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Static tensile and cyclic tension-tension fatigue testing investigation of 3D printed ABS materials: a comparative study of different infill orientation and infill density with statistical analysis
Diese Studie untersucht die Auswirkungen der Füllungsorientierung und -dichte auf die mechanischen Eigenschaften von 3D-gedruckten ABS-Materialien, wobei der Schwerpunkt auf statischen Zug- und zyklischen Zugspannungsermüdungsprüfungen liegt. Die Forschung untersucht systematisch, wie unterschiedliche Rasterwinkel und Fülldichten Zugfestigkeit, Streckgrenze, Young's Modul und Ermüdungslebensdauer beeinflussen. Zu den wichtigsten Ergebnissen zählen die überlegene Leistung des Rasterwinkels von 30 ° / -60 ° bei 100% Fülldichte für die Zugfestigkeit und der Rasterwinkel von 45 ° / -45 ° für Ermüdungslebensdauer und Duktilität. Die Studie unterstreicht auch den signifikanten Einfluss der Belastungshäufigkeit auf die Ermüdungsleistung, wobei höhere Frequenzen im Allgemeinen die Lebensdauer der Ermüdung erhöhen. Statistische Analysen, einschließlich ANOVA und Tukeys HSD-Tests, bestätigen die Ergebnisse und bieten eine solide Grundlage für die Optimierung von 3D-Druckparametern. Die praktischen Implikationen dieser Erkenntnisse werden diskutiert und bieten Anleitungen zur Anpassung von FDM-Prozessen an spezifische mechanische Anforderungen. Zukünftige Forschungsrichtungen werden ebenfalls vorgeschlagen, darunter die Erforschung anderer einflussreicher FDM-Parameter und die Expansion auf verschiedene polymere Materialien.
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Abstract
The effects of 3D printing process parameters on the mechanical behavior of ABS (Acrylonitrile Butadiene Styrene) materials, specifically focusing on static tensile and cyclic tension-tension fatigue testing, are analyzed in this investigation. The study examines how infill orientation (raster angle) and infill density influence the mechanical behavior of 3D printed ABS specimens. The study investigates the influence of different raster angles (0°/90°, 30°/ − 60°, + 45°/ − 45°, and 75°/ − 15°) and infill densities (20%, 50%, 80%, and 100%) on the overall tensile behavior of FDM-printed ABS specimens. In addition to the raster angles and infill densities, several maximum stress levels (90%, 70%, 60%, and 50% of UTS) are also incorporated in fatigue testing. The effect of frequency ranging from 0.25 to 20 Hz was also analyzed for 100% infill density with 50% stress level for various raster angles. The research employs statistical analysis methods, including ANOVA and post-hoc Tukey’s HSD tests, to analyze the effect of infill orientation, infill density, and their interactions on the mechanical behavior (p < 0.001; R2 > 0.95) and fatigue life (p < 0.001; R2 = 0.967) of 3D printed ABS materials. Statistical analyses revealed significant influences of infill orientation and infill density, with the 30°/− 60° orientation showing superior tensile performance across all infill densities, while + 45°/− 45°orientation provided superior fatigue performance across all stress levels and frequencies. Fatigue life improved significantly at higher cyclic frequencies, particularly between 0.25 to 5 Hz, with marginal gains above 5 Hz. Fatigue data closely followed a power-law (\(N= a{S}^{m}.\)) relationship, where S–N (Fatigue Stress-Fatigue Cycle) and inverse Log–Log S–N graph with negative m value validate the strong fatigue stress-fatigue life correlations (R2 > 0.94). These findings provide statistically supported insights for optimizing FDM process parameters for ABS components with grid infill patterns and dogbone geometries, serving as a reference framework for similar materials and conditions rather than universal guidelines.
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1 Introduction
Additive manufacturing (AM) is a technique that constructs objects by incrementally depositing material, layer by layer, based on a digital blueprint, whereas subtractive manufacturing creates an object by removing material [1, 2]. Rapid prototyping, on-demand manufacturing, digital fabrication, desktop manufacturing, solid unstructured manufacturing, layer manufacturing, direct manufacturing methods, and 3D printing are other names for additive manufacturing. [3, 4]. According to the American Society for Testing and Materials (ASTM), 3D printing processes are classified into seven categories. These include material extrusion, vat polymerization, material jetting, powder bed fusion, direct energy deposition, sheet lamination, and binder jetting [5]. These techniques use distinct materials, such as plastics, ceramics, metals, liquids, powders, and even living cells [6]. AM is widely employed in industries and is popular among researchers because of its cost-effectiveness, rapid prototyping, and vast application area. Its applications have expanded from the aerospace and automobile industries to the medical and food industries [7]. However, AM parts usually require post-processing to improve the microstructure, reduce porosity and roughness, and meet geometric tolerance [8].
Although a variety of materials can be used in AM/3D printing processes, plastic materials are the most common and widely utilized in research and industry. Plastics are broadly categorized as Thermoplastics and Thermosets. Usually, the Material Extrusion AM/3D printing process is required for plastic materials, and this process is categorized as Fused Filament Fabrication (FFF) and Fused Deposition Modeling (FDM). Most of the research focuses on the mechanical characteristics of FDM parts, which are a popular AM method for producing plastic parts [9]. Prototyping and functional component production are two uses for this technology in the automobile, aerospace, and healthcare sectors [2]. Thermoplastic filament materials are melted first, and then they are extruded layer by layer on the hot build platform to make a particular shape in the FDM process [10]. However, FDM requires post-processing because of the filament voids from the nozzle diameter, which result in poor surface accuracy. FDM is a major participant in the additive manufacturing sector because it can produce lightweight structures and intricate geometries with little waste.
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Based on molecular structure, thermoplastics can be categorized as amorphous polymers and semicrystalline polymers. Thus, the plastics are listed as amorphous polymers, semicrystalline polymers, and thermosets [8]. Acrylonitrile Butadiene Styrene (ABS), Polyvinyl chloride (PVC), Polycarbonate (PC), etc., are amorphous polymers. Polylactic Acid (PLA), Polylactic Acid Plus (PLA +), etc., are semicrystalline polymers, and Phenolic Resin, Silicone, Epoxy, etc., are thermosets. Most of the amorphous and semicrystalline polymers use the FDM process. Among these polymers, the properties of ABS parts printed using FDM processes have been extensively studied [11‐13]. ABS is a great thermoplastic amorphous polymer with high stress and strain values, chemical resistance, and dimensional stability [14].
Researchers are focusing on enhancing the mechanical properties of 3D printed items by analyzing the impact of processing parameters, such as printing speed, layer thickness, nozzle temperature, raster angle, infill pattern, infill density, etc. [15‐18]. Such as Agarwal et al. [19] found that printing speed and layer thickness enhance the tensile properties of ABS specimens. Brackett et al. [20] outline that increased infill density (20% to 100%) resulted in higher elastic modulus and ultimate tensile strength. Orientation of the raster angle (00, 300, 450, 600, or 900) has a notable impact on the mechanical characteristics [2, 16‐18, 21]. Agarwal et al. [22] concluded that concentric infill patterns had 123% and 115% higher ultimate tensile strength than linear and triangular infill patterns, respectively. Bhuiyan and Khanafer [2] found that grid infill patterns with 00 raster angle showed higher yield strength and ultimate tensile strength with increasing infill density. Moreover, various finite element models have been developed to simulate the process of ABS 3D printing and to facilitate parameter selection [23].
