the closest theoretical type of the flexural stress distribution of the zirconium oxide specimens tested.

Criterion	Distribution Type
	Normal	Lognormal	Logistical	Gamma	Weybull	Exponential	Gumbel	Cauchy
Akaike	1994.148	1969.620	1990.064	1970.721	1986.989	2170.777	1969.973	2029.095
Bayesian	2000.335	1975.807	1996.252	1976.909	1993.177	2173.871	1976.160	2035.283

.

Table 5. The evaluation of the closest theoretical type of strain distribution corresponding to the maximum force of the zirconium oxide ceramic specimens tested.

Criterion	Distribution Type
	Normal	Lognormal	Logistical	Gamma	Weybull	Exponential	Gumbel	Cauchy
Akaike	−585.945	−651.194	−614.515	−641.083	−611.167	−479.935	−647.446	−584.931
Bayesian	−579.757	−645.006	−608.327	−634.896	−604.980	−476.841	−641.258	−578.743

shows the results of estimating the closest theoretical distribution law to the strain distribution corresponding to the maximum force.

The analysis of the results of the information criteria application shows that the closest theoretical distribution is the log-normal distribution law of the flexural stress and deformation corresponding to the maximum force.

Figure 10 shows the results of the Monte Carlo method [44] calculation of the average power of the evaluation criteria for the compliance of the data distribution with the normal distribution law. The calculation was performed for the log-normal law of data distribution.

An analysis of the results of average power calculations shows that the Kolmogorov–Smirnov criterion has a maximum power for any number of tested samples.

Table 6. The results of testing the data for conformity to the normal distribution law using the Kolmogorov–Smirnov test *.

Kolmogorov–Smirnov Statistic	DFDM, mm	Ds, mm	HFDM, mm	Hs, mm	WFDM, g	Ws, g	Fmax, N	ε, mm	σF, MPa
D	1.000	1.000	0.848	0.803	0.928	0.891	1.000	0.511	1.000
p-value	<0.000001	<0.000001	<0.000001	<0.000001	<0.000001	<0.000001	<0.000001	<0.000001	<0.000001

* The interpretation of the abbreviations is provided in the Abbreviations list.

presents the results of testing the data for compliance with the normal distribution law (the level of statistical significance was assumed to be 0.05).

An analysis of the results of the Kolmogorov–Smirnov test shows that all of the analyzed data statistically significantly differ from the normal distribution law (p-value < 0.05). Based on this conclusion, non-parametric methods will be applied for further analysis.

The Kruskal–Wallis and Dunn criteria were applied to evaluate the statistical significance of differences in the mechanical properties of zirconium dioxide samples tested in biaxial compression depending on the infill pattern, nozzle diameter, and layer thickness. The results of the application of these criteria are presented in

Table 7. The results of applying the Kruskal–Wallis and Dunn’s criteria to evaluate statistically significant differences in the flexural stress of specimens whose blanks were manufactured using nozzles of different diameters.

Nozzle Diameters	0.6 (p-Value)	0.8 (p-Value)
0.8 (p-value)	0.001	—
1 (p-value)	0.289	0.008
Kruskal–Wallis (p-value)	0.010

(the level of statistical significance p-value was taken as 0.05).

Table 8. The results of applying the Kruskal–Wallis criterion and Dunn’s criterion to evaluate statistically significant differences in the flexural stress of specimens whose blanks were manufactured with different layer thicknesses.

Layer Height	0.2 (p-Value)	0.3 (p-Value)
0.3 (p-value)	0.018	—
0.4 (p-value)	0.006	0.361
Kruskal–Wallis (p-value)	0.030

shows the results of applying the Kruskal–Wallis test and Dunn’s criterion to evaluate statistically significant differences in the flexural stress of specimens whose blanks were manufactured with different layer thicknesses.

Table 9. The results of applying the Kruskal–Wallis criterion and Dunn’s criterion to evaluate statistically significant differences in the flexural stress of specimens whose blanks were manufactured with different types of filling.

Filling Type	ZigZag (p-Value)	Concentric (p-Value)
Concentric (p-value)	0.084	—
Linear (p-value)	0.312	0.186
Kruskal–Wallis (p-value)	0.370

shows the results of applying the Kruskal–Wallis test and Dunn’s criterion to evaluate statistically significant differences in the flexural stress of specimens whose blanks were manufactured with different types of filling.

