An in-line rheometer and data acquisition system are used to monitor the melt pressure, melt temperature, and environmental temperatures while producing parts via fused filament fabrication (FFF). Melt pressures are observed to increase when printing parts with small layer heights, which is attributed to the confined space created between the nozzle and the previous layer (i.e., an exit pressure). These exit pressures (referred to as contact pressure) and the resulting interlayer contact areas are analyzed for 2863 layers created at 21 different processing conditions. The measured contact pressure was found to directly influence the shape of the layers and the resulting interlayer contact. An intimate contact model based on contact pressure is combined with a wetting model to accurately predict the interlayer contact of FFF parts. This pressure-driven intimate contact model for FFF shows strong agreement with the observed interlayer contact. No theoretical model has previously existed for predicting interlayer contact, so this research provides a critical component for developing a comprehensive part strength model. Both the measurements and proposed model are sufficiently simple and accurate for real-time analysis of FFF quality, so the described in-line sensors provide valuable quality insights and are recommended for future researchers, printer manufacturers, and end-users.
I. INTRODUCTION
Fused filament fabrication (FFF), also known as fused deposition modeling (FDM®), is a form of additive manufacturing where layers of polymeric filament are oriented into a desired shape by pushing the material through a heated nozzle as is described more thoroughly in other works [1–4]. Upon exiting the nozzle, the polymer melt meets the previously deposited layer and immediately begins to cool and solidify. The rapid cooling prevents the layers and roads (in this context, roads refer to adjacent material strands printed on the same layer) from fully fusing, which often leads to voids and weak mechanical properties. Parts are typically weakest in the vertical, z-direction due to a weak interlayer bond strength, resulting in anisotropic properties [1–9]. A review of parts made from acrylonitrile butadiene styrene (ABS) (a common material used in FFF) indicates that complete strength is typically not achieved along the z-axis [10], motivating our focus on interlayer strength and the physical contact between layers.
Many studies have used the healing model initially proposed by Wool and O'Connor [11,12] to model and understand the bond strength between FFF layers and roads [4–9,13–16]. The healing model includes five sequential steps: surface rearrangement, surface approach, wetting, diffusion, and randomization [11,17]. Surface approach and wetting both describe different mechanisms behind how two separate materials come into contact; surface approach is caused by an external force while wetting is caused by surface tension. In the case of FFF, the wetting step has been extensively studied in an attempt to describe interlayer contact, which is a measure of the contact area connecting two separate layers. The wetting between FFF layers has been most popularly predicted using a sintering model initially developed by Frenkel [18] and then modified by Pokluda et al. [19]. The sintering model was first applied to FFF by Li et al. [20], and it has continued to gain popularity in the FFF literature [4,5,21,22]. Recently, Hart et al. proposed a wetting equation with a similar form to the sintering model that was used to provide a reasonable prediction of the fracture toughness [14]. However, the work by Sun et al. showed that wetting did not significantly contribute to the interlayer contact of ABS because the rapid cooling and corresponding viscosity increase prevented interlayer contact growth. Therefore, they proposed that diffusion was likely the dominant factor in determining strength [5].
Diffusion across FFF layers and roads has also been extensively studied [6,8,9,14–16,23–25] with most of the diffusion models stemming from Wool's healing model [11,12] and de Gennes' reptation theory [26]. According to the healing model, which had great success in describing many polymer welding processes [11,12,17,27,28], strength develops proportionally to interlayer diffusion to the ¼ power until a critical interpenetration depth is achieved, corresponding to the strength of the virgin material. This model has also been successfully applied to the FFF process [6,9,16,23]. Thomas and Rodriguez first applied the healing model to FFF, proving that it could be used to predict the isothermal healing process while post-annealing printed parts [6]. The diffusion healing model was next applied to predicting strength of as-printed parts by simulating the nonisothermal cooling and diffusion processes [9]. Many other authors have correlated the strength of FFF parts to various theoretical diffusion models [8,15,16,23,24].
Despite the extensive work related to wetting and diffusion, no comprehensive model exists for predicting FFF interlayer bond strength. In fact, there is much discrepancy in the literature regarding the importance of both wetting and diffusion. Many researchers state that wetting and interlayer contact are critical whereas interlayer diffusion is typically complete by the time the layer cools [14,16,29,30]. Other authors claim that diffusion is crucial while wetting is either not considered or negligible because the polymer quickly becomes too viscous to allow for wetting growth [5,6,9,23–25]. Recent results from the authors of this work have indicated that the interlayer strength can be predicted extremely well by diffusion, but only if the interlayer contact is known (interlayer contact was previously measured but not modeled) [9]. In order to be fully effective, any model must predict both the interlayer contact and the diffusion.
Currently, no theoretical model has been able to accurately predict the interlayer contact of printed parts, and it has only very recently been suggested that the pressure required to force the layers into contact is critical to strength development [1,9,14,29]. This article proposes that pressure-driven intimate contact is the missing link to predicting interlayer contact and strength. Intimate contact is a combination of the first two steps of the healing process (surface rearrangement and surface approach). It describes when the two surfaces come together due to an externally applied force/pressure, and it is complete once all the physical space (including any surface texture) between the surfaces is gone [31]. Many healing models have focused on wetting and diffusion because intimate contact can typically be ignored for microscopic crack healing, pressure-free healing, or in processes where the surfaces instantaneously come into intimate contact due to high initial pressures or low material viscosities [17]. However, the high viscosity of many thermoplastic systems can prevent instantaneous intimate contact [31]. Work on thermoplastic composites has shown that pressure is needed to create strength across composite plies. For example, a pressure-driven intimate contact model initially developed by Lee and Springer [32] has been successfully applied for predicting composite strength [31–33].