Any material’s fatigue characteristics are also impacted by printing parameters. In their analysis of the fatigue behavior of samples with 0°, 45°, and 90° directions, Letcher et al. [24] discovered that the 45° angle exhibits a longer fatigue life than the other two. The impact of print orientations on the PLA’s tensile fatigue behavior was examined by Afrose et al. [25]. The findings showed that samples constructed in the 45° direction had greater fatigue lifetimes, cycle softening, and modulus of toughness than samples constructed in both X and Y directions. In their study of fatigue data for various ABS material printing orientations, Lee and Huang [26] examined the total strain energy absorbed during cycling loading. Moreover, Ziemian et al. [27] found that + 450/− 45° direction presented a higher fatigue lifetime and a higher storage modulus, followed by the 0, 450, and 90° directions for the same applied loads. Magri et al. [28] printed ABS and PLA materials with + 450/− 45° infill orientation and conducted cyclic testing with 10, 40, and 80 Hz. As the frequency is very high, there was a temperature effect that caused the earlier breakdown of the specimen. Reis et al. [29] conducted a fatigue test with a 2 mm/min displacement rate and load ranging from 0 to 90% of the maximum average load obtained from the static tensile tests. Jap et al. [30] studied the effect of raster orientation on the static and fatigue properties of filament deposited ABS polymer. Their results indicated that the − 45°/45° raster orientation exhibited a greater number of cycles to failure by as much as 63.5%. Dudescu et al. [31] investigated the influence of infill pattern on the fatigue behavior of 3D-printed ABS specimens. Standard samples with a 100% infill rate were fabricated using various patterns, including rectilinear (0° and 90°), grid (0°–90° and ± 45°), triangular (60°), fast honeycomb, full honeycomb, and wiggle. The results showed that patterns with filaments inclined relative to the tensile axis—such as grid ± 45°, rectilinear 0°, and triangular 60°—exhibited the longest fatigue life, whereas those with filaments primarily perpendicular to the loading direction—such as fast honeycomb, full honeycomb, and rectilinear 90°—demonstrated shorter fatigue life. El-Deeb et al. [32] examined how part-build directions (Upright, On Edge, Flat) and build orientation angles affect the fatigue behavior of ABS material fabricated via Fused Filament Fabrication (FFF) with a 50% infill density. The study’s results indicated that the On-Edge printing direction exhibited a markedly higher fatigue life compared to the other orientations under cyclic loading, achieving 1,592 cycles when printed at orientation angles of 15°–75°. In contrast, the Flat and Upright directions produced only 290 and 39 cycles, respectively, at the same orientation angles.
It is evident from the reviewed literature that most studies on the fatigue behavior of FDM-printed ABS have mainly examined the effect of raster angle, while other parameters such as infill pattern and density were often kept constant or explored only in basic configurations (e.g., linear, triangular, or ± 45° orientations). To the best of Authors’ knowledge, limited attention has been given to the combined influence of infill density, loading frequency, stress amplitude, and raster orientation on both static and fatigue performance. Furthermore, prior research has rarely addressed the interaction between printing parameters and loading conditions in defining fatigue life and failure mechanisms. To fill these research gaps, the present study systematically explores how 3D printing parameters (infill density and raster angle) and experimental conditions (loading–unloading frequency and stress amplitude) collectively affect the mechanical and fatigue behavior of FDM-printed ABS.
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2 Materials and methods
This study conducted research with 3D-printed ABS materials to perform several mechanical analyses. For that, this section outlines the manufacturing procedure and specifications of the test samples, methods, manufacturing parameters, tensile and cyclic test settings, etc.
2.1 Specimen construction
For the static tensile and cyclic testing, dog bone specimens were built with 3D-printed ABS materials by following the ASTM D638 standard (Type IV specimen). ASTM D638 Type IV specimen geometry is the standard geometry was used to ensure comparability with prior studies, provide uniform stress distribution in the gauge section, and this size is compatible with tensile and fatigue testing machine. A 3D model of the specimen was created using SolidWorks 2025 software. A detailed overview of the specimen is depicted in Fig. 1.
Fig. 1
Schematic diagram of ASTM D638 (Type IV) standard dog-bone specimen (All dimensions are in mm)
This design was converted to an STL file to import into GrabCAD, which is a 3D printing software. In GrabCAD, the default infill pattern is the grid. However, different infill orientations and infill densities can be incorporated. Infill density and orientation significantly influence the modulus of elasticity of 3D-printed materials [33]. As the infill pattern is the grid, 00/900, 300/-600, + 450/-450, 750/-150 infill orientation (or raster angle) was selected for printing with 20%, 50%, 80%, and 100% infill density for each infill orientation. The selected infill densities (20–100%) represent the practical range from lightweight prototypes to fully solid parts. The chosen raster orientations span from highly anisotropic (0°/90°) to quasi-isotropic (± 45°), with additional intermediate angles (30°/ − 60°, 75°/ − 15°) included to capture off-axis effects and stress redistribution mechanisms. As seen in Fig. 2, the Stratasys F370 CR Printer (Eden Prairie, MN, USA), an FDM-based 3D printer, was used to produce these specimens. Table 1 compiles the manufacturing parameters used in 3D printing. All the specimens were constructed with their minimal part dimensions aligned with the machine’s z-axis while resting flat on the 3D printer tray (Fig. 3).
Fig. 2
a Stratasys F370 CR 3D printer, b 3D printed specimen for different infill orientations
The mechanical tensile tests of the 3D printed specimen were performed using an INSTRON machine (Norwood, MA, USA) by following ASTM D638 standards, as depicted in Fig. 4. The maximum load capacity of this machine is 10 kN. The crosshead speed applied to the samples was 5 mm/min (Speed is recommended by ASTM D638 for semi-rigid and rigid plastic materials), and the test ended with a rupture. Tensile tests were performed to determine Ultimate tensile strength (UTS), Yield Strength, Young’s modulus, and elongation for each raster angle and infill density. Two printing process parameters are considered for different printing variations. Infill orientations (00/900, 300/-600, + 450/− 450, and 750/− 150) and Infill densities (20%, 50%, 80%, and 100%) are two printing process parameters, and they create 16 printing variations. Table 2 describes all 16 printing variations (i.e., 20% infill density for 00/900 raster angle, 40% infill density for 00/900 raster angle, etc.). At least four specimens of each printing variation (a total of 64 specimens) were tested.
Fig. 4
a Instron E10000 series tensile and fatigue testing machine; b closer picture with dogbone sample
Static tensile tests were therefore conducted in this study using a 42 (4 × 4) factorial experimental design, with two components examined at four levels each, for a total of 16 treatment combinations. Factor A, infill orientation, included 00/900, 300/-600, + 450/-450, and 750/-150, and Factor B, Infill densities, included 20%, 50%, 80%, and 100%. For each infill percentage, four tensile tests were conducted, with the mean result chosen for each infill density. The slope of the linear part of the stress–strain curves was used to determine the elastic modulus for each specimen.
2.2.2 Tension-tension fatigue testing
At least four replicates were examined for every factor combination, according to the ASTM D7791 standard. Tension-tension uniaxial fatigue tests were performed for 00/900, 300/− 600, and + 450/− 450 raster angles with varying infill densities (20%, 50%, 80%, and 100%). For each case, maximum stress levels are 90%, 70%, 60%, and 50% of UTS. Tests were conducted using sinusoidal stress variation in time, and the minimum cycle stress in each case was 10% of the maximum load (stress ratio R = 0.1, R = \(\frac{Max Stress}{Min Stress}\)). To reduce the chance of localized heating from hysteresis, testing was done at room temperature at a low frequency. Thus, in this study, tension-tension fatigue testing was performed according to a 31 × 42 (3 × 4 × 4) factorial experimental design, with one factor analyzed at 3 levels and two factors analyzed at 4 levels each, i.e., 48 total experimental combinations. Factor A, infill orientation, included 00/900, 300/− 600, and + 450/− 450, and Factor B, infill densities, included 20%, 50%, 80%, and 100%, and Factor C, maximum stress level, included 90%, 70%, 60%, and 50% of UTS. Fatigue Testing was also performed with 0.25 Hz, 0.5 Hz, 1 Hz, 2 Hz, 5 Hz, 10 Hz, and 20 Hz for 00/900, 300/− 600, and + 450/− 450 raster angles with 100% infill density (ID). There was no specific run-out time of testing, however, test was conducted until specimen breaks. Figure 5 depicts a sample of a sinusoidal wave for stress distribution of fatigue testing.
