Effect of Process Parameters on Tensile Strength of FDM Printed Carbon Fiber Reinforced Polyamide Parts

Abstract

Reinforcing the polymer with nanoparticles and fibers improves the mechanical, thermal and electrical properties. Owing to this, the functional parts produced by the FDM process of such materials can be used in industrial applications. However, optimal parameters’ selection is crucial to produce parts with optimal properties, such as mechanical strength. This paper focuses on the analysis of influential process parameters on the tensile strength of FDM printed parts. Two statistical methods, RSM and ANN, were applied to investigate the effect the layer thickness, printing speed, raster angle and wall thickness on the tensile strength of test specimens printed with a short carbon fiber reinforced polyamide composite. The reduced cubic model was developed by the RSM method, and the correlation between the input parameters and the output response was analyzed by ANOVA. The results show that the layer thickness and raster angle have the most significant influence on tensile strength. As for machine learning, among the nine different tested ANN topologies, the best configuration was found based on the lowest MAE and MSE test sample result. The results show that the proposed model could be a useful tool for predicting tensile strength. Its main advantage is the reduction in time needed for experiments with the LOSO (leave one subject out) k-fold cross validation scheme, offering better generalization ability, given the small set of learning examples.

1. Introduction

According to the ISO/ASTM 52900, additive manufacturing (AM) is defined as the joining materials process to make parts from three-dimensional model data, usually layer by layer, as opposed to subtractive manufacturing methodologies. It is also known as additive fabrication, used for direct digital manufacturing, rapid prototyping, etc. Additive manufacturing has many advantages over the conventional manufacturing method. AM enables the production of products with very complex details without any special planning of the manufacturing process, preparation of devices, complex manufacturing operations or any additional tools and accessories. In addition, a significant advantage of these processes is the production of parts without any loss of material, or this loss of material is minimized, thus reducing the production cost. Many researchers have shown the experimental application and the advantages of this process over conventional manufacturing [1,2,3]. Depending on the type of materials used and the process physics, many AM systems are accessible in the market, such as fused deposition modeling (FDM), stereolithography (SLA), selective laser sintering (SLS), ink jet modeling, etc.

FDM is a widely used additive manufacturing technology for the fabrication of complex geometric parts in various engineering applications. In the FDM technique, printers use a thermoplastic type of filament, which is melted and extruded through the nozzle, which travels on a prescribed path to fabricate a certain 3D structure. Materials such as acrylonitrile butadiene styrene (ABS), polyamide (PA), polylactic acid (PLA), poly carbonate (PC), thermoplastic polyurethane (TPU), and polyethylene terephthalate (PET), are used commonly as filaments in the FDM process [4,5,6,7]. Although a relatively wide range of polymers are in use in FDM, a common disadvantage of all of them is the limited functionality of the manufactured parts due to the inadequate mechanical properties of these materials. A possible solution to this problem is the use of composite materials, comprised of a polymer base, with particles made of metal, ceramics, carbon, glass and wood [8,9]. Recently, research has focused on the use of different composite materials and optimizing their process parameters for FDM, to improve different mechanical properties and other desired properties of the FDM components. Parts made using these composites have higher mechanical, thermal and electrical properties, compared to the unreinforced polymer printed parts [10,11,12]. Peng et al. [13] investigated the effect of process parameters on interlayer adhesion and mechanical properties of the FDM CF/PA6 fabricated parts. CF/PA6 printed along the tensile load direction has been shown to exhibit higher tensile properties than the other two printing directions, indicating a strong anisotropy of mechanical properties. In ref. [14], the authors investigated the effect of short carbon fiber on the mechanical, electrical and piezoresistivity properties of 3D-printed polyamide composite parts. It was shown that the reinforcing of neat polyamide with short carbon fibers improved the mechanical properties of the material. In the XY build orientation, 3D-printed composites exhibited significantly increased tensile strength and tensile modulus in compared to the neat PA. Belei et al. [15] concluded that the layer height and printing bed temperatures are the most influential parameters, while the extrusion temperature and printing speed had a lower influence on the performance of FFF (fused-filament fabrication) printed short-fiber-reinforced polyamide parts under uniaxial tensile loading. Liao et al. [16] found that the reinforcing of polyamide PA12 with 10% short carbon improved the tensile and flexural strength of printed parts in compared with the pure PA12. Sedlacek F. and Lasova V. [17] analyzed the influence of the short carbon fibers in nylon PA6 polymer used in the FDM process for two build directions, horizontally and vertically printed specimens. The results showed that a significant influence of the short carbon fibers on the strength and heat deflection temperature of the parts was found in PA6. It was also shown that the strength and tensile modulus of the PA6 reinforced with short carbon fibers in the longitudinal direction of the material are up to 39% higher than for the transverse direction. Badini et al. [18] investigated the effect of the orientation of reinforcing fibers in polymer-based composites on the mechanical properties of FDM-printed parts. The results showed that the best strength and stiffness were achieved when the fibers and the layer interfaces were parallel to the sample axis, while these properties were about 60% lower when measured in the direction perpendicular to the fibers. Ning et al. [19] investigated the effects of the FDM process parameters on the tensile properties of carbon fiber-reinforced plastic. The results revealed that samples with 0° and 90° raster angles exhibited higher Young’s modulus, yield and tensile strengths, whereas samples with raster angles of −45° and 45° exhibited higher toughness and ductility. The study optimized the process parameters of research examples to specify the infill speed of 25 mm/s, and layer thickness of 0.15 mm for high tensile and yield strengths, whereas a 0.25 mm layer thickness was specified to achieve high toughness and ductility. Tian et al. [20] investigated the effect of process parameters (melting temperature, fiber content, hatch spacing and layer thickness) and the performance of 3D-printed continuous carbon fiber reinforced PLA composites. The results showed that the mechanical properties improve with increasing the melting temperature, but the surface accuracy is affected by increasing the temperature above 240 °C.