An analysis of the results of the Kruskal–Wallis test and Dunn’s criterion show the presence of four groups of differences, two groups related to layer thickness and two groups related to nozzle diameter. Based on this result, a hierarchical method was applied to classify the results of the three-point bending test of the specimens. The Spearman correlation coefficient between the cohesion distance and Euclidean distance between the actual data and the classification results was 0.843. Figure 11 shows the results of the separation of the flexural stress and strain corresponding to the maximum force depending on the membership of the new group.

Table 10. A comparison of the tensile strength of zirconium oxide ceramic specimens subjected to biaxial loading in the groups obtained from the hierarchical classification results.

Group Number	1 (p-Value)	2 (p-Value)	3 (p-Value)
2 (p-value)	0.000	—	—
3 (p-value)	0.000	0.000	—
4 (p-value)	0.007	0.314	0.000
Kruskal–Wallis (p-value)	0

shows the results of comparing the flexural stress of the specimens in the new groups by the Kruskal–Wallis test and Dunn’s test (the level of statistical significance was assumed to be 0.05).

An analysis of the results of applying the Kruskal–Wallis criterion shows that the differences between the mechanical properties of the samples in the new groups are statistically significantly different. An application of Dunn’s criterion shows that the differences are not statistically significant in groups 2 and 4. In all other cases, the differences are statistically significant.

Figure 12 shows the results of the Spearman correlation analysis for all of the variables considered in the paper.

From the results of the correlation analysis, it follows that in three groups (Figure 12A–C) there is a weak correlation between the nozzle diameter of the workpiece used in FDM printing and the biaxial strength of zirconium oxide ceramic samples. In the fourth group (Figure 12D), a very strong correlation is observed between all of the investigated parameters except for the diameter of the workpiece and the diameter of the sample.

To determine the central parameter, the correlation graphs presented in Figure 13 were constructed.

Table 11. The centralization of the graph of statistically significant correlation for the samples belonging to the first group *.

Parameters Analyzed	Group 1
	Degree Centrality, Equation (1)	Closeness Centrality, Equation (2)	Betweenness Centrality, Equation (3)
Lh	7	0.769	6.744
HFDM	7	0.769	6.762
HS	7	0.769	5.720
WFDM	6	0.714	5.637
Fmax	6	0.714	4.018
FS	5	0.625	1.917
WS	4	0.588	0.476
ND	3	0.526	0.000
DFDM	3	0.556	0.000
DS	3	0.556	0.726
EFmax	3	0.526	0.000
Centralization	0.256	0.148	0.094

* The interpretation of the abbreviations is provided in the Abbreviations list.

shows the results of calculating the centrality of the correlation graph.

The same centrality values are obtained from the graphs of the other groups and the ranking of the parameters by centrality does not change. It follows from the analysis that the greatest number of statistically significant correlations is possessed by the thickness of the filling layer, the thickness of the workpiece, and the thickness of the ceramic sample obtained after the heat treatment of the workpiece.

Table 12. A comparison of regression relationships by Akaike’s criterion for the different groups of samples.

Dependence Type	Group 1	Group 2	Group 3	Group 4
Linear	857.785	265.939	506.130	34.179
Exponential	857.813	265.921	506.034	34.368
Logarithmic	857.670	266.002	506.419	33.439
Polynomial	858.388	267.736	504.587	−158.421

shows a comparison of the dependencies of flexural stress on the thickness of the fill layer according to the Akaike criterion.

It follows from the results of the analysis that the lowest value of Akaike’s criterion has the logarithmic dependence for group 1, exponential dependence for group 2 and polynomial dependence for groups 3 and 4. However, given the closeness of the Akaike criterion values, it is necessary to check the linear, exponential, and logarithmic types for sensitivity to data scatter for groups 1 and 2.

Figure 14 shows four models for the first group of the dependencies of the flexural stress of ceramic samples on the thickness of the fill layer during the FDM printing of the workpiece. For each robust regression model, 95% confidence intervals were constructed by bootstrapping.

Figure 15 shows four models for the second group of the dependencies of the flexural stress of the ceramic samples on the thickness of the fill layer during the FDM printing of the workpiece. For each model, robust regressions are constructed with a 95% confidence level by the bootstrapping method.

