Investigation of the Fabrication Parameters’ Influence on the Tensile Strength of 3D-Printed Copper-Filled Metal Composite Using Design of Experiments

Abstract

The present study investigates the effects of fabrication parameters such as the nozzle temperature, the flow rate, and the layer thickness on the tensile strength of copper-filled metal-composite specimens. The selected material is a polylactic acid (PLA) filament filled with 65% copper powder. Two sets of 27 specimens each were fabricated, and equivalent tensile experiments were carried out using a universal testing machine. The experiments were planned according to the full factorial design, with three printing parameters, as well as three value levels for each parameter. The analysis revealed that the temperature and the flow rate had the greatest impact on the yielded tensile strength, with their contribution percentages being 42.41% and 22.16%, respectively. In addition, a regression model was developed based on the experimental data to predict the tensile strength of the 3D-printed copper-filled metal composite within the investigated range of parameters. The model was evaluated using statistical methods, highlighting its increased accuracy. Finally, an optimization study was carried out according to the principles of the desirability function. The optimal fabrication parameters were determined to maximize the tensile strength of the specimens: temperature equal to 220 °C, flow rate equal to 110%, and layer thickness close to 0.189 mm.

1. Introduction

The tensile testing of 3D-printed specimens is a crucial method for assessing the mechanical properties and structural integrity of materials produced through additive manufacturing. It involves subjecting a specimen to uniaxial tension until failure to determine key properties such as tensile strength, elasticity, elongation, and Young’s modulus. With the increasing adoption of 3D-printing technologies across industries, understanding the tensile behavior of printed materials has become essential for predicting their performance in real-world applications. One key factor influencing tensile properties is the material used for 3D printing.

Filaments such as polylactic acid (PLA) and acrylonitrile butadiene styrene (ABS) have been extensively studied because they are widely available, can be used in numerous applications, and have a low cost. Srinivasan et al. [1] employed a central composite design (CCD) to investigate the effects of infill pattern and density, as well as layer thickness, on the tensile strength of ABS specimens. Rezaeian et al. [2] examined the effect of printing speed on tensile and fracture properties of ABS material. Tzotzis et al. [3] applied similar methodologies to evaluate the tensile strength and strength-to-mass ratio of ABS test pieces with respect to four structural characteristics. Hikmat et al. [4] employed the Taguchi method to investigate the influence of various printing parameters on the tensile strength of PLA workpieces. Atakok et al. [5] presented a study related to tensile testing, three-point bending, and impact strength of both PLA and recycled PLA parts by utilizing statistical methodologies. Shbanah et al. [6] investigated the effect of heat treatment on PLA specimens subjected to tensile testing. Several studies dealt with other typical polymer testing, including acrylonitrile styrene acrylate (ASA) [7], polycarbonate (PC) [8], thermoplastic polyurethane (TPU) [9,10], nylon [11], and polyethylene terephthalate glycol (PETG) [12,13]. Most studies employed statistical methodologies to assess a range of fabrication parameters relating to the generated tensile strength, bending resistance, or impact strength.

The advent of technologies that enabled the production of composite filaments contributed to the expansion of the filament market. In addition, the idea that manufacturers can use 3D-printed parts made of composite materials paved the way for a new research area. The investigation of the behavior of fiber-reinforced polymers and metal matrix composites is the main research topic regarding composite filaments because of their improved strength-to-weight ratio compared to pure polymeric filaments. Yavas et al. [14] investigated the fracture behavior of a 3D-printed carbon fiber reinforced polymer (CFRP) during tensile and tension testing with respect to the build orientation. Bendine et al. [15] worked on tensile and tensile fatigue tests of 3D-printed CFRP parts. The authors evaluated the mechanical properties of the parts, assessed their microstructure, and investigated the effect of the fiber volume fraction. Kumar Mishra and Jagadesh [16] investigated the tensile behavior of additively manufactured nylon-based CFRP parts. The authors validated the stiffness of the fabricated parts by using the volume average stiffness model, as well as experimental data. Jia et al. [17] studied the thermal effects on the mechanical properties and failure mechanisms of 3D-printed CFRP materials for varying fiber angles. Similar works [18,19] focus on the mechanical behavior of 3D-printed CFRP.