The applications of various optimization and modeling techniques were adopted in FDM, such as the Taguchi method, the response surface method (RSM), grey relational, fractional factorial, artificial neural networks (ANNs), genetic algorithm (GA) and fuzzy logic. These methods give good and reliable results and offer improvement of the quality characteristics of parts made by FDM technology [21,22]. Ref. [23] demonstrated the use of RSM for the modeling and optimization of the FDM process parameters. The authors of this paper identified the influence of four important process parameters: thickness of layer, infill density, printing temperature and wall thickness, on the tensile strength of test specimens printed from PLA material. Kamoona et al. [24] presented an investigation on the effect of three process parameters on the flexural strength of the FDM Nylon 12 fabricated parts. RSM was used to analyze the results. To test the significance of the parameters, the analysis of variance (ANOVA) method was used. The results showed that the raster angle and air gap have a significant effect on the flexural strength. Srivastava et al. [25] developed a statistical model using the RSM method integrated with GA to predict the optimal FDM process parameters. According to the central composite design (CCD), 86 experiments were performed, considering 6 process parameters, such as air gap, slice height, raster angle, raster width, contour width and orientation.

Artificial intelligence plays an essential role in the research and development of manufacturing processes. It became an integral part of optimizing process parameters and in predicting output values based on inputs. The use of artificial neural networks as one of the machine learning methods has also proven to be useful for the modeling of the FDM process. Yadav et al. [26] studied the effect of process parameters on the mechanical properties of FDM printed parts made of different materials, where infill density and extrusion temperature were optimized to increase the tensile strength of the FDM fabricated units. ANN combined with GA into a hybrid tool (GA ANN) was used for model generation and optimization purposes. Deswal et al. [22] optimized the significant process parameters of FDM 3D printer parts to increase their dimensional accuracy by using hybrid tools such as ANN and GA-ANN. In ref. [27], the authors performed a characterization of the influence of five manufacturing parameters on the tensile strength (UTS) and tensile modulus (E) of a part, and data were later used for ANN construction. The resulting methodology was used to create two load-bearing components with satisfactory performance after only a few iterations. On the other hand, the study by Mahapatra and Sood [28] proposed an ANN model to determine the relationship between five input parameters and three output responses, namely, the roughness of the top, bottom and side surfaces of the component. Ahmed et al. [29] proposed a new class of design of experimental techniques for an integrated second-order definitive screening design (DSD) and an ANN to design experiments for evaluating and predicting the effects of six important operating variables. By determining the optimal manufacturing conditions to achieve better dimensional accuracies for cylindrical parts, this study significantly reduces the time and number of complex experiments. Moreover, the results indicate potential in the integration of second-order DSD with ANN for additive manufacturing applications.

