Optimization of Flexural Performance of PETG Samples Produced by Fused Filament Fabrication with Response Surface Method

Additive manufacturing (AM), particularly fused filament fabrication (FFF), has gained significant attention for its design flexibility and cost-effectiveness. This study focuses on optimizing FFF parameters that employ response surface methodology (RSM) to enhance the flexural performance of polyethylene terephthalate glycol (PETG) parts. Three essential parameters—layer height, print speed, and nozzle temperature—were varied, and their effects on flexural strength, flexural modulus, flexural toughness for ultimate strength, flexural toughness at 5% strain, and strain at ultimate strength were evaluated. Based on a Box–Behnken design, the experiments revealed significant effects of these parameters on the mechanical responses. The analysis of variance (ANOVA) indicates that layer height predominantly affects flexural modulus and toughness, while nozzle temperature significantly impacts flexural strength. The RSM models exhibited high accuracy, with R2 values exceeding 99%. Optimal parameter combinations yield remarkable improvements: flexural strength reached 39.55 MPa, flexural modulus peaked at 1344.60 MPa, flexural toughness for ultimate strength reached 218.22 J/mm3, flexural toughness at 5% strain reached 381.47 J/mm3, and strain at ultimate strength reached 3.50%. Validation experiments confirm the effectiveness of the optimization, with errors below 3.17%.


Introduction
AM is becoming progressively influential in shaping the direction of industry development.The advantages of AM are design flexibility, customization, waste minimization, and the capability to produce complex structures.There has been a significant focus on advancing AM technologies in recent years.There are many different AM technologies available today.One of the most popular and widely used is FFF [1][2][3][4].FFF is a cost-effective AM method that uses polymer materials.It builds products layer by layer and is widespread for creating components from thermoplastics and fiber-reinforced composites.Current studies examine the quality, build time, surface finish, part quality, mechanical properties, and production costs of parts produced using FFF.Optimal parameter selection affects product quality, and the properties of FFF-produced parts correlate with changing print parameters [5,6].
A wide variety of polymer filaments such as ABS, PLA, Nylon, PC, TPU, and PET can be printed with good dimensional flexibility using FFF.Among these, PET is a widely used thermoplastic.PETG, derived from PET and glycol, boasts attractive mechanical and chemical properties, including robust chemical resistance, considerable impact strength, and material flexibility, owing to its chemical composition.PETG is ideal for AM as it has a lower viscosity than PET.Although PETG demonstrates a higher glass transition temperature (Tg), the mechanical characteristics exhibit similarities, approximately 67 • C [7,8].
technique.In their study, the infill density varied between 60-80%, and the highest flexural strength (77.65 MPa) was obtained at a 60% infill density.Taguchi analysis showed that higher flexural strength values can be obtained for 60% infill density compared to 70% and 80%.Based on the study of Durgashyam et al. [21], and to save weight, the infill density was kept constant at 50% in our current study.Guessasma et al. [22] analyzed the printability and tensile performance of 3D-printed PETG, demonstrating significant improvements in mechanical properties with optimized printing parameters.Another study by Hanon et al. [23] evaluated the anisotropy of different raster directions, spatial orientations, and fill percentages in 3D-printed PETG, highlighting the material's versatility and potential for various applications.These recent advancements emphasize the growing interest and potential in optimizing PETG for diverse applications through material modifications and advanced printing techniques.
Three-dimensional printing technologies, especially the FFF method, are of great interest in optimizing the mechanical properties of polymers.Studies in this field show that careful optimization of printing parameters can significantly improve print quality and mechanical properties.Deswal et al. [24] optimized key process parameters to improve the dimensional accuracy of FFF printing devices.Hybrid statistical tools such as RSM-Genetic Algorithm (RSM-GA), Artificial Neural Network (ANN), and ANN-GA were used.Srinivasan et al. [25] applied RSM to predict the tensile strength of ABS parts printed with FFF, which significantly improved mechanical properties by determining the optimum printing parameters.Selvam et al. [26] used particle swarm optimization (PSO) to enhance the strength of AM components.They improved part performance with carbon fiber reinforcement and bio-inspired interlock sutures.Saad et al. [27] used RSM, particle search algorithms (PSO), and symbiotic organism search (SOS) algorithms to optimize the surface roughness in FDM 3D printing and achieved significant improvements in surface quality.Naveed and Anwar [28] applied experimental techniques and ANOVA-based statistical analysis to optimize 3D printing parameters to determine the optimal parameters for high-quality and consistent 3D-printed components.Das et al. [29] investigated the crystallization and rheological behavior of short carbon fiber-reinforced polyamide 6 (CF-PA6) filaments in the process of melt layer-by-layer deposition.The effects of printing parameters such as layer thickness, raster angle, and filler pattern on tensile properties were evaluated using the Taguchi method.Moradi et al. [30] investigated the process parameters of FFF-printed nylon parts.The effects of layer thickness, filler percentage, and number of contours were evaluated and optimized using RSM.Layer thickness was found to be the most influential parameter.Tunçel et al. [31] used the Taguchi method and GRA to optimize FFF parameters for 30% ceramic-reinforced composite PLA material.The results increased the tensile strength by 20.55% and reduced the production time by 43.75%.According to the literature, traditional optimization techniques such as the Taguchi method have effectively determined the appropriate printing parameters, but multi-objective optimization techniques such as RSM, GA, GRA, PSO, and ANN have been used for more complex materials and processes.
Recently, there has been a significant focus among researchers to investigate the mechanical properties of materials produced by FFF technology, a trend that continues to grow in importance.The literature review revealed a gap in research regarding the comprehensive analysis of the flexural performance of FFF components fabricated using PETG, which served as the driving force behind this study.This research aims to increase the durability and reliability of structural components used in automotive, aerospace, and medical industries by improving the flexural performance of PETG materials.The findings may enable the production of lighter and more durable parts in these fields.The current research proposes a parametric optimization study using RSM for the FFF fabrication of PETG material to improve the performance and applicability of 3D-printed objects in specific use cases.In particular, it focuses on determining the optimal FFF process parameters that result in the superior flexural performance of 3D-printed PETG parts.The study considers three key process parameters: layer height, print speed, and nozzle temperature.Flexural performance responses were evaluated using a three-point flexure test, including flexural strength, modulus, ultimate flexural toughness, flexural toughness at 5% strain, and strain.