Although it has not been previously modeled, the strength of FFF and FDM processes is also limited by pressure-driven intimate contact. Previous observations of FFF printed cross sections (as will also be discussed in Fig. 5) indicate that macroscopic separations exist between layers [1,5,29,30]. In fact, certain FFF processing conditions that generate minimal contact pressure can result in very little interlayer contact [Fig. 5(d)]. Although wetting improves interlayer contact with enough time at elevated temperatures, pressure can force the layers together much more rapidly than wetting. Therefore, interlayer contact is believed to be a combination of intimate contact followed by wetting. The current paper will extend the model by Lee and Springer [32] to predict intimate contact during the FFF process. This approach combines rheological analyses, transient heat analyses, an intimate contact model, and a wetting model to predict interlayer contact and to address the relative importance of both wetting and intimate contact.
The intimate contact model is enabled by a custom in-line rheometer implemented onto an FFF printer [34]. The in-line rheometer includes a melt pressure transducer, a filament encoder for measuring flow rate, and a melt thermocouple. All these sensors are shown to be crucial for understanding the FFF printing process and for ensuring part quality. Mackay has recently pointed out that rheological investigations of the FFF process are crucial for printer design and for improving print speed and part strength [35]. The use of the in-line rheometer in our paper confirms Mackay's statement by using rheology and in-line pressure measurements to develop a model for intimate contact, which is crucial for predicting part strength. The remainder of the current paper develops the intimate contact model, which future researchers can implement into strength predictions, and the paper describes the use of crucial in-line sensors that printer end-users and researchers should implement to achieve better understanding of their process.
II. MATERIALS AND METHOD
A. Approach
Pressure-driven intimate contact models may have been previously ignored in the FFF literature due to difficulties measuring contact pressure. The novelty of this research comes from measuring FFF contact pressures with an in-line rheometer and using the contact pressures to accurately predict intimate contact in FFF for the first time. This recently developed in-line rheometer [34] provides an intrusive melt thermocouple and pressure transducer to measure the melt states during real-time FFF printing. A previous publication has thoroughly characterized the extrusion pressures, P, and viscosities while extruding material from the nozzle into open space (i.e., not while printing actual parts) [34], creating a pressure called the open extrusion pressure. The in-line rheometer is now used while printing parts. As described subsequently, subtracting the open extrusion pressure from the in-print pressure provides a measurement for the exit pressure, which is referred to as the contact pressure, Pcontact, which drives the intimate contact process. This paper describes and validates the Pcontact measurements and correlates them to the interlayer contact. Additionally, the contact pressures are used in an intimate contact model to predict the interlayer contact, which is compared to measurements from the printed parts. This paper explores the combination of intimate contact and wetting, and how both components create the interlayer contact necessary to achieve both part finish and mechanical properties.
B. FFF printer
An FFF printer (Lulzbot Taz 6 v 2.1, Loveland, CO) with a single extruder is used in this research. The system was customized with an in-line rheometer comprising of a pressure transducer and a thermocouple both in direct contact with the melt as it passes through the nozzle; the in-line rheometer combines the melt pressure measurements with volumetric flow rate measurements (based on the filament velocity calculated from the stepper motor speed) to calculate viscosity as a function of shear rate after applying corrections including the Bagley, temperature, Rabinowitsch, and pressure corrections [34]. The inset of Fig. 1 shows the hollow pressure pin (acting as part of the pressure transducer) with a thermocouple welded with silver solder so that it is in direct contact with the melt [34]. The pressure transducer measures the pressure drop across the 0.5 mm diameter and 1.85 mm length nozzle tip by applying Bagley corrections, providing viscosity results that are accurate enough to replicate measurements from off-line rheometers, making it a very capable in-line rheometer [34]. A few thermocouples are located throughout the system to aid with the heat transfer analysis developed in this paper. Along with the thermocouple measuring the temperature of the melt, Tmelt, one thermocouple is adhered to the build platform to measure its temperature, Tbuild, and another is located approximately 1 cm above and 1.5 cm to the right of the nozzle to measure the approximate environmental temperature, T∞, experienced by the recently deposited roads. The in-line data from these three temperature readings (Tmelt, T∞, and Tbuild) were all used to predict the transient temperature profile for every layer printed during this study, enabling a more accurate heat analysis that accounts for the actual processing temperatures and their inherent fluctuations. A fourth thermocouple was in contact with the load cell of the pressure transducer, measuring the temperature of the load cell, Tload, for temperature corrections. The customized system is shown in Fig. 1, and the design and validation of the entire setup is described in detail in previous work [34].
Custom FFF sensor system, including an in-line melt pressure transducer and thermocouples, measuring Tmelt, Tload, T∞, and Tbuild.
Custom FFF sensor system, including an in-line melt pressure transducer and thermocouples, measuring Tmelt, Tload, T∞, and Tbuild.
C. Materials
High impact polystyrene (HIPS) filament was studied because it is capable of printing over a wide range of layer heights, print speeds, and extrusion rates, so it enabled evaluating interlayer contact over a very large and stable processing window. HIPS Natural filament (Esun, Shenzhen, China) was selected because the authors found its dimensional precision to be excellent relative to most commercial filaments, with a diameter specification of 2.95 ± 0.05 mm. The close tolerances on diameter are critical for maintaining a consistent and accurate flow rate and shear rate through the nozzle [34]. HIPS was also selected because it exhibits a classic rheological behavior with both Newtonian and shear thinning regimes and typical storage modulus, G′, and loss modulus, G″, cross-over points as shown in Fig. 2. The HIPS material properties shown in Table I were used for the modeling and analyses in this paper. The glass transition temperature, Tg, was characterized using differential scanning calorimetry (DSC).
