1 Introduction

The fast-changing customer demands, the need for high-quality products at the lowest possible cost and the elegant aesthetic effect have emerged the FDM 3D printing technology. FDM 3D printing is a well-known technique for producing tangible prototypes from various materials [1, 2]. This technology is vastly favored in today’s high-speed design-to-market workplaces for its quick and inexpensive prototypes. Having the ability for direct manufacturing, producing products with complex geometry, freedom for innovative design, economical use of material, and being environmentally friendly that surpasses traditional manufacturing limitations has been the core reason for this evolution [3]. In FDM, as shown in Fig. 1, the thermoplastic filament is melted using a heating cartridge placed in the block, extruded through a nozzle with the help of a pinch feed mechanism, and deposited on the hotbed layer-by-layer up until the formation of an intended product [4]. The most common materials utilized in this technology are amorphous thermoplastics such as Acrylonitrile Butadiene Styrene (ABS) and Polylactic Acid (PLA) [5,6,7]. Due to their lightweight, inexpensive and formability, these thermoplastics have been highly preferred in the engineering and medical fields [8].

Fig. 1
figure 1

A schematic diagram of the FDM extrusion and deposition process [11]

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Since mechanical properties are essential for functional parts, it is necessary to study and understand how such properties may vary with different materials and processing parameters. Thus, improvement can be made suitably during the fabrication phase to improve its properties [9]. The printed component properties were reported to depend on the layer fusions' strength. The interface strength is the most significant as the two layers' thermal gradient determines the functional components' final properties. This fusion's strength depends on many factors such as temperature gradient, polymer structure (molecular weight, branching, heat of fusion, glass transition temperature), and bead geometry [10].

Apart from the fusion strength, FDM's properties also reliant on six critical printing factors such as layer height, air gap, extrusion temperature, raster angle, printing speed, and infill percentage [12,13,14]. These factors are defined as follows: (1) Layer height: the Z-axis's height relative to the printing bed directly reflects the deposited layer's thickness. The layer height should not be greater than the nozzle diameter. (2) Air gap: the space between the beads. Positive gap results in a loosely packed structure that builds rapidly. Meanwhile, the negative gap allows two beads to partially occupy the same space. These results in a more dense structure, which requires a longer build time. The negative gap settings were also shown could minimize the voids. (3) Extrusion temperature: the temperature at which the filament is melted and extruded for deposition on the hotbed. (4) Raster angle: the angle or direction of the beads of material about the part's loading. The different modes and directions used will affect the part's mechanical properties. (5) Printing speed: the speed of extruder motion in the x- and y-axis during the printing process. (6) Infill percentage: The amount of deposited material on each surface layer.

As to date, quite a number of studies have been performed to investigate the effect of printing parameters on 3D printed parts' mechanical behavior. A study conducted by B.M Tymrak et al. shows that the tensile strength changes with the extruded filament alignment on the loading direction due to different build orientations [15]. The tested ABS printed specimen showed higher tensile strength at the layer height of 0.2 mm and 45° raster angle. In another study conducted by Sung-Hoon et al., the effect of raster pattern and air gap on the printed ABS specimen's tensile strength was investigated [16]. Their finding reports that at zero air gap, the specimen built at 0° has greater tensile strength than the specimen made at 90°. Also, at -0.003 air gaps, all the tested specimens showed an increase in the overall tensile strength. In another investigation, the tensile properties of polyetherimide (PEI) specimens reveal that each build direction has different tensile strength and strain characteristics. Test specimens produced in the X-direction were reported to have the best strength and elongation before the failure, followed by Y-direction and Z-direction [17]. Hongbin Li et al. investigated the effects of layer thickness, deposition velocity, and infill rate on PLA bonding strength. They found that layer thickness plays a predominant role in affecting the bonding strength, followed by deposition velocity and infill rate [18].

Es-Said et al. examined the effect of raster orientation on ABS's mechanical properties. They reported that raster orientation significantly influences the polymer molecules [19]. Habbeb et al. conducted a study on the relationship between PLA material's strength and porosity in FDM 3D printing through standard tensile tests. Their findings show that the printed parts' highest average tensile strength was 45.56 MPa at 0.2 mm layer height for PLA. The porosity of PLA was found to be increasing with layer height [20]. Xunfei Zhou et al. evaluated the printing pattern and infill density effects on the ultimate tensile strength and elastic modulus. Their experimental results revealed minimizing air gaps and using a triangular infill pattern consequences good UTS [21].

