Mechanical Properties of AM Polymer Specimens Under Bending Stress

Abstract

Additive Manufacturing, or 3D Printing, is based on manufacturing physical objects by sequential deposition of layers of material. Although the usage of AM is growing, no straightforward methodology exists to produce parts with specific, or optimized, mechanical properties. In this work, an approach for optimizing the mechanical properties of AM specimens under bending stress is presented, using DOE. For the experimental procedure, Fused Deposition Modeling (FDM) technology was used along with Polylactic acid (PLA) as the in-process material. Nozzle temperature, printing speed, infill pattern and printing orientation were selected as manufacturing factors to be optimized to achieve so maximum load and deflection to be acquired. Both optimized sets of values were increased by 53% and 28%, respectively, and were experimentally checked to validate the accuracy of the approach.

1. Introduction

Additive Manufacturing (AM) is a term that describes the technology which manufactures three dimensional objects by adding material instead of removing material from an existing billet (Subtractive). In comparison with traditional manufacturing methods, Additive Manufacturing is relatively fast, simple and cheap, making the manufacturing procedure ideal for prototyping. It does not involve tools, dies or complex machinery and therefore has a wide range of applications in the aerospace, automotive, healthcare and product development industries. In addition, additive manufacturing has the advantage of creating complex geometries that cannot be reproduced by any other manufacturing method. This advantage makes AM a unique manufacturing process, as models can be designed and manufactured specifically for certain applications with enhanced mechanical behavior, without geometrical restrictions based on the manufacturing process [1].

Despite the innovation and the simplicity behind AM technology, most AM manufacturing industries for polymers are mostly focused on producing specimens that do not require substantial mechanical properties. Therefore, information regarding mechanical properties and how the manufacturing procedure affects the mechanical behavior of the component is scarce. The research community demonstrates strong interest in this field, as the number of papers is quite high [1,2,3,4,5,6,7]. Thus, it is crucial to track and understand the importance of the 3D printing parameters to model and predict the mechanical properties of an AM produced component.

Fused Deposition Modeling (FDM) is a broadly implemented AM technology due to its competent accuracy, low cost and large material selection. FDM manufacturing is an AM technique that extrudes thermoplastic polymer in filament form and deposits it in required areas. The material passes through a heated nozzle of specific diameter, so the item can be manufactured through a layer-by-layer procedure. If the nozzle diameter is reduced, the printing accuracy and the level of detail is increased; however, at the same time, the time required to finish the manufacturing process is increased.

FDM is an AM approach which depends on many variables and parameters which might affect the mechanical behavior of the produced component. As the FDM procedure is based on building a component layer-by-layer, the overall mechanical properties and the behavior of the component are subject to the bonding strength between the layers; consequently, all factors selected for the analysis will be focused on that aspect.

A number of recent studies have investigated the mechanical properties of PLA, particularly under bending stress. A closer look at the latest literature provides a clearer understanding of the strengths and limitations of current research in this area. Recent studies have reaffirmed that print orientation plays a pivotal role in determining the mechanical properties of AM parts. A study by Zhang et al. [8] found that the bending strength of PLA printed along the Z-axis (vertical direction) is notably weaker compared to the X- and Y-axis due to weaker interlayer adhesion. This aligns with earlier findings by Zhou et al. [9], who concluded that parts printed in the horizontal orientation (X- and Y-axis) exhibit higher flexural strength. However, both studies fail to investigate how the layer thickness interacts with orientation affecting the overall bending performance. Moreover, while these studies provide useful insights into print orientation, they often neglect the complex interplay between orientation and infill patterns, a factor that has been shown to influence mechanical properties significantly, as demonstrated by Lee et al. [10].

The recent literature emphasizes the importance of process parameters in influencing the mechanical properties of PLA. Martínez et al. [11] explored the effects of infill density on the flexural strength of PLA and observed a direct correlation between higher infill densities and increased strength, with diminishing returns beyond certain density thresholds. Similarly, Singh et al. [12] found that layer height has a noticeable effect on flexural stiffness · with smaller layer heights improving both strength and stiffness due to better interlayer bonding. However, these studies also reported inconsistent results across different print speeds, with some showing improved mechanical properties at slower print speeds (due to better layer bonding) while others found little to no interrelationship. This inconsistency may be attributed to differences in the printing equipment and material batches used, further complicating our understanding of how printing speed influences bending resistance in PLA.