HIPS material properties used for the analyses in this paper.
Property . | Value . |
---|---|
Density, ρ (kg/m3) | 1040 |
Thermal conductivity, k [W/(m/K)] | 0.19 |
Specific heat capacity, Cp [J/(kg/K)] | 2340 |
Glass transition temperature, Tg (°C) [34] | 98 |
Property . | Value . |
---|---|
Density, ρ (kg/m3) | 1040 |
Thermal conductivity, k [W/(m/K)] | 0.19 |
Specific heat capacity, Cp [J/(kg/K)] | 2340 |
Glass transition temperature, Tg (°C) [34] | 98 |
D. Print conditions
Hollow boxes, as previously used in the literature [1,9] were printed with four walls (A–D) as shown in Fig. 3. Each wall is made of a single road, so the wall thickness is nominally equal to the road width, W. Twenty-one boxes were printed while varying the nominal melt temperature, Tm, the layer height, H, the road width, W, and the print speed (aka, the transverse nozzle velocity), S, as shown in Table II. In-line pressures (P and Pcontact) and temperatures (Tmelt, Tbuild, and T∞) were recorded while printing each part. As described previously [34] and verified by the Tmelt measurements, the set point temperature was set slightly higher than the intended melt temperature to achieve a desired Tm; for example, the melt temperature set point was 262 °C to achieve a Tm of 250 °C, according to the Tmelt measurements. Unless otherwise noted, the temperatures reported in this paper refer to the Tmelt observed with the melt thermocouple values rather than the printer set point. The volumetric flow rate, Q, and the apparent shear rate at the nozzle wall, , through the 0.5 mm nozzle are correlated to the pressure readings, so they are also listed in Table II. Q is calculated as the product of W, H, and S. The values shown in Table II were calculated based on Q, assuming a Newtonian velocity profile (though the shear rate values were later adjusted using the Rabinowitsch correction when calculating in-line viscosity [34]).
DOE of printed conditions, including non-linear main effects, interactions, and direct comparisons of various layer heights while maintaining constant flow rate and shear rate.
Design intent . | Condition . | Tm (°C) . | H (mm) . | W (mm) . | S (mm/min) . | Q (mm3/s) . | . |
---|---|---|---|---|---|---|---|
Main effects | 1 | 250 | 0.25 | 0.5 | 2500 | 5.21 | 356 |
Main effects | 2 | 250 | 0.25 | 0.65 | 2500 | 6.77 | 463 |
Main effects | 3 | 250 | 0.25 | 0.35 | 2500 | 3.65 | 249 |
Main effects | 4 | 250 | 0.4 | 0.5 | 2500 | 8.33 | 570 |
Main effects | 5 | 250 | 0.1 | 0.5 | 2500 | 2.08 | 143 |
Main effects | 6 | 250 | 0.25 | 0.5 | 4000 | 8.33 | 570 |
Main effects | 7 | 250 | 0.25 | 0.5 | 1000 | 2.08 | 143 |
Main effects | 8 | 275 | 0.25 | 0.5 | 2500 | 5.21 | 356 |
Main effects | 9 | 225 | 0.25 | 0.5 | 2500 | 5.21 | 356 |
Interactions | 10 | 275 | 0.4 | 0.35 | 4000 | 9.33 | 639 |
Interactions | 11 | 225 | 0.4 | 0.35 | 4000 | 9.33 | 639 |
Interactions | 12 | 225 | 0.1 | 0.65 | 4000 | 4.33 | 296 |
Interactions | 13 | 275 | 0.1 | 0.35 | 4000 | 2.33 | 160 |
Interactions | 14 | 275 | 0.1 | 0.35 | 1000 | 0.58 | 40 |
Interactions | 15 | 275 | 0.1 | 0.65 | 4000 | 4.33 | 296 |
Replicate | 16 | 250 | 0.25 | 0.5 | 2500 | 5.21 | 356 |
Layer height | 17 | 250 | 0.1 | 0.5 | 4034 | 3.36 | 232 |
Layer height | 18 | 250 | 0.175 | 0.5 | 2305 | 3.36 | 232 |
Layer height | 19 | 250 | 0.25 | 0.5 | 1614 | 3.36 | 232 |
Layer height | 20 | 250 | 0.4 | 0.5 | 1009 | 3.36 | 232 |
Layer height | 21 | 250 | 0.55 | 0.5 | 733 | 3.36 | 232 |
Design intent . | Condition . | Tm (°C) . | H (mm) . | W (mm) . | S (mm/min) . | Q (mm3/s) . | . |
---|---|---|---|---|---|---|---|
Main effects | 1 | 250 | 0.25 | 0.5 | 2500 | 5.21 | 356 |
Main effects | 2 | 250 | 0.25 | 0.65 | 2500 | 6.77 | 463 |
Main effects | 3 | 250 | 0.25 | 0.35 | 2500 | 3.65 | 249 |
Main effects | 4 | 250 | 0.4 | 0.5 | 2500 | 8.33 | 570 |
Main effects | 5 | 250 | 0.1 | 0.5 | 2500 | 2.08 | 143 |
Main effects | 6 | 250 | 0.25 | 0.5 | 4000 | 8.33 | 570 |
Main effects | 7 | 250 | 0.25 | 0.5 | 1000 | 2.08 | 143 |
Main effects | 8 | 275 | 0.25 | 0.5 | 2500 | 5.21 | 356 |
Main effects | 9 | 225 | 0.25 | 0.5 | 2500 | 5.21 | 356 |
Interactions | 10 | 275 | 0.4 | 0.35 | 4000 | 9.33 | 639 |
Interactions | 11 | 225 | 0.4 | 0.35 | 4000 | 9.33 | 639 |
Interactions | 12 | 225 | 0.1 | 0.65 | 4000 | 4.33 | 296 |
Interactions | 13 | 275 | 0.1 | 0.35 | 4000 | 2.33 | 160 |
Interactions | 14 | 275 | 0.1 | 0.35 | 1000 | 0.58 | 40 |
Interactions | 15 | 275 | 0.1 | 0.65 | 4000 | 4.33 | 296 |
Replicate | 16 | 250 | 0.25 | 0.5 | 2500 | 5.21 | 356 |
Layer height | 17 | 250 | 0.1 | 0.5 | 4034 | 3.36 | 232 |
Layer height | 18 | 250 | 0.175 | 0.5 | 2305 | 3.36 | 232 |
Layer height | 19 | 250 | 0.25 | 0.5 | 1614 | 3.36 | 232 |
Layer height | 20 | 250 | 0.4 | 0.5 | 1009 | 3.36 | 232 |
Layer height | 21 | 250 | 0.55 | 0.5 | 733 | 3.36 | 232 |