In recent years, composite filaments have gained attention for offering enhanced mechanical and thermal characteristics. Carbon-fiber-reinforced-polymer (CFRP) composite filaments have been widely studied [20] due to their superior mechanical properties and low weight compared to typical polymers intended for 3D printing. Copper-filled filaments [21,22], on the other hand, are a popular choice due to copper’s excellent thermal conductivity, electrical properties, and aesthetic appeal. These filaments are typically composed of a base polymer, such as PLA or ABS, infused with fine copper particles. The inclusion of copper enhances the filament’s stiffness and can provide added durability compared to standard polymer-based materials. However, the copper content also introduces complexities in tensile testing, as it can impact the material’s brittleness, ductility, and fracture behavior. When testing copper-filled 3D-printed specimens, factors like print orientation, layer adhesion, and the distribution of copper particles within the filament play a significant role in the resulting mechanical properties. Variations in printing parameters, such as nozzle temperature and layer thickness, further affect the material’s tensile response. Several studies have investigated the behavior of the copper-filled filaments to varying degrees. Kottasamy et al. [23] focused on the effect of different copper compositions and different infill patterns on the tensile properties of copper-filled PLA. Ambruş et al. [24] examined the printing orientation, infill pattern, and density influence on the mechanical behavior of 3D-printed Cu-PLA composite parts. Adibi and Hashemi [25] employed a Taguchi design to study the behavior of copper-filled ABS during tensile testing under a range of parameters, including temperature, infill pattern, and layer thickness. Another study on copper-filled ABS polymer by Singh et al. [26] utilized similar techniques and methodologies to examine the effects of the nozzle temperature, the pattern, and the layer thickness on the generated tensile strength of additively manufactured parts. Similar works [27,28] focus mostly on the printing orientation, infill pattern, infill percentage, and layer. The anisotropic nature of 3D-printed parts complicates the interpretation of test results. Therefore, tensile testing not only provides a measure of the material’s inherent strength but also offers insights into optimizing printing processes to achieve better performance in copper-filled composites. Understanding the tensile properties of 3D-printed materials, particularly composites like copper-filled filaments, is essential for designing parts that are both functional and reliable in demanding applications. Defects of 3D-printed copper/polymer composites are another topic that draws increased attention. Molefi et al. [29] investigated the influence of the micro and nanoparticles on the tensile strength of polyethylene/copper composite filaments with respect to the surface defects. Côté et al. [30] worked on the correction strategies for eliminating the dimensional inaccuracies and defects of highly filled 3D-printed polymers. Zhang et al. [31] evaluated the internal defects and crack propagation of 3D-printed polymer-based materials used in construction. Similar works investigated the generation mechanism of defects and equivalent treatments for a variety of polymers and the derived composites [32,33].

The present study deals with the tensile strength investigation of copper-filled PLA parts manufactured with the 3D-printing method by utilizing a full factorial design. The copper composition of the filament is approximately 65%. The studies that are available in the literature primarily examine filaments with either 25% or 80% copper composition and focus on parameters such as the printing orientation, the infill pattern, and density, as well as the layer thickness. With the aforementioned findings in mind, this research investigates the flow rate, in addition to the nozzle temperature and layer thickness, aiming at the mechanical evaluation of the specific filament. The specific combination of parameters tends toward the fabrication process itself rather than focusing on the structural characteristics of the specimens found in the most recent research. Therefore, the specific copper composition and the process parameter combination constitute a part of the composite filament evaluation research area that requires attention.

2. Materials and Methods

2.1. Experimental Workflow and Apparatus

The experimental workflow of the study comprises five basic steps, as shown in Figure 1. First, the design of the experiments was carried out with the three fabrication parameters and three corresponding values in mind. Therefore, 27 different combinations were generated. This allows for testing every possible combination, contributing to the development of more accurate models [34,35]. Next, the fabrication of the tensile test specimens was performed using a CreatBot D600 Pro 3D-printer (Henan Creatbot Technology Limited, Zhengzhou, Henan, China).