One critical challenge in the field is the lack of standardized testing methods across studies. Many recent studies, including those by Sánchez et al. [13] and Gao et al. [14], employed different testing geometries (e.g., three-point vs. four-point bending) and specimen dimensions, making it difficult to compare results. Inconsistencies in testing speeds and environmental conditions (such as temperature and humidity) further complicate the interpretation of results. Standardizing the testing conditions for PLA specimens under bending stress is essential to achieve reliable and comparable data across different research efforts.

2. Materials and Methods

In order to be able to model an FDM manufacturing procedure, the most important controllable parameters will be selected so as to retrieve information about (a) the impact of each individual parameter and (b) how each parameter affects and contributes to the overall mechanical properties to predict the mechanical properties of the produced components. The specimens were tested under bending stress and, therefore, the model which will be created will be based on a specific type of stress.

Furthermore, Taguchi’s Design of Experiment (DOE) will be used to model the FDM manufacturing process. The specific statistical tool is able to analyze each selected parameter’s impact and its contribution to the overall control parameter, which, in this case, is the mechanical properties acquired. By dictating a pre-set and a minimum number of experiments, each level of the parameter selected is evaluated independently. As a result, Taguchi’s DOE can predict the outcome of an experiment given certain pre-sets of values [15], and, therefore, modelling mechanical properties regarding certain parameters is possible.

2.1. Parameters

2.1.1. Temperature

The first selected parameter is the hot-end temperature of the nozzle, to which the filament is heated prior to its extrusion. During filament extrusion, the temperature of the extruded material is significantly higher compared to the previous layer due to cooling [2]. By increasing the temperature of the nozzle, both layers’ atomic diffusion mechanism is increased, resulting in a stronger bond between the layers. Simultaneously, the temperature difference between these consecutive layers causes the hot layer to expand while the colder layer contracts. As both layers cool down, they are contracting at different rates, provoking the development of shear forces between them, causing the layers to bend and in some cases leading to delamination. The exerted stresses between layers have a detrimental impact both on mechanical behavior and printing quality, as well as causing cracking or warping which can be visible macroscopically from the outer layer. Therefore, temperature selection is crucial to achieve better mechanical performance by decreasing stress development and enhancing bonding. The selected range of the hot-end temperature is between 180 °C and 210 °C, fulfilling the filament manufacturer’s recommendations and ensuring the printability of the specimens.

2.1.2. Speed

The second selected parameter is the printing speed. In terms of mechanical properties, printing speed has an ambiguous aspect in rapid prototyping. High printing speeds generally have a negative impact on the quality outcome of the produced component as they exacerbate inertia forces by increasing the moving parts’ momentum [16]. When printing speed increases, the force required to stop each carriage is increased as well. Therefore, when a change of movement is required, the jerk is higher, reducing the quality of the produced component. At the same time, high printing speed reduces the time between each nozzle pass from the same point along the horizontal plane. Therefore, the temperature difference of the two sequential layers is reduced and the effect of layer separation and warping is reduced, increasing mechanical properties.

The range of printing speed is selected between 25 and 50 mm/s, ensuring the printability of the specimens. In general, 50 mm/s is considered fast while 25 mm/s is generally a slow speed. As the printing speed is reduced, the filament driving motor is required to slow down to prevent over-extrusion. A 25 mm/s printing speed is neatly above the lower limit of the extruder stepper motor. If the speed is decreased even further, the motor might not be able to provide a consistent flow of extruded filament.

2.1.3. Infill Pattern

Infill pattern describes the internal structural geometry of an AM produced component. In order to limit material consumption and allow a reduced-weight component to be produced, all AM processes have the ability to print partially hollow or even hollow components by applying structural geometry to the inner part of the component. Therefore, mechanical properties are highly related to the infill pattern and the density of the pattern, as both variables are adjustable [3]. The rigidity and the mechanical properties are enhanced by increasing the infill percentage. Infill pattern density will remain constant for this experiment.

The shape of each infill pattern causes different force allocations and, consequently, different patterns have varying effects on the mechanical properties of the component based on stress distribution (Figure 1) [3]. Furthermore, by giving the same infill percentage, each pattern has different amount of material deposited and, therefore, each pattern has a unique material/infill ratio, which affects the mechanical performance [17]. In the present study, three patterns were selected, each one with a different orientation (

Table 1. Selected DOE levels of the infill patterns.

Factor	Level 1	Level 2	Level 3
Pattern	Rectilinear	Full Honeycomb	Triangle
Orientation	45°/−45°	0°/120°/−120°	0°/60°/−60°

) [18].