All the boxes in this work were printed with a brim consisting of 10 roads to aid in adhesion while enabling the bottom layer to remain in contact with the build plate, which was held constant at 80 °C (the set point closely matched the actual Tbuild measurements) for all the prints because the Tbuild was previously found to be a relatively insignificant parameter in determining the strength of these boxes [1,9]. The first layer of all the conditions was always printed at 660 mm/min with an H of 0.25 mm to maintain consistent adhesion to the build plate. At the end of each print, the nozzle moved up and away from the completed box to extrude into open space for 15–30 s at the same used while printing that condition to obtain the equilibrium open pressure, Popen.
The conditions in Table II were all printed within a 14-h timeframe to minimize variations in equipment and environment (the temperature was controlled between 20 and 22 °C). The experiments were designed such that conditions 1–9 change one-factor-at-a-time (OFAT) at three levels to study the nonlinear main effects of Tm, H, W, and S. Conditions 10–15 were designed by augmenting conditions 1–9 with a D-optimal design to explore interactions as well as the extremes of the FFF processing window. Condition 16 was a replicate of condition 1 to evaluate repeatability and potential drifts during the day. Conditions 17–21 maintained a constant Tm, W, Q, and while systematically varying H, which was hypothesized as being the most influential variable in determining Pcontact.
One box, each providing eight test specimens, was printed per condition rather than printing multiple replicates for each condition to maximize the variety of process conditions explored through this design of experiments (DOEs). Moreover, previous replicate testing as well as the replicate test done during this DOE (comparison of condition 1 versus condition 16) showed that replicate boxes had statistically indistinguishable interlayer contact and interlayer strength. Processing defects were monitored by analyzing filament slip as well as variations in the melt pressure and temperature, indicating that all parts were produced consistently.
E. In-line pressure measurements
The printing process was videotaped during some of the conditions from Table II. The supplementary multimedia file associated with Fig. 4 shows the video of the live printing process from condition 6 (Tm = 250 °C, H = 0.25 mm, W = 0.5 mm, S = 4000 mm/min) side-by-side with the collection of the real-time pressure data. The still images in Fig. 4 (Multimedia view) show an image of the custom printing nozzle while printing a layer close to the bottom of condition 6 [Fig. 4(a) (Multimedia view)] and a 100 s window of the pressure curves at the end of the print, immediately after printing into open space [Fig. 4(b) (Multimedia view)]. The open pressure, Popen, is subtracted from the layer pressure, P, which is obtained from the equilibrium pressure plateau for each layer, to calculate the contact pressure, Pcontact, for every layer of the part (102 layers in the case of condition 6, which is printed with H = 0.25 mm).
Condition 6 (a) depiction of the printing process and (b) last 100 s of the in-line pressure data; the supplementary video shows the printing process with the simultaneous data collection, demonstrating how the real-time pressure curves match up to the actual printing process. Multimedia view: https://doi.org/10.1122/1.5093033.1
Condition 6 (a) depiction of the printing process and (b) last 100 s of the in-line pressure data; the supplementary video shows the printing process with the simultaneous data collection, demonstrating how the real-time pressure curves match up to the actual printing process. Multimedia view: https://doi.org/10.1122/1.5093033.1
As shown in Fig. 4(b) (Multimedia view), there is a cyclic pattern of pressure drops of about 0.5 MPa that occur every 3–3.5 s, which is due to a momentary pause in extrusion while the nozzle moves vertically upward while transitioning to the next layer (this is described in more detail with regard to Fig. 11 in Sec. IV). Therefore, each pressure plateau corresponds to a different layer, which is why the plateau pressures are called the layer pressures in this work. Each layer pressure is calculated as the average of the last 50–90% of the pressure plateau to remove the transient effects caused by changing layers. Also shown in Fig. 4(b) (Multimedia view), a series of four oscillations occur during each pressure plateau where the pressure drops by about 0.15 MPa. These four oscillations correspond to the four walls of the printed box because the nozzle and the extrusion rate decelerate slightly around each corner. These oscillations are most severe for condition 6 [Fig. 4 (Multimedia view)] because it was printed at the fastest print speed of 4000 mm/min; the acceleration around the corner is less severe for parts printed at slower speeds as shown in Fig. 11, which will be discussed later.