Materials and Methods
The three-point flexural samples were produced using the Creality Ender 3-S1 Pro printer (Shenzen, China), which prints using the FFF method and has a nozzle diameter of 0.4 mm.The printing process used a Creality PETG filament with a diameter of 1.75 mm and a density of 1.27 g/cm 3 .The experimental design and the RSM analyses were conducted using Minitab, Version 20.3.The flexure tests were performed on a custom-built table-top testing machine designed for low-strength materials (Figure 1).The device is controlled by an Atmega2560 microcontroller (Microchip, Chandler, AZ, USA) and uses C++ for its software development.The user interface software was developed in C# (Microsoft Visual Studio 2022).Although the test device has a maximum load-carrying capacity of up to 1.5 kN, a 0.3 kN capacity load cell (Tedea, Shaanxi, China) is used to get more accurate measurements.A stepper motor was used to drive the loading head.This allowed the system to be controlled using open-loop control.The configuration settings for the motor drivers were set to 1600 pulses per revolution with a screw pitch and reduction ratio of 5, allowing precise loading head positioning in increments as small as 1/1600 mm.Displacement data acquisition involved tracking the position of the loading head.The data-acquisition card, which employed an ADS1256 from Texas Instruments, USA, was configured to operate at a sampling rate of 30 data points per second.
Polymers 2024, 16, x FOR PEER REVIEW 4 of 1 considers three key process parameters: layer height, print speed, and nozzle temperature Flexural performance responses were evaluated using a three-point flexure test, including flexural strength, modulus, ultimate flexural toughness, flexural toughness at 5% strain and strain.