Apart from the experimental investigation, the mathematical model development has also gained importance in estimating the mechanical properties of parts produced via an FDM 3D printer. However, it is still limited compared to the number of experimental investigations. Pires et al. [22] developed a prediction model to explore the critical printing factors such as mass, mass variation, printing time, and porosity on the printed specimen properties. They realized that the size scale, printlet format, and print temperature influence the printlet mass, while the printing time was impacted by size scale, printing speed, and layer height. Meanwhile, Anitha et al. used Taguchi and ANOVA analysis to investigate the relationship of parts’ layer thickness, road width, and deposition speed with the surface roughness and conclude that the significant factor is layer thickness [23]. Ang et al., from their analysis using full factorial design, proved that all input parameters consist of an air gap, raster width, build orientation, build laydown pattern and build layer are significant to the response, which is porosity, compressive strength, and compressive modulus [24, 25]. Thus, the present work investigates the PLA's tensile behavior using the FDM 3D printing technique [7] and proposes a mathematical model to predict those properties.

2 Materials and Methods

Rainstorm Desktop 3D Multicolor Printing Printer Reprap Prusa i3 with a 0.4 mm nozzle diameter was used to fabricate the tensile test specimen using a 1.75-mm PLA filament. Arduino Mega 2560 was used as the microcontroller and RAMPS 1.4 attached to the Arduino Mega 2560 to expand pin inputs. The Marlin firmware open-source software and the Repetier Host slicing software were used to generate G-code files and control the FDM 3D printer to fabricate the desired parts. The tensile test was performed using INSTRON 3367 machine. The maximum load which can be applied to this machine is 50kN. According to the ASTM D638 standard, the suggested speed of testing is 5 mm/min. The test was conducted at the Materials Laboratory of Universiti Malaysia Pahang. Table 1 lists the parameters which have been kept constant during the printing process.

Table 1 Printing parameters and their values
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2.1 Part Fabrication Using FDM 3D Printer

The specimen design is created using a CAD program (SolidWorks 2017 edition) and saved into an (STL) file format. The STL file stores every surface of the 3D design and shows it as triangulated segments. The FDM 3D printer reads the digitally supplied coordinates resultant from the STL file by transforming it into a G-file via slicer software present in the FDM 3D printer. The G-code file divides the 3D STL file into a sequence of two-dimensional (2D) horizontal cross-sections (25–100 μm) depending on the fabrication technique [26]. During fabrication, the thermoplastic polymer's filament is fed into an extruder containing a heater to liquefy the filament. The filament is dragged inward with a pinch feed mechanism's help and extrudes the molten bead of material through a circular nozzle. The moveable FDM head then deposits the extruded material layer-by-layer onto the substrate. The melting of the material performed 1 degree above its melting point, allowing it to solidify immediately upon deposition [27]. These allow for good bondage between the layers. The extruder head moves according to the layer height and repeats the layer deposition cycle until the original CAD file's full physical representation is formed [28]. Figure 2a shows the printed specimen used for the mechanical tests, while Fig. 2b depicts the geometry of the Type 1 specimen according to the ASTM D638 standard. Table 2 lists the dimension of the Type 1 specimen adapted according to the ASTM D638 standard.

Fig. 2
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a PLA printed tensile specimen, b Type 1 specimen geometry according to ASTM D638 standard

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Table 2 Dimensions of the Type 1 specimen geometry according to ASTM D638 standard
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2.2 Design and Realization of the Experiment