Cross sections of (a) condition 5 (H = 0.1 mm, W = 0.5 mm, Tm = 250 °C, S = 2500 mm/min), (b) condition 1 (H = 0.25 mm, W = 0.5 mm, Tm = 250 °C, S = 2500 mm/min), (c) condition 4 (H = 0.4 mm, W = 0.5 mm, Tm = 250 °C, S = 2500 mm/min), and (d) condition 11 (H = 0.4 mm, W = 0.35 mm, Tm = 225 °C, S = 4000 mm/min).
Cross sections of (a) condition 5 (H = 0.1 mm, W = 0.5 mm, Tm = 250 °C, S = 2500 mm/min), (b) condition 1 (H = 0.25 mm, W = 0.5 mm, Tm = 250 °C, S = 2500 mm/min), (c) condition 4 (H = 0.4 mm, W = 0.5 mm, Tm = 250 °C, S = 2500 mm/min), and (d) condition 11 (H = 0.4 mm, W = 0.35 mm, Tm = 225 °C, S = 4000 mm/min).
As can be seen from Fig. 4(b) (Multimedia view), the pressure data, P, collected while printing the layers is higher than Popen despite being extruded at the same Q, and . Intuitively (and as theoretically described in Sec. III F), this increase in pressure, Pcontact, can be considered as being due to the greater pressure at the nozzle outlet caused by extruding material into the confined space created by the previous layer. Conditions 17–21 were important because they were printed with a constant Q and while varying only H (of course, the traversing print speed S had to also be varied to keep Q and consistent). A constant Q maintains a constant Popen, enabling direct comparison of P and Pcontact, so conditions 17–21 are often compared when analyzing Pcontact. The resulting pressure curves are later analyzed in Sec. IV.
The data for each print are saved, including the extrusion pressure, P, viscosity, η, and extrusion shear rate, , which are recorded every 4 ms, and Tmelt, T∞, and Tbuild, which are recorded every 1 s. An average P, η, , Tmelt, T∞, and Tbuild were recorded for every layer after filtering out the data from the first 50% and last 10% of that layer to remove any effects created from starting and stopping, thus ensuring that only the equilibrium values were considered. Taking the average values from all layers and conditions produced in Table II resulted in a total of 2884 measurements (parts made with H = 0.1 mm had 253 layers, H = 0.25 mm had 102 layers, H = 0.4 mm had 64, H = 0.175 mm had 145, and H = 0.55 mm had 47 layers).
As detailed in previous work [34], both Q and were measured from the stepper motor pulses and verified with a separate filament encoder to monitor for filament slip or skipped motor steps. The average from both the stepper motor and filament encoder matched within 3% of one another for nearly all conditions. Only conditions 9, 11, and 12 showed a larger mismatch where the filament encoder measured a that was 4.5% lower than that of the stepper motor. These conditions likely had slight filament slippage or skipped motor steps because they also had the highest measured pressures as shown later in Table IV. Nonetheless, this amount of error is acceptable for statistical analysis given that all conditions resulted in fully printed FFF specimens.
Summary of average values for all conditions from Table II; values in parentheses indicate standard deviation; P, Pcontact, and Wbond are measurements; Wbond_IC and Wbond_pred are model predictions.
Condition . | P (MPa) . | Pcontact (MPa) . | Wbond (mm) . | Wbond_IC (mm) . | Wbond_pred (mm) . |
---|---|---|---|---|---|
1 | 1.31 (0.019) | 0.087 (0.019) | 0.40 (0.029) | 0.3837 (0.017) | 0.3839 (0.017) |
2 | 1.58 (0.037) | 0.12 (0.037) | 0.53 (0.031) | 0.5287 (0.040) | 0.5288 (0.040) |
3 | 1.14 (0.017) | 0.012 (0.017) | 0.23 (0.019) | 0.1279 (0.032) | 0.1287 (0.032) |
4 | 1.64 (0.023) | 0.10 (0.023) | 0.32 (0.021) | 0.3743 (0.017) | 0.3747 (0.017) |
5 | 1.08 (0.070) | 0.19 (0.070) | 0.44 (0.026) | 0.4817 (0.023) | 0.4817 (0.023) |
6 | 1.59 (0.040) | 0.14 (0.040) | 0.38 (0.025) | 0.4019 (0.038) | 0.4020 (0.038) |
7 | 0.93 (0.016) | 0.043 (0.016) | 0.40 (0.027) | 0.3596 (0.036) | 0.3598 (0.036) |
8 | 1.01 (0.025) | 0.084 (0.025) | 0.40 (0.025) | 0.4047 (0.031) | 0.4050 (0.031) |
9 | 1.87 (0.060) | 0.17 (0.060) | 0.38 (0.027) | 0.4000 (0.027) | 0.4001 (0.027) |
10 | 1.24 (0.016) | 0.056 (0.016) | 0.19 (0.016) | 0.2382 (0.014) | 0.2393 (0.014) |
11 | 2.19 (0.031) | 0.23 (0.031) | 0.13 (0.029) | 0.2719 (0.008) | 0.2720 (0.008) |