Equation (1), also known as the Power law, was utilized in this investigation to determine the parameters of fatigue properties to assess the material’s fatigue behavior. The properties of the stress-life curve were determined by fitting the curve on the logarithmic scale.
$$N = aS^{m}$$
(1)
where,
Fatigue exponent, m
Fatigue coefficient, a
Number of cycles to fatigue failure, N
Maximum stress level expressed in % of UTS, S
2.3 Statistical data analysis
A fixed-effects model of analysis of variance (ANOVA) was used to compare the mean values of the UTS yield stress, Young’s modulus, and fatigue life of the various specimen types. [34]. The MS Excel and IBM SPSS software were used to study the statistical analysis of the obtained results through tensile testing.
2.3.1 Two-way ANOVA
A two-way ANOVA was used to assess the effect of the specimen’s infill orientations and infill density, on the different tensile test variables (UTS, Yield strength, Young’s modulus, etc.) resulting from tensile tests to assess the level of anisotropic behavior. There are two printing process parameters (Infill orientation/Raster angle and Infill density) that create sixteen printing variations, and each variation has at least four tensile testing experiments. Thus, there are sixteen algebraic means for each printing variation. In two-way ANOVA, three hypotheses are being tested, and so three null hypotheses and three alternative hypotheses. Here, hypotheses for tensile testing are,
Null hypothesis (H0),
H01
There is a significant effect of one factor (Raster angle) on the dependent variable.
H02
There is a significant effect of another factor (Infill density) on the dependent variable.
H03
There is no interaction between the two factors (Raster angle and Infill density).
Alternative hypothesis (Hi),
H1
There is no effect of one factor (Raster angle) on the dependent variable.
H2
There is no effect of other factors (Infill density) on the dependent variable.
H3
There is an interaction between the two factors (Raster angle and Infill density).
2.3.2 Three-way ANOVA
A three-way ANOVA was also analyzed to evaluate the equivalence of the mean number of cycles to failure for the treatment factors of specimen’s infill orientation (00/900, 300/− 600, + 450/− 450), infill density (20%, 50%, 80%, and 100%) and maximum fatigue stress level (90%, 70%, 60%, and 50% of UTS). Thus, there are 48 testing categories, and each category has at least four fatigue testing experiments. In three-way ANOVA, seven hypotheses are being tested (three independent factors, three two-way interactions, and one three-way interaction), so seven null hypotheses and seven alternative hypotheses.
2.4 Regression analysis
The unknown parameters of Eq. (1) must be found using a conventional regression analysis method. The Leveneberg–Marquardt approach is frequently used for nonlinear regression because of the equation’s nonlinearity [34]. The squared error between measurements and estimates is minimized by the ideal parameters [2]. The results of the linear regression are shown in the following sections, where the experimental data is represented by black dotted lines and the fit curve is shown by solid-colored lines. In addition to the relative errors between computed and experimental data, the coefficient of determination (R2) could be utilized to assess the accuracy of projected models [35]. A statistical overview to measure R-squared (R2) is defined below:
The following sections present a comparison of all applied models and their respective R2 values in the figure.
3 Results and discussion
3.1 Static tensile test
3.1.1 Comparative analysis of static tensile test variables
Tensile test data were collected, and the outcomes were carefully examined to see how the process parameters affected the printed specimens. They were computed using the stress–strain curves displayed in Fig. 6 and the data that were recorded. Table 3 provides an overview of the tensile test results for the examined specimens.
Fig. 6
Stress–Strain graph of tensile testing for different printing variations: a 20% infill density; b 50% infill density; c 80% infill density; d 100% infill density
Tension test results for different infill orientations and infill density (standard deviations are shown in parentheses)
Printing process parameter
Mean young’s modulus [MPa]
Mean yield stress (offset 0.2%) [MPa]
Mean ultimate tensile stress [MPa]
Mean elongation [%]
Raster angle
Infill density
00/900
20%
3053.78 (8)
27.94 (0.19)
28.79 (0.14)
2.19 (0.23)
50%
3156.24 (32.89)
28.73 (0.19)
28.91 (0.2)
2.09 (0.35)
80%
3334.71 (25.67)
30.89 (0.75)
30.65 (0.05)
2.82 (0.37)
100%
3511.72 (72.8)
32.34 (0.11)
35.45 (0.21)
2.61 (0.27)
300/ − 600
20%
3007.57 (4.41)
30.52 (0.02)
30.79 (0.04)
3.42 (0.52)
50%
3278.11 (10.79)
32.86 (0.2)
32.96 (0.21)
3.03 (0.23)
80%
3443.46 (17.8)
34.65 (0.15)
34.78 (0.12)
3.04 (0.39)
100%
3673.1 (12.09)
36.99 (0.71)
37.20 (0.76)
4.19 (0.85)
450/ − 450
20%
3041.59 (13.11)
29.25 (1.05)
30.94 (0.6)
3.35 (0.44)
50%
3171.75 (46.5)
30.65 (1.72)
31.66 (0.75)
3.93 (0.75)
80%
3377.34 (42.05)
32.19 (0.7)
33.37 (0.22)
4.02 (0.62)
100%
3496.54 (142.94)
34.66 (0.41)
35.57 (0.05)
5.79 (0.31)
750/ − 150
20%
3063.625 (0.42)
30.66 (0.16)
30.7425 (0.17)
1.6 (0.06)
50%
3211.91 (1.5)
30.87 (0.05)
30.99 (0.04)
1.67 (0.02)
80%
3404.89 (17.9)
32.31 (0.47)
32.76 (0.12)
1.56 (0.08)
100%
3611.34 (7.8)
35 (0.03)
35 (0.04)
1.96 (0.02)
Figure 7 summarizes Table 3 data and shows how raster angle and infill density affect several static tensile testing variables, such as UTS, yield strength, young’s modulus, and elongation.
Fig. 7
Static tensile testing variables for different printing variations: a UTS; b yield strength; c young’s modulus; d elongation
Young’s Modulus increases with infill density (ID) across all raster orientations. For instance, at 0°/90°, the modulus rises from 3053.78 MPa (20% ID) to 3511.72 MPa (100% ID). The highest modulus (3673.1 MPa) is observed at 30°/ − 60° with 100% ID, suggesting superior stiffness with this raster angle at full density. At 100% ID, the ranking of stiffness is: 30°/ − 60° > 75°/ − 15° > 0°/90° > 45°/ − 45°. This indicates that oblique raster angles (e.g., 30°/ − 60°) enhance interlayer bonding and load distribution, improving stiffness more effectively than transverse (0°/90°) or symmetric (45°/ − 45°) patterns. The yield stress exhibits a consistent rise with increasing infill for all raster angles. At 100% ID, 30°/ − 60° achieves the highest yield stress (36.99 MPa), followed closely by 75°/ − 15° (35.00 MPa) and 45°/ − 45° (34.66 MPa). 0°/90° records the lowest (32.34 MPa), reinforcing that oblique angles provide more resistance to initial plastic deformation. The superior yield behavior at 30°/ − 60° and 75°/ − 15° raster angles is likely due to enhanced stress distribution pathways that reduce early failure onset.
UTS also improves with increasing infill density across all raster orientations. 30°/ − 60° at 100% ID exhibits the highest UTS (37.20 MPa), followed by 45°/ − 45° (35.57 MPa) and 0°/90° (35.45 MPa). 75°/ − 15° presents a consistent but slightly lower UTS (~ 35 MPa), despite its high modulus. This suggests that 30°/ − 60° raster orientation at 100% ID offers the optimal tensile strength, likely due to its favorable fiber alignment and reduced internal voids. Elongation provides insight into ductility and energy absorption before fracture. The highest elongation (5.79%) is recorded at 45°/ − 45° with 100% ID, indicating excellent ductile behavior. 30°/ − 60° also performs well at 100% (4.19%), confirming its balanced strength-ductility profile. In contrast, 75°/ − 15° demonstrates consistently low elongation, e.g., 1.96% at 100% ID, suggesting a more brittle behavior despite high strength. Thus, 45°/ − 45° raster angles offer better deformation before failure, suitable for applications requiring toughness.