The experiment design starts with parameter selection, the type of test to be conducted, and the number of specimens required for the analysis. A total combination of 3 values from 3 types of the parameter was chosen. Three chosen parameters for the investigation are layer height, raster angle, and infill density. Infill density is the amount of material (in percentage) used to print the part. The higher the infill percentage, the higher the amount of material used to print the part. The infill density chosen for the present investigation is 20, 50, and 80%. The layer height is the thickness of each layer of material deposition during the printing process. The chosen layer height for the present work is 0.1, 0.2, and 0.3 mm. Raster angle is the angle of material deposition referencing the printing axis. The chosen value for the raster angle is 40, 60 and 80°. The mechanical test to be undertaken is a tensile test. The samples were printed and tested according to the ASTM D638 Type 1 standard [29]. All the parameters are set in slicing software before converted into a G-code file. Using DOE, the total amount of combination for all three parameter value variations is obtained to be 27 sets of data, as shown in Table 3. 27 different combined parameters were printed to study how differently each combination affects the PLA specimen's mechanical properties. Three samples were prepared for each set of data required and averaged. In total, 81 specimens were printed for the experimental analysis. The tensile testing was performed to assess the tensile property of each sample upon completion of the printing. The finding was analyzed in the form of the tabulation of ultimate tensile strength, fracture strain, and elastic modulus. The generated graph was studied, and the necessary information was extracted.

Table 3 The list of ultimate tensile strength, fracture strain, elastic modulus yield strength, and energy absorption of each specimen
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2.3 Design of Experiment Analysis Using Response Surface Methodology (RSM)

Statistical analysis was done using the obtained experimental data for validation purposes to support this experiment's reliability. The analysis was completed using a full factorial approach using MINITAB software. This statistical evaluation aims to evaluate the effect of three combined printing parameters: infill layer height, raster angle, and infill density towards the tensile properties of the FDM 3D printed PLA and the development of a mathematical model for tensile properties prediction. From the statistical evaluation, an ANOVA of variance table was generated to depict the p-value of the involved factors. The confidence level for the analysis was set to be 95%; thus, any p-value higher than 0.05 is considered an insignificant effect on the resulting tensile property. The generated regression equation reliability was determined by calculating the error percentage between the experimental and predicted value. If the average error percentage is below 10%, then the model is considered reliable. Finally, a response optimizer is used to determine the maximum individual and overall mechanical response with regard to printing parameter combination.

3 Results and Discussion

Five different groups of graphs denoting specific tensile behavior have been plotted according to each printing parameter. The plot is generated to visualize any observable trend that could be concluded related to the effect of selected parameter combinations on tensile properties.

As shown in Table 3, the tensile properties, which are the ultimate tensile strength, elastic modulus, yield strength (0.2% offset), fracture strain, and energy absorption, are deduced from stress–strain curves individually. The overall stress–strain curve of all the specimens is shown in Fig. 3. Meanwhile, Figs. 4 and 5 depict the fractured images captured using a light microscope.

Fig. 3
figure 3

Stress versus strain curves for all 27 combinations

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Fig. 4
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Polymer chains across the interface

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Fig. 5
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Brittle fracture of PLA specimen

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3.1 Ultimate Tensile Strength (UTS): Effect of Infill Percentage, Raster Angle, and Layer Thickness

The ultimate tensile strength (UTS) is the material's maximum resistance to fracture. It is equal to the maximum load that can be carried by one square inch of the cross-sectional area when the load is applied in tension. The UTS can differ depending on the type of material. The UTS is usually obtained by performing a tensile test and plotting the engineering stress versus strain curve. The highest point of the stress–strain curve is UTS. It is an intensive property; therefore, its value does not depend on the test specimen's size. However, it is dependent on other factors, such as preparation parameters, the presence of surface defects, the temperature of the test environment, and the material.

In this project's context, the plot reflects the average from findings for all 81 FDM 3D printed PLA specimens. Figure 6 shows that the UTS values fall between 9.737220 and 35.61776 MPa, which denotes the highest and lowest of all recorded values. The maximum tensile strength was achieved by specimen printed at 25th combination, where else the lowest was specimens printed at the 10th combination. The graphs above show the relationship between the UTS and infill percentage, raster angle, and layer thickness. It can be observed that specimens printed with 80% infill percentage resulted in higher UTS than the lower infill percentage specimen. The trend shows that when the infill density increases, the UTS also increases. Higher infill implies higher material availability to overcome the applied stress internally. From the UTS versus layer thickness graph, a strong relationship could not be construed. However, the 25th combination with 0.1 mm layer height recorded the highest UTS. The resultant increase may due to the increase in the diffusion between adjacent layers. The present findings are in favor of the previous research finding reported by BM. Tymrak, whereby he found tensile strength to be highest at lowest layer height. Meanwhile, the high-temperature gradient that increases the distortion effect, which accumulates the residual stresses, might be why the reduced UTS for a few specimens. From the UTS versus raster angle graph, there was also no apparent trend observed. However, a high raster angle is preferred due to the raster's inclination along the loading direction, offering more resistance for strength improvement [30].