Materials and Methods
The three-point flexural samples were produced using the Creality Ender 3-S1 Pro printer (Shenzen, China), which prints using the FFF method and has a nozzle diamete of 0.4 mm.The printing process used a Creality PETG filament with a diameter of 1.75 mm and a density of 1.27 g/cm 3 .The experimental design and the RSM analyses were conducted using Minitab, Version 20.3.The flexure tests were performed on a custom built table-top testing machine designed for low-strength materials (Figure 1).The device is controlled by an Atmega2560 microcontroller (Microchip, Chandler, Arizona, USA) and uses C++ for its software development.The user interface software was developed in C# (Microsoft Visual Studio 2022).Although the test device has a maximum load-carrying capacity of up to 1.5 kN, a 0.3 kN capacity load cell (Tedea, Shaanxi, China) is used to ge more accurate measurements.A stepper motor was used to drive the loading head.Thi allowed the system to be controlled using open-loop control.The configuration setting for the motor drivers were set to 1600 pulses per revolution with a screw pitch and reduc tion ratio of 5, allowing precise loading head positioning in increments as small as 1/1600 mm.Displacement data acquisition involved tracking the position of the loading head The data-acquisition card, which employed an ADS1256 from Texas Instruments, USA was configured to operate at a sampling rate of 30 data points per second.Three-point flexural test samples were prepared by ISO 178 standards using the Solidworks 2020 computer-aided design program [32,33].Samples for this standard have dimensions of 80 mm × 10 mm × 4 mm.The Cura 5.5.0 software was used for slicing.The parameters that remained constant during the printing processes are provided in Table  Three-point flexural test samples were prepared by ISO 178 standards using the Solidworks 2020 computer-aided design program [32,33].Samples for this standard have dimensions of 80 mm × 10 mm × 4 mm.The Cura 5.5.0 software was used for slicing.The parameters that remained constant during the printing processes are provided in Table 1.RSM is a method for statistically analyzing engineering problems to model the relationships among multiple variables and facilitate improvements in design and manufacturing processes [25,34].The variables identified in this study affecting the responses to be used in RSM modeling were layer height, print speed, and nozzle temperature (Table 2).Three levels of layer height were considered: 0.15 mm, 0.20 mm, and 0.25 mm.The printing speed varied over a wide range, equal to 20 mm/s, 50 mm/s, and 80 mm/s.Additionally, three distinct nozzle temperatures were investigated: 230  Critical responses such as flexural strength, flexural modulus, flexural toughness at ultimate flexural strength, flexural toughness at 5% strain, and strain at ultimate flexural strength are depicted in Figure 2a below.Also, a schematic representation of the flexural experiment is provided in Figure 2b.
The relevant formulas used in the calculations are shown in the equations below (Equations ( 1)-( 4)) [35,36].Flexural strength (σ) and flexural strain (ε) can be obtained as follows: Here, P, δ, L, b, and h represent load, deflection of the center point of the beam, span length, width, and thickness of the test beam, respectively.The flexural modulus (E f ) can also be calculated by the following equation: where θ is the slope obtained by considering two points in the elastic region of the loaddeflection curve.Flexural toughness up to ultimate stress and 5% strain points have been calculated for assessment, as shown in the equation below.

Results and Discussions
Flexural tests are essential to understand the material's behavior under bending and its resistance to loads from different directions.Flexural properties are preferred in this study because 3D-printed parts are often subjected to complex loading conditions, and these tests better reflect the material's performance under actual conditions of use.Furthermore, flexural tests are critical in understanding interlayer bonding problems, which are especially common in AM methods.

