Effects of voids and raster orientations on fatigue life of notched additively manufactured PLA components

In this study, the fatigue life of notched polylactic acid (PLA) samples fabricated through the fused deposition modeling (FDM) technique was studied experimentally and numerically. The volumetric method based on the theory of critical distance was employed for fatigue life predictions. The effects of influential process parameters including raster orientation and FDM-induced defects such as voids or gaps inside the parts were examined on the fatigue strength reduction factors and fatigue lives. Circular and elliptical-shaped notch geometries were considered with various dimensions. Fatigue tests were conducted on notched and un-notched samples at the load ratio of 0.1. Predicted results were compared with experimental fatigue test data. Results revealed that the raster orientation parameter had a substantial impact on fatigue strength reduction factors and fatigue lives. The stress concentrations induced by the FDM process on the surfaces and inside the parts for the samples with 90° raster angles acted similar to the sharp notches, resulting in no substantial difference in fatigue life of notched and un-notched 3D-printed samples. In contrast, un-notched 3D-printed specimens with 0° raster orientations possessed higher fatigue lives as compared to the notched samples. While the volumetric approach efficiently predicted the fatigue lives of the samples with 90° raster orientations, it moderately underpredicted the fatigue lives of the samples with 0° raster angles.


Introduction
With the development of additive manufacturing (AM) techniques, also known as three-dimensional (3D) printing, the need for fabricating components with complex geometries is increasing. Several AM techniques have been developed for manufacturing metallic and polymeric parts [1]. The most commonly used material extrusion-based printing method for fabricating plastic components is fused deposition modeling (FDM). This technique has gained extensive popularity due to its simplicity, broad filament availability, and low cost [2,3]. In this technique, the raw plastic material passes through a heated nozzle; then, the filament is deposited over the previously laid layer of the part to form a desired shape [3]. During the FDM process, filament temperature reaches to the melting point to help the filaments stick easily to each other, followed by a relatively rapid cooling. Rapid solidification may cause residual stresses in the part, and often results in forming micro-cracks, distortion, deformation, and other types of defects [4]. Missing filament materials during the FDM process and air gaps or voids after the process are other type of defects in FDM-produced polymeric parts as compared to the conventionally manufactured plastic components. Defects such as voids or air gaps as well as rough surfaces of the parts can adversely affect the mechanical performance of the components [5][6][7]. Fayazbakhsh et al. showed that defects in the form of missing extrudates during the FDM process reduced the tensile strength of the AM PLA parts significantly [8]. Kerekes et al. [9] studied the damage and deformation of FDM-processed AM parts through conducting several tensile tests and employing inverse identification analysis. They observed that the area with premature pores in the intersection of infill and filament outline shell was the region where failures initiated from. In the FDM process, depending on the nuzzle diameter while fabricating the parts, surface roughness as well as the percentage of the voids or gaps inside the part can vary. Surface roughness and the stress concentrations induced by the intrinsic voids in the FDM-processed parts can have detrimental effects on the mechanical properties of the AM parts.