In summary, a review of the current research shows that the process parameters of FDM have a significant impact on the tensile strength of printed parts. However, most of these studies were conducted for commonly used FDM materials (PLA, ABS, PA, etc.). A lack of sufficiently reliable models was observed for the prediction of mechanical properties of FDM printed parts of the new composite polymers, as well as the insufficient research of these materials. Therefore, the objective of this study was to investigate the influence of the FDM process parameters on the tensile strength and predict the tensile strength of new polymer composites using RSM and ANN methods based on varying values of the FDM process parameters. The RSM method was applied because this method, with a not-fully experimental design, gives the right answers and offers proper analysis of the interaction and significance of the influential process parameters on the output response. ANN was adopted since it ensures arbitrary levels of adjustment to the underlying model. Thus, this study focuses on developing a reliable model for the prediction of the tensile strength of FDM printed parts with a short carbon fiber reinforced polyamide composite since this material is one of the new and insufficiently researched FDM materials.

2. Materials and Methods

2.1. Experimental Setup Description

The specimens for testing tensile strengths used in this experiment were designed in accordance with the ISO 527 Standard, as shown in Figure 1. Models of the test specimens were saved in STL formats and imported into the 3D printing software Ultimaker Cura 4.8.0 (Ultimaker B.V., Utrecht, The Netherlands) for slicing the representative CAD model into layers, whereby the printing path and all process parameters for each specimen were defined (Figure 2). This software also serves for the generation of support structures, if necessary, for the setup of the process parameters, and for the adjustment of the part position on the 3D printer’s bed.

In this study, all the samples were printed with an Ultimaker S3 3D printer machine. The print material used was short carbon fiber reinforced polyamide PA6/66 (Novamid^® ID1030 CF10, Royal DSM, Heerlen, The Netherlands), and its physical and mechanical properties are shown in

Table 1. Material properties for Novamid^® ID1030 CF10 [30].

Material Properties	Test Method	Value
Tensile modulus (flat X-X orientation)	ISO 527	7625 MPa
Stress at yield (flat X-X orientation)	ISO 527	112 MPa
Strain at yield (flat X-X orientation)	ISO 527	2.5%
Stress at break (flat X-X orientation)	ISO 527	110 MPa
Strain at break (flat X-X orientation)	ISO 527	2.2%
Tensile modulus (flat Y-X orientation)	ISO 527	2720 MPa
Stress at yield (flat Y-X orientation)	ISO 527	63 MPa
Strain at yield (flat Y-X orientation)	ISO 527	3%
Stress at break (flat Y-X orientation)	ISO 527	58 MPa
Strain at break (flat Y-X orientation)	ISO 527	4.5%
Printing temperature		270 ± 10 °C
Melting temperature		200 °C

. According to the ISO 527 Standard, the universal testing machine Shimadzu AGS–X-10kN (Shimadzu Corporation, Kyoto, Japan) was used for tensile strength measurements.

2.2. Design of the Experiment Based on the RSM Method

The RSM method [31], based on the circumscribed central composite design (CCCD) was adopted, to study the relationship between the process parameters and the output response, to construct a mathematical model that can predict the output response of an actual process. To develop the mathematical model for tensile strength, an experiment was implemented in accordance with CCCD with four input parameters (ǀαǀ = 2.0). The influence of four process parameters, namely, layer thickness, printing speed, raster angle and wall thickness on tensile strength, was assessed in this study. Other process parameters, such as infill, printing temperature, part orientation and build plate temperature, were kept constant and are depicted in

Table 2. Fixed parameters and their levels.

Process Parameters	Level	Unit
Printing temperature	270	°C
Part orientation	Flat x-x direction	degree
Build plate temperature	110	°C
Infill	100	%

. The printing temperature and build plate temperature were adopted according to the recommendations of the material manufacturer. The research recognizes that high tensile strengths can be achieved with flat orientation at a 100% infill [13,32]. Variations of the input parameters were performed on 5 levels. The zero level (center point) was created in between the high and low levels. The range of parameter variation was selected through a preliminary experiment so that it was possible to create a test sample with any combination of selected parameters.

Table 3. Control process parameters and their levels.

Process Parameters	Symbol	Unit	Levels
			−2	−1	0	1	2
Layer thickness	A	mm	0.1	0.15	0.2	0.25	0.3
Printing speed	B	mm/s	60	70	80	90	100
Raster angle	C	°	0	30	45	60	90
Wall thickness	D	mm	0.8	1.1	1.4	1.7	2

shows the control process parameters, along with their levels in terms of uncoded form in accordance with CCCD. The experimental data for 31 runs with four control input parameters and one output response are given in

Table 4. The experimental data.