Overall trends and comparative ranking of UTS, Yield Stress, Young’s Modulus, Ultimate Stress at Break, and Elongation are shown below. Table 4 shows the comparison for 100% infill density.
30°/ − 60° emerges as the most optimized raster angle for strength and stiffness.
45°/ − 45° excels in ductility, which may be favorable in fatigue or impact-prone applications.
75°/ − 15° presents a high-strength but low-ductility profile, potentially prone to brittle fracture.
0°/90° performs consistently lower in all metrics, affirming the limitations of this raster configuration.
As four experiments were conducted for each case (i.e., 4 experiments of 20% ID for 00/900 raster angle, 4 experiments of 40% infill density for 00/900 raster angle, etc.), statistical validation was also conducted to validate the gathered data. Moreover, the level of anisotropic behavior of ABS materials can also be assessed from statistical analysis.
3.1.2 Statistical analysis of static tensile testing data
3.1.2.1 ANOVA analysis
For the analysis of static tensile test data, a two-way ANOVA was incorporated to compare the tensile test variables (mean UTS, Yield Strength, Young’s modulus) associated with the 2-printing process parameter, which included 16 different printing variations. The two-way ANOVA test results for the tensile test variables (UTS, Yield strength, and Young’s modulus) are shown in Tables 5, 6, and 7, respectively. This analysis was conducted at a confidence level (CI) of 95%. All the tensile test data for ANOVA tests are shown in Appendix 1 1.
Table 5
ANOVA test result for ultimate tensile strength (UTS)
Source of variation
SS
df
MS
F
P-value
F crit
Raster angle
74.04
3
24.68
230.98
< 0.001
2.80
Infill density
283.46
3
94.49
884.26
< 0.001
2.80
Raster angle × infill density
19.44
9
2.16
20.21
< 0.001
2.08
Error
5.13
48
0.11
Total
382.07
63
R2 = .987 (Adjusted R2 = .982)
Table 6
ANOVA test result for yield strength
Source of variation
SS
df
MS
F
P-value
F crit
Raster angle
116.68
3.00
38.89
92.81
< 0.001
2.80
Infill density
241.50
3.00
80.50
192.11
< 0.001
2.80
Raster angle × infill density
9.98
9.00
1.11
2.65
0.01
2.08
Error
20.11
48.00
0.42
Total
388.28
63.00
R2 = .948 (Adjusted R2 = .932)
Table 7
ANOVA test result for young’s modulus
Source of variation
SS
df
MS
F
P-value
F crit
Raster angle
82,291.09
3.00
27,430.36
13.45
< 0.001
2.80
Infill density
253,7425.39
3.00
845,808.46
414.86
< 0.001
2.80
Raster angle × Infill density
69,923.62
9.00
7,769.29
3.81
0.001
2.08
Error
97,860.62
48.00
2,038.76
Total
2,787,500.72
63.00
R2 = .965 (Adjusted R2 = .954)
(I)
ANOVA analysis of UTS.
The ANOVA test results for the UTS of the ABS specimen are shown in Table 5. Since the F > Fcritical and P values < 0.05 for two process parameters independently and combinedly, it rejects the null hypothesis and accepts the alternative hypothesis. Both raster angle and infill density have statistically significant effects on UTS. Infill density exhibits a much stronger effect (F = 884.26) than raster angle (F = 230.98), suggesting that UTS is more sensitive to density-related material continuity than to orientation. The interaction term (Raster Angle × Infill Density, F = 20.21, p < 0.05) is also statistically significant, indicating that the influence of raster angle on UTS depends on the infill density level.
It is clear from Table 5 analysis that the model’s capabilities, as indicated by its R2, exceed 0.90. There isn’t a significant departure from normalcy in the residuals’ normal probability plot (Fig. 8a). The fundamental premise of our analysis—that errors are regularly distributed—is confirmed by this outcome. Moreover, Fig. 8b shows an upward trend in residuals, indicating a violation of homoscedasticity, with increasing variance in residuals as UTS increases, suggesting heteroscedasticity. While there are some residuals beyond ± 2, none are extreme enough to be considered strong outliers, and this supports the validity of the data points and model fit.
Fig. 8
a Normal P-P Plot of regression standardized residual, b residual plot for UTS
The ANOVA test results for the Yield Strength of the ABS specimens are shown in Table 6. Since the F > Fcritical and P < 0.05 for two process parameters independently and combinedly, it rejects the null hypothesis and accepts the alternative hypothesis. Thus, varying raster angle and infill density have a significant influence on the Yield Strength of ABS specimens. However, the dominant factor is infill density, with an F-value more than twice that of raster angle, suggesting yield stress is more controlled by internal structure density. The interaction (Raster Angle × Infill Density) term is significant at α = 0.05 (F = 2.65, p < 0.05), although its influence is more modest compared to UTS. This implies some conditional dependency, albeit weaker, between raster orientation and density in governing the onset of plasticity.
It is clear from the examination of Table 6 that the model’s R2 factors and capabilities are adequate. The yield strength’s normal probability curve is displayed in Fig. 9a. With the residuals distributed in a straight line, this graphic validates the normality assumption of errors. Figure 9b shows the residuals exhibit a systematic upward pattern, rather than a random scatter around the horizontal axis, which reindicates variance of residuals is not constant. While a few data points are beyond ± 2, none appear extreme enough to be clear outliers. This supports data reliability.
Fig. 9
a Normal P-P plot of regression standardized residual, b residual plot for yield strength
The ANOVA test results for the UTS of the ABS specimen are shown in Table 7. Since the F > Fcritical and P values < 0.05 for two process parameters independently and combinedly, it rejects the null hypothesis and accepts the alternative hypothesis. Thus, varying raster angle and infill density have a significant influence on the Young’s modulus of ABS specimens, and they show different Young’s modulus values. Both factors are again statistically significant, with infill density having an overwhelming influence (F = 414.86) compared to raster angle (F = 13.45). This reaffirms that stiffness is predominantly dictated by infill, likely due to enhanced material continuity and load path distribution. Interaction (Raster Angle × Infill Density) is significant at α = 0.05 (F = 3.81, p = 0.001), confirming a non-additive relationship where the effect of raster angle on modulus changes based on infill level.
The model shows a very high explanatory power with R2 = 0.965 and Adjusted R2 = 0.954, indicating that the majority of the variation in Young’s Modulus is explained by these probability plots (Fig. 10a), and it shows no significant deviation from the normality. The fundamental premise of our analysis is that errors are normally distributed, which is confirmed by this outcome. In Fig. 10b, the data points follow a non-random, structured pattern rather than a uniform scatter around the horizontal axis. There appear to be three visually distinct clusters, potentially corresponding to categorical variables (e.g., infill levels, raster angles, or both). The grouping may also suggest that some categorical effects (like printing process combinations) have disproportionately influenced the variance. A few points lie far to the left (residual < − 3, suggesting possible outliers or high-leverage observations.
Fig. 10
a Normal P-P plot of regression standardized residual of young’s modulus, b residual plot for young’s modulus
A post hoc analysis is required and appropriate as two-way ANOVA shows significant interaction effects, and it needs to be determined which specific group means differ from each other. From ANOVA results, Ultimate Tensile Strength (UTS), Yield Strength, and Young’s Modulus have interaction effects, and post hoc analysis is applied to find out which specific raster angle and infill density combinations differ significantly after observing significant two-way ANOVA results. Though there are many post-hoc analyses, Tukey’s HSD (Honestly Significant Difference) was chosen to compare all group means. ANOVA showed significant effects, and the data appear to meet assumptions (normality, equal group sizes, etc.). It balances power (power = 1—β, it is the probability of a Type II error) and Type I error control effectively. Table 8 (Raster angle) and Table 9 (Infill density) showed the Post-Hoc Tukey’s HSD analysis for UTS. The rest of the analysis is shown in the Appendix in Tables 1-19, 20, 21 and 22.