Fig. 6
figure 6

a Ultimate tensile strength versus infill density; b Ultimate tensile strength versus layer thickness; c Ultimate tensile strength versus raster angle plot. Note: ID infill density, LH layer thickness, RA raster angle

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3.2 Fracture Strain: Effect of Infill Percentage, Raster Angle, and Layer Thickness

Fracture strain is the maximum strain value achieved by a specimen before it fractures. It denotes the ratio between changed length and initial length after breakage of the test specimen. The fracture strain is influenced by several factors, such as strain speed, temperature, specimen geometry, and material type. The stress–strain curve for brittle materials is typically linear over their full range of strain, eventually terminating in fracture without appreciable plastic flow.

In the present study, the range of fracture strain achieved is from 0.03667 to 0.08012 mm/mm, which denotes the highest and lowest fracture strain recorded among all parameter combinations. As seen in Fig. 7, the highest fracture strain is achieved by specimens printed with the 9th combination, and the lowest is from specimens printed at the 10th combination. Upon observation from the plot, it is found that the higher infill percentage contributes to the higher fracture strain for all samples. Noticeably, the 9th combination printed with 80% infill has the highest fracture strain, while the 10th combination has the lowest fracture strain printed at 20% infill density. Generally, the higher infill specimen is more robust due to their higher degree of resistance [7]. When the specimen is more robust, the amount of strain needed to fracture the specimen is higher. Meanwhile, the raster angle shows no significant trend with respect to the resulting fracture strain. High raster angle increases the stress accumulation along the deposition's direction, resulting in more distortion and weak bonding. The fracture strain versus layer thickness chart displays increased fracture strain with increased layer height. This can be related to a lower distortion effect resulting from a lower temperature gradient at the bottom layer due to the higher layer height. Specimen printed with 10th combination results in the lowermost fracture strain due to the lowest infill percentage, higher raster angle, and lowest layer height.

Fig. 7
figure 7

a Fracture strain versus infill chart; b Fracture strain versus layer thickness; c Fracture strain versus raster angle plot. Note: ID infill density, LH layer thickness, RA raster angle

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3.3 Elastic Modulus: Effect of Infill Percentage, Raster Angle, and Layer Thickness

An elastic modulus, or modulus of elasticity, is a number that measures an object or substance's resistance to being deformed elastically when a force is applied. The elastic modulus is defined as the slope from the stress–strain curve in the elastic deformation region. It is also defined as a constant of proportionality, which varies for different materials. It is a measure of the stiffness of a given material. A stiffer material will have a higher elastic modulus. If the slope is steep, the sample is anticipated to have a high tensile modulus. If the slope is gentle, then the sample is predicted to have a low tensile modulus.

As shown in Fig. 8, the range of elastic modulus values obtained in the present study falls between 952.1736 and 277.74950 MPa, whereby it denotes the highest and lowest elastic modulus value. The highest elastic modulus is achieved by specimens printed at the 27th combination, and the lowest was the 10th combination. From the graph, it can be noticeably seen that when the infill percentage increased, the resulting elastic modulus increases. On a side note, the elastic modulus is always directly proportional to the UTS. The 27th combination printed using 80% infill is seen to have the most significant elastic modulus, while the 10th combination printed with 20% infill has the lowest elastic modulus. It also observed that when the layer height increases from 0.1 to 0.3 mm, the elastic modulus correspondingly increases. Besides that, both 40° and 80° raster angles resulted in averagely the identical elastic modulus. The lower inclination raster angle opposite the loading direction reduces the degree of resistance, affecting their overall strength and vice versa. The maximum value of the elastic modulus is reached when all fibers are oriented along the loading line. In this condition, the specimen shows the highest stiffness as each fiber takes the load, and the effects of the fiber-to-fiber bonding are minimized. Infill orientation close to 0° reduces strength and stiffness because the bonding surfaces take part in the tensile load among fibers, weaker, and more prone to fail [1].