Exp. No.	Process Parameters				Tensile Strength (MPa)
	A	B	C	D
1.	0.25	70	30	1.7	58.07
2.	0.1	80	45	1.4	73.93
3.	0.2	80	45	2	59.2
4.	0.2	80	45	1.4	61
5.	0.2	80	45	1.4	64.37
6.	0.2	80	45	1.4	65.97
7.	0.2	80	0	1.4	58.9
8.	0.25	70	60	1.1	54.73
9.	0.2	80	45	1.4	61.53
10.	0.15	70	30	1.7	72.53
11.	0.2	80	45	1.4	60.6
12.	0.2	80	45	1.4	65.43
13.	0.2	80	45	0.8	52.53
14.	0.25	90	60	1.1	46.13
15.	0.15	90	30	1.7	65.2
16.	0.15	90	60	1.7	71.77
17.	0.2	80	45	1.4	64.7
18.	0.2	80	90	1.4	91.53
19.	0.3	80	45	1.4	45.77
20.	0.15	70	60	1.1	82.73
21.	0.15	70	30	1.1	67.07
22.	0.25	90	30	1.7	49.6
23.	0.15	90	60	1.1	80.6
24.	0.25	70	30	1.1	52.53
25.	0.15	70	60	1.7	85.27
26.	0.25	70	60	1.7	65.13
27.	0.2	100	45	1.4	64.57
28.	0.25	90	60	1.7	53.8
29.	0.25	90	30	1.1	47.53
30.	0.15	90	30	1.1	74.33
31.	0.2	60	45	1.4	71.97

.

Design Expert software was used to analyze the experimental data. The quadratic model is generally used in the modeling of FDM process parameters [25,33,34].

In this study, quadratic and cubic regression models were adopted to assess the overall FDM process parameters. The process parameters were the output response variable (tensile strength, $R_m$) and input parameters. The input parameters, used further on for RMS and ANN modeling, are depicted as layer thickness (A), print speed (B), raster angle (C), and wall thickness (D) in Table 3 and Table 4, which were analyzed by a set of experimental data using the RSM method.

2.3. Artificial Neural Networks Based Prediction Model

Artificial neural networks (ANNs) [35] were selected as the method for generating a predictive model. The ability to detect all possible interactions between the independent variables and the implicit ability to detect complex nonlinear relationships are the main advantages of predictive modeling by neural networks. This is achieved by using multi-layered ANNs, which serve as a black box prediction model. The ANN’s drawback is that possible causal relationships can only be detected to a limited extent [36]. Since ANNs are data-driven, self-adaptive methods, they can adapt the model of the system arbitrarily without having to explicitly specify the functional form of the underlying model. Consequently, they can represent any function with arbitrary accuracy [37]. The weight matrix and the threshold vector coefficients are iteratively adjusted using a special training procedure to minimize the sum of squared differences [38].

The feedforward ANN’s architecture represents an important factor, since ANNs with different topologies lead to different results. There is no simple formula to determine the number of neurons and hidden layers. The topology of an ANN depends critically on the number of training cases, the amount of noise and the overall complexity of the given problem [39].

The pre-processing step was performed with a normalization mapping of the input variable values to (−1, 1). The leave one subject out (LOSO) k-fold cross-validation procedure was adopted in the performance evaluation of the proposed ANNs. According to the LOSO procedure, the data were divided into 25 subsets (k = 25). All of the data points except one (k−1 = 24) were used in the ANN training, and the remaining one was used for testing the ANNs performance. It should be stressed that the main experimental database consisted of 31 samples. However, in creating the learning database of an ANN, samples with the same four input variables (CCCD’s zero level, center point) and their respective initial tensile strength values were averaged into a single sample. Therefore, the learning database consisted of 25 data points, as indicated in

Table 5. ANN’s database.

Exp. No.	Process Parameters				Tensile Strength (MPa)
	A	B	C	D
1.	0.25	70	30	1.7	58.07
2.	0.1	80	45	1.4	73.93
3.	0.2	80	45	2	59.20
4.	0.2	80	45	1.4	63.40
5.	0.2	80	0	1.4	58.90
6.	0.25	70	60	1.1	54.73
7.	0.15	70	30	1.7	72.53
8.	0.2	80	45	0.8	52.53
9.	0.25	90	60	1.1	46.13
10.	0.15	90	30	1.7	65.20
11.	0.15	90	60	1.7	71.77
12.	0.2	80	90	1.4	91.53
13.	0.3	80	45	1.4	45.77
14.	0.15	70	60	1.1	82.73
15.	0.15	70	30	1.1	67.07
16.	0.25	90	30	1.7	49.60
17.	0.15	90	60	1.1	80.60
18.	0.25	70	30	1.1	52.53
19.	0.15	70	60	1.7	85.27
20.	0.25	70	60	1.7	65.13
21.	0.2	100	45	1.4	64.57
22.	0.25	90	60	1.7	53.80
23.	0.25	90	30	1.1	47.53
24.	0.15	90	30	1.1	74.33
25.	0.2	60	45	1.4	71.97

. The performance metrics included mean average error (MAE) and mean squared error (MSE).