The orientation of the filament deposition during the process as well as the part build direction can also have major impact on mechanical characteristics of the AM parts [10,11]. It has been observed through various research studies that different AM plastic materials undergoing static or cyclic loadings behave differently with respect to the raster orientation. Ziemian et al. [12] reported anisotropic effects in both tensile strength and fatigue performance of acrylonitrile butadiene styrene 3D-printed parts. The authors showed that fatigue life of the samples in longitudinal (0°) and default (45/45°) raster orientations was noticeably higher than that of diagonal (45°) or transverse (90°) orientations. Afrose et al. [13] studied the influence of raster orientation on fatigue performance of PLA 3D-printed components. They observed that the parts in 45° build orientation possessed higher fatigue life than those fabricated with 0° and 90° raster angle while the samples were undergoing the same percentage of applied static loads. FDM manufacturing technique has other process parameters which can have significant impact on static and fatigue strength of the AM parts.
Most of the components in service contain at least one feature of geometrical discontinuities including key holes, notches, and grooves. These geometrical discontinuities adversely affect the performance of the parts being subjected to various load conditions including static, dynamic, impact, or cyclic loads. Due to distinct manufacturing characterizations, 3D-printed parts behave differently as compared to those parts manufactured through traditional techniques such as casting or injection molding. It is well known that existing a notch in a component can dramatically reduce its fatigue strength. A number of research studies can be found in the literature dealing with the effects of notches on static and fatigue performance of AM metallic parts [14][15][16][17][18] and polymeric components [19][20][21][22]. However, since the nature of 3D-printed metallic and polymeric parts fabricated through specific AM techniques is totally different, these components behave differently with respect to the notches as well. The Murakami model based on the √ area approach was successfully employed for predicting fatigue life of notched and un-notched Inconel 718 AM samples [23,24]. Molaei and Fatemi [25] studied fatigue characteristics of notched Ti-6Al-4 V and 17-4 PH stainless steel additively manufactured samples undergoing axial and combined axial-torsion variable amplitude loads. They reported that due to rough surface of the as-built sample, both notched and un-notched specimens could be treated as notched sample having different values of fatigue notch factors.
It is well known that the FDM fabrication technique involves many process parameters including anisotropy, surface roughness, and voids/gaps. While literature holds some research studies on the effects of FDMrelated intrinsic defects on the overall mechanical performance of the AM plastic parts [26,27], the influence of the voids or residual gaps on the fatigue response of the notched FDM-processed 3D-printed parts is yet to be fully understood. In this study, the focus is placed on the influence of the raster orientation factor and its effects on fatigue life of notched PLA samples fabricated through the FDM technique, taking into account the effects of intrinsic voids or residual air gaps in the samples. The numerical simulations were used to obtain the stress distributions along the line starting from the notch roots toward the edges of the notched specimens. These simulations take into account the effects of voids, since the voids between filaments are precisely simulated in FE models. The void geometrical features were taken from the scanning electron microscopy (SEM) images of the actual samples. The effects of raster orientations on fatigue response of the notched 3D-printed samples were considered both empirically and through the use of FE simulations and fatigue life predictions using volumetric approach. To do so, cycle-dependent fatigue strength reduction factors K � f (N) are employed to predict the fatigue life of notched samples based on a theory of critical distance (TCD) and using the available fatigue reference curve of the smooth neat PLA material. In the end, predicted fatigue lives using this approach are compared with those obtained via experiments, and the discrepancies in the results have been interpreted based on the manner of the failures in the specimens.