Fig. 8
figure 8

a Elastic modulus versus infill chart; b Elastic modulus versus layer thickness; c Elastic modulus versus raster angle plot. Note: ID infill density, LH layer thickness, RA raster angle

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3.4 Yield Strength (0.2% Offset): Effect of Infill Percentage, Raster Angle, and Layer Thickness

Yield strength is defined as the yield stress, which is the stress level at which permanent deformation of 0.2% of the material's original dimension occurs. It is also defined as the stress level at which a material can withstand before it deformed permanently. Before reaching the yield point, the material will distort elastically and return to its original shape upon removing repression and stress. Beyond the yield point, the deformation will be permanent and cannot be reversed. There will be little or no plastic deformation in brittle materials, and fracture occurs around the end portion of the linear elastic curve.

From Fig. 9, the highest yield strength achieved is 26.08234 MPa and ranges down to 9.02682 MPa. The 7th combination records the maximum yield strength, and the 10th combination records the lowest. Specimens with the 7th combination printed with 80% infill again result in the highest yield strength. However, there are several specimens that shown an opposite trend, whereby the smaller infill percentage has resulted in higher yield strength. From the graph, it can be inferred that infill density has a varied effect on yield strength. A uniform trend can only be noticed for the infill density from 20 to 50%. The yield strength increases with the increase in infill density. From the yield strength versus raster angle graph, the lowest raster angle, which is 40° resulted in considerably high yield strength compared to higher raster angle. The intermediate raster angle has mostly been seen to cause a significant drop in yield strength. While evaluating the effect of layer height on the yield strengths, it can be concluded that there is no legit trend. The impact of layer height is disseminated with respect to the printing parameter combination. The 10th combination recorded the lowest value of ultimate strength, fracture strain, elastic modulus, and yield strength on a side note.

Fig. 9
figure 9

a Yield strength versus infill chart; b Yield strength versus layer thickness; c Yield strength versus raster angle plot. Note: ID infill density, LH layer thickness, RA raster angle

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3.5 Toughness (Energy Absorption)

Toughness is defined as a material's ability to deform plastically and absorb energy in the process before fracturing. In other words, resistance to fracture. Toughness is directly proportional to the combination of strength and ductility. For instance, a material with high strength and ductility will be tougher than a material with low strength and high ductility. Strength refers to the ability to resist deformation upon the placement of stress. Ductility is the strain experienced before fracture, whereby the percentage of elongation is the indicator in a uniaxial tensile test. Calculation of area under the stress–strain curve is one way to measure the toughness. The calculated area value is denoted as “material toughness,” and it has units of energy per volume (J/m3).

Figure 10 shows the highest toughness achieved is 1.82228 J/m3 and ranges down to 0.18207 J/m3. The maximum toughness is recorded by the 18th combination, while the lowest is from the 10th combination. Specimens with 18th combination are printed with 80% infill, 60° raster angle, and 0.3 mm layer thickness. Toughness shows an increasing trend with infill percentage and layer thickness. Raster angle shows a varied effect with all the parameter combinations, whereby in some cases, 40° raster angle resulted in higher toughness compared to other raster angles and vice versa.

Fig. 10
figure 10

a Toughness versus infill density; b Toughness versus raster angle; c Toughness versus layer thickness plot. Note: ID infill density, LH layer thickness, RA raster angle

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4 Design of Experiment Analysis using Response Surface Methodology (RSM)

4.1 Ultimate Tensile Strength (UTS)

Table 4 shows that the p-value of layer height and infill percentage is lesser than the alpha value, which is 0.05, indicating its significant effect on the ultimate tensile strength. The infill density is the most significant parameter influencing the UTS and is followed by layer thickness. The 2-way interaction is insignificant since its p-value is more than 0.05. Other combinations of the parameters are also seen to be inconsequential since the p-value more than 0.05. The R2 is more than 80% suggesting reliable experimental data. The developed second-order mathematical model is shown in Eq. 1. The contour plot shown in Fig. 11 suggests the maximum UTS can be obtained with a higher layer height and high raster angle.