3. Results and Discussions

3.1. Modeling of Tensile Strength by ANOVA and RSM

The results of the tensile strength test were collected and used to generate a representative mathematical model. Statistical processing and ANOVA were adopted to obtain reliable mathematical models based on the previously described procedures and experimental data, obtained by the CCCD. The significance of the model and the members of the response polynomial was determined with ANOVA.

Table 6. Model summary statistics.

Source	Lack of Fit p-Value	R2	Adjusted R2	Predicted R2	Remarks
Linear	0.0103	0.7502	0.7102	0.6137
2FI	0.0096	0.8137	0.7157	0.6012
Quadratic	0.0460	0.9298	0.8643	0.6237	Suggested
Cubic	0.8003	0.9929	0.9708	0.9040	Aliased
Reduced Cubic	0.6037	0.9860	0.9663	0.9000	Selected

presents the data of the initial ANOVA analysis, with a recommendation for selection of the appropriate model for the tensile strength $R_m$ prediction.

A quadratic model for the tensile strength ($R_m$) prediction was proposed, based on the recommendation for the selection of the appropriate model. The cubic model has more terms than the number of unique points in the design, because some terms were aliased, and the model was aliased. By reducing the number of terms in the cubic model (eliminating insignificant terms), the adequate reduced cubic model was found to have the best Lack of Fit p-value, R², Adjusted R², and Predicted R² values compared to the other three considered models (linear, 2FI and quadratic).

Table 7. ANOVA for the reduced cubic model.

Source	Sum of Squares	df	Mean Square	F-Value	p-Value	Remarks
Model	3894.31	17	229.08	49.84	<0.0001	significant
A-A	396.49	1	396.49	86.27	<0.0001
B-B	170.13	1	170.13	37.02	<0.0001
C-C	532.36	1	532.36	115.83	<0.0001
D-D	35.19	1	35.19	7.66	0.0171
AB	19.58	1	19.58	4.26	0.0613
AC	53.22	1	53.22	11.58	0.0052
AD	79.39	1	79.39	17.27	0.0013
BC	30.31	1	30.31	6.59	0.0246
BD	64.64	1	64.64	14.06	0.0028
CD	3.84	1	3.84	0.8358	0.3786
A2	22.04	1	22.04	4.80	0.0490
B2	40.06	1	40.06	8.72	0.0121
C2	237.86	1	237.86	51.75	<0.0001
D2	98.26	1	98.26	21.38	0.0006
ABD	24.40	1	24.40	5.31	0.0399
A2C	124.23	1	124.23	27.03	0.0002
AB2	73.36	1	73.36	15.96	0.0018
Residual	55.15	12	4.60
Lack of Fit	29.65	7	4.24	0.8304	0.6037	not significant
Pure Error	25.50	5	5.10
Cor Total	3949.46	29

presents the ANOVA analysis of the selected reduced cubic model.

The Model F-value of 49.84 implies the model’s significance. There is only a 0.01% chance that an F-value this large could occur due to noise. In this study, p-values less than 0.0500 indicate that the model’s terms are significant enough. In this case, A, B, C, D, AC, AD, BC, BD, A², B², C², D², ABD, A²C, and AB² are significant model terms. Terms AB and CD were retained, due to the model’s hierarchy. The Lack-of-Fit p-value of 0.6037 implies that the lack of fit is not significant relative to the pure error. There is a 60.37% chance that a lack-of-fit p-value this large could occur due to noise.

The calculations of the basic statistical parameters for the selected reduced cubic model are given in

Table 8. Basic statistical parameters for the selected reduced cubic model.

Parameters	Std. Dev.	Mean	C.V.%	R2	Adjusted R2	Predicted R2	Adequate Precision
Value	2.14	64.12	3.34	0.9860	0.9663	0.9000	27.5558

. The values of R², adjusted R², and predicted R² indicate a strong relationship between the model and the experimental data. Adequate precision is a measure of the predicted response range in relation to the error, i.e., it represents the signal-to-noise ratio. In this case, a ratio of 27.556 indicates an adequate signal.

