1. Introduction
In recent years, the field of the Additive Manufacturing (AM) or 3D printing has experienced an uninterrupted rise [
1]. This technology consists of adding material in a layer-by-layer fashion to fabricate the final three-dimensional part, normally from a CAD model. The main causes of its growth are its design freedom, which enables the production of complex-shaped components that are hardly obtainable by other manufacturing methodologies, as well as its cost-effectiveness [
2]. The AM technologies can be classified based on many criteria [
3]. According to the deposition method, a wide variety of printing technologies exist: Multi-Jet Fusion (MJF) [
4], Selective Laser Melting (SLM) [
5], Electron Beam Melting (EBM) [
6], and Fused Filament Fabrication (FFF) [
7], among others. This work was focused on FFF, also called Fused Deposition Modeling (FDM), which is one of the best established AM technologies.
In FFF, a thermoplastic filament is heated a few degrees above its glass transition temperature and extruded through the heated nozzle, then placed to form a layer. This newly deposited layer solidifies and bonds with previously deposited ones, forming the desired 3D geometry [
8]. The main setting parameters are sample orientation, printing pattern, and layer thickness. The most remarkable features of FFF encompass reduced weight and material use to operating with a wide range of polymeric materials [
9]. Furthermore, FFF parts are extensively used for rapid prototyping in many industries such as aerospace, automobile, medical, electronics, etc. [
10].
In contrast, one of the key characteristics of AM materials, which is not an exception for FFF, is that the properties of the final parts differ from those of their raw material. It has been shown that these properties strongly depend on the manufacturing process parameters [
11,
12], but this dependency is not yet fully understood. This lack of knowledge regarding the process properties’ dependency increases the printing randomness and causes a dispersion of the mechanical properties of the final printed parts [
13], making the FFF technology less attractive from the industrial point of view.
This issue has been extensively studied in recent years. Related investigations can be basically classified between those that study the dependency and the influence of the process parameters on the final properties of the printed part [
14,
15,
16,
17,
18,
19,
20,
21,
22] and those that explicitly characterize these properties for a set of specific process parameters [
23,
24,
25]. Their main findings conclude that, on the one hand, the stiffness in the build direction is the weakest one due to inter-layer unions (also known as the inter-layer adhesion issue) and, on the other hand, the resistance in the direction of the extruded filament is higher than the one of the intra-layer unions. Moreover, the properties of FDM parts in the direction perpendicular to the deposition orientation have been found to be more dependent on the bonding effect than on the properties of the raw material itself [
26]. Finally, several rheology-centric investigations have been carried out [
27,
28,
29,
30]. These investigations express the need for careful rheological knowledge to achieve stronger 3D-printed parts, highlight the importance of viscosity, temperature, pressure, and shear rate in material extrusion processes [
31]. A common aspect in all these studies is the fact that the whole 3D-printed part is considered as a single material that shows an anisotropic behavior. Since multiple printing patterns are employed during the manufacturing process, this approximation does not truly represent the underlying physics of the case.
In this work, the mechanical behavior of FFF parts was represented by a three-zone model distinguishing among the following zones: cover, contour, and inner (
Figure 1). Each zone corresponded to a different printing pattern: covers were printed with crossed filaments; contours were printed with aligned filaments; and inner zones could adopt several different patterns, the most common being the ±45° pattern. The distinction between covers (horizontal surfaces) and contours was made based on the surface angle with respect to the horizontal printing plane: covers had a slope below 30° and contours above that threshold. Two different types of inner zones existed: in-fill and lattice structures. The in-fill type refers to a standard pattern defined by both its geometry and air gap, while the lattice consists of a structure made of a periodically repeated unit cell.
In previous papers [
32,
33], this three-zone model was used in order to characterize the properties of printed parts for Polylactic Acid (PLA) and General Purpose Acrylonitrile Butadiene Styrene (ABS/GP), respectively. The novelty of this paper was to extend this background to Polycarbonate Acrylonitrile Butadiene Styrene (ABS/PC) and to use dimensional analysis to reduce the number of required experiments and to generalize the non-dimensional mechanical properties for different materials. The major advantages of using dimensional analysis are the reduction of the number of parameters involved in the problem, the possibility to extrapolate the results to non-tested materials, and a better understanding of the dependencies among the involved parameters [
34]. The study of the inter-layer adhesion effect is of special interest, which depends to a large extent on the material through temperature-dependent properties [
35,
36]. Thus, this work also aimed at a better understanding of the adhesion phenomena and the identification of which mechanical properties were adhesion independent. ABS/PC was the chosen raw polymer used in this paper because polycarbonate materials are known to exhibit poor adhesion strength [
37].