Experimental Results
Three bending force-deflection curves with the same manufacturing process parameters are shown in Figure 3 as representative curves.This pattern was observed across other experimental groups as well.When repeated tests yield highly similar results, the standard deviation within the experimental groups will be low.This indicates reliable outcomes and suggests that fewer experiments may be necessary for a robust experimental design.So, Box-Behnken design type, which requires fewer experiments, was chosen for the response surface analysis [37].
Table 2 presents the input parameters, along with their corresponding levels.Additionally, Table 3 provides details regarding the responses and the Box-Behnken design employed.The RSM model was generated using the Minitab 20.3 software.Table 3 illus

Results and Discussions
Flexural tests are essential to understand the material's behavior under bending and its resistance to loads from different directions.Flexural properties are preferred in this study because 3D-printed parts are often subjected to complex loading conditions, and these tests better reflect the material's performance under actual conditions of use.Furthermore, flexural tests are critical in understanding interlayer bonding problems, which are especially common in AM methods.

Experimental Results
Three bending force-deflection curves with the same manufacturing process parameters are shown in Figure 3 as representative curves.This pattern was observed across other experimental groups as well.When repeated tests yield highly similar results, the standard deviation within the experimental groups will be low.This indicates reliable outcomes and suggests that fewer experiments may be necessary for a robust experimental design.So, Box-Behnken design type, which requires fewer experiments, was chosen for the response surface analysis [37].
Table 2 presents the input parameters, along with their corresponding levels.Additionally, Table 3 provides details regarding the responses and the Box-Behnken design employed.The RSM model was generated using the Minitab 20.3 software.

Anova Results
ANOVA provides quantitative data on the effects of the input parameters and their interactions with the responses [38].Tables 4-6 show the ANOVA results for flexural strength, flexural modulus, flexural toughness for ultimate flexural strength, flexural toughness for 5% strain, and strain responses at ultimate flexural strength.The ANOVA results calculate two critical values.A 95% confidence level was chosen in the model setup [39].The higher the F-values, the more influential the input parameter is on the response

Anova Results
ANOVA provides quantitative data on the effects of the input parameters and their interactions with the responses [38].Tables 4-6 show the ANOVA results for flexural strength, flexural modulus, flexural toughness for ultimate flexural strength, flexural toughness for 5% strain, and strain responses at ultimate flexural strength.The ANOVA results calculate two critical values.A 95% confidence level was chosen in the model setup [39].The higher the F-values, the more influential the input parameter is on the response [40].The most effective parameter on flexural modulus (79.38%), flexural toughness for ultimate flexural strength (67.36%), and strain at ultimate flexural strength (73.23%) is layer height.Nozzle temperature is the most influential parameter on flexural strength (56.64%) and flexural Polymers 2024, 16, 2020 8 of 18 toughness for 5% strain (33.62%).On the other hand, print speed is generally less influential on responses.RSM significantly decreases the number of experiments and can detect factor interactions based on the selected model, necessitating the examination of experimental results using a second-order polynomial response-regression model for precise prediction.The second-order equations of the output responses (flexural strength, flexural modulus, flexural toughness for ultimate flexural strength, flexural toughness for 5% strain, and strain at ultimate flexural strength according to the input parameters) are provided in Table 7.An explanation of the system and the necessary equations can be found in the study by Yaman et al. [41].The list of R 2 values (coefficient of determination of the equation) that is used in evaluating the models is provided in Table 8.All output parameters have R 2 values greater than 0.99, which is indicative of a good fit.Similarly, the adjusted R 2 and predicted R 2 values, which indicate the accuracy of the model, were also found to be acceptably high.According to the results obtained from the model, R 2 values were determined as 99.33%, 99.40%, 99.32%, 99.46%, and 99.12% for flexural strength, flexural modulus, and flexural toughness for ultimate flexural strength, flexural toughness for 5% strain, and strain at ultimate flexural strength, respectively, as shown in Table 8.The detailed formulas used to explain R 2 , adjusted R 2 , and predicted R 2 are presented in the Çalhan et al. study [42].