Table 8
Post-Hoc Tukey’s HSD test of UTS for raster angle
Raster angle (I) (degree)
Raster angle (J) (degree)
Mean difference (I-J)
Std. error
P-values
95% confidence interval
Lower bound
Upper bound
0
30
− 2.99
0.12
< .001
− 3.30
− 2.68
45
− 1.94
0.12
< .001
− 2.24
− 1.63
75
− 1.43
0.12
< .001
− 1.73
− 1.12
30
0
2.99
0.12
< .001
2.68
3.30
45
1.05
0.12
< .001
0.74
1.36
75
1.56
0.12
< .001
1.25
1.87
45
0
1.94
0.12
< .001
1.63
2.24
30
− 1.05
0.12
< .001
− 1.36
− 0.74
75
0.51
0.12
< .001
0.20
0.82
75
0
1.43
0.12
< .001
1.12
1.73
30
− 1.56
0.12
< .001
− 1.87
− 1.25
45
− 0.51
0.12
< .001
− 0.82
− 0.20
The error term is Mean Square(Error) = .107
The mean difference is significant at the .05 level
Table 9
Post-Hoc Tukey’s HSD test of UTS for infill density
Infill density (I) (%)
Infill density (J) (%)
Mean difference(I-J)
Std. error
P-values
95% confidence interval
Lower bound
Upper bound
20
50
− 0.81
0.12
< .001
− 1.12
− 0.50
80
− 2.57
0.12
< .001
− 2.88
− 2.26
100
− 5.49
0.12
< .001
− 5.80
− 5.18
50
20
0.81
0.12
< .001
0.50
1.12
80
− 1.76
0.12
< .001
− 2.07
− 1.45
100
− 4.68
0.12
< .001
− 4.99
− 4.37
80
20
2.57
0.12
< .001
2.26
2.88
50
1.76
0.12
< .001
1.45
2.07
100
− 2.92
0.12
< .001
− 3.22
− 2.61
100
20
5.49
0.12
< .001
5.18
5.80
50
4.68
0.12
< .001
4.37
4.99
80
2.92
0.12
< .001
2.61
3.22
The error term is Mean Square(Error) = .107
*The mean difference is significant at the .05 level
(I)
Ultimate tensile strength (UTS).
Post hoc analysis of raster angle demonstrated that all orientations differ significantly in mean UTS (p < 0.001 for every pair), with the 30°/–60° raster yielding the highest strength, followed in descending order by 75°/–15°, 45°/–45°, and 0°/90°. Similarly, infill density comparisons showed a clear static increase in UTS with density: each density level (20%, 50%, 80%, 100%) differed significantly from all others (p < 0.001), confirming that material continuity exerts a dominant effect on tensile capacity.
(II)
Yield strength.
For yield strength, Tukey’s HSD indicated that the 30°/–60° orientation again outperforms all others (p < 0.001), with 0°/90° and 45°/–45° also significantly lower than 30°/–60° (p < 0.001). The only non-significant raster comparison was between 45°/–45° and 75°/–15° (p = 0.116), suggesting comparable resistance to plastic deformation for these two off-axis patterns. Infill density exhibited highly significant pairwise differences (p < 0.001 for all comparisons), reinforcing that higher densities uniformly enhance yield strength.
(III)
Young’s modulus.
Stiffness exhibited a similar density dependence: every infill comparison from 20 to 100% was significant (p < 0.001), with modulus increasing in the order 20% < 50% < 80% < 100%. Raster angle effects on modulus were more nuanced: 30°/–60° displayed significantly greater stiffness than 0°/90° and 45°/–45° (p < 0.001), while the differences between 0°/90° vs. 45°/–45° (p = 0.963) and 30°/–60° vs. 75°/–15° (p = 0.320) were not significant. This indicates that both 30°/–60° and 75°/–15° orientations yield comparable stiffness at high infill, whereas 0°/90° and 45°/–45° produce similarly lower modulus values. Collectively, these post hoc results confirm that infill density is the primary determinant of tensile and stiffness properties, with raster angle playing a secondary but still significant role. For applications requiring maximum strength, the 30°/–60° raster at 100% infill is recommended; when stiffness is paramount, either 30°/–60° or 75°/–15° at high densities will yield optimal performance. These insights provide clear guidance for tailoring FDM process parameters to meet specific mechanical requirements.
3.2 Tension-tension fatigue test with constant frequency
Tension-Tension fatigue test with constant frequency was conducted at 0.5 Hz frequency with three process parameters. The experiment was conducted by changing raster orientation, infill density, and maximum stress level.
3.2.1 Comparative analysis of fatigue test data
This section will analyze how raster angle and infill density influence the fatigue life of 3D-printed ABS specimens under tension–tension cyclic loading at various stress levels (normalized to UTS). The fatigue behavior of FDM-printed ABS specimens was evaluated under tension–tension cyclic loading at four normalized stress levels: 90%, 70%, 60%, and 50% of UTS. As no study was found for the chosen raster angle, infill pattern, and infill densities, fatigue result can not be compared to existing literatures. As fatigue stress levels are related to UTS of the specimen, UTS data validation is required. It is shown in Table 10 for comparison with different literature. Table 10 showed that the UTS value of this study and other literatures are consistent.
The influence of raster angle (45°/− 450, 0°/90°, and 30°/ − 60°) and infill density (20%, 50%, 80%, and 100%) was systematically investigated. The results, summarized in Tables 11 and visualized via S–N curves in Fig. 11, provide clear insights into how these printing parameters affect fatigue life.
Table 11
Mean number of fatigue cycles for various infill orientations and infill densities in tension-tension fatigue testing (standard deviations are shown in parentheses)
Max% of UTS
20% infill density
50% infill density
450/ − 450
00/900
300/ − 600
450/ − 450
00/900
300/ − 600
90
104 (12)
68 (5)
94 (10)
103.5 (17)
75 (12)
83.5 (13)
70
1094 (96)
1025 (77)
1357.25 (57)
1277 (159)
1018 (45)
1337.25 (26)
60
2906 (154)
2072 (151)
3132.25 (274)
3148 (402)
2601(155)
3097.25 (134)
50
6065 (691)
4518 (507)
6592 (701)
7858 (655)
5314 (175)
6697 (5)
Max% of UTS
80% Infill Density
100% Infill Density
450/ − 450
00/900
300/ − -600
450/ − 450
00/900
300/ − 600
90
107 (7)
76 (12)
70.5 (16)
96 (5)
66.25 (6)
53 (2)
70
1630 (139)
1153 (171)
1244.5 (19)
1392 (215)
662.25 (68)
992 (90)
60
3426 (322)
2437 (368)
2896 (198)
3450 (510)
1581 (59)
2467 (153)
50
7494 (139)
6906 (599)
6911 (701)
7564 (415)
4053 (105)
6652 (10)
Fig. 11
S–N curves of fatigue testing for different raster angles: a 20% infill density; b 50% infill density; c 80% infill density; d 100% infill density
Across all raster angles and infill densities, a consistent inverse relationship between the maximum stress level and the number of cycles to failure was observed, characteristic of classical S–N fatigue behavior. As the stress level decreased, the fatigue life significantly increased, highlighting the material’s greater ability to withstand lower cyclic loads. 450/-450 infill orientation generally yields the longest fatigue life for most infill densities and stress levels, particularly at moderate to high infill (40%, 80%, 100%). The only exception occurs at the lowest infill density (20%) and lower stress levels (70%, 60%, and 50% UTS), where the 30°/–60° orientation slightly outperforms 450/-450. This suggests that when the internal material volume is minimal, the more oblique (30°/–60°) paths can interrupt crack growth more effectively under cyclic loads. The S–N curves reveal a clear progression in fatigue performance as infill density increases and raster orientation shifts. At the lowest density, overall endurance is poor, and no single orientation dominates across all stress levels. 450/-450 excels under the highest loads, but 30°/–60° overtakes it as stresses drop, with 0°/90° consistently lagging. Once infill rises, 450/-450 emerges as the superior pattern throughout, delivering noticeably longer lives and a more gradual decline in endurance with increasing load. Further increasing density continues to elevate fatigue cycle and flattens the curves, underscoring reduced sensitivity to stress changes after 60% or less stress level of UTS.