Notch effects
The S-N curve of notched components can be predicted using the S-N curve of un-notched samples. It can be considered that fatigue strength of un-notched samples at a certain life is K t times greater than that of notched specimen, where K t is the elastic stress concentration factor. This is the simplest and most conservative method of fatigue life prediction of notched samples. It is well known that fatigue notch factor ( K f ), which is defined as the ratio of smooth fatigue limit to the notched fatigue limit, is always smaller than the elastic stress concentration factor. One reason for this fact is that the stresses in the notched samples exceed the elastic limit even at low load levels, resulting in expanding plastic strain zone in the vicinity of the notch instead of increasing stress value. Fatigue notch factor can also be expressed based on notch sensitivity (q) as follows [28]: For an elastic-perfectly plastic model, three different values for K f can be determined based on the applied load level and yielding condition. For the cases of (i) no yielding, (ii) local yielding, and (iii) full yielding (completely reversed), , and K f = 1 , respectively [28]. In this equation, a is the stress amplitude, and y is the yield stress. However, for a wide variety of materials, the elastic-perfectly plastic model is not a suitable plasticity model and leads to erroneous results.

Strain-based approaches to fatigue
In this method, the total strain component which is the summation of elastic and plastic strain values is related to the number of cycles to failure. There are an extensive number of strain-based models and criteria which have been proposed to predict fatigue life. The conventional Smith-Watson-Topper (SWT) model [29] is one of the most commonly used strain-based approaches that can be used for fatigue life estimations of wide variety of materials. The SWT model can be expressed as follows: In this equation, , and c are the strain-based fatigue parameters related to both elastic and plastic lines of the − N curve. In order to use strain-based approaches such as SWT model to predict fatigue life, the above-mentioned fatigue parameters should be known. These parameters can be found in the literature for a wide variety of metals and alloys such as steels and aluminum alloys; however, they can rarely be found for AM materials due to the manufacturingrelated complexity and anisotropy of these components. Some strain-based fatigue parameters for a number of AM materials can be found in reference [30]. However, these parameters are limited for certain conditions and cannot be generalized.

Theory of critical distance
The most basic concepts on what is known as the theory of critical distance were proposed by Neuber [31] and Peterson [32]. Neuber assumed that the mean stress over a certain structural size which is also known as "critical distance" ahead of the notch could be used for evaluating notch sensitivity [31]. Based on the Neuber's relation, notch sensitivity can be obtained as follows: where is a material constant that can be determined through experiments, and is the radius of the notch root. Peterson assumed that fatigue failure occurs when the stress at a certain point ahead of the notch root reaches to the fatigue strength of the un-notched component [32]. Based on the Peterson's assumption of reducing stress in the vicinity of the notch tip linearly, the notch sensitivity can be expressed as follows: In Peterson's relation is a material constant and should be obtained experimentally. Although for some materials such as steels or aluminum alloys there can be found some empirically obtained material constants of Peterson's and Neuber's models, for other materials, these constants are not available and need to be determined through experiments. These material constants are not available for AM plastic materials, as well. Similar to the models proposed by Neuber and Peterson, there are other methods that can determine critical length parameters for cracks and can be adopted for assessing notch fatigue limits [33,34]. Research studies on fatigue assessments of AM materials based on the TCD theory are very limited [22,25].

Volumetric approach
To have a more precise fatigue life prediction of notched AM samples especially for notch-sensitive materials such as PLA, it is necessary to utilize a method which does not require complex constitutive models, and can be implemented for notches with different geometrical features. Volumetric approach which has been proposed by Pluvinage [35] is based on the theory of critical distance approach and can be considered a powerful candidate for fatigue life prediction of the notched components. In this approach, determining the magnitudes of effective stress and the effective distance is of great importance. The effective distance is a length measured from the notch root at which the fatigue phenomenon is expected to occur. The effective stress is defined as the average of the weighted stresses over effective distance [35]. Figure 1 shows a typical elastic-plastic stress distribution and stress gradient ahead of a typical notch in a notched specimen. The relative stress gradient can be defined as follows: Three distinct zones in Fig. 1 are recognized each having important characteristics. These zones are named as zones I, II, and III. Zone I corresponds to a distance calculated from the notch root to the point with maximum stress value. The stress value experiences a reduction in zone II until its value reaches to the effective stress. This point corresponds to the minimum stress gradient. The effective distance has been found to be the limit between zones II and III. For the cases where plastic strain components do not exist, the stress value at the notch tip is the maximum, and zone I vanishes. According to this method, fatigue notch factor can be obtained using the following formula: In this equation, X eff is the effective distance, n is the net stress, and yy is the stress along the loading direction. After obtaining fatigue notch factors, the reference fatigue curve of smooth specimens can be utilized for fatigue life prediction of the notched samples.

Materials and specimens
The AM samples were fabricated at 0° and 90° raster orientations. The nozzle diameter of conventional FDM 3D printer devices varies usually between 0.2 and 0.8 mm. This parameter impacts the quality and overall mechanical properties of the plastic specimens being 3D printed. In this research, the largest possible nozzle diameter (D = 0.8 mm) was chosen in order to highlight and to have a better understanding of the effects of residual gaps or voids on fatigue performance of 3D-printed notched samples. Also, three different notch shapes were selected, one circular shaped with r = 2 mm, and two elliptical shaped with b/a ratio of respectively 0.5 and 0.25 (a = 4 mm is the large diameter and b is the small diameter of the ellipse). Figure 2 shows the schematic views of the samples at 0° and 90° raster orientations as well as the geometry of the samples and notches.