12 | 2.05 (0.15) | 0.60 (0.15) | 0.56 (0.053) | 0.6500 (0.000) | 0.6500 (0.000) |
13 | 0.69 (0.020) | 0.012 (0.020) | 0.32 (0.028) | 0.1910 (0.053) | 0.1912 (0.053) |
14 | 0.38 (0.026) | 0.033 (0.026) | 0.31 (0.028) | 0.2663 (0.060) | 0.2664 (0.060) |
15 | 1.27 (0.094) | 0.37 (0.094) | 0.58 (0.030) | 0.6499 (0.001) | 0.6499 (0.001) |
16 | 1.31 (0.022) | 0.094 (0.022) | 0.40 (0.027) | 0.3886 (0.018) | 0.3887 (0.018) |
17 | 1.23 (0.077) | 0.21 (0.077) | 0.46 (0.030) | 0.4756 (0.028) | 0.4756 (0.028) |
18 | 1.19 (0.031) | 0.097 (0.031) | 0.44 (0.032) | 0.4080 (0.030) | 0.4081 (0.030) |
19 | 1.10 (0.023) | 0.060 (0.023) | 0.40 (0.033) | 0.3683 (0.030) | 0.3685 (0.030) |
20 | 1.04 (0.019) | 0.031 (0.019) | 0.31 (0.021) | 0.3138 (0.052) | 0.3145 (0.052) |
21 | 1.11 (0.024) | 0.027 (0.024) | 0.27 (0.045) | 0.3033 (0.069) | 0.3046 (0.069) |
Condition . | P (MPa) . | Pcontact (MPa) . | Wbond (mm) . | Wbond_IC (mm) . | Wbond_pred (mm) . |
---|---|---|---|---|---|
1 | 1.31 (0.019) | 0.087 (0.019) | 0.40 (0.029) | 0.3837 (0.017) | 0.3839 (0.017) |
2 | 1.58 (0.037) | 0.12 (0.037) | 0.53 (0.031) | 0.5287 (0.040) | 0.5288 (0.040) |
3 | 1.14 (0.017) | 0.012 (0.017) | 0.23 (0.019) | 0.1279 (0.032) | 0.1287 (0.032) |
4 | 1.64 (0.023) | 0.10 (0.023) | 0.32 (0.021) | 0.3743 (0.017) | 0.3747 (0.017) |
5 | 1.08 (0.070) | 0.19 (0.070) | 0.44 (0.026) | 0.4817 (0.023) | 0.4817 (0.023) |
6 | 1.59 (0.040) | 0.14 (0.040) | 0.38 (0.025) | 0.4019 (0.038) | 0.4020 (0.038) |
7 | 0.93 (0.016) | 0.043 (0.016) | 0.40 (0.027) | 0.3596 (0.036) | 0.3598 (0.036) |
8 | 1.01 (0.025) | 0.084 (0.025) | 0.40 (0.025) | 0.4047 (0.031) | 0.4050 (0.031) |
9 | 1.87 (0.060) | 0.17 (0.060) | 0.38 (0.027) | 0.4000 (0.027) | 0.4001 (0.027) |
10 | 1.24 (0.016) | 0.056 (0.016) | 0.19 (0.016) | 0.2382 (0.014) | 0.2393 (0.014) |
11 | 2.19 (0.031) | 0.23 (0.031) | 0.13 (0.029) | 0.2719 (0.008) | 0.2720 (0.008) |
12 | 2.05 (0.15) | 0.60 (0.15) | 0.56 (0.053) | 0.6500 (0.000) | 0.6500 (0.000) |
13 | 0.69 (0.020) | 0.012 (0.020) | 0.32 (0.028) | 0.1910 (0.053) | 0.1912 (0.053) |
14 | 0.38 (0.026) | 0.033 (0.026) | 0.31 (0.028) | 0.2663 (0.060) | 0.2664 (0.060) |
15 | 1.27 (0.094) | 0.37 (0.094) | 0.58 (0.030) | 0.6499 (0.001) | 0.6499 (0.001) |
16 | 1.31 (0.022) | 0.094 (0.022) | 0.40 (0.027) | 0.3886 (0.018) | 0.3887 (0.018) |
17 | 1.23 (0.077) | 0.21 (0.077) | 0.46 (0.030) | 0.4756 (0.028) | 0.4756 (0.028) |
18 | 1.19 (0.031) | 0.097 (0.031) | 0.44 (0.032) | 0.4080 (0.030) | 0.4081 (0.030) |
19 | 1.10 (0.023) | 0.060 (0.023) | 0.40 (0.033) | 0.3683 (0.030) | 0.3685 (0.030) |
20 | 1.04 (0.019) | 0.031 (0.019) | 0.31 (0.021) | 0.3138 (0.052) | 0.3145 (0.052) |
21 | 1.11 (0.024) | 0.027 (0.024) | 0.27 (0.045) | 0.3033 (0.069) | 0.3046 (0.069) |
F. Cross-sectional dimensions
Cross sections were obtained by cutting each of the four walls through the center-line of each wall. Comparison of cross sections cut with industrial shears, a razor blade, and a punch die indicated that shears (Heritage 108, Klein Cutlery, Bolivar, NY) were found to minimize cross-section distortion. The entire 25.4 mm height of each sample was analyzed by taking images with an SZX16 microscope (Olympus, Tokyo, Japan) and measuring the dimensions using imagej software. Wbond, which is the width of interlayer contact as shown in Fig. 5, was the primary dimension of interest. The layer height, H, and the total road width, Wmax, were also measured as shown in Fig. 5. Wbond was measured between every layer of every part produced in Table II, resulting in a total of 2863 measurements (parts made with H = 0.1 mm had 252 interfaces, H = 0.25 mm had 101 interfaces, H = 0.4 mm had 63, H = 0.175 mm had 144, and H = 0.55 mm had 46 interfaces). During the analysis, these 2863 interface measurements were matched to the 2884 real-time pressure, viscosity, shear rate, and temperature measurements described in Sec. II E. The first layer of each of the 21 parts, which was printed with different conditions from the rest of the part, was neglected from the 2884 measurements to match the Wbond measurements to the real-time layer measurements.