$$ \begin{aligned} {\text{Ultimate}}\;{\text{tensile}}\;{\text{strength}}\;\left( {{\text{MPa}}} \right) & = 21.9 + 78.9\;{\text{Layer}}\;{\text{height}}\;\left( {{\text{mm}}} \right) \\ & \quad - 0.559 \;{\text{Raster}}\;{\text{angle}}\, \left(^\circ \right) + 6.0\;{\text{Infill}}\;{\text{density}}\, \left( \% \right) \\ & \quad - 10\;{\text{Layer}}\;{\text{height }}\;\left( {{\text{mm}}} \right)*{\text{Layer}}\;{\text{height}} \;\left( {{\text{mm}}} \right) \\ & \quad + 0.00455\;{\text{Raster}}\;{\text{angle }}\;\left(^\circ \right)*{\text{Raster}}\;{\text{angle }}\;\left(^\circ \right) \\ & \quad + 16.6\;{\text{Infill}}\;{\text{density }}\;\left( \% \right)*{\text{Infill}}\;{\text{density}} \;\left( \% \right) \\ & \quad - 0.262\;{\text{Layer}}\;{\text{height}} \;\left( {{\text{mm}}} \right)*{\text{Raster}}\;{\text{angle}} \;\left(^\circ \right) \\ & \quad - 74.2\;{\text{Layer}}\;{\text{ height}} \;\left( {{\text{mm}}} \right)*{\text{Infill}}\;{\text{density}} \;\left( \% \right) \\ & \quad + 0.197\;{\text{Raster}}\;{\text{angle}} \;\left(^\circ \right)*{\text{Infill}}\;{\text{density}} \;\left( \% \right) \\ \end{aligned} $$
(1)
Table 4 ANOVA table for UTS
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Fig. 11
figure 11

Contour plot of UTS

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Response optimizer was used to optimize the predicted ultimate tensile strength value within the range inserted printing parameter combination. From this analysis, the maximum ultimate tensile strength was found to be 34.07 MPa at a printing combination of 0.1 mm layer height, 80° raster angle, and 80% infill density.

5 Elastic Modulus

Table 5 shows that the p-value of layer height and infill percentage is lesser than the alpha value of 0.05, indicating its significant effect on the ultimate tensile strength. The infill density (F-value 364.83) most significantly affects elastic modulus and is followed by layer thickness. The combination of the layer height (mm) * infill density (%) and raster angle (°) * Infill density (%) was found to be significant for 2-way interaction as the p-value is less than 0.05. For the square, it is substantial for the raster angle (°) * raster angle (°), and infill density (%) * infill density (%). These findings show that doubling the value of infill density and raster angle will affect the elastic module. The R2 is more than 90% suggesting reliable experimental data. The developed second-order mathematical model is shown in Eq. 2. The interaction plots can be seen in Fig. 12. This graph demonstrates that the parameters interact with each other in few points. The contour plot is shown in Fig. 13.

$$ \begin{aligned} {\text{Elastic}}\;{\text{modulus}}\;\;\left( {{\text{MPa}}} \right) & = 1331 + 1536\;{\text{Layer}}\;{\text{height}} \;\left( {{\text{mm}}} \right) - 36.90\;{\text{Raster}}\;{\text{angle}} \;\left(^\circ \right) \\ & \quad - 138\;{\text{Infill}}\;{\text{density}} \;\left( \% \right) - 720\;{\text{Layer}}\;{\text{height}} \;\left( {{\text{mm}}} \right)*{\text{Layer}}\;{\text{height}} \;\left( {{\text{mm}}} \right) \\ & \quad + 0.2801\;{\text{Raster}}\;{\text{angle}} \;\left(^\circ \right)*{\text{Raster}}\;{\text{angle}} \;\left(^\circ \right) + 565\;{\text{Infill}}\;{\text{density}} \;\left( \% \right) \\ & \quad *{\text{Infill}}\;{\text{density}} \;\left( \% \right) + 1.77\;{\text{Layer}}\;{\text{height}} \;\left( {{\text{mm}}} \right)*{\text{Raster}}\;{\text{ angle }}\;\left(^\circ \right) \\ & \quad - 1422\;{\text{Layer}}\;{\text{height}} \;\left( {{\text{mm}}} \right)*{\text{Infill}}\;{\text{density}} \;\left( \% \right) + 6.51\;{\text{Raster}}\;{\text{angle }}\;\left(^\circ \right)*{\text{Infill}}\;{\text{density}} \;\left( \% \right) \\ \end{aligned} $$
(2)
Table 5 ANOVA table for elastic modulus
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Fig. 12
figure 12