Static and fatigue tests
Quasi-static tests of 3D-printed samples were conducted using SANTAM STM-150 universal testing machine to obtain the stress-strain curves of the un-notched samples. Three tests according to ASTM D638 standard were carried out for each condition and the average value of the ultimate tensile strength (UTS) was calculated. The tensile strength of the PLA filament or that of injection molded could be quite different with the strength of 3D-printed parts [13].
Fatigue tests were carried out using Instron 5900 series fatigue testing machine at frequency of 0.5 Hz and load ratio of R = 0.1. Cyclic loads were selected based on certain percentages of the UTS values of the samples. Experimental fatigue test data is the average of three tested specimens at each load level.

FE simulations
During the FDM process, the filaments are deformed and some gaps or voids remain between the filaments, producing a part with a density lower than 100%. This phenomenon is shown schematically in Fig. 3a. The gaps have been observed in actual PLA specimens using SEM technique, as shown in Fig. 3b. The average distance between the edges of the voids was found to be approximately 0.2 mm. It is well known that most FDM-processed AM components show large level of anisotropy; however, in numerical simulations, these parts may be treated as isotropic materials. In this study, the gaps between the filaments are simulated in FE analyses to obtain more accurate results. Figure 4 shows the way samples with 0° and 90° raster orientations were modeled in FE simulations. In Fig. 4a, filaments are parallel to the loading direction, while in   Fig. 4b, the load is applied perpendicular to the filament direction. The numerical simulations were performed using the ABAQUS software to obtain stress distributions along the lines starting from the notch tip toward outside of the notched samples.
In this study, the static and fatigue properties of pure PLA material are used for respectively (i) FE simulations to obtain stress distributions, and (ii) fatigue life predictions based on the volumetric approach. The stress-strain curve of the generic pure PLA material available in ref. [36] was used in FE simulations to define the kinematic hardening model. Figure 5 illustrates the stress-strain curves of un-notched samples at 0° and 90° raster orientations. The standard divisions (SD) of test samples with 0° and 90° raster orientations were 1.8 MPa and 2.2 MPa, respectively. The monotonic response of neat PLA [36] has also been included in Fig. 5. The ultimate tensile strength of the 3D-printed sample at 0° raster angle was 68% of the neat PLA material. Afrose et al. [13] reported that this ratio could roughly vary between 60 and 64%. Figure 6 shows the S-N curves of un-notched and notched samples as well as the reference fatigue curve of PLA material. The reference curves, which will be used to predict fatigue life of notched samples, were plotted based on the fatigue test data for the neat PLA samples available in ref. [36]. Since the fatigue test data of 3D-printed samples and that of reference fatigue curve are in different load ratio, both sets of fatigue test data were converted to the completely reversed condition loading (R = − 1) using the SWT parameter ar = √ max a [29]. The S-N curves of the samples with 90° raster orientation clearly indicate that the impact of stress concentration caused by the FDM process was greater than that of notches, as evidenced in Fig. 6b. In fact, 3D-printed un-notched samples with 90° raster orientation behave similarly to the notched samples. This is mainly due to poor bonding between the filaments where the load tends to separate filaments from each other. In such case, micro-cracks initiated in the vicinity of the notch holes where the filaments poorly bonded to each other and then propagated very rapidly through the interface of the filaments, as evidenced schematically in Fig. 7a. A crack initiation site as well as its propagation path is shown in Fig. 7b, indicating that the effects of intrinsic cracks and discontinuities were more prominent than that of notches. This effect was observed to be more dominant in low cycle fatigue regime. This was not the case for the samples with 0° raster orientation. Fatigue strength of un-notched samples at 0° raster angle was noticeably higher than those of notched specimens (see  Fig. 6a). For the case of samples with 0° raster angle, cracks need to propagate along a line perpendicular to the filament direction, resulting in an increased number of cycles to failure as compared to the samples with 90° raster orientations. Since 3D-printed PLA material acts similar to brittle materials, the components of plastic strains compared to the elastic ones can be negligible. Therefore, the S-N curves of the un-notched PLA samples can be used for determining fatigue strength coefficient and fatigue strength exponent based on the Coffin-Manson relation [28]:

Results
In this equation, ar is the stress amplitude for the completely reversed loading condition. The calculated fatigue parameters based on the experimental fatigue  [36] test data of the smooth specimens are summarized in Table 1. The data presented in Table 1 can be implemented for fatigue life prediction purpose for any notched samples at 0° and 90° raster angles. These data are based on the best curve fit of the average fatigue data of the unnotched 3D-printed PLA samples. However, the maximum stress at the notch root could be noticeably greater than the effective stress value at which fatigue occurs. Therefore, to obtain more accurate results, the effective stress at the effective distance should be used for fatigue life predictions. Figure 8 illustrates the stress distributions and relative stress gradients for notched samples at 0° raster orientation undergoing the same nominal stress of 12.3 MPa. Similar graphs have been plotted for samples with 90° raster orientation at all load levels ranging roughly between 50 and 80% of the UTS values.

Discussions
The diameter of filaments was the same for all notched 3D-printed samples. However, during FDM fabrication process due to pressure and gravity, the filaments deform and partially merge with previously laid filaments, producing layers with thickness less than filament diameter. It was found that the effective distances for the notched samples varied roughly between 0.05 and 0.18 mm for the samples with 0° raster angle and 0.18-0.25 mm for the sample with 90° raster orientations. The stress distributions and relative stress gradients as well as the effective distances were utilized to obtain the notch strength reduction factors for all notched samples and at all load levels. Figure 9 illustrates the notch strength reduction factor values versus the parameter b/a for the samples with respectively 0° and 90° raster orientations.
As seen in Fig. 9 and as expected, the notch strength reduction factors decrease with increasing notch tip radius. A drop in the value for the case of 0° raster angle at S = 19.6 MPa is due to the larger plastic strain component as compared to the other cases. Notch strength reduction factors can be used to predict the fatigue life of the notched samples as long as the smooth fatigue reference curve is known. Fatigue life predictions were fulfilled for the notched samples based on the available fatigue test data of the neat PLA material and cycledependent fatigue strength reduction factors. The predicted fatigue lives were compared with experimental fatigue test data, as evidenced in Fig. 10. In this figure, the dashed lines indicate the upper and lower scatter bands with the factor of ±2.
The majority of predicted life data through the use of volumetric approach fell within the factor of ± 2. This approach was efficient in estimating the fatigue life of samples with 90° raster orientation having elliptical notch shape. A slight overestimation for the case of circular notched samples with 90° raster angle is due to the effects of discontinuities between the filaments and stress concentrations in these areas. The impact of stress concentrations due to the rough surface for the samples with 0° raster orientations was much less than that of the samples with 90° raster angles. That is why the predicted life results through this approach showed slightly underestimation for the elliptical notched specimens with 0° raster orientations. A relatively similar phenomenon can be found in ref. [25] in which rough surface of the unnotched as-built surface of AM metallic specimens acted as a local notch, resulting in decreased fatigue life.

Conclusions
Fatigue life of FDM-processed notched PLA samples was studied experimentally and numerically. The volumetric approach based on the theory of critical distance was utilized to obtain effective distances, fatigue notch factors, and fatigue lives. The effects of two different raster orientations were studied on the fatigue life taking into account the influence of voids between the filaments in the samples. Overall, the fatigue life predictions through the use of volumetric approach were closely agreed with those obtained through experiments. It was observed that FDMinduced stress concentrations in the specimens acted similar to a notch, and were more noticeable for the samples with 90° raster orientation as compared to those samples with 0° raster angles.
Funding This research was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC under grant RGPIN-217525). The authors are grateful for their support.

Data availability
The data presented in this study are available on request from the corresponding author.

Declarations
Ethics approval All professional ethics have been followed.

Consent to participate Not applicable.
Consent for publication Not applicable.

Conflict of interest
The authors declare no competing interests.