The repeatability of the dimensional measurement via imagej was found to be within ±2% as determined by measuring the same feature 15 times. The dimensions in this paper are based on measurements from wall C for each box. Other walls were also analyzed, but as discussed in the supplementary material [45], the dimensions and pressures were very similar for all four walls of the printed boxes. Figure 5 shows some example cross sections for the three different layers heights (conditions 1, 4, and 5) as well as for condition 11, which was printed at extreme conditions that results in very small Wbond values.
III. ANALYSIS
A. 2D transient heat modeling
Immediately after exiting the nozzle, the HIPS begins to rapidly cool and solidify. This temperature profile must be known for the wetting analysis, which continues throughout the cooling process until the polymer becomes too viscous. Therefore, a transient heat model was developed to calculate the temperature profile for all 2884 layers.
The temperature analysis in this work is two-dimensional (2D), making the cooling profile dependent on both the nominal layer height, H, and the nominal road width, W. The third dimension, corresponding to conduction down the length of the road, was neglected based on previous work by Costa et al. [36] who used finite element analysis (FEA) to determine all the significant contributions to heat transfer during FFF; they found that convection with the environment and conduction with adjacent printed material had the largest effects on layer cooling while conduction down the length of the road (as well as other effects such as radiative heat transfer) had a minimal influence on the temperature profile [36].
A finite difference method was programmed using matlab R2018a (Mathworks, Cambridge, MA) to calculate the 2D transient temperature profile of each deposited layer and the previously deposited layers. The analysis uses Tmelt, T∞, and Tbuild, measured for each layer of the corresponding condition in Table II, meaning that each of the 2884 layers has a unique cooling profile that is used to analyze its interlayer contact. Figure 6 depicts the iterative progression of the numerical method used to predict the 2D cooling profile of each individual layer. The initial condition for the first layer is the Tmelt measured while printing that first layer. Convective boundary conditions were based on the T∞ and Tbuild measured for that first layer with convection coefficients described in the supplementary material [45].
Illustration of layer-by-layer, 2D cooling model; a new layer, n, is added at the end of each step.
Illustration of layer-by-layer, 2D cooling model; a new layer, n, is added at the end of each step.
After predicting the cooling profile over the amount of time, t, required to print a single layer (t is calculated based on part dimensions and print speed, S), another layer, n, is added to the first layer, and the cooling analysis is repeated by considering the cross section of both combined layers. As shown in Fig. 6, this process repeats by adding an additional layer after each time increment, t, until N layers are achieved. N is the number of layers required to achieve a printed height of 2 mm, which was found to be the height at which previous layers can be neglected without inducing prediction errors (this analysis is provided in the supplementary material [45]). Yin et al. similarly found that previous layers become negligible in terms of heat transfer after printing a few subsequent layers [23]. Once N layers are reached, the Tbuild measurement is neglected and the bottom boundary condition is based on T∞ as described in the supplementary material [45]. For all subsequent layers, when the new layer is added, the oldest layer is removed from the model until all the layers in the printed part are analyzed.
The finite difference calculations were based on the material properties in Sec. II C. Spatial resolutions of Δx = Δz = 0.0125 mm were used, and a time domain resolution, Δt, was calculated as shown in the following equation:
where M is a dimensionless quantity set as 0.2 to enable the solution to converge accurately while maintaining efficient computation [Eq. (1) resulted in Δt ≈ 0.0004 s]. The model used in this work assumes rectangular layers with a width equal to the nominal road width, W. The supplementary material [45] provides much more detail about the transient heat analysis, validating the assumptions as well as the accuracy of this temperature model, and it discusses the sensitivity analysis for selecting the resolution as well as the number of layers, N.
B. Viscosity analysis
Viscosity is a critical parameter for both the intimate contact and wetting models. The process of intimate contact occurs at different shear rates depending on the processing conditions, and Wbond growth due to wetting occurs during the nonisothermal cooling process. Therefore, the Cross-Williams-Landel-Ferry (WLF) model was chosen for modeling viscosity, since it combines the shear rate dependent Cross model [Eq. (2)] and the temperature dependent WLF model for predicting the zero-shear viscosity, , as shown in Eq. (3) [41],
where is the critical shear stress at which the viscosity profile moves from Newtonian to shear thinning, n is the power law index ( and n are fit to experimental data), T* is a reference temperature (the glass transition temperature in Table I was used), and A1, A2, and D1 are fit to experimental data. The parameters for the Cross-WLF equation are shown in Table III, which were fit to the measurements taken from the in-line rheometer [34]. The fitted Cross-WLF model was used to calculate the viscosity values for the intimate contact and wetting models.
C. Intimate contact
Intimate contact is the initial stage of welding across an interface and is the process governing the initial contact of the two bodies during pressure-driven deposition. The pressure-driven intimate contact process has been ignored in previous FFF literature possibly because the driving pressure has never been previously measured or characterized. This paper, therefore, focuses on measuring Pcontact and characterizing the interlayer contact length by considering both intimate contact and wetting.