Then, the two sets of specimens were numbered according to the corresponding test number. During the fourth step, the specimens were tested in terms of their tensile strength by performing the tensile test with the Instron 3345 Universal Testing Machine, equipped with a 5 kN load cell, at a constant 25 mm/min speed. Finally, the acquired data were analyzed, and a regression model was developed. Moreover, the interaction between the variables, as well as the effect of each variable on the measured tensile strength was investigated.

Table 1. Fabrication parameters for the copper-filled PLA filament printing.

Printing Parameter	Value
Nozzle temperature	Varying
Build plate temperature	50 °C
Filament diameter	1.75 mm
Nozzle diameter	0.6 mm
Printing speed	30 mm/s
Infill	100%
Pattern	Rectilinear
Infill angle	45%
Build orientation	Horizontal

presents the values of the typical printing parameters. The test pieces were designed according to the guidelines of the ASTM-D638 standard [36,37], which describes the tensile test method for plastic parts, as well as the recommended dimensions of the specimens. The Type IV specimen was selected, with a gauge length of 33 mm, a width of 6 mm, and a thickness of 3.6 mm. The material selected for the fabrication of the specimens is a copper-filled PLA composite containing 65% copper powder.

Table 2. Basic mechanical properties of the copper-filled PLA filament.

Property	Value
Tensile strength	18.69 MPa
Tensile elongation	1.27%
Flexural strength	17.60 MPa
Flexural modulus	1.026 GPa
Impact strength	49.66 J/m

contains the standard mechanical properties of the filament, whereas Figure 2 illustrates the infill density, pattern, and printing orientation of the specimens.

2.2. Design of Experiments

In the present study, three fabrication parameters were applied: the nozzle temperature (T), the flow rate (F), and the layer thickness (L). The values for each factor are summarized in

Table 3. Specimen fabrication parameters and the corresponding levels.

Level	Nozzle Temperature T (°C)	Flow Rate F (%)	Layer Thickness L (mm)
+1	220	130	0.3
0	210	120	0.2
−1	200	110	0.1

. Due to the full factorial design, the total number of tests was 27. Therefore, 54 specimens were produced to perform each trial twice, and the mean value of the maximum load for each test was calculated. The sets were produced on two consecutive days, and the experiments were carried out right after the specimens were documented.

Table 4. The design of experiments and the tensile test results.

Test	T (°C)	F (%)	L (mm)	s (MPa)
1	200	110	0.1	16.29
2	200	120	0.1	17.57
3	200	130	0.1	18.86
4	210	110	0.1	18.35
5	210	120	0.1	18.35
6	210	130	0.1	19.04
7	220	110	0.1	19.59
8	220	120	0.1	19.31
9	220	130	0.1	19.28
10	200	110	0.2	17.24
11	200	120	0.2	18.26
12	200	130	0.2	19.74
13	210	110	0.2	18.77
14	210	120	0.2	19.03
15	210	130	0.2	20.10
16	220	110	0.2	20.40
17	220	120	0.2	19.68
18	220	130	0.2	20.23
19	200	110	0.3	16.37
20	200	120	0.3	17.49
21	200	130	0.3	19.43
22	210	110	0.3	17.93
23	210	120	0.3	18.46
24	210	130	0.3	19.30
25	220	110	0.3	19.57
26	220	120	0.3	18.84
27	220	130	0.3	19.46

shows the combinations of the printing parameters for each trial, as well as the results of the tensile strength. The temperature range was selected according to the recommendations of the manufacturer, whereas the layer thickness was chosen according to recent, similar works [38,39]. Notably, the tensile strength was calculated as the result of the measured maximum load and the cross-section of the specimens, which was equal to 21.6 mm². Before proceeding with the experiments, a preliminary test was carried out to identify the range of flow rates that did not clog the nozzle due to the abrasive nature of copper-filled PLA.