2.1.4. Print Orientation

The last selected DOE parameter is printing orientation. Printing orientation is an important aspect regarding the mechanical properties of a manufactured component, as the infill and the outer shell orientation depend on the placement of the component upon the printing bed [19,20]. In general, the infill pattern is virtually a 2D pattern extruded along the vertical axis. Therefore, the produced components display anisotropic behavior which affects the mechanical properties [21]. By changing the printing orientation, the direction of the infill pattern is affected as well as the mechanical properties of the tested object [22]. Overall, the strongest produced specimen is obtained when the fused filament deposition coincides with the pull direction; however, not all ranges of coincidence have been analyzed [19]. There are three possible options regarding the infill orientation (Figure 2). The blue arrows indicate the direction of the infill pattern, and each direction is parallel to one of the three vectors of the coordinate system. In addition, the assumption that the stress load will be placed along the Z-axis for each specimen is made. The orientation levels are given in

Table 2. DOE—Orientation Levels.

Level 1	Level 2	Level 3
Along X-axis (a)	Along Y-axis (b)	Along Z-axis (c)

.

During manufacturing of the specimens, different placements of the bed can be arranged for each individual specimen. In case (a), the bottom of the specimen is placed at the printing bed’s surface (Figure 2). In case (c), the cross section of the specimen is placed at the bed’s surface and the length of the specimen is therefore printed along the Z-axis. However, in case (b), the orientation was difficult to accurately manufacture as the infill pattern direction needed to be along the Z-axis. To compensate for this limitation, the printing orientation will be the same as case (a), but, during bending test, the specimen will be rotated 90° along the Y-axis.

2.2. AM Model Settings

FDM has numerous parameters that can be adjusted for the manufacturing procedure. Instead of the four controlled parameters, all other selected settings were kept the same for all experiments so as to exclude their effects on the mechanical performance [18]. Regarding the hardware selection, the nozzle-end diameter was selected equal to 0.4 mm. The specific nozzle selection dictates an optimal layer height of 0.2 mm [17]. Furthermore, the infill percentage was set to 60%, the outline overlap was set to 15% and the outer shell consisted of 2 solid layers, while both the bottom and the upper layer consisted of 3 solid layers with a rectilinear infill pattern. Lastly, during the deposition of the first layer, the cooling was disabled and the speed was rated down to 10% so better adhesion with the built platform to be achieved.

As presented in the clause 2.1, based on the selected factors and their levels, an L9 orthogonal Taguchi Array was used as the base for the DOE. The values of each factor are presented in

Table 3. Taguchi L9 DOE.

Experiment (S/N)	Temperature (°C)	Speed (mm/s)	Infill Patterns	Orientation
1	180	25	Rectilinear	X
2	180	37.5	Honeycomb	Y
3	180	50	Triangle	Z
4	195	25	Honeycomb	Z
5	195	37.5	Triangle	X
6	195	50	Rectilinear	Y
7	210	25	Triangle	Y
8	210	37.5	Rectilinear	Z
9	210	50	Honeycomb	X

for each of the 9 experiments based on the L9 Taguchi orthogonal Array and the above analysis.

2.3. Three-Point Bending Experiments

The experimental procedure and the specimen design were based on the ASTM D790 specification. A Galdabini QUASAR 100 of max load of 100 kN, which is a dual column benchtop testing machine, was used. All specimens had an 8 mm square section and were 120 mm in length. The load rate was set to 0.1 mm/s and the support pins were placed at a distance of 60 mm; thus, the active length of the specimen was the half of its total length (Figure 3).

3. Results

All three-point bending experiments were implemented and the results (max Load, max Deflection) along with the parameters of each experiment are given in

Table 4. Taguchi L9 DOE with results.

Experiment (S/N)	Temperature (°C)	Speed (mm/s)	Infill Pattern	Orientation	Max Load (N)	Max Deflection (mm)
1	180	25	Rectilinear	X	174.5	3.50
2	180	37.5	Honeycomb	Y	169.0	2.50
3	180	50	Triangle	Z	170.0	1.76
4	195	25	Honeycomb	Z	108.0	1.38
5	195	37.5	Triangle	X	194.0	3.50
6	195	50	Rectilinear	Y	191.0	3.25
7	210	25	Triangle	Y	215.0	2.42
8	210	37.5	Rectilinear	Z	126.5	1.73
9	210	50	Honeycomb	X	192.5	3.50

. Moreover, flexural stress–strain diagrams were created (Figure 4).

The maximum Load and maximum Deflection prior to fraction are presented for each experiment (Figure 5).

DOE Analysis

Applying Taguchi’s analysis, it is possible to determine the impact of each parameter on the mechanical performance of the specimen. Therefore, it is possible to model the engineering behavior and predict the mechanical properties for any combination of the manufacturing settings.

The procedure is applied for both load and deflection and, therefore, two optimal conditions with enhanced behavior can be predicted.