Figure 3 presents the normal probability plot of residuals, and the predicted values vs. actual plot for tensile strength. It is evident that all the residuals are clustered in a straight line, implying that the errors are normally distributed. Additionally, since the points are clustered around a straight line, the predicted values are in close adherence to the actual values. For an analyzed response, the mathematical model is generated according to the reduced cubic model, as given below in Equation (1):

$$\begin{array}{ll}{R}_m=942.64296& -5324.78333\mathrm{A}-21.97483\mathrm{B}-2.88104\mathrm{C}+215.28704\mathrm{D}+104.94083\mathrm{A}\mathrm{B}+32.69889\mathrm{A}\mathrm{C}\\ & -510.16667\mathrm{A}\mathrm{D}-0.006117\mathrm{B}\mathrm{C}-2.31667\mathrm{B}\mathrm{D}+0.072593\mathrm{C}\mathrm{D}+3502.41667{\mathrm{A}}^2\\ & +0.160435{\mathrm{B}}^2+0.005817{\mathrm{C}}^2-21.03009{\mathrm{D}}^2+8.23333\mathrm{A}\mathrm{B}\mathrm{D}-85.8{\mathrm{A}}^2\mathrm{C}-0.74175\mathrm{A}{\mathrm{B}}^2\end{array}$$

(1)

3.2. Influence of the Process Parameters on Tensile Strength

The interaction influences of each input parameter on the tensile strength are shown on the 3D response surface plots (Figure 4a–f).

It can be concluded that the most significant influence on the tensile strength is contributed by the layer thickness and raster angle. For parts with a 100% infill structure, the wall thickness has no significant effect on the tensile strength. Slight increases in tensile strength values were observed with an increase in the wall thickness (Figure 4c,e,f).

The results of the tensile strength tests as well as the generated surface plots clearly show that the analyzed process parameters have a significant influence on the mechanical behavior of polyamide reinforced with short carbon fibers. Based on the experimental data in Figure 5a, it was presented the stress–strain curve for the test specimens with the best and worst conditions of analyzed process parameters. It can be observed that the properly selection of optimal process parameters leads to a significant increase in the tensile strength. The range of maximum stress varies from 45.77 MPa (sample 19 from Table 4) to 91.53 MPa (sample 18 from Table 4) for the highest tensile strength value, which is improved by 99.98%. It can also be seen that polyamide reinforced with short carbon fibers shows extremely brittle behavior with very small deformations before fracture, ranging from 2.6% (sample 21 from Table 4) to 5% (sample 19 from Table 4), in contrast to neat polyamide which shows plastic behavior under tensile stresses [14,17]. Hence, it can be concluded that the presence of carbon fibers reduced the ductility of polyamide and improved the tensile strength.

Figure 5b presents the stress–strain curves for three different layer thicknesses at the constant values of other process parameters. A trend of a significant increase in the value of the tensile strength from 45.77 MPa at the layer thickness of 0.3 mm (sample 19 from Table 4) to 73.93 MPa at the layer thickness of 0.1 mm (sample 2 from Table 4) can be observed. Thus, by increasing the layer thickness, the tensile strength significantly decreases. It also confirmed by the generated surface plots in Figure 4a–c. The decrease in the value of tensile strength by increasing the layer thickness can be explained by the increase in porosity between individual layers. As the raster width increases with increasing of the layer thickness, the air gap increases due to the technique of deposition the material. The air gaps are clearly visible at the layers thickness of 0.3 mm, as shown in Figure 6b. When the raster width is smaller, it allows better raster stacking, resulting in better interlayer cohesion and a larger effective cross-surface area, as shown in Figure 6a.