3. Results and Discussion

Upon finalizing the experimental stage, the acquired data were organized, processed, and analyzed. The analysis is presented in the next sections. Before proceeding with the analysis, the fracture mechanism of the specimens was observed, and the equivalent stress–strain curves were generated. Figure 3a illustrates a macro image of the fracture area of specimen number 6, as well as the generated curve. Similarly, Figure 3b–d correspond to specimens 10, 13, and 18. Since the structural characteristics of the fabricated specimens remained the same for all pieces, the produced stress–strain curves were almost identical, as well as the fracture pattern. The only exception was the load at which the fracture occurred due to the varying fabrication parameters.

3.1. Regression Analysis

The experimental data were used to develop a regression equation for the prediction of the tensile strength s. Equation (1) can be used to approximate the tensile strength in MPa, based on the model constant, the three fabrication parameters (temperature, flow rate, and layer thickness), and the squared values of these parameters: Τ², F², and L², as well as the interaction between these parameters: Τ × F, Τ × L, and F × L.

$$\begin{array}{l}\mathrm{s} \left(\mathrm{MPa}\right)=-170.1+1.215\mathrm{T}+0.766\mathrm{F}+31.4\mathrm{L}-0.000581{\mathrm{T}}^2+0.003329{\mathrm{F}}^2-74.44{\mathrm{L}}^2\\ \hspace{1em}\hspace{1em}-0.007273\mathrm{T}\times \mathrm{F}-0.0729\mathrm{T}\times \mathrm{L}+0.1148\mathrm{F}\times \mathrm{L}\end{array}$$

(1)

To analyze the regression equation, the response data were first analyzed using an analysis of variance (ANOVA).

Table 5. Analysis of variance results for the tensile strength.

Source	Degree of Freedom	Sum of Squares	Mean Square	f-Value	p-Value	Contribution %
Model	9	29.8700	3.3189	146.63	0.000
Error	17	0.3848	0.0226
Total	26	30.2548
R-sq = 98.73%  R-sq (adj) = 98.05%  R-sq (pred) = 96.48%
Term
Τ	1	12.6672	12.6672	559.64	0.000	42.41
F	1	6.6208	6.6208	292.50	0.000	22.16
L	1	0.0028	0.0028	0.12	0.729	0.01
Τ2	1	0.0203	0.0203	0.90	0.357	0.07
F2	1	0.6650	0.6650	29.38	0.000	2.23
L2	1	3.3247	3.3247	146.89	0.000	11.13
Τ × F	1	6.3472	6.3472	280.42	0.000	21.25
Τ × L	1	0.0638	0.0638	2.82	0.111	0.21
F × L	1	0.1582	0.1582	6.99	0.017	0.53

presents the ANOVA results for the tensile strength model, which was analyzed for goodness of fit, variance, and prediction accuracy. Moreover, the contribution level of each term to the response was checked by using a 95% confidence level. The coefficient of determination (R-sq) was computed as 98.73%, with adjusted and predicted values of 98.05% and 96.48%, respectively. The increased values of the three coefficients indicate a strong fit for the model, suggesting that the model terms are sufficient and that the model can predict the tensile strength with increased reliability within the scope of the study.

The p-values provided by the ANOVA indicate the statistical significance of the studied terms [40]. However, they do not measure the significance of each term. Therefore, each term with a p-value lower than α = 1 − 0.95 = 0.05 is statistically significant, and hence, we can assume that its contribution to the response is considerable. All terms included in Table 5, with the exceptions of the terms L, T², and Τ × L, are significant. Lastly, the determined f-value for each term, which essentially represents the ratio of the term mean square to the error mean square, provides their contributions. It was found that the temperature, the flow rate, the terms Τ × F, and L², as well as F², contribute to the tensile strength generation with percentages equal to 42.41%, 22.16%, 21.25%, 11.13%, and 2.23%, respectively.