The calculation of the confidence intervals of the coefficients of the robust regression models shows that for the first and second groups, the ordinary linear model explains the dependence of the flexural stress on the thickness of the filling layer inside, covering the largest number of test results.

Table 13. Robust regression equations describing the dependence of the flexural stress on fill layer thickness in the FDM printing of blanks.

Group Number	Robust Regression Equation	Standard Deviation
Group 1	${\sigma }_{FS}=300.356-39.172\times H_L$	42.96
Group 2	${\sigma }_{FS}=474.772-88.459\times H_L$	62.79
Group 3	${\sigma }_{FS}=175.660+24.201\times H_L+68.643\times H_L^2$	36.75
Group 4	${\sigma }_{FS}=628.492-52.134\times H_L+45.902\times H_L^2$	0

shows the robust regression equations describing the dependence of the flexural stress of ceramic specimens in biaxial tests on the thickness of the fill layer used in the FDM printing of the workpiece.

An analysis of the results of the model building shows that with an increasing layer thickness, the flexural stress of the zirconium oxide ceramics sample decreases in groups 1 and 2. In groups 3 and 4, the flexural stress of the zirconium oxide samples nonlinearly depends on the thickness of the filling layer with a minimum at a layer thickness of 0.3 mm. Given the small number of test results in group 4, the description of the model may not be quite adequate and requires careful application in practice.

3.3. Analyzing the Structure of Samples

The results of the statistical analysis show that the group of zirconia samples subjected to the biaxial test has a flexural strength comparable to samples obtained by other technological processes. Such high values can be obtained due to the low defectivity of the samples. Figure 16 shows the results of a fracture analysis of three sintered zirconia samples belonging to different groups and subjected to biaxial tests. Yellow circles indicate the presence of triangular defects between the layers, characteristic of the FDM technology, which negatively affect the values of the density and strength of the samples.

An analysis of the fracture surface image shows the presence of triangular-shaped defects (Figure 16, sample 1) on the interlayer boundary (Figure 16, sample 3) in the ceramic samples inherited after FDM printing. In addition, there are a small number of macro defects located on the same lines as the FDM printing defects.

Figure 17 shows an enlargement of the fractures of samples belonging to groups 2 and 4.

A refined analysis of the surface shows that interlayer defects on the fracture surface are extremely rare (Figure 17A,B). In particular, the main defects are inherited from FDM printing (triangular defect in Figure 17C,D) and oval- and round-shaped defects where crack development is observed (Figure 17E,F). The refinement of the fracture image near the indenter impact area shows that the crack development goes along the interlayer boundary (Figure 17C) with further fracture development with a stepped (the step has a wave shape) crack development, which indicates the ductile–brittle nature of the fracture (Figure 17D).

Figure 18A,B shows the surface of the specimen from group 1, selected according to the results of the hierarchical classification.

Figure 18 clearly shows extended longitudinal interlayer defects (Figure 18A), microcracks oriented along the direction of sample filling (Figure 18B), and agglomerations of point defects located randomly across the surface. Figure 18C,D shows the surface images of three zirconium oxide ceramic samples belonging to group 4 and group 2 allocated according to the results of the hierarchical classification. The surface analysis of the zirconium oxide samples belonging to groups 2 and 4 after three-point bending tests showed the absence of microcracks and pronounced delaminations on the sample surface, in contrast to the sample belonging to the first group.

A comparative microstructural analysis of the sintered specimens revealed two typical defects. One of them is insufficient adhesion between the layers, which manifests itself in the form of pores or cracks (Figure 18). Another typical defect is the triangular voids formed between the layers (Figure 16), which is mainly related to the printing mode and the filling orientation [32]. The first type of defect can be eliminated by increasing the nozzle temperature or lowering the viscosity of the feedstock. By adjusting the infilling pattern and printing parameters such as layer height and nozzle movement speed, the occurrence of triangle-shaped defects can be avoided [59].

Figure 19 shows the tomography of zirconium dioxide samples belonging to different groups of samples, divided according to the flexural strength.

An analysis of the tomographic study results shows that the sample from the third group has a high defectivity on the surface and in the volume (Figure 19C,D). It is also evident from the tomographic analysis results that the infill pattern is preserved only on the surface of the specimens and is not inherited in the volume, except for the specimens from the second group (Figure 19E,F).