3.2.2 Statistical analysis of tension-tension fatigue testing data
3.2.2.1 ANOVA analysis
A three-way ANOVA was conducted on the total fatigue cycles in tension–tension fatigue testing, with raster angle, infill density, and stress level as fixed factors (48 different categories). ANOVA test results for the fatigue data are depicted in Table 12. This analysis is also carried out at a CI of 95%. All the fatigue test data for ANOVA tests are shown in Appendix 1-23.
Table 12
ANOVA test result for fatigue cycle
Source of variation
SS
df
MS
F
P-value
Raster angle
25,180,821.22
2
12,590,410.61
47.043
< .001
Infill density
9,790,906.52
3
3,263,635.51
12.194
< .001
Stress Level
1,045,847,671.27
3
348,615,890.43
1302.571
< .001
Raster angle × infill density
5,790,976.91
6
965,162.82
3.606
.002
Raster angle × stress level
19,254,115.53
6
3,209,019.26
11.990
< .001
Infill density × stress level
15,706,273.63
9
1,745,141.51
6.521
< .001
Raster angle × infill density × stress level
9,568,716.51
18
531,595.36
1.986
.014
Error
38,539,684.25
144
267,636.69
Corrected total
1,169,679,165.83
191
R2 = .967 (Adjusted R2 = .956)
Stress level exerts the strongest influence (F = 1302.57, p < 0.001), confirming that higher cyclic stresses dramatically reduce fatigue life. Raster angle also significantly affects life (F = 47.04, p < 0.001), demonstrating that filament orientation alters crack‐initiation and propagation paths. Infill density shows a smaller yet still highly significant effect (F = 12.19, p < 0.001), with denser specimens generally enduring more cycles before failure. The interaction effect of Raster Angle × Stress Level (F = 11.99, p < 0.001) and Infill Density × Stress Level (F = 6.52, p < 0.001) indicates that the detrimental effect of increasing stress is modulated by both orientation and internal material volume. Raster Angle × Infill Density (F = 3.61, p = 0.002) shows that the optimal raster pattern depends on specimen density, such as oblique patterns (300/-600) yield the greatest benefit only above certain infill thresholds. A three-way interaction of the combined Raster Angle × Infill Density × Stress Level term is also significant (F = 1.99, p = 0.014), revealing a subtle but real three-factor dependency. Thus, the best printing strategy for maximizing fatigue life shifts depending on both the applied load and the chosen infill. This panel of scatter plots, shown in Fig. 12, assesses the fit and assumptions of the three‐way ANOVA model (factors: raster angle, infill density, stress level, and their interactions) predicting cycles to failure. From Table 12, the model explains 96.7% of the variance in fatigue life (R2 = 0.967, adjusted R2 = 0.956), indicating an excellent fit.
Fig. 12
a Diagnostic plots for the three‐way ANOVA model on fatigue life, b residual plot for the mean number of cycles
On Fig. 12(a), Observed vs. Predicted (top‐center) points lie closely along a rising trend, demonstrating that the model captures most of the variation in fatigue life. Observed vs. Standardized Residual (bottom‐left), residuals cluster around zero without systematic curvature, indicating no gross nonlinearity or omitted‐variable bias. Predicted vs. Standardized Residual (bottom‐center), Residuals are randomly scattered across the horizontal axis, supporting the assumption of independence. A slight widening of the cloud at higher predicted values hints at minor heteroscedasticity, but no extreme outliers are apparent. Observed vs. Observed (upper‐left) and Predicted vs. Predicted (center‐center), which are Identity plots, emphasize the same one-to-one alignment between observations and confirm uniform coverage of the predicted range without systematic gaps. Standardized Residuals Distribution (right column) depicts a vertical stack of standardized residuals, showing most of the points lying within ± 2 SD, with a few mild outliers, indicating that assumptions of normality and variance are reasonably met, that also validated by Fig. 12(b). According to Fig. 12(b), residuals are symmetrically distributed around zero across the full span of observed cycle counts, indicating the model is not systematically over- or under-predicting. The vertical spread of residuals shows specimens with very high cycle counts, suggesting the variance of fatigue life may increase at higher fatigue cycles. Apart from that single outlier around -4 and slight widening at high cycle counts, the residuals appear randomly scattered, supporting assumptions of independence and approximate homoscedasticity.
3.2.2.2 Post Hoc Tukey’s HSD analysis
A post hoc analysis is required and appropriate as three-way ANOVA shows significant individual and interaction effects, and it needs to be determined which specific group means differ from each other. Thus, Tukey’s HSD (Honestly Significant Difference) was chosen to compare all group means. The Tukey HSD results (Table 13 and Appendix 1-24 and 25) provide clear, pairwise insights into how each factor, such as raster angle, infill density, and stress level, affects fatigue life.
Table 13
Post-Hoc Tukey’s HSD test of fatigue cycle for raster angle
Raster angle (I) (degree)
Raster angle (J) (degree)
Mean difference (I-J)
Std. error
P-values
95% confidence interval
Lower bound
Upper bound
0/90
30/ − 60
− 534.02
91.45
< .001
− 750.59
− 317.44
45/ − 45
− 880.44
91.45
< .001
− 1097.02
− 663.86
30/ − 60
0/90
534.02
91.45
< .001
317.44
750.59
45/ − 45
− 346.42
91.45
< .001
− 563
− 129.84
45/ − 45
0/90
880.44
91.45
< .001
663.86
1097.02
30/ − 60
346.42
91.45
< .001
129.84
563
The error term is Mean Square (Error) = 267,636.7
The mean difference is significant at the .05 level
As P-values < 0.001 in Table 13 for raster orientation, all three orientations differ significantly from each other. The substantial mean differences (45°/− 450–0°/90° ≈ 880 cycles; 30°/–60°–0°/90° ≈ 534 cycles) validate that 30°/–60° alignment markedly improves fatigue endurance compared to 0°/90°. Thus, 45°/-450 yields the highest mean cycles, followed by 30°/–60°, with 0°/90° the lowest.
Appendix 1-24 depicts the summary of the Post-hoc Tukey’s HSD test of Fatigue Cycle for infill density. 20% infill was significantly different from all higher densities (p < 0.001), reflecting poor fatigue performance due to insufficient or less internal volume and load-bearing pathways. 50% vs. 80% and 20% vs. 100% infill density showed no statistically significant difference (p > 0.05), indicating that gains in fatigue life begin to plateau around 80% infill. However, 50% vs. 100% showed significant differences, suggesting that the jump from mid to maximum density yields measurable benefit, but less consistently than from low to mid-density. Thus, fatigue life improves with increasing infill density, especially from 20 to 50%, but benefits taper off beyond 80%, indicating diminishing returns in very high-density structures.
Appendix 1-24 depicts the summary of the Post-hoc Tukey’s HSD test of Fatigue Cycle for stress level. Every pair of stress levels differs highly significantly (p < 0.001) because fatigue decreases as stress level increases from 50 to 90% of UTS (Almost 6180 cycles). Thus, Lower cyclic stresses dramatically prolong life, underscoring stress level as the dominant fatigue driver. Even small increases in stress (e.g., 70% to 90%) caused significant fatigue degradation, consistent with typical S–N behavior in polymer-like ABS.After analyzing all three factors, stress level has the strongest individual effect, with fatigue life dropping sharply as load amplitude increases, regardless of infill orientation and densities. These results highlight the importance of jointly optimizing infill orientation and infill density when designing FDM parts for fatigue-critical applications, especially under high-load conditions where fatigue degradation is most severe.