The paper is organized as follows. First,
Section 2 presents the three-zone constitutive model.
Section 3 describes the experimental procedures followed (i) to characterize, through tensile tests, the contour and top and bottom covers and (ii) to validate, through bending tests, the obtained data. In
Section 4, the solution strategy used for the computational simulations employed to obtain the inner zone properties is explained.
Section 5 discusses the obtained results, and
Section 6 introduces the proposed dimensional analysis of the three-zone model. Finally, the paper’s concluding remarks and possible future research lines are presented in
Section 7.
2. Material Characterization
The raw material used in this paper was ABS/PC for 3D printing manufactured by ELIX Polymers, which behaves as an isotropic material with mechanical properties
MPa and
[
38,
39]. Polymers’ raw properties strongly depend on factors such as the manufacturing process, polymer chain type, or additives and, therefore, can vary among different providers [
40]. Nevertheless, due to the AM procedure, final 3D-printed parts do not behave isotropically; they exhibit noticeable orthotropic mechanical properties [
41].
For the characterization of printed parts, in this paper, the component was divided into three different zones to treat them as
different materials. It is convenient to define the standard coordinate system for a 3D-printing process (shown in
Figure 2) where XY denotes the horizontal printing plane and Z is the vertical direction (also called the printing direction).
To fully characterize each zone, either the constitutive tensor
or its inverse, the compliance tensor
, must be obtained. An orthotropic elastic material requires nine material properties for its complete characterization. However, if the previous distinction among zones is considered, the material properties of each separate region can be considered transversely isotropic, meaning that the material presents an isotropic behavior in a certain plane. Due to the symmetry presented in this plane, the required number of material parameters is reduced from nine to five for each zone. For an XY isotropic material, the transversely isotropic compliance tensor, using Voigt’s notation, is:
where
accounts for Young’s modulus in the
i direction,
for Poisson’s ratio that describes the relation between the deformations in the
j and
i directions when a load is applied in the
i direction, and
for the shear modulus in direction
j in the plane normal to direction
i. Note that for the XY transversely isotropic tensors are
,
,
, and
.
The isotropic plane for the cover zone is the printing plane (XY), while for the contour zone, it is the one perpendicular to the filament (which depends on the shape of the part). Because of this, it is convenient to adapt the nomenclature shown in Equation(
1) for each respective zone as shown in
Table 1. For the cover case,
and
are Young’s modulus in the direction perpendicular to the isotropic plane (printing plane) and in the isotropic plane, respectively,
and
Poisson’s ratio in the printing direction and in the plane of isotropy, and
G and
the shear modulus in the printing direction and in the plane of isotropy. For the contour zone,
relates to Young’s modulus in the direction parallel to the filament (X direction in the case shown in
Table 1), and the remaining parameters present an analogous description.
The inner zone is also considered a transversely isotropic material, XY being its isotropic plane. Thus, its compliance tensor matches the one in Equation (
1).
6. Dimensional Analysis on the Three-Zone Model
For comparison, the mechanical properties of PLA, ABS/GP, and ABS/PC were expressed as a ratio to their respective raw material properties.
Figure 10 shows the non-dimensional comparison for the cover and contour zones. The properties of PLA and ABS/GP were taken from the previous works [
32,
33], where the experimental methodology of this paper was used. Their non-dimensional properties were within the expected range, all ratios being below unity. For this case, they can also be called normalized properties since all of them were of the same order of magnitude [
34]. Two main material properties groups were distinguished: the ones unaffected by inter-layer adhesion (
,
,
) and the affected ones (
,
,
,
,
). This distinction was made a priori based on whether the inter-layer unions were stressed or not in their corresponding property test. For example,
was adhesion independent since the fibers, and consequently the inter-layer joining, were aligned with the applied force in the corresponding test. In contrast, layer unions in
formed 90° with respect to the applied force in the test, and therefore, adhesion effects may emerge.
In relation to properties independent of inter-layer adhesion, it can be seen in
Figure 10 that all of them showed similar values for the three tested materials, with the mechanical properties of PLA the highest ones and the ABS/PC properties the lowest ones.