The sintered samples exhibited a density of 95% from theoretical. This value is due to the presence of defects that occur during the printing process. Representative X-ray diffraction patterns corresponding to the polished and fracture surface of the sintered specimens are shown in Figure 20.

The patterns show that no contaminants or new phases were detected after the sintering. The XRD analysis revealed that the surface of the samples consists of tetragonal zirconia. On the other hand, the presence of a monoclinic phase on the fractured surface may indicate the presence of a phase transformation toughening mechanism, thereby increasing the ceramic’s strength and fracture toughness.

Figure 21 shows the SEM-EDS elemental distribution maps and EDS spectrum for the sintered samples. The EDS analysis showed the presence of Zr, Y, and O elements only as expected as shown in Figure 20, which is an EDS spectrum of the specimen taken from the observed area. In addition, EDS mapping confirmed a homogeneous distribution of the Zr, O, and Y in the volume as no areas of concentration of the elements were observed. The EDS technique deals only with elements, not phases. However, based on the EDS-mapping results, it can be anticipated that the phases are also distributed uniformly in the sintered material.

The average content of the components in the samples of each of the four groups is shown in

Table 14. The average content of the components in the samples of each of the four groups.

	Sample Number	Average Content of Constituents, wt.% 1
		Zr	O	Y
Group 1	1	62.89	29.68	7.43
	2	63.09	30.52	6.39
	3	62.57	30.42	7.01
Group 2	1	63.96	30.12	5.92
	2	62.73	30.06	7.21
	3	62.12	30.98	6.9
Group 3	1	63.69	29.69	6.62
	2	62.72	30.82	6.46
	3	62.28	29.47	8.25
Group 4	1	63.79	29.78	6.43
	2	63.51	29.26	7.23
	3	62.98	30.43	6.59

¹ the average values of the five measurements on each sample.

. Three samples from each group were analyzed. The content calculation is performed automatically in the Aztec 2.0 software, provided with the EDS detector, based on counting the number of quanta with specific energy emitted by the atoms of the elements. The reported values represent the average concentration of elements in the studied area with a confidence interval of σ ≤ 0.3% by mass. The investigation was conducted on a polished surface at an accelerating voltage of 20 kV to excite all characteristic lines of the elements. These results are sufficient for a reliable comparison of the samples against each other, conclusions about concentration changes, and ongoing processes, but are arguable for asserting absolute concentration. In this context, the significance of deviations is lower. Since all of the samples were sintered and studied under identical conditions, the results are taken as reliable.

4. Discussion

The statistical analysis of the results of the biaxial test on the ceramic samples showed statistically significant differences between the sintered samples obtained from the printed samples made with 0.6 mm and 0.8 mm nozzles, as well as between 0.6 mm and 1 mm. Whereas, no statistically significant differences were found between the strength properties of the specimens whose blanks were manufactured using 1 mm and 0.8 mm nozzles. When investigating the differences in the strength of zirconium dioxide samples depending on the thickness of the filling layer, it was found that statistically significant differences were observed for sintered samples made from printed samples with filling layer thicknesses of 0.2 mm and 0.3 mm, as well as 0.2 mm and 0.4 mm. Whereas, the differences between 0.3 mm and 0.4 mm were found not to be statistically significant.

The analysis of differences in the strength of the ceramic samples depending on the type of filling did not reveal statistically significant differences. The obtained result of the analysis of the differences in strength in the groups of zirconia samples agrees with the previously obtained results for alumina [28]. This may indicate a general trend for this technology of manufacturing ceramics products.

Based on the revealed statistically significant difference in the flexural strength of zirconia, a hierarchical classification of samples according to their strength was carried out and four groups were identified, three of which had statistically significant differences in strength. Each of the groups included samples of blanks, which were manufactured using different nozzle diameters and layer thicknesses. The group with the maximum compressive strength values included samples manufactured using nozzle diameters of 0.6 mm and 1 mm and layer thicknesses of 0.4 mm, 0.3 mm, and 0.2 mm. The maximum value of strength was found in the specimen made with a nozzle diameter of 1 mm and layer thickness of 0.2 mm. Because only the test results of three specimens were included in group 4, it is not possible to make a conclusion, and it is possible to attribute the results obtained to anomalies of the experiment. However, the results of the flexural tests of specimens in group 2 are not statistically significantly different from the results in group 4 and the largest number of specimens in group 2 had a layer thickness of 0.2 mm. The results obtained in our study are similar to the results presented in [34,35], which suggests that there is a general pattern of the effect of layer thickness on the strength of products obtained by FDM printing. The study of correlations between the thickness of the filling layer and the nozzle diameter with strength and geometrical parameters of zirconia samples shows that the thickness of the filling layer shows the greatest number of correlations. Whereas, the nozzle diameter has a much smaller number of correlations. The number of correlations is maintained regardless of belonging to one or another group of samples with different mechanical properties, which indicates the stability of the identified correlations.

