Additive Manufacturing (AM) is a group of technologies that produce three-dimensional physical objects by gradually adding material [1
]. Since the 1980s these technologies became adopted for a growing number of medical/engineering applications and have gradually entered our lives with the development of low-cost 3D printers [3
]. In Fused Filament Fabrication (FFF) (also often denoted as Fused Deposition Modeling), parts are made layer by layer, each layer being obtained by the extrusion through a nozzle and the deposition of a molten plastic filament [5
]. The nozzle movements are controlled by a computer, in accordance with a previously defined deposition sequence. Thus, FFF can produce a prototype or a finished product from a Computer Aided Design (CAD) model without the use of molds.
Despite the potential disruptive character of FFF, in practice 3D printed parts often show unsatisfactory mechanical resistance [7
]. This is generally due to insufficient bonding between adjacent filaments, which in turn is determined by the temperature history upon cooling [8
]. Consequently, knowledge of the temperature evolution during the deposition/cooling stage is valuable for process set-up and optimization.
The objective of this work was to compute the temperature evolution during deposition and cooling of FFF parts, taking into consideration the amorphous or semi-crystalline nature of polymers. This unique tool will not only enable an estimation of the magnitude of the effect of the phase change occurring during cooling/solidification of partially crystalline polymers, but will also give generality to the thermal model. The paper is organized as follows. Section 3
presents the algorithm for dealing with cooling of materials with a phase change, as well as the resulting computer code. Section 4
deals with the deposition and cooling of simple geometries, in order to gauge the differences in cooling of amorphous and semi-crystalline polymers. Section 5
studies the cooling of a large part, assuming all possible build orientations.
2. Related Work
Until recently, a limited range of materials was commercially available for FFF, but the situation is changing rapidly [9
]. Acrylonitrile Butadiene Styrene (ABS) and Polylactic Acid (PLA) remain the most popular [11
]. ABS, an amorphous polymer, exhibits good impact resistance and toughness, heat stability, chemical resistance, and long service life [13
]. PLA, a partially crystalline polymer, is biodegradable (compostable) and has low melting temperature but has limited thermal stability [14
]. The performance of these two materials for 3D printing has been assessed [15
], particularly in terms of dimensional accuracy [19
], surface roughness [21
], mechanical performance [22
] and emission of volatile organic compounds (VOC) [23
]. For the 3D printing of a compact omnidirectional wheel, Rubies and Palacín [25
] observed that when using 100% infill density, PLA yielded a better mechanical performance than ABS. Conversely, Shabana et al. [26
] concluded that ABS parts exhibited better properties but released organic volatile compounds. However, upon combining alternate layers of the two materials, optimal results were attained. Mudassir [27
] proposed a selection methodology for the two materials.
Often, both ABS and PLA 3D printed parts exhibit deficient performance, due to poor bonding between their various individual filaments. In fact, adequate bonding requires that contacting filaments are sufficiently hot during sufficient time in order to enable the necessary macromolecular diffusion [28
]. Local temperatures and their time evolution depend on the geometry of the part, the printing conditions adopted and the thermo-physical properties of the polymer.
In a previous work, the authors developed a simulation methodology to predict the temperature history at any location of a 3D printed part. This entailed the development of an algorithm to define/up-date automatically contacts and thermal/initial conditions as the deposition proceeds, as well as a criterion to compute the degree of bonding between adjacent filaments [28
]. Despite the practical usefulness and the general good agreement between theoretical predictions and experimental data [29
], the method can only be used for amorphous materials such as ABS, which do not exhibit a phase transition from the melt to the solid state. In the case of partially crystalline polymers like PLA, the enthalpy of fusion (also known as latent heat of fusion), must be considered [30
]. Zgryza et al. [31
] showed experimentally by means of Infrared Thermography that differences in the surface temperature of 3D printed samples of ABS and PLA were smaller for ABS.
4. Application of the Code to Simple 3D Printed Structures
This section deals with using the code to predict the cooling of simple 3D parts. The first example concerns the deposition of a single filament (Figure 5
a), whereas the second considers the structure with 10 filaments illustrated in Figure 5
b. Table 1
presents the main properties of ABS (P400 ABS, Stratasys®
, Edina, MI, USA) and PLA (881N PLA, Filkemp®
, Algueirão–Mem Martins, Portugal). Table 2
identifies the process parameters and computational variables. The heat transfer coefficient hconv
was deduced using the correlation of Churchill and Chu [36
], a high conductance between adjacent filaments was assumed, and an intermediate value for the extrusion temperature was considered to be suitable for both ABS and PLA. The version 220.127.116.116344 (R2017a) of MatLab®
shows the temperature evolution of the cross-section of a single PLA filament (at x
= 30 mm, i.e., at a section in the middle of the filament) from an initial temperature of 230
, with and without phase change, as predicted by the code presented above. The latter starts at t
= 3.25 s and lasts 0.75 s. During this period, the temperature remains constant, whereas it decreases continuously if the phase change is not considered. This results in a temperature difference of 13.9
= 4 s) between the two cooling processes.