The Pareto chart of Figure 4 visualizes the standardized effects of the three 3D-printing fabrication parameters on the tensile strength of the printed material, further supporting the ANOVA results. Each bar represents the effect of a factor or interaction between factors on the response variable, which in this case is the tensile strength. In addition, the length of the bar indicates the magnitude of the effect. The red vertical line represents the threshold value for statistical significance. For the present study, with the confidence level set at 95% and 17 degrees of freedom, the critical t-value is approximately 2.11. Bars that exceed this threshold indicate factors or interactions that significantly affect the tensile strength. In contrast, any factor that does not exceed this threshold is not considered statistically significant, and its effect can be neglected. Such terms are the Τ × L, Τ² and L, as already identified by the ANOVA results. It should be noted that the term F × L is statistically significant; however, its contribution to the response is very low (Table 5). Summarizing, the nozzle temperature and the flow rate, both make substantial contributions to the response. However, the temperature has the largest effect on tensile strength. Moreover, the interaction between nozzle temperature and flow rate suggests that this combination influences tensile strength significantly.

The regression modeling was evaluated in terms of the residuals as well. Figure 5 illustrates the results of the residual analysis. Specifically, Figure 5a depicts the normal probability graph, which plots the position of the data points with respect to the fitted line. It is evident that the data points are very close to the fitted line, and no serious departures are present. Figure 5b plots the residuals versus the fitted values. This graph indicates that the residuals are randomly scattered on both sides of the reference line (dashed reference line). Moreover, the plot shows the points are evenly distributed on both positive and negative sides of the graph. Figure 5c represents the error histogram, which shows the residual distribution in the model. By observing the histogram, a relative uniformity is evident. In addition, it shows that 12 out of 27 residuals are gathered towards the central error bin. Finally, Figure 5d supports the normality of the model as the residuals versus the order of observation do not highlight any specific pattern or trends. Moreover, the absence of clustering further supports the absence of systematic faults in the model.

The mean effects plot illustrated in Figure 6 analyzes the influence of the three 3D-printing parameters on the tensile strength. By observing the plot, it is shown that the tensile strength increases consistently as the temperature rises from 200 °C to 220 °C. The largest increase in strength is observed between 210 °C and 220 °C, suggesting that higher temperatures significantly improve tensile strength. Similar findings were reported by Kumar et al. [39] regarding the PLA/copper composite for a temperature range of 230 °C to 250 °C. Regarding the flow rate, it is evident that the tensile strength improves as the flow rate increases from 110% to 130%. The most notable increase occurs between 120% and 130%, with the mean tensile strength peaking around 19.5 MPa at 130%. This suggests that increasing the flow rate beyond 120% has a noticeable positive impact on tensile strength. Finally, tensile strength peaks at a layer thickness of 0.2 mm but drops when the thickness is reduced to 0.1 mm or increased to 0.3 mm. The sharpest decrease occurs between 0.2 mm and 0.3 mm, indicating that beyond 0.2 mm, thicker layers may negatively affect strength. In addition, the highest mean tensile strength value observed is approximately 19.3 MPa for 0.2 mm. A similar effect pattern related to layer thickness was reported by Darsin et al. [41], with thickness values between 0.3 mm and 0.4 mm. In contrast, Kumar et al. [38] identified a constant increase in tensile strength as layer thickness rises from 0.1 mm to 0.3 mm.

To summarize, temperature and flow rate have the most significant and positive influence on tensile strength. Conversely, layer thickness shows an optimum of around 0.2 mm, with both thinner and thicker layers decreasing the strength. Similar findings for the temperature, as well as the layer effect have been reported by Darsin et al. [41] and Kumar et al. [38]. Additionally, Dobrescu et al. [42] measured tensile strength of approximately 30 MPa for similar copper-filled PLA at 100% infill density.

Figure 7 includes three interaction plots showing the interaction between the fabrication parameters. Figure 7a illustrates the interaction between the nozzle temperature and the flow rate. It is observed that the tensile strength increases with increasing temperature for all flow rates. The highest tensile strength is observed at the maximum temperature (T = 220 °C) and the lowest flow rate (F = 110%) while increasing the flow rate to 120% or 130% results in slightly lower tensile strength values. Contrary to typical assumptions provided by the mean effects plot, a combination of high temperature (220 °C) and low flow rate (110%) gives the best tensile strength. However, higher flow rates at this temperature slightly reduce the strength. Figure 7b depicts the temperature versus the layer thickness interaction.