The analysis of the regression equations shows that the relationship between the strength of zirconia for most of the groups decreases with an increasing thickness in the filling layer during the fabrication of the workpiece. This result diverges from the findings obtained in [28]. The observed discrepancy may be due to the concentration of ceramics in the filament used in the manufacture of blanks; this hypothesis will be tested by us in future work. Previously, the effect of ceramic particles distribution on the strength properties of the filament during tensile tests was considered [26,27]. It was shown that changing the distribution of ceramic inclusions leads to a change in strength. In the case of obtaining ceramic samples from blanks made by FDM printing technology using a ceramic–polymer filament, the inhomogeneity of ceramic particles distribution in the volume of the specimen can decrease with increasing concentration, which can ultimately increase the flexural strength of the ceramic sample.

The analysis of the surface of zirconia samples belonging to different groups showed that samples belonging to group 1 have a large number of cracks on the surface along the fill lines, which is not observed in samples belonging to groups 2 and 4. The fracture surface of the samples of groups 2 and 4 contain a small number of macro-defects inherited from the blanks produced by FDM printing technology and macro-defects of an arbitrary shape concentrated on the lines of the interface of printing layers. Some of the defects are the source of a crack initiation developing in the interlayer direction.

The obtained results of the structure analysis coincide with the results presented in [30,31] and allow us to conclude that the cause of defects is the under- or over-extrusion of the filament during the fabrication of blanks by the FDM printing technology from ceramic plastic at the same thickness of the printing layer.

The analysis of the fracture character shows its ductile–brittle nature, which can be related to the inhomogeneity of the ceramic structure in the interlayer regions and the presence of a phase transition from the crystal lattice with a tetragonal structure to a monoclinic one. In favor of this statement are the results of X-ray diffraction (Figure 16). The absence of the monoclinic phase on the sintered sample surface and its presence on the fracture surface indicate the formation of the monoclinic phase under the influence of stresses occurring at the crack tip [11].

5. Conclusions

This study on the relationship between the technological parameters of FDM printing and the mechanical properties of the final product is of great importance to produce high-quality products with a low cost. In our work, we demonstrated how the technological parameters of the FDM printing of blanks affect the biaxial compression strength of the ceramics obtained after plastic burning. Within the framework of the study, it was established that, as follows:

• In the manufacture of FDM ceramic samples from zirconium dioxide, the thickness of the filling layer has the greatest effect on the bending strength.
• The effect of nozzle diameter on the flexural strength properties of zirconia has no significant influence. The obtained result may be related to the concentration of ceramics in the filament used in the manufacture of the workpiece.
• An analysis of the differences in the flexural strength of zirconia depending on the type of filling of the workpiece showed that there were no statistically significant differences in the groups of samples. This may also be due to the inhomogeneous distribution of the ceramic phase in the manufactured filament.
• The occurrence of defects in the structure of the ceramic sample is due to the under- and over-extrusion of the filament during the fabrication of the samples using FDM printing technology from a PLA/ZrO₂ composite filament.
• The fracture mechanism of zirconia under the biaxial test is ductile–brittle in nature. The presence of a ductile component in the fracture character can be associated with the phase transition from tetragonal to monoclinic phases of zirconia under the action of stresses arising at the crack tip and sample heterogeneity (the presence of defects inherited from the discs obtained by FDM printing technology).

Further studies to establish the influence of the layer thickness, nozzle diameter, and filling scheme on the mechanical properties of the obtained ceramics will be aimed at establishing the relationship between the technological parameters and the concentration of ceramics in the filament. Considering the previously identified published works, a study will be conducted on the influence of the filler layer width during the printing of blanks using FDM printing technology on the reduction of defectivity and improving the microstructure of zirconium dioxide samples obtained by multistage technology.