3.2.3 Fatigue life analysis with power law
An S–N (“fatigue stress–fatigue life”) curve is the fundamental tool for characterizing the fatigue behavior of polymers, such as ABS. Typically, it is assumed that the logarithm of the controlling stress S is linearly dependent on the logarithm of the constant amplitude fatigue life, N. The 10-base log–log graph for the mean number of fatigue cycles (N) on the y-axis and the percentage of the UTS (S) defining the maximum stress level per cycle on the x-axis was created using the S–N curves in Fig. 11. Figure 13 presents a transformed graph for 20% and 100% infill density.
Fig. 13
Transformed (log–log) S–N curves with least squares linear approximation: a 20% infill density, b 100% infill density
Figure 13 depicts that these data are in a linear relationship. Based on this transformation, the S–N curves for the power law of the FDM printed ABS specimen expressed in Eq. (1) can be rewritten as,
$$Log\left( N \right) = Log\left( a \right) + m Log\left( S \right)$$
(5)
A least squares regression fit (Curve fitting) is used to empirically calculate the material parameters m and a from the experimental fatigue data. An example is depicted in Fig. 13 for 20% and 100% infill density. The results of the regression analysis for 20%, 50%, 80%, and 100% are shown in Table 14.
Table 14
Material parameters estimated using a power law model for ABS specimen fatigue life
Infill density (%)
Raster angle (degree)
Fatigue exponent, m
Fatigue coefficient, a
R2
20%
0/90
− 7.1084
10 15.885
0.9402
30/ − 60
− 7.248
10 16.29
0.9469
45/ − 45
− 6.986
10 15.784
0.9651
50%
0/90
− 7.3035
10 16.292
0.9519
30/ − 60
− 7.469
10 16.678
0.9519
45/ − 45
− 7.3705
10 16.536
0.9689
80%
0/90
− 7.5504
10 16.774
0.9601
30/-60
− 7.7882
10 17.229
0.9495
45/ − 45
− 7.2086
10 16.276
0.9425
100%
0/90
− 6.993
10 15.585
0.9769
30/ − 60
− 8.2007
10 17.902
0.9591
45/ − 45
− 7.4585
10 16.703
0.9537
The log–log S–N data shown in Table 14 for ABS fatigue life fit very well to a power‐law model, as shown in Eqs. 1 and 5, with all regressions yielding R2 > 0.94. Increasing infill density steepens the slope (m becomes more negative) and raises the intercept (Log a), indicating that denser specimens both live longer at low stresses and are more sensitive to increases in stress. For example, at 100% infill, the fatigue exponent (m) for the 30°/–60° raster reaches 8.20 (the steepest slope), and its fatigue coefficient is highest (a = 1017.90). On the other hand, raster orientation modulates these effects; the 45°/-450 pattern consistently shows a less negative m (flatter S–N slope) and moderate Log a compared to 30°/–60°, delivering balanced fatigue endurance across stress levels. In contrast, 0°/90° specimens exhibit the least negative slopes (e.g., –6.99 at 100% infill), reflecting more gradual life loss but overall lower endurance. These parameters quantitatively capture how both infill density and raster orientation govern fatigue performance in FDM printed ABS.
3.3 Tension-tension fatigue test with variable frequency
Tension-Tension fatigue test with variable frequency was conducted with 0.25 Hz, 0.5 Hz, 1Hz, 2 Hz, 5Hz, 10 Hz, and 20Hz frequency for 100% infill density and three raster orientations (00/900, 300/-600, and 450/-450). The experiment was conducted with a maximum stress level of 50% of UTS.
3.3.1 Comparative analysis of fatigue test data with changing frequency
This section will analyze how raster angle and tension-tension fatigue testing frequency influence the fatigue life of 3D-printed ABS specimens under tension–tension cyclic loading at 50% stress of UTS. The results, summarized in Tables 15 and 11 and visualized in Fig. 14, provide clear insights into how these process parameters affect fatigue life.
Table 15
Mean number of fatigue cycles: 100% infill density with changing frequency (standard deviations in parentheses)
Raster angle
Frequency (Hz)
0.25
0.5
1
2
5
10
20
00/900
3536 (166)
4053 (105)
4539 (169)
5465.5 (264)
7202.75 (288)
8173 (115)
12,086 (208)
300/ − 600
5237 (196)
6652 (10)
7228 (258)
7908.5 (225)
8870.5 (287)
11,136.5 (767)
14,344 (482)
450/ − 450
7285 (456)
7564 (421)
8213 (206)
8539.5 (179)
13,353.25 (406)
14,206.75 (492)
18,453 (543)
Fig. 14
Effect of fatigue testing frequency on fatigue cycle
Fatigue life goes up for all raster orientations as the test frequency increases from 0.25 Hz to 20 Hz (Table 15 and Fig. 14), which indicates frequency sensitivity of ABS materials. At the slowest frequency (0.25 Hz), all three specimens fail after a few thousand cycles and are clustered together. As frequency rises, all the curves diverge, and 45°/− 45° specimens show the largest gains, the 30°/–60° specimens rise more moderately, and 0°/90° remains the lowest. Between 1 and 5 Hz, the ± 45° specimens jump ahead sharply, likely because faster cycling gives less time for cracks to grow and slight self‐heating that may enhance polymer toughness. Above 5 Hz, fatigue lives continue to increase but at a slower rate, indicating diminishing returns from further frequency increases. Through all frequencies, the order remains the same (45°/-45° > 30°/–60° > 0°/90°), showing that filament angle has the strongest effect on how long parts last under repeated loading. Thus, higher cyclic rates amplify the absolute endurance differences between orientations.
3.3.2 Statistical analysis of fatigue test data with changing frequency
3.3.2.1 ANOVA analysis
A two-way ANOVA was conducted on the total fatigue cycles in tension–tension fatigue testing, with raster angle and frequency as fixed factors (21 different experimental categories). ANOVA test results for the fatigue data are shown in Table 16. This analysis is carried out at a confidence level (CI) of 95%. All the fatigue test data for ANOVA tests are shown in Appendix 1-26.
Table 16
ANOVA analysis for fatigue cycle in changing frequency
Sources of variation
SS
df
MS
F
P-values
Fcritical
Raster angle
302,887,726.6
2
1.51 × 108
1273.799
< .001
3.14
Frequency
847,658,362.5
6
1.41 × 108
1188.28
< .001
2.25
Raster angle × frequency
38,999,355.91
12
3,249,946
27.335
< .001
1.9
Error
7,490,163.75
63
118,891.5
Total
119,7035,609
83
R2 = .994 (Adjusted R2 = .992)
Table 16 reports a two-way ANOVA on mean fatigue cycles (50% UTS) across three raster angles and seven test frequencies (0.25–20 Hz). The model explains 99.4% of the variation in fatigue life (R2= 0.994, adj R2= 0.992), showing an excellent fit. As raster angle and test frequency both have F = 1273.799 > Fcritical and F = 1188.28 > Fcritical, respectively, P < 0.05, they have highly significant effects on fatigue life. P < 0.05 for both factors individually validates their strong effect on fatigue life. Thus, infill orientation and test speed each strongly influence endurance. Moreover, their interaction (Raster Angle × Frequency) is also significant as F = 27.335 > Fcritical and P < 0.05, meaning the benefit of a given raster angle depends on the test frequency. For example, 45°/− 45° gains more fatigue cycles at higher speeds compared to 0°/90°. The diagnostic plots in Fig. 15 (a) show observed vs. predicted points cluster tightly around the diagonal in both low-frequency and high-frequency groups, confirming accurate predictions across the board. Standardized residuals appear randomly scattered with no clear pattern or trend in the Observed–Residual or Predicted–Residual plots, supporting the assumptions of linearity and independence. A slight increase in vertical spread at higher predicted values hints at minor heteroscedasticity (variance growing with cycle life), but no extreme outliers threaten model validity. The residual plot in Fig. 15b further confirms that errors are symmetrically distributed around zero for all cycle counts, with only one point beyond ± 3 standard deviations.