RSM Results
This study highlights the critical presence of interaction effects, showing how the combined effects of different input parameters exceed (or fall short of) their individual effects and simultaneously influence at least one output response.Understanding how the processing parameters of a 3D printer affect the flexural performance of printed samples depends on recognizing these interactions [27].The simultaneous effects of layer height, print speed, and nozzle temperature variations on flexural strength, flexural modulus, flexural toughness at ultimate flexural strength, flexural toughness at 5% strain, and strain at ultimate flexural strength are shown in the 3D plots generated by RSM in Figures 4-8.
Pareto plots are also shown in Figures 4-8 to better evaluate the individual and combined effects of each selected parameter.240 °C nozzle temperature parameters (Table 3).The lowest toughness was obtained as 166.26J/mm 3 in Sample 7.This sample has 0.15 mm layer height, 50 mm/s print speed, and 230 °C nozzle temperature parameters (Table 3).Sample 6 has a 36.6% higher toughness value than Sample 7. When the toughness values in Table 3 are examined, the results for flexural toughness reach a 5% strain change over a much narrower range than the flexural toughness at ultimate strain and converge.

Flexural Toughness for 5% Strain Results
Figure 7 shows the Pareto chart and 3D plots of flexural toughness for 5% strain according to layer height, print speed, and nozzle temperature.As shown in Figure 7a, the maximum effect on flexural toughness at 5% strain is due to nozzle temperature and the interaction of nozzle temperature with layer height and print speed.According to Table 5, which shows the results of ANOVA, the nozzle temperature has an effective rate of 33.62%, the layer height is 0.91%, and the printing speed is 1.57%.The nozzle temperature/layer height interaction had an effect of 23.68%, while the print-speed interaction had an impact of 19.28%.Flexural toughness at 5% strain increased with increasing nozzle temperature.In particular, for the 0.25 mm layer height and 80 mm/s print speed parameters, the increase in flexural toughness at 5% strain was more significant with increasing nozzle temperature (Figure 7c,d).Changes in layer height and print-speed parameters have mixed effects regarding the increases and decreases in flexural toughness at 5% strain (Figure 7b-d).The highest flexural toughness for the 5% strain value was obtained as 368.48J/mm 3 at 0.20 mm layer height, 80 mm/s print speed, and 250 °C nozzle temperature.

Strain at Ultimate Flexural Strength Results
Figure 8 shows the simultaneous effects of layer height, print speed, and nozzle temperature on strain at ultimate flexural strength.In addition, the degree of influence of the variables on the strain (%) is provided in Figure 8a.The Pareto plot for strain shows that layer height is the most influential parameter, followed by print speed and nozzle temperature.The ANOVA results show that the contribution of layer height to strain is 73.23%, the print speed is 16.91%, and the nozzle temperature is 2.62%.The simultaneous effects of the variables show that increasing layer height promotes an increase in strain while

RSM Prediction vs. Experimental Results
This section draws a contrast to assess the degree of agreement between the predictions generated by the regression equations and the 15 experiments used to construct the RSM model.Tables 9-11 compare the prediction results of the RSM model and the experimental results, along with the corresponding error percentages for each output response.When the error means between the test results and the RSM predictions are analyzed, the results are in good agreement with very low error percentages.The best fits were found for flexural toughness at 5% strain with an error of 0.13%, while the worst fit was found for flexural modulus with an error of 0.83%.

Flexural Strength Results
Flexural strength provides information on the strength of the material using the ultimate load generated during the flexure test.Figure 4 shows the Pareto chart and the effects of layer height, print speed, and nozzle temperature on flexural strength.Figure 4a presents the Pareto plot of flexural strength.According to the Pareto plot of flexural strength, the order of influence is nozzle temperature, layer height*layer height, and print speed*nozzle temperature.The ANOVA results in Table 4 reveal that this effect is caused by 56.64% nozzle temperature, 14.24% layer height*layer height, and 9.99% print speed*nozzle temperature.The p-value of layer height for flexural strength (0.056) is higher than 0.05, indicating that the effect of the layer height on flexural strength is insignificant.Figure 4b-d shows the simultaneous impacts of layer height, print speed, and nozzle temperature on flexural strength.Figure 4c,d illustrates flexural strength increases with increasing temperature.It was also observed that the compression speed of about 50 mm/s provided the highest flexural strength (Figure 4b,d).The highest flexural strength value was obtained as 38.91 MPa in Sample 3 with a 250 • C nozzle temperature, 50 mm/s print speed, and 0.25 mm layer height parameters (Table 3).