As observed, at T = 220 °C, the tensile strength peaks when the layer thickness is 0.2 mm. Both increasing and decreasing the layer thickness from 0.2 mm results in a reduction in tensile strength. This trend is also present at T = 210 °C, although the overall strength is lower. For T = 200 °C, the tensile strength remains low across all layer thicknesses. Finally, Figure 7c presents the interaction between the flow rate and layer thickness. This interaction shows that the highest tensile strength is achieved at F = 130% and L = 0.2 mm. For lower flow rates (F = 120% and 130%), the strength still peaks at L = 0.2 mm, but the overall tensile strength is lower compared to F = 130%. To summarize, increasing the temperature improves tensile strength, with T = 220 °C producing the best results. Regarding the flow rate, it was found that the lowest flow rate (110%) yields the best tensile strength when combined with higher temperatures. Specifically, the highest tensile strength is achieved with T = 220 °C, F = 110%, and L = 0.2 mm.

Figure 8 depicts the contour plots, which provide a visual representation of the interactions between the three 3D-printing parameters and their combined effect on the tensile strength of the printed test pieces. Each subplot represents different parameter combinations. In addition, the contour lines and colors represent different tensile strength values, with green shades indicating higher tensile strength, moving towards dark blue shades for lower values. Figure 8a illustrates the interaction between temperature (x-axis) and flow rate (y-axis). It is observed that the tensile strength increases with both increasing temperature and flow rate. The highest tensile strength (green area, >20 MPa) occurs at the top-right corner or bottom-right corner, where the temperature is at its maximum value and flow rate is either at its minimum or maximum value (T ≈ 220 °C, F ≈ 110% or F ≈ 130%). At lower flow rates and temperatures (bottom left), the tensile strength drops significantly (blue regions, <18 MPa). The gradient is smooth, indicating that both parameters positively affect tensile strength, but high values of both temperature and flow rate are required to achieve the best results.

Figure 8b shows the interaction between temperature (x-axis) and layer thickness (y-axis). It is evident that the tensile strength improves with increasing temperature across all layer thicknesses. The highest strength values (green area, >20 MPa) are observed in the center-right area, where the temperature is high (approximately 220 °C), and layer thickness is moderate (L ≈ 0.2 mm). Lower temperatures and thinner layers (left-hand side, blue regions) result in much lower tensile strength (<18 MPa). The plot shows that temperature has a more dominant impact on tensile strength compared to layer thickness, as tensile strength increases sharply with temperature, while changes in layer thickness have a more gradual effect. Finally, Figure 8c illustrates the interaction between flow rate (x-axis) and layer thickness (y-axis). It is noted that the highest tensile strength (green region, >20 MPa) is observed in the center-right area, where the flow rate is high (F ≈ 130%) and layer thickness is moderate (L ≈ 0.2 mm). Very thin layers (L < 0.12 mm) or very thick layers (L > 0.24 mm) lead to lower tensile strength (blue regions, <18 MPa). There is a notable effect from both parameters, with an optimal combination occurring when the flow rate is close to 130% and layer thickness is around 0.2 mm.

In summary, nozzle temperature has a strong positive effect on tensile strength in combination with both flow rate and layer thickness, with higher temperatures (T > 215 °C) consistently yielding better results. Flow rate is also important, with higher flow rates (F > 125%) or lower levels (F = 110%) leading to improved tensile strength when paired with high temperature or optimal layer thickness. Layer thickness, on the other hand, has a more moderate effect, with the best tensile strength obtained at approximately 0.2 mm. Thinner or thicker layers tend to reduce strength, especially when combined with lower flow rates or temperatures. The generalized effect patterns and the magnitude of the measured response were also observed by Moradi et al. [43] for a PLA/copper composite.