Fig. 15
a Diagnostic plots for the two‐way ANOVA model on fatigue life, b Residual Plot for the Mean number of cycles with changing frequency
The ANOVA analysis confirms that both raster angle and test frequency, and their combination, are key drivers of fatigue performance, and the diagnostic checks validate that the model assumptions hold.
3.3.2.2 Post Hoc Tukey’s HSD test
A two-way ANOVA shows significant individual and interaction effects, but it did not show which specific group means differ from each other and which group has a more significant effect. Thus, Tukey’s HSD (Honestly Significant Difference) was chosen to compare all group means. The Tukey HSD results (Table 17 and Appendix 1-27) provide clear, pairwise insights into how each factor, such as raster angle and frequency, affects fatigue life.
Table 17
Post-Hoc Tukey’s HSD test of fatigue cycle for raster angle
Raster angle (I)
Raster angle (J)
Mean difference (I− J)
Std. error
P− values
95% confidence interval
Lower bound
Upper bound
0
30
− 2331.57
92.15
< .001
− 2552.77
− 2110.37
45
− 4651.32
92.15
< .001
− 4872.52
− 4430.12
30
0
2331.57
92.15
< .001
2110.37
2552.77
45
− 2319.75
92.15
< .001
− 2540.95
− 2098.55
45
0
4651.32
92.15
< .001
4430.12
4872.52
30
2319.75
92.15
< .001
2098.55
2540.95
The error term is Mean Square (Error) = 118,891.488
The mean difference is significant at the .05 level
The Tukey’s HSD results for raster angle in Table 17 confirm that all three orientations differ significantly in mean fatigue life (Standard Error = 118 891.5, p < 0.001 for each pair). Specifically, 45°/-45° specimens endure on average 4,651 cycles more than 0°/90°. However, 30°/–60° parts last 2,332 cycles longer than 0°/90°. On the other hand, 45°/− 45° still holds a 2,320-cycle advantage over 30°/–60°. Thus, fatigue resistance ranks 45°/− 45° > 30°/–60° > 0°/90°, with each step statistically robust. For frequency, every pairwise comparison shown in Appendix 1-27 across the seven test speeds (0.25, 0.5, 1, 2, 5, 10, 20 Hz) is also highly significant (all p < 0.001). The mean life rises statistically with frequency increases. The smallest jump is from 0.25 Hz to 0.5 Hz (737 cycles). Moderate increases occur between mid‐range speeds (e.g., 1 Hz to 2 Hz, 645 cycles). The largest gain is between 0.25 Hz and 20 Hz (9,608 cycles). These contrasts confirm that higher fatigue testing frequency steadily boosts fatigue life, with the greatest marginal benefit seen when going from the slowest to the fastest test frequency.
3.4 Specimen inspection after fatigue testing
Fatigue testing was conducted for three raster angles (00, 300°, and 450°) with 20%, 50%, 80%, and 100% infill density for different stress levels (90%, 70%, 60%, and 50% of UTS). As the infill structure is a grid (Depicted in Fig. 3c), all the specimens break traversely, as shown in Fig. 16. Figure 16 depicts specimens of 00 raster angle with 100% infill density for maximum fatigue stress levels of 90%, 70%, 60%, and 50% of UTS (From left to right).
Fig. 16
ABS specimen with 00 raster angle with 100% infill density for different maximum fatigue stress levels of 90%, 70%, 60%, and 50% of UTS (From left to right)a
When maximum fatigue stress is 50% of the UTS, it is much less than the yield stress of an ABS specimen. Thus, the ABS specimen shown in Fig. 16 (Right) with a 50% stress level falls under the elasticity limit, and it perfectly behaves as an elastic material. Thus, it does not show any increment or an insignificant increment of length before breaking. On the other hand, 90% stress level showed a noticeable increment of length before breaking and gauge width shrinks (White mark on the narrow specimen on the left in Fig. 16). Because 90% stress level has almost similar stress as yield stress (e.g., 00 infill orientation and 100% infill density specimen has yield stress of 32.34 MPa, and 90% stress level of UTS is 31.905 MPa), and after some fatigue cycles, it exceeded the elastic limit. 70% stress levels also fall under the elastic limit, with stresses less than the yield stress. As a result, they also show very little noticeable increment in length before fracture. Though specimen analysis is shown for only the ABS specimen with a 00 raster angle with 100% infill density, this analysis is also valid for other specimens as well. Because all the specimen has similar stress levels, and they show similar surface behavior.
4 Conclusion and future direction
This comprehensive study investigated the effects of infill orientation, infill density (ID), stress amplitude, and loading frequency on the static tensile and tension-tension fatigue behavior of FDM-printed ABS specimens. Increasing ID from 20 to 100% consistently enhanced ultimate tensile strength (UTS), yield strength, and Young’s modulus across all raster orientations. At 100% ID, UTS improved by up to 23% compared to 20% ID. 30°/ − 60° delivered the highest strength metrics due to oblique interlayer bonding and load distribution. 45°/ − 45° maximized ductility (elongation: 5.79%), making it ideal for impact and fatigue-prone applications. However, 0°/90° consistently underperformed, while 75°/ − 15° showed high strength but low ductility. Two-way ANOVA confirmed significant individual and interactive effects of raster angle and ID (all p < 0.05). Post hoc Tukey’s HSD affirmed that 30°/ − 60° outperformed other orientations at 100% ID. Fatigue life decreased exponentially with increasing stress amplitude from 50 to 90% UTS) as stress level was the dominant factor (ANOVA F = 1302.57, p < 0.05). 45°/ − 45° generally maximizes fatigue life, especially at ≥ 50% ID, due to balanced stress redistribution. 30°/ − 60° excelled at low density (20%) under moderate stress, while 0°/90° exhibited the shortest fatigue life. Moreover, Log–log S–N curves fitted the fatigue data excellently (R2 > 0.94). Higher infill density increased the fatigue coefficient a’ (life at low stress) and steepened the slope m’ (sensitivity to stress). In addition to that, fatigue life increased with loading frequency ranging from 0.25 Hz to 20 Hz, attributed to reduced crack propagation time and mild hysteresis-induced heating. 45°/ − 45° showed the highest frequency sensitivity (e.g., 18,453 cycles at 20 Hz and 7285 at 0.25 Hz), followed by 30°/ − 60° and 0°/90°. Two-way ANOVA confirmed significant individual factors and interaction effects (p < 0.05). In practical implications, a 30°/ − 60° raster with 100% ID for optimal UTS, yield strength, and stiffness can be considered for strength-critical Applications. On the other hand, a 45°/ − 45° raster with ≥ 80% ID to maximize fatigue life and elongation, and it can be adopted in fatigue/ductility-critical applications. Low-frequency tests (≤ 0.5 Hz) minimize thermal artifacts, while higher frequencies (> 5 Hz) may overestimate service life in real-world dynamic loading.
Future studies may expand on the current work by examining other influential FDM parameters such as nozzle temperature, layer thickness, print speed, and build orientation. Investigations could also include fatigue crack propagation analysis through advanced microscopic characterization and fractography to gain insights into failure mechanisms at different raster orientations and densities. Additionally, expanding the scope to different polymeric materials (e.g., PLA, PETG, Nylon, and composites) would generalize these findings and inform broader engineering design standards. Exploring environmental effects, such as temperature, humidity, and long-term aging, would further enhance practical applicability, particularly in industrial and outdoor environments. Finally, implementing numerical modeling and simulation studies using finite element analysis could complement experimental data, enabling efficient prediction and optimization of fatigue behavior for complex FDM structures.
Declarations
Competing interest
The authors declare no competing interests.
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Static tensile and cyclic tension-tension fatigue testing investigation of 3D printed ABS materials: a comparative study of different infill orientation and infill density with statistical analysis
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