As can be observed in

Table 5. Impact Analysis—Maximum Load.

Level (S/N)	Temperature (°C)	Speed (mm/s)	Infill Pattern	Orientation
1	171	165.7	163.8	186.8
2	164.3	163.2	156.5	191.7
3	178	184.5	193	134.8
Delta	13.7	21.3	36.5	56.8
Impact	10.7%	16.6%	28.4%	44.3%
Rank	4	3	2	1

, orientation is the most crucial parameter, regarding maximum load, by affecting 44.3% of the total maximum load. In addition, when orientation is set along Z plane, the component becomes brittle and the maximum load diminishes, while the other two present just a small difference between each other while Y orientation is the best option.

The next most important factor is the infill pattern, by affecting 28.4% of the maximum load. The triangle pattern is the best option compared to the other two, and has the most beneficial effect on maximum load. In comparison, the rectilinear and honeycomb patterns interact by reducing the maximum load, while, of the two, rectilinear is a better option.

Printing speed is the third most important factor, by affecting 16.6% of the maximum load. Maximum speed of 50 mm/s has the most positive impact on maximum load. The other two options related to speed have less impact on the maximum load

Finally, printing temperature is the least significant factor, affecting 10.7% of the maximum load. The optimal option for maximum load is the highest temperature of 210 °C, and the temperature of 180 °C followed. This behavior indicates that the effect of temperature on the mechanical properties of the produced component is not single-dimensional. The significance of the printing parameters can be verified by the impact analysis on Figure 6.

By combining the best outcome for each parameter, the overall load can be maximized. The optimal parameter combination can be seen in

Table 6. Settings for Maximum Load (Prediction).

Temperature (°C)	Speed (mm/s)	Infill Pattern	Orientation	Predicted Load (N)
210	50	Triangle	Along Y	233.7

. Then, by using these parameters as inputs in Minitab 19, a prediction of the maximum load can be made, resulting in 233.7 N, which is 8.7% higher than the maximum tested case.

Based on the data in

Table 7. Impact Analysis—Maximum Deflection.

Level (S/N)	Temperature (°C)	Speed (mm/s)	Infill Pattern	Orientation
1	2.587	2.433	2.827	3.5
2	2.71	2.577	2.46	2.723
3	2.55	2.837	2.56	1.623
Delta	0.16	0.403	0.367	1.877
Impact	5.7%	14.4%	13.1%	66.9%
Rank	4	2	3	1

for optimal deflection, the major parameter affecting the elastic property of the specimen is the orientation. In comparison to the study of optimal load, orientation is responsible for 67% of the total deflection and therefore outperforms the other parameters. By observing Figure 7, we can observe that orientation along the X-axis is the optimal, while the other two options give lesser results. The worst case is the Z-axis orientation. Similarly, as the Z-axis makes the component brittle, the deflection is minimized and therefore a behavior like this is expected [23]. Furthermore, Y-axis orientation is almost in the middle point of the other two values, producing lesser results compared to X-axis, but better compared to Z-axis values.

The second most important parameter is the printing speed. Speed is responsible for 14.4% of the deflection, while the 50 mm/s values give the best maximum deflection. The other two values give lesser results, while the relationship of the values is close to linear.

In addition, the infill pattern parameter is the third most important parameter. The rectilinear value is the best option for maximum deflection, while honeycomb and triangle have nearly the same effect, with the triangle value being slightly better. Both speed and infill pattern have similar impacts on the overall deflection value, as the infill accounts for 13.1% of the deflection.

Finally, printing temperature is the parameter with the least significance, accounting for 5.7% of the deflection. The best deflection can be expected at 195 °C, while both other values produce similar results, with 180 °C being slightly better.

By combining the best outcome for each parameter, the overall deflection can be maximized. The optimal parameter combination is given in

Table 8. Settings for Maximum Deflection (Prediction).

Temperature (°C)	Speed (mm/s)	Infill Pattern	Orientation	Predicted Deflection (N)
195	50	Rectilinear	Along X	4.03

. Then, using these parameters as inputs in Minitab 19, the maximum deflection can be predicted as 4.03 mm, which is 15.1% higher than the maximum tested case.

As the final step of the analysis, a validation run for both the optimal specimens was implemented to verify the findings and evaluate whether the optimal conditions for both cases had been met (

Table 9. Experimental Results on Optimal Predicted Specimens.

Optimal Predicted Force		Optimal Predicted Deflection
Force (N)	Deflection (mm)	Force (N)	Deflection (mm)
330	3.6	279.5	4.78

).