When 10 filaments are deposited, contacts with adjacent filaments and support arise. Figure 7
shows the temperature evolution of the cross-section of filament 2 at x
= 30 mm, with and without phase change, again for PLA and an initial temperature of 230
. In the computations, the travel time along the
-axis is not considered (Figure 5
), that is, the deposition of a new layer starts immediately after concluding the deposition of the previous one. The phase change occurs at t
= 3.68 s and lasts 0.4 s, due to the thermal contacts with filaments 1 and 3. The peak initiated at t
= 10 s is created by the new thermal contact with filament 7. The maximum temperature difference of 18.9
between the two curves is observed at approximately t
= 8 s. This difference is higher than in the previous example (Figure 6
) due to the contacts developing between filaments. As the temperature of each filament remains constant during its phase change, those filaments that are in contact with filaments that are undergoing a phase change cool more slowly, i.e., the temperature of each filament is influenced by its own phase change and by the phase change of the other filaments.
ABS and PLA having distinct thermal properties (Table 1
) apart from their amorphous/partially crystalline character, their cooling rates should also differ. As seen in Figure 8
, which shows the temperature evolution of the cross-section of filament 2, at x
= 30 mm, the ABS filament cools faster, a maximum temperature difference of 39.1
being obtained for the two materials at approximately t = 6 s. In principle, this would mean that this particular PLA is a better option for FFF, as slower cooling favors bonding between filaments [28
5. Applied Case Study
This section considers the manufacture by FFF of a rectangular tile with 90 × 60 × 30 mm using PLA or ABS. 3D printing will be carried out using a unidirectional and aligned strategy (i.e., filaments will be deposited along the x
axis direction). Six build orientations (labelled P1 to P6) are feasible, as demonstrated in Figure 9
. Orientations P1 and P2 entail the longest filaments (90 mm), whilst P5 and P6 require the shortest filaments (30 mm). If the filaments are circular (with a diameter of 0.25 mm) and the deposition velocity is set to 30 mm/s, it will take 24 h to perform the 3D printing of this part. Each build orientation will involve a different number of filaments and contact area with the support, as presented in Table 3
. The materials properties (PLA and ABS) and the process parameters are defined in Table 1
and Table 2
Given the high number of filaments necessary to perform the 3D printing of the part, in order to identify more easily the differences in cooling associated with each build orientation, as well as understand the rates of cooling of ABS and PLA (here representing the behavior of amorphous and partially crystalline polymers, respectively), the temperature evolution for one filament will be followed. The data presented in Figure 10
and Figure 11
concerns the central filament on the 20th layer counting from the support of the 3D printer. This corresponds to filament no. 2341 for orientations P1 and P4, no. 4681 for P2 and P5, and no. 7021 for orientations P3 and P6. As before, the data presented refers to the cross-section in the middle of the filament length, that is, at
for orientations P1 and P2,
for orientations P3 and P4 and
for orientations P5 and P6.
For an easier comparison of the thermal history associated with each material and build orientation, Figure 9
exhibits the temperature evolution during the first 3800 s from the instant the cross-section of the filaments highlighted was deposited. The actual time elapsed since building of the part started is identified in the figures labels. Figure 11
uses the real time scale to study in greater detail the temperature development during cooling, again for the six build orientations (this is why the time values in the x
axis change with build orientation), and directly comparing the curves for ABS and PLA. The insets in the figures are magnifications of the progress of temperature during short time periods, evidencing either specific features of the curves or differences between the two materials.