2-Way interaction plot

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Fig. 13
figure 13

The contour plot of elastic module

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Response optimizer was used to optimize the predicted elastic modulus value within the range inserted printing parameter combination. From this analysis, the maximum elastic modulus was found to be 936 MPa at a printing combination of 0.3 mm layer height, 80° raster angle, and 80% infill density.

6 Fracture Strain

Table 6 shows that the p-value of layer height and infill percentage is lesser than the alpha value of 0.05, indicating the significant effect on the ultimate tensile strength. The layer height (F-value 37.44) most significantly affects the fracture strain and is followed by infill density and raster angle. The combination of the layer height (mm) * infill density (%) was found to be substantial for the 2-way interaction since its p-value is less than 0.05. The findings also indicate that the increase of infill density and layer thickness for the square is insignificant. The R2 is more than 85% suggesting reliable experimental data. The developed second-order mathematical model is shown in Eq. 2. The interaction plots can be seen in Fig. 14. The graph shows that the parameters interact with each other in few points. The contour plot is shown in Fig. 15.

$$ \begin{aligned} {\text{Fracture}}\;{\text{strain}}\;\;\left( {{\text{mm}}/{\text{mm}}} \right) & = 0.0365 + 0.0417\;{\text{Layer}}\;{\text{height}} \;\left( {{\text{mm}}} \right) - 0.000066\;{\text{Raster}}\;{\text{angle}} \;\left(^\circ \right) \\ & \quad + 0.0228\;{\text{Infill}}\;{\text{density}} \;\left( \% \right) + 0.113\;{\text{Layer }}\;{\text{height }}\;\left( {{\text{mm}}} \right)*{\text{Layer}}\;{\text{height}} \;\left( {{\text{mm}}} \right) \\ & \quad + 0.000003\;{\text{Raster}}\;{\text{ angle}} \;\left(^\circ \right)*{\text{Raster}}\;{\text{angle}} \;\left(^\circ \right) + 0.0016\;{\text{Infill}}\;{\text{density}} \;\left( \% \right)*{\text{Infill}}\;{\text{density}} \;\left( \% \right) \\ & \quad - 0.001165\;{\text{Layer}}\;{\text{height}} \;\left( {{\text{mm}}} \right)*{\text{Raster}}\;{\text{angle}} \;\left(^\circ \right) \\ & \quad + 0.1142\;{\text{Layer}}\;{\text{height}} \;\left( {{\text{mm}}} \right)*{\text{Infill}}\;{\text{density}} \;\left( \% \right) \\ & \quad - 0.000439\;{\text{Raster}}\;{\text{angle }}\;\left(^\circ \right)*{\text{Infill}}\;{\text{density}} \;\left( \% \right) \\ \end{aligned} $$
(3)
Table 6 ANOVA table for fracture strain
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Fig. 14
figure 14

2-way Interaction of fracture strain

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Fig. 15
figure 15

The contour plot of fracture strain

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Response optimizer was used to optimize the predicted fracture strain value within the range inserted printing parameter combination. From this analysis, the maximum fracture strain was found to be 0.0796 mm/mm at a printing combination of 0.3 mm layer height, 40° raster angle, and 80% infill density.