By reviewing the optimal maximum force specimen, we observed that the mechanical properties were enhanced, as the maximum force was 330 N, which is the highest measured value out of all nine DOE experiments, approximately 53.5% higher than the maximum value of the tested experiments.

As observed in Figure 8, the “optimal load” specimen displays unexpected brittle behavior, as it failed almost instantly after passing the maximum force point. This kind of behavior was not expected, as specimens with Y-axis-level orientation tend to have ductile behavior. Further observation on the “optimal deflection” specimen revealed that the same pattern appears, as the specimen has enhanced mechanical properties that are even higher than the DOE estimation. The measured deflection was 4.38 mm, which is the highest measured deflection out of all examined specimens, increased by approximately 25.1% related to the maximum value of the tested experiments.

4. Discussion

During experimental design and the experimental procedure, a few issues arose which made the experimental procedure challenging, as the 3D printer used was not an industrial printer but rather an open-source desktop printer. One such challenging problem was faced during the manufacturing procedure of the specimens that were printed along the Z-axis. These specimens did not manage to have adequate bed adhesion, and many prints therefore failed to achieve the manufacturing tolerances complying with the related standards; thus, these specimens were reprinted until they were within tolerances.

Regarding data analysis, modelling both maximum load and deflection parameters, it is possible to predict the mechanical behavior of each component under bending stress.

Regarding each parameter independently, the most crucial parameter for both models is the printed orientation. When Z-axis orientation was selected in both cases, the mechanical behavior was the least. Z-axis orientation made the specimen brittle and both maximum force and deflection were significantly reduced. Regarding maximum load, two values produced similar results; however, regarding elongation, the best option was the X-axis orientation.

The printing speed parameter was the second most important parameter for deflection and the third regarding the load. However, printing speed has a similar impact on both properties by accounting for 14.4% of total elongation and 16.6% of total load. For both properties, a 50 mm/s value has the most beneficial effect. As mentioned, by maintaining a higher velocity along the horizontal plane, the time required for each pass from the same point is decreased.

Therefore, during deposition, the temperature of the sub-layer is higher and the rate of diffusion is increased, increasing the adhesion strength between the two bonding layers. Additionally, infill pattern is the second most important parameter regarding maximum load and the third most important parameter regarding deflection. Infill pattern is considered one of the most important factors regarding strength, which is confirmed as it accounts for 28.4% of the total maximum load, while it accounts for 13.1% of the total deflection.

For both optimized cases, the honeycomb pattern produced the worst results, indicating that the shape of the pattern has more impact compared to material density. Honeycomb is the pattern with the highest material consumption as, for the same infill percentage, it deposits more material compared to other options. The rectilinear pattern is the best option regarding optimal deflection, while the triangle pattern is the best option for optimal load.

To determine the interaction between the infill pattern and the infill percentage, further study is needed. This can be carried out by reviewing the total pass of the same specimen with the same infill percentage but a different pattern. Using this method, the infill percentage–pattern efficiency can be determined.

Finally, hot-end temperature is the least important aspect for both studies. This is probably due to the selected range, which was determined according to the manufacturer’s suggestions to preserve consistency. The selected temperature range was relatively small. Thus, the provided ranges are optimal in order to maintain stable manufacturing conditions and therefore the impact is minimal. Further research could consider an extended temperature range in order to obtain a better overview of the best selected temperature range regarding enhanced mechanical behavior.

Furthermore, upon reviewing all constructed specimens, no significant delamination was presented. The delamination effect may be visible in lower infill percentages, as the accumulative bonding strength is lower. Other studies could examine the possibility of delamination by adjusting the printing settings that could affect material bonding, such as temperature, printing speed, infill pattern and infill percentage [22,23].

However, a variation was observed between the experimental optimal values and the predicted values from DOE for both models. The selected optimal models have the best mechanical performance out of all experiments and the mechanical behavior was even greater compared to what was expected.

Additive manufacturing and especially FDM-based AM displays anisotropic behavior. The models demonstrated that predicting the mechanical properties of a component produced by a specific AM manufacturing method is rather challenging, as there are a lot of variances taking effect at the same time.

Taguchi’s analysis is heavily based on a mean-based model to both calculate parameter impacts and estimate values for each selected case; consequently, the prediction and the impact data retrieved from the experiment only have quantitative value and not qualitative. Further research to determine the actual reason for the variances encountered and potential models to be applied is ongoing.

In summary, it is safe to assume that the selected model has enhanced mechanical behavior and it is safe to consider the impact of each parameter quantitatively. In future work, an AI tool is proposed to predict the mechanical properties of AM specimens subjected to standard mechanical tests.