Each of the two graphs of Figure 10
essentially displays 3 sets of curves, which are due to the similitudes in heat transfer between P1 and P2, P3 and P4 and P5 and P6. In the initial seconds, the cooling rate is higher for P1 and P2, followed by P3 and P4, and finally by P5 and P6. This is directly related to the length of the filaments for each build orientation (90, 60 and 30 mm, respectively), which leads to different deposition times (3, 2 and 1 s, respectively) and determines the period of time elapsed between contacts. Indeed, the figures clearly show that the cooling of the filament is influenced by the physical contact with filaments that are deposited later, as well as by heat transfer from newer filaments belonging to other more recent layers. The peaks around 500 s are a good example of the latter effect. Also, a comparison between the two graphs will show that at analogous cooling times the filament temperatures are generally higher for PLA, due to the occurrence of a phase change (and the inherent thermal properties of each material), but this is more clearly seen in Figure 11
As discussed above, Figure 11
reveals in more detail how the temperature of the mid cross-section of the filament selected evolves with time for the various build orientations and for the two materials. In each graph, the initial sharp temperature decrease results from the deposition of the filament. The inset clearly shows that the differences in the cooling rate between ABS and PLA are due to their intrinsic thermal properties (influencing the slope of the curve) as well as by their crystalline character, with PLA exhibiting a plateau due to the phase change. In the same inset, the first temperature peak arises due to the physical contact with the next filament being deposited. The remaining peaks in each graph were caused by the heat transfer developing due to the deposition of new hotter filaments in the same layer and in the layers above.
The magnitude of the initial peak is small, but varies with build orientation. Also, the time at which it develops differs with build orientation. The longer the filament, the larger the time elapsed between the successive contributions to heat transfer from new filaments, and consequently the lower the re-heating effect. As the deposition of the part continues, the filament being studied reaches the environment temperature. From then onwards, the intensity of the temperature peaks decreases, because the distance between this filament and any new filament being deposited also increases.
quantifies some of the features of the curves in Figure 11
, thus evidencing the temperature differences upon cooling of ABS and PLA for the part being considered. It includes the maximum temperature difference between the two materials that was observed during the global deposition/cooling sequence. This amounts to approximately 40
and depends little on build orientation. Once the filament reaches the environment temperature, the temperatures of the next 3 peaks (denoted A, B and C in Figure 11
) were also registered and are included in the Table. As expected, the magnitude of these peaks decreases as the deposition of the 3D part proceeds, because the new individual filaments that are deposited are gradually more distant from the cross-section being monitored. Naturally, the temperature differences between the two materials also decrease (from approximately 10
for peak A, to circa
for peak B, to around 4
for peak C). Also, the temperatures for PLA are consistently higher than those for ABS, obviously due to the phase change undertook by the former. Build orientation has an effect on the temperature of peaks A to C, particularly for the first. A difference of almost 20
was registered for orientation P1 (64.8
) relative to P5 (83.6
). Again, the higher temperatures occur for the build orientations dealing with shorter filaments, where the contacts between filaments at any given vertical cross-section of the part are more frequent. These re-heating peaks may contribute significantly to the quality of the 3D printed part, because if sufficiently high temperatures are attained, bonding between contiguous filaments is favored.
A simulation method to predict quantitatively the temperature evolution of filaments during deposition and cooling in FFF, capable of dealing with both amorphous and semi-crystalline polymers, was implemented. The simulation can be applied to any thermoplastic or composite as long as its thermal properties are known. When depositing a single filament of PLA, a temperature difference of almost 14 °C is observed when considering a phase chance relative to ignoring it. In the case of structures with several filaments, the temperature difference can raise to about 20 °C, due to the re-heating effects of neighboring filaments. The differences between the two types of materials were highlighted studying the deposition of a single filament and a simple structure with 10 filaments, made with ABS or PLA. The evolution of temperature with time can become significantly different for the two polymers (differences of up to 40 °C), especially when several filaments come into contact with each other.
An applied case study was also presented, by considering the 3D printing of a 90 × 60 × 30 mm brick-like part, which would take 24 h to manufacture under the usual deposition velocity of 30 mm/s. The influence of the build orientation selected was investigated. It was shown that the time evolution of the filaments temperature depends on their length, as this determines the frequency at which heat transfer from newly deposited filaments contributes to re-heating. Temperature differences of around 30 °C were predicted. The temperature of PLA filaments was always higher than that of ABS for all the 3D printing orientations, due to the inherent thermal properties of the two materials and the existence of a phase change in PLA.
The work presented is a first step towards predicting the properties of parts produced by FFF. Knowing the evolution of temperature with time as the deposition proceeds, it is possible to predict bonding between contiguous filaments by means of a healing criterion, as well as part shrinkage and warpage arising due to local temperature gradients. As a further step, the mechanical properties of 3D parts could be estimated; for example, with the use of sintering models.