Flexural Modulus Results
Flexural modulus is the stress ratio to the corresponding strain within elastic limits.Figure 5 shows the Pareto chart and 3D plots of flexural strength for different layer heights, print speeds, and nozzle temperature levels.Figure 5a shows that the maximum effect on the flexural modulus is due to the layer height.According to Table 4, where ANOVA results are displayed, the layer height has an effective rate of 79.38%, the layer height*layer height is 11.59%, and the print speed is 6.20%.Figure 5b-d shows the simultaneous effect of the variables on the flexural modulus.Flexural modulus increased with the increase in print speed and nozzle temperature.However, it decreased with an increase in layer height.
The highest flexural modulus value was 1468.18MPa for Sample 8, with the parameters of 0.15 mm layer height, 80 mm/s printing speed, and 240 • C nozzle temperature (Table 3).

Flexural Toughness for Ultimate Flexural Strength Results
Analyzing the Pareto chart in Figure 6a, the order of the effect of the parameters on flexural toughness for ultimate flexural strength is layer height, print speed, and nozzle temperature.The effect of the interactions of the parameters remained small.In the ANOVA table in Table 5, it was previously shown that the linear effect of the parameters was very high at 93.96%.In the same table, it was also seen that the layer height reached 67.36%.Analyzing the interactions in Figure 6b,c, it can be seen that increasing the layer height causes an increase in toughness.While the rise in nozzle temperature increased the toughness, as did the increase in layer height, while the toughness decreased with the increase in print speed (Figure 6b,c).The highest toughness was obtained as 227.11J/mm 3 in the sample coded 6.This sample has 0.25 mm layer height, 20 mm/s print speed, and 240 • C nozzle temperature parameters (Table 3).The lowest toughness was obtained as 166.26J/mm 3 in Sample 7.This sample has 0.15 mm layer height, 50 mm/s print speed, and 230 • C nozzle temperature parameters (Table 3).Sample 6 has a 36.6% higher toughness value than Sample 7. When the toughness values in Table 3 are examined, the results for flexural toughness reach a 5% strain change over a much narrower range than the flexural toughness at ultimate strain and converge.

Flexural Toughness for 5% Strain Results
Figure 7 shows the Pareto chart and 3D plots of flexural toughness for 5% strain according to layer height, print speed, and nozzle temperature.As shown in Figure 7a, the maximum effect on flexural toughness at 5% strain is due to nozzle temperature and the interaction of nozzle temperature with layer height and print speed.According to Table 5, which shows the results of ANOVA, the nozzle temperature has an effective rate of 33.62%, the layer height is 0.91%, and the printing speed is 1.57%.The nozzle temperature/layer height interaction had an effect of 23.68%, while the print-speed interaction had an impact of 19.28%.Flexural toughness at 5% strain increased with increasing nozzle temperature.In particular, for the 0.25 mm layer height and 80 mm/s print speed parameters, the increase in flexural toughness at 5% strain was more significant with increasing nozzle temperature (Figure 7c,d).Changes in layer height and print-speed parameters have mixed effects regarding the increases and decreases in flexural toughness at 5% strain (Figure 7b-d).The highest flexural toughness for the 5% strain value was obtained as 368.48J/mm 3 at 0.20 mm layer height, 80 mm/s print speed, and 250 • C nozzle temperature.

Strain at Ultimate Flexural Strength Results
Figure 8 shows the simultaneous effects of layer height, print speed, and nozzle temperature on strain at ultimate flexural strength.In addition, the degree of influence of the variables on the strain (%) is provided in Figure 8a.The Pareto plot for strain shows that layer height is the most influential parameter, followed by print speed and nozzle temperature.The ANOVA results show that the contribution of layer height to strain is 73.23%, the print speed is 16.91%, and the nozzle temperature is 2.62%.The simultaneous effects of the variables show that increasing layer height promotes an increase in strain while increasing print speed promotes a decrease (Figure 8b-d).Nozzle temperature has a limited effect on strain.Based on the test results in Table 3, the highest strain at the ultimate flexural strength value is 3.66% for the parameters of 0.25 mm layer height, 20 mm/s print speed, and 240 • C nozzle temperature.