7 Yield Strength

Table 7 shows that the p-value of layer height, raster angle, and infill percentage is more than the alpha value of 0.05, indicating all the parameters are insignificant. This is due to yield strength is affected by other parameters.

$$ \begin{aligned} {\text{Yield}}\;{\text{strength}}\;\;\left( {{\text{MPa}}} \right) & = 32.8 + 62.3\;{\text{Layer }}\;{\text{height }}\;\left( {{\text{mm}}} \right) \\ & \quad - 1.188\;{\text{Raster}}\;{\text{angle}} \;\left(^\circ \right) + 56.1 \;{\text{Infill}}\;{\text{density}} \;\left( \% \right) \\ & \quad + 34 \;{\text{Layer }}\;{\text{height}} \;\left( {{\text{mm}}} \right)*{\text{Layer}}\;{\text{ height}} \;\left( {{\text{mm}}} \right) + 0.01010\;{\text{Raster}}\;{\text{angle }}\;\left(^\circ \right)*{\text{Raster}}\;{\text{angle}} \;\left(^\circ \right) \\ & \quad - 31.6 \;{\text{Infill}}\;{\text{density}} \;\left( \% \right)*{\text{Infill}}\;{\text{ density}} \;\left( \% \right) \\ & \quad - 0.299\;{\text{Layer}}\;{\text{height}} \;\left( {{\text{mm}}} \right)*{\text{Raster}}\;{\text{ angle}} \;\left(^\circ \right) \\ & \quad - 91.8 \;{\text{Layer}}\;{\text{ height}} \;\left( {{\text{mm}}} \right)*{\text{Infill}}\;{\text{density}} \;\left( \% \right) \\ & \quad - 0.045\;{\text{Raster}}\;{\text{angle }}\;\left(^\circ \right)*{\text{Infill}}\;{\text{density}} \;\left( \% \right) \\ \end{aligned} $$
(4)
Table 7 ANOVA table for yield strength
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8 Comparison of the Experimental and Predicted Mechanical Response

The comparative results of experimental and predicted responses of tensile properties are summarized in Table 8. Table 8 shows that the average error between the experimental value and the predicted value is minimal, ranging from 0.041 to 0.1135%. Hence, all the mathematical models can be highly accounted for reproducing similar tensile properties with minimum deviation.

Table 8 Overall comparison between the experimental and predicted response
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9 Multiple Response Prediction

In the previous subtopic, all four responses were optimized individually to determine the maximum achievable value. However, using multiple response prediction, the optimized overall response in conjunction with one printing parameter combination can be determined. This analysis found that the best parameter combination for optimum tensile properties was 0.3-mm layer thickness, 40° raster angle, and 80% infill density. The values are listed in Table 9.

Table 9 Comparison of the overall optimized mechanical response
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10 Conclusion

In this research work, 81 specimens with 27 different printing parameter combinations were successfully printed using the low-cost FDM 3D printer. Tensile testing was performed to evaluate each specimen's tensile properties and investigate the effect of printing parameters on the tensile behavior. The highest UTS, strain, elastic modulus, yield strength, and toughness obtained in the present study is 35.61776 MPa, 0.08012 mm/mm, 952.1736 MPa, 26.08234 MPa, and 1.82228 J/m3, respectively. From the observation of the trends, it can be concluded that ultimate tensile strength is predominantly affected by the infill percentage and very least affected by raster angle and layer thickness. On the other hand, it is found that fracture strain, elastic modulus, and toughness are more influenced by the infill percentage and layer thickness. The best-suited combined parameter for optimum tensile properties from the experimental analysis is 0.3 mm layer height, 40° raster angle, and 80% infill density. The resulting properties are 28.45150 MPa for UTS, 0.08012 mm/mm for fracture strain, 828.0600 MPa for elastic modulus, 20.19923 MPa for yield strength and 1.72182 J/m3 for toughness. The RSM analysis further affirms that’s infill density is the primary factor influencing the tensile behavior. The R2 value for all the examinations obtained to be more than 80%, suggesting reliable experimental data. A second-order mathematical model is developed for each tensile property for estimation of the properties. Validation of the model reveals very minimal error ranging from 0.041 to 0.1135%. Thus, the models can be highly accounted for reproducing similar tensile properties with minimum deviation. Finally, the multiple response prediction reveals the possible parameter combination for the best tensile properties. The best parameter combination for optimum tensile properties was 0.3 mm layer thickness, 40° raster angle, and 80% infill density.