Figure 11 shows the same results, but referred to
instead, and there, it can be seen that these small variations vanished. With this procedure, the dispersion of the provider’s data was disregarded. Consequently, and according to
Table 6, experiments with horizontally printed specimens are no longer required to characterize the aforementioned properties, and they can be computed using the non-dimensional relationships established in
Table 7.
Moreover, regarding
and
, considered as potentially adhesion-affected properties, the adhesion effect on them was also negligible since their non-dimensional values did not vary for the three tested materials. Therefore, based on
Table 6, it was confirmed that the 45-Contour tests could be omitted. In addition, V-Contour samples were not needed either since
was obtained using Equation(
3). Contrariwise, dimensionless properties
and
varied for different materials, as shown in
Figure 11a, which indicated that the physical process of adhesion was relevant.
In light of the above, the number of required experiments could be reduced to one third from the six initial configurations to just V-Cover and 45-Cover, a significant reduction that implies considerable cost savings.
The non-dimensional values for the ±45° in-fill referred to
are depicted in
Figure 12 as a function of in-fill density. Values corresponding to an in-fill density above 70% were not considered in order to avoid possible intra-layer phenomena. Poisson’s ratios were not plotted due to their lower influence on the material mechanical behavior. It can be seen that Young’s modulus in the Z direction showed a linear relationship with in-fill density, as expected, since stiffness in this direction and the area in the printing plane are directly proportional properties. In contrast, Young’s modulus in the isotropic plane showed a non-linear correlation with in-fill density due to the fact that the effective area of the RVE in X and Y directions had a more complex relation to in-fill density. Finally, it can be seen that the non-dimensional properties did not depend on the material. On account of that, computational homogenizations for the in-fill characterization can be replaced by charts as those in
Figure 12, obtained experimentally or computationally.
Inter-layer adhesion needs to be further investigated in order to fully understand the mechanical behavior of FFF parts. In this context, the use of Scanning Electron Microscopy (SEM) imaging could help to evaluate the inter-layer bonding performance [
56]. Up-to-date research suggests that major influential factors for inter-layer strength are a combination of both inter-layer contact and diffusion processes [
57]. Coogan and Kazmer [
58] developed a model that describes the interlayer bond strength of the parts in terms of two non-dimensional numbers: one related to the thermal diffusion across layers and the other quantifying the interlayer contact influence. This approach may be extended to characterize the influence of inter-layer strength in the elastic moduli of the AM components. Furthermore, Machine Learning (ML) is becoming increasingly used in the AM field for both properties’ prediction and optimization [
59,
60].
7. Conclusions
In this study, the mechanical properties of 3D-printed parts made of ABS/PC were characterized experimentally and computationally. The reported results put in evidence that the considered three-zone model was a reliable approximation for the characterization of 3D-printed parts and confirmed the direct impact of process parameters such as printing pattern and build orientation.
Results from tensile tests confirmed that both stiffness and strength at the inter-layer unions were lower than at the intra-layer joining and on the filament direction. The mechanical properties of horizontally printed parts were the closest to those of the raw material due to the absence of inter-layer bonding effects. Moreover, parts horizontally manufactured and with a cross-pattern showed the highest strength because they were the only specimens that underwent ductile fracture.
Results from bending tests reflected the influence of both the build orientation and the in-fill density on the mechanical performance of the 3D-printed part. An increase of in-fill density increased the stiffness of the component and decreased the influence of the build orientation on the mechanical properties of the part. The results from the computational simulations showed close agreement with the experiments and demonstrated the high fidelity of the three-zone model. Furthermore, the transversely isotropic behavior for cover, contour, and inner zones was verified.
It was concluded that non-dimensional relationships could be established for adhesion-independent mechanical properties, which implies that the number of testing configurations required to fully characterize the 3D-printed parts was reduced from six to two. These relationships must be referred to the 3D-printed part properties instead of the raw material ones to avoid manufacturing data dispersion.
Future research needs to address the better understanding of the inter-layer adhesion issue. If a quantitative relationship is established between adhesion-dependent properties and inter-layer stiffness properties, such as inter-layer contact or polymer chain diffusion, a significant decrease of the needed tests will be achieved through modelization or ML.
Finally, this research helped to establish new design-for-manufacturing techniques through the use of high-fidelity computational simulations. These low-cost simulations enable a high degree of customization of the parts by modifying printing parameters such as build orientation or in-fill density, optimizing their mechanical properties and subsequent performance.