RSM Prediction vs. Experimental Results
This section draws a contrast to assess the degree of agreement between the predictions generated by the regression equations and the 15 experiments used to construct the RSM model.Tables 9-11 compare the prediction results of the RSM model and the experimental Polymers 2024, 16, 2020 14 of 18 results, along with the corresponding error percentages for each output response.When the error means between the test results and the RSM predictions are analyzed, the results are in good agreement with very low error percentages.The best fits were found for flexural toughness at 5% strain with an error of 0.13%, while the worst fit was found for flexural modulus with an error of 0.83%.

Optimization and Validation of Responses
In this study, the multiple responses listed in Table 11 were optimized using the response optimizer according to the stated objectives and as part of the RSM analyses.The main objective was to find the maximum values for all responses.Figure 9 shows the results of the RSM optimizer.The optimum values for strain, toughness at 5% strain, toughness at ultimate FS, flexural modulus, and flexural strength were obtained as 3.45%, 369.74 J/mm 3 , 215.86 J/mm 3 , 1336.27MPa, and 39.05 MPa for optimum input parameters of 0.25 mm layer height, 58.18 mm/s print speed, and 250 • C nozzle temperature, respectively.In optimization studies, the desirability value is expected to be close to 1.The value of 0.7018 in the present study shows an acceptable desirability value.Nevertheless, verification experiments were conducted to prove the accuracy of the optimization study, and the results obtained were compared with those obtained as a result of the optimization.Table 12 shows the optimization results, the validation experiment results, and the error rates between them.The results of the validation experiments were above the predicted values for all outputs.In the verification experiments, for the optimal parameters 3.50%, 381.47 J/mm 3 , 218.22 J/mm 3 , 1344.60 MPa, and 39.55 MPa strain, toughness for 5% strain, toughness for ultimate FS, flexural modulus, and flexural strength, respectively, were obtained.When the error rates are analyzed, it can be seen that all of them are less than 1.5% except for toughness at 5% strain.The lowest error rate was obtained in flexural modulus with 0.62%, while the highest error occurred in toughness at 5% strain with 3.17%.between them.The results of the validation experiments were above the predicted values for all outputs.In the verification experiments, for the optimal parameters 3.50%, 381.47 J/mm 3 , 218.22 J/mm 3 , 1344.60 MPa, and 39.55 MPa strain, toughness for 5% strain, toughness for ultimate FS, flexural modulus, and flexural strength, respectively, were obtained.When the error rates are analyzed, it can be seen that all of them are less than 1.5% except for toughness at 5% strain.The lowest error rate was obtained in flexural modulus with 0.62%, while the highest error occurred in toughness at 5% strain with 3.17%.

Conclusions
The study focused on optimizing FFF process parameters for PETG material and evaluated various mechanical responses such as flexural strength, flexural modulus, and flexural toughness through three-point flexure tests.Key process parameters included layer height, print speed, and nozzle temperature.This study used Box-Behnken design within RSM to create models representing the relationships between variables and responses.The main results obtained are presented below.
According to the results, increasing the layer height and nozzle temperature increased the mechanical properties of PETG material under the flexural load.Increasing layer height decreased printing time and thermal stress, while increasing nozzle temperature led to better fusion of the layers, resulting in more robust and high-integrity final products.The ANOVA analysis revealed the quantitative effects of input parameters and their interactions with responses.Layer height predominantly affected flexural modulus (79.38%), flexural toughness for ultimate flexural strength (67.36%), and strain at ultimate flexural strength (73.23%).Conversely, nozzle temperature significantly impacted flexural strength (56.64%) and flexural toughness for 5% strain (33.62%).
Experimental data were used to construct second-order polynomial response-regression models that yielded high coefficients of determination (R 2 ) ranging from 99.12% to 99.46%.
Desirability was high at 0.7018, validated by verification experiments closely matching predicted values with minimal errors (0.13% to 3.17%).
Future research could further explore additional 3D-printing parameters, such as different fill patterns, structure orientations, and post-processing techniques, to enhance the mechanical properties of FFF-printed PETG parts.Furthermore, evaluating the optimized parts' long-term durability and environmental impact will provide valuable insights.Comparing the performance of FFF-printed PETG parts with commercial and conventionally produced PETG parts will also be helpful for broader practical applications and sustainability considerations in additive manufacturing.