Figure 5c presents the stress–strain curves for five different raster angles. It can be seen that the trend of a significant increase in the value of the tensile strength from 58.9 MPa for raster angle 0° (sample 7 from Table 4) to 91.53 MPa for raster angle 90° (sample 18 from Table 4). Thus, by increasing the raster angle, the tensile strength increases. It is also confirmed by the generated surface plots in Figure 4b,d,f. The significant increase in the tensile strength was observed at the raster angle of 90°. This significant increase in tensile strength can be explained by the orientation of the carbon fibers. In the case of the raster angle of 90°, the load direction is in the direction of deposition of the material and fibers are mostly oriented in same direction, so the tensile strength is mainly dependent of the strength of the carbon fibers. It can be also confirmed by the mechanism of the material fracture that was mainly caused by the tearing mechanism, as shown in Figure 7a. However, in the case of the raster angle of 0°, the load direction was perpendicular to the raster direction, so the tensile strength depended on the cohesion forces between rasters. Thus, the material fracture was caused by the mechanism of stratification between individual rasters. This mechanism results in flat fracture surfaces, as shown in Figure 7b. Additionally, for any other raster angle less than 90 degrees, one component of the load force acts in the direction of the raster, creating shear stresses between the individual rasters, while the other component of the load force acts perpendicular to the raster direction and causes stratification between individual rasters, as well as in the case when the raster angle is 0 degrees. Therefore, the maximum tensile strength will depend on the cohesion force between the individual rasters, so the fracture that occurs in this case will be caused primarily the mechanism of stratification (Figure 7c.). Thus, at the raster angle of 60°, the load force component acting perpendicular to the raster direction and causing the stratification mechanism between individual rasters is smaller than when the raster angle of 30°, resulting in the increase in tensile strength, as shown in Figure 5c. Based on all the above, it can be concluded that the short carbon fibers have a significant impact on the reinforcement of polyamide when the load direction is in the direction of the deposition of the material.

Figure 5d presents the stress–strain curves for three different printing speed at the constant values of other process parameters (at zero level for layer thickness, raster angle and wall thickness). It can be seen that by decreasing the printing speed, the tensile strength increases. The influence of the printing speed is related to the heat input, which has an impact on interlayers cohesion and cohesion between individual rasters. At lower printing speeds, the heat input is higher, so the previous layers are heated more intensively, resulting in stronger cohesion between the layers. The maximum tensile strength of 71.97 MPa is achieved at a minimum printing speed of 60 mm/min, which is an increase in tensile strength of 11.46% compared to the tensile strength of 64.57 MPa achieved at a printing speed of 100 mm/min. It can be observed that the printing speed has a secondary impact on the tensile strength while the layer thickness and the raster angle have a primary impact. Figure 8 presents the stress–strain curves for printing speeds of 70 mm/s and 90 mm/s at different layer thicknesses and raster angles. Thus, the tensile strength increases by decreasing printing speed and layer thickness and by increasing the raster angle.

To increase the tensile strength of CFPR parts, it is necessary to select smaller values for the layer thickness and printing speed (in this case, a layer thickness of 0.1 mm and printing speed of 60 mm/s), and higher values of raster angle and wall thickness (in this case, a raster angle of 90° and wall thickness of 2 mm).

3.3. Modelling of Tensile Strength by ANN

The initially tested feedforward ANN configurations with training and testing results are presented in

Table 9. Tested feedforward ANN configurations.

ANN Information	Config 1	Config 2	Config 3	Config 4	Config 5	Config 6	Config 7	Config 8
Training procedure	trainlm	trainlm	trainscg	trainscg	traingda	traingda	trainbr	trainbr
Learning epochs	100	100	100	100	100	100	100	100
Transfer function	tansig	logsig	tansig	logsig	tansig	logsig	tansig	logsig
Architecture	ANN 6	ANN 6	ANN 6	ANN 6	ANN 6	ANN 6	ANN 6	ANN 6
Cross validation	25-fold	25-fold	25-fold	25-fold	25-fold	25-fold	25-fold	25-fold
MAE test	0.3243	0.316	0.2129	0.2157	0.2662	0.2618	0.21	0.2267
RPD (MAE test)	1.7213	1.7665	2.6217	2.5877	2.097	2.1321	2.6584	2.4624
MAE train	0.0001	0.0001	0.0255	0.0476	0.1578	0.2355	0.0549	0.0619
MSE test	0.1341	0.1854	0.0869	0.0725	0.1115	0.124	0.0674	0.0928
RPD (MSE test)	4.1631	3.0102	6.4213	7.7042	5.0072	4.5016	8.2797	6.0144
MSE train	0.0001	0.0001	0.0016	0.0043	0.0389	0.09	0.0075	0.0087
Time [s]	3.6	3.2	3.9	3.9	3.6	3.7	5.4	5.3

. Training procedures and transfer functions were tested in eight different configurations. The training procedures included the Levenberg–Marquardt (“trainlm”), scaled conjugate gradient (“trainscg”), gradient descent with adaptive learning rate (“traingda”), and Bayesian regularization backpropagation (“trainbr”). The adopted transfer functions were tangential (“tansig”) and logarithmic (“logsig”). The best results for test samples (MAE test = 0.2100, MSE test = 0.0674) were obtained with the Bayesian regularization learning method and the tangential transfer function; the specified configuration was adopted further on. To confirm the previous statement and to complement the prediction accuracy, the ratio of prediction to deviation (RPD) was calculated by dividing the standard deviation of the reference test data by the standard error of the prediction [40]. The highest value was obtained with the 7th ANN configuration (for MAE and MSE test).