3.2. Optimization Study

In this study, the parameter combination that maximizes the formula that predicts the tensile strength was identified. It was revealed that the 220 °C temperature, 110% flow rate, and 0.1889 mm contribute towards maximizing the tensile strength within the scope of the study. A second solution, with the temperature set at 220 °C, 110% flow rate, and 0.2030 mm layer, was also responsible for maximizing the response, with a slightly different result. The maximized response for the first solution was calculated to be approximately equal to 20.333 MPa, and for the second one, 20.317 MPa.

The desirability function was employed to identify the optimal solutions for the developed regression model. This function is usually employed on models derived from a design of experiments (DOE) and has been widely applied in similar studies [3,44,45]. The implementation of this function requires the identification of the response variables to be optimized (i.e., tensile strength) and the specification of the desired goals for each response (i.e., maximize). Next, each response is transformed into a desirability score (d) ranging from 0 to 1. When d = 1, the desired outcome is achieved completely. The opposite, d = 0, means an unacceptable outcome. The individual desirability scores for each response Y are combined into a single overall desirability score (D), often calculated as the geometric mean represented by Equation (2) for k responses.

$$\mathrm{D}={({\mathrm{d}}_1({\mathrm{Y}}_1){\mathrm{d}}_2({\mathrm{Y}}_2){\mathrm{d}}_3({\mathrm{Y}}_3)\mathrm{\dots }{\mathrm{d}}_k({\mathrm{Y}}_k))}^{1/k}$$

(2)

Table 6. Constraints of the optimization study.

Factor	Goal	Lower Limit	Upper Limit
T (°C)	In range	200	220
F (%)	In range	110	130
L (mm)	In range	0.1	0.3
s (MPa)	Maximize	16.29	20.40

presents the constraints and limits for the optimization study, whereas

Table 7. Optimization solutions according to the desirability function.

	Solution
Parameter	1	2
T (°C)	220	220
F (%)	110	110
L (mm)	0.1889	0.2030
s (MPa) Fit	20.333	20.317
Desirability	0.983428	0.979509

displays the two best solutions generated, both yielding approximately 20.3 MPa.

4. Conclusions

This study presents an investigation of the tensile strength of a copper-filled metal composite material with respect to the nozzle temperature, flow rate, and layer thickness, covering a research gap related to composite filament strength evaluation. More specifically, it is related to the performance optimization of 65% copper/PLA in terms of the fabrication process. A set of experiments was conducted according to the full factorial design of experiments (DOE), and a prediction model was developed based on the acquired data. The ANOVA methodology was utilized to evaluate the effect of the aforementioned parameters on the tensile strength and assess the effectiveness of the developed regression model. In addition, an optimization method was carried out to identify the optimal combination of parameters. With these findings in mind, the following conclusions can be drawn:

• The parameter with the most significant effect on the response is temperature, with a contribution percentage of 42.41%. It is followed by the flow rate, which contributes 22.16% to the generated response.
• Following the previously mentioned factors, Τ × F contributes 21.25% to the response and, L² contributes 11.13%.
• The ANOVA results, specifically the p-values, highlighted the terms Τ × L, Τ², and L as not statistically significant. Therefore, their contribution to the response is negligible.
• The combination of parameters that yielded the highest value of tensile strength (s = 20.40 MPa), based on the experimental testing, is T = 220 °C, F = 110%, and L = 0.2 mm.
• Both the temperature and flow rate act increasingly on the generated tensile strength. Layer thickness, however, seems to have a more complex behavior. In particular, the medium value is responsible for higher levels of tensile strength, whereas the other two layer thicknesses yield lower values for the response.
• Moreover, it was found that the combination of T = 220 °C and F = 110% generated the highest mean tensile strength compared to every other combination of temperature and flow rate.
• The developed regression model exhibits a high predicted R² value, equal to 96.48%, supporting the reliability of the model.
• Finally, the optimal solution for maximizing the tensile strength with the regression equation is the combination of 220 °C nozzle temperature, 110% flow rate, and 0.1889 mm layer thickness.

Future research will include more comprehensive experimental work focused on additional material testing, such as compression and bending, with respect to a wider range of process parameters, aiming to develop a plasticity model that can be used in simulation methodologies.