Figure 2 .
Figure 2. (a) A stress-strain graph of a flexural sample.(FS: flexural strength, E f flexural modulus, T: toughness) (b) schematic diagram of a sample under a three-point flexure.

Figure 2 .
Figure 2. (a) A stress-strain graph of a flexural sample.(FS: flexural strength, E f flexural modulus, T: toughness) (b) schematic diagram of a sample under a three-point flexure.

Polymers 2024 , 19 Figure 4 .
Figure 4. (a) Pareto chart and (b-d) simultaneous impacts of layer height, print speed, and nozzle temperature on flexural strength.

Figure 5 .
Figure 5. (a) Pareto chart and (b-d) simultaneous impacts of layer height, print speed, and nozzle temperature on flexural modulus.

Figure 4 . 19 Figure 4 .
Figure 4. (a) Pareto chart and (b-d) simultaneous impacts of layer height, print speed, and nozzle temperature on flexural strength.

Figure 5 .
Figure 5. (a) Pareto chart and (b-d) simultaneous impacts of layer height, print speed, and nozzle temperature on flexural modulus.

Figure 5 .
Figure 5. (a) Pareto chart and (b-d) simultaneous impacts of layer height, print speed, and nozzle temperature on flexural modulus.

Figure 6 .
Figure 6.(a) Pareto chart and (b-d) simultaneous impacts of layer height, print speed, and nozzle temperature on flexural toughness for ultimate flexural strength.

Figure 6 .
Figure 6.(a) Pareto chart and (b-d) simultaneous impacts of layer height, print speed, and nozzle temperature on flexural toughness for ultimate flexural strength.

Figure 7 .
Figure 7. (a) Pareto chart and (b-d) simultaneous impacts of layer height, print speed, and nozzle temperature on flexural toughness for 5% strain.

Figure 7 .
Figure 7. (a) Pareto chart and (b-d) simultaneous impacts of layer height, print speed, and nozzle temperature on flexural toughness for 5% strain.

Figure 8 .
Figure 8.(a) Pareto chart and (b-d) simultaneous impacts of layer height, print speed, and nozzle temperature on strain at ultimate flexural strength.

Figure 8 .
Figure 8.(a) Pareto chart and (b-d) simultaneous impacts of layer height, print speed, and nozzle temperature on strain at ultimate flexural strength.

Table 1 .
Constant printing parameters of the flexural test samples.
• C, 240 • C, and 250 • C. Throughout the experiments, the parameters outlined in Table 1 remained constant.

Table 2 .
Three-dimensional-printing process parameters and their levels.

Table 3 .
The Box-Behnken design of experiments and the response of the outputs.

Table 3 .
The Box-Behnken design of experiments and the response of the outputs.

Table 4 .
ANOVA results of flexural strength and flexural modulus.

Table 5 .
ANOVA results of flexural toughness for ultimate flexural strength and flexural toughness for 5% strain.

Table 6 .
ANOVA results of strain at ultimate flexural strength.

Table 8 .
R 2 values of responses from ANOVA results.

Table 9 .
Comparison of test and RSM responses for ultimate flexural strength, flexural modulus, and flexural toughness for ultimate FS.

Table 9 .
Comparison of test and RSM responses for ultimate flexural strength, flexural modulus, and flexural toughness for ultimate FS.

Table 10 .
Comparison of test and RSM responses for flexural toughness for 5% strain and strain for ultimate FS.