Feedforward ANNs were tested with nine different topologies, namely, ANN 4, ANN 5, ANN 6, ANN 2_4, ANN 4_6, ANN 6_4, ANN 2_4_6, ANN 4_6_4, and ANN 6_4_2, comprising one to three hidden layers. For example, the ANN 4 topology contains one hidden layer with four neurons, the ANN 2_4_6 contains three hidden layers with two neurons in the first hidden layer, four in the second, and six in the third hidden layer. As mentioned earlier, all neurons in the hidden layers adopted the tangential (“tansig”) transfer function and the Bayesian regularization backpropagation learning method (“trainbr”). The LOSO k-fold cross-validation with 25 folds was used for the ANN’s validation, wherein each fold contained 24 training data points and 1 test data point. The learning procedure lasted for six different epoch durations (10, 50, 100, 200, 400 and 800 iterations). After the training procedure, the performance of ANN was calculated as the average values of MAE and MSE for both test and training data of all 25 folds. The results for MAE test and MAE train are presented in Figure 9 and Figure 10, and for MSE test and MSE train, are presented in Figure 11 and Figure 12.

The ANN 6 configuration achieved the best result for the test set after 400 epochs (MAE test = 0.1745, MSE test = 0.0469). A higher number of epochs was not necessary, since the MAE and MSE converged after 800 epochs in all the adopted ANN configurations. The graphs above indicate that a higher number of hidden layers in ANNs is not suitable for this application. ANNs with two or three hidden layers are prone to overfitting, since the results do not change with a higher number of epochs.

Figure 13 shows the comparison between the experimental and predicted values of tensile strength for all 25 data points. The predicted values were obtained with the ANN 6 configuration (trained for 400 epochs) and the mathematical model (generated according to the reduced cubic model) as described in the paragraph above. The average percent error (APE) between the predicted tensile strength values and the experimental values was calculated, where APE was 1.3016% for ANN 6 and 2.1948% for RSM predicted values. The RPD of the ANN6 configuration was 3.1985 for the MAE test and 11.9024 for the MSE test.

A preliminary investigation was performed based on the results of ANOVA and RSM. Feature selection was adopted, wherein the B and D parameters were excluded. According to the eight tested configurations (similar to Table 9) of ANN 6, the best test MAE and MSE results were also achieved with the “trainbr” training algorithm and “logsig” transfer function of 0.2557 and 0.1039, respectively.

4. Conclusions

This study investigates the influence of process parameters on the tensile strength of FDM manufactured CFRP composite parts. Besides RSM, also ANN methods were introduced as a useful tool for predicting the tensile strength of FDM fabricated CFRP composite parts. A significant difference between ANN and RSM was found based on the paired t-test for the presented data. There should also be stressed that there is a fundamental difference between RSM and ANN test outputs since RMS adopts all the data in model building and ANN does not (the ANN success rate is tested on unseen data via the LOSO k-fold cross-validation technique).

The following conclusions were drawn:

• Analyzed process parameters have a significant influence on the mechanical behavior of CFRP composite parts. The tensile strength can be significantly increased and improved by the selection of the optimal process parameters.
• Presence of carbon fibers in polyamide decreased the ductility of polyamide and improved the tensile strength.
• Carbon fibers have a significant effect on the tensile strength only in the case that the load direction was in the direction of deposition of the material (at raster angle of 90 degrees).
• The layer thickness has the most significant influence on the tensile strength. The value of tensile strength increases with decreasing layer thickness, it can be explained by the increase in air gap between individual layers and rasters.
• The raster angle also has a significant effect on tensile strength, it can be explained by different mechanisms that cause the fracture material.
• The wall thickness and printing speed have a secondary effect on the tensile strength. Nevertheless, a slight increase in tensile strength can be achieved with an increase in wall thickness and with a decrease in printing speed;
• Among the nine different tested ANN topologies, the ANN 6 model was recognized as the most appropriate.
• The average percentage error between the predicted tensile strength values and the experimental values was assessed.
• The main benefits of the introduced methods also include the future reduction in experimentation time, especially since CFRP belongs to the new and insufficiently researched FDM materials.

The future research is to investigate the influence of process parameters on the compressive and flexural properties of FDM fabricated CFRP composite parts, as well as the effect of the percentage of carbon fibers on the properties of the printed parts.