An objective of the FFF process is to produce a rectangular cross section with a circular nozzle, so the inherent shape of the melt exiting the nozzle does not match the desired layer shape [29]. The flow fields during this transition from a circular to rectangular shape have been modeled by McIlroy and Olmsted [37] and are also described in the supplementary material [45]. To put it concisely, the melt must abruptly change flow patterns as it goes from flowing through a constrained, cylindrical pipe to being deposited onto a flat surface where the final desired shape is a rectangle with height, H, and a nominal width, W. If allowed to form under no pressure (extruding into open space), the layers would be deposited as transverse cylinders with diameters approximately equal to the nozzle diameter. However, the lateral surface of the nozzle tip (proximal to the nozzle orifice) can be considered as a small plate, providing a constraining surface and contact pressure downwards onto the recently deposited extrudate, flattening it and forcing it down onto the previous layer as it passes overhead.
For modeling purposes, the initial profile of the newly deposited layer can be simplified to a tall rectangle with initial height, H0, and initial width, Wbond0, as shown in Fig. 7. This rectangular simplification has been successfully applied to thermoplastic composites, which are also formed from near-circular contact points between their composite plies [31–33,38]. Intuitively, one expects that the interlayer contact will increase with pressure, time, and temperature (increasing temperature resulting in viscosity reduction). The following model, as initially derived by Lee and Springer [32], explicitly describes the relationship between intimate contact, pressure, time, viscosity, and the initial material state (i.e., H0 and Wbond0).
(a) Idealized depiction of the initial profile of the recently deposited layer prior to be shaped by Pcontact; (b) model depiction of pressure-driven intimate contact; F is force, and f is force per unit length.
(a) Idealized depiction of the initial profile of the recently deposited layer prior to be shaped by Pcontact; (b) model depiction of pressure-driven intimate contact; F is force, and f is force per unit length.
Based on Fig. 7(b), the initial length not in contact, W0, is defined by Eq. (4). The degree of intimate contact, Dic, is then defined by Eq. (5).
As the recently deposited material is pushed downward, H will decrease, and the material will flow out in the x-direction (transverse to the print velocity). Assuming the volume of the flowing rectangle remains constant, applying the conservation of mass, and solving the one-dimensional momentum balance for flow in the x-direction result in Eq. (6) as is initially presented by Lee and Springer [32],
Equation (6) was analyzed for the various conditions in Table II, and it was discovered that the second term in brackets ranges between 200 and 25 000 for the assortment of conditions printed in the DOE from Table II, making the first term (which is equal to 1) negligible. Note that Eq. (6) is not a function of surface tension because intimate contact is a pressure-driven phenomenon assumed to occur more rapidly than surface tension wetting [31], which is calculated with a separate model (described in Sec. III E). W0, Wbond0, and H0 are all constants, so they can be combined into one empirically determined constant called the roughness parameter, Rc [38],
Finally, combining Eqs. (5)–(7), and replacing the Newtonian viscosity term, μ, with the temperature and shear dependent viscosity, η, produces the following equation:
Equation (8) is the pressure-driven intimate contact model used in this work to predict Wbond. Pcontact is the previously described contact pressure measured by the in-line rheometer; Rc was held constant at 0.75 for all conditions as determined by statistically fitting Rc to the Wbond measurements for condition 1 as described in the supplementary material [45]; tP is the time the layer is exposed to the pressure, which is calculated based on the length, L, of the contact surface adjacent to the nozzle orifice, and the print speed, S, as described by the following equation:
where Router is the outer radius of the solid nozzle tip and Rinner is the radius of melt channel in the nozzle tip, which are both defined in Fig. 10. Router was measured to be 0.475 mm, while Rinner was 0.265 mm for the custom nozzle. Taking L equal to Router minus Rinner provides a conservative estimate for L. Typical values for tP are on the order of 4 ms but can vary significantly with the print conditions.
The intimate contact step can be assumed to be isothermal because tP is on the order of Δt from the transient heat analysis, making it a nearly instantaneous process where the temperature of the layer remains at Tmelt. The shear rate experienced by the deposited layer, , during the intimate contact process can be described as a sliding plate system [Eq. (10)] where the nozzle is moving at speed, S, and the previous layer is stationary,
D. Cross-sectional dimensions
In order to calculate the transient wetting process as described in Sec. III E, the maximum road width, Wmax, must be characterized. Once Wbond is calculated from the intimate contact process [Eq. (8)], Wmax is calculated by using the geometrical relation in Eq. (11) where the nominal cross-sectional area [Fig. 8(a)] is set equal to the actual cross-sectional area [Fig. 8(b)],
where W and H are the nominal road width and layer height, respectively. As verified in this work and described in the supplementary material [45], H is well controlled by the printer, making it reasonable to use the same value of H for the nominal dimensions [left side of Eq. (11)] and actual dimensions [right side of Eq. (11)]. The actual cross-sectional area of representative printed layers is composed of a rectangle of height, H, and length, Wbond, with half an ellipse on both ends of the rectangle as geometrically defined in Fig. 8(b).
E. Wetting
Once the intimate contact step is complete, Wbond can continue to grow via wetting. The wetting model [Eq. (12)] was initially developed by Frenkel [18] and Pokluda et al. [19] and validated by observing the coalescence of a rotomolding grade of polyethylene. The model assumes two molten spheres, experiencing no external force, coalesce due to the work of surface tension balanced by the work of viscous dissipation as shown in Fig. 9. This model has since been widely used in the literature to predict wetting in FFF [4,5,20–22],
where σ is surface tension and . Maintaining the definitions used by Sun et al. for the FFF process [5], , , and . is Wmax after the intimate contact step (t = 0), which was calculated from Eq. (11).
The form of Eq. (12) indicates that surface tension, viscosity, and the layer dimensions are critical in determining the rate of wetting. However, during rapidly cooling processes like FFF, the effect of surface tension is minimal, since surface tension only varies slightly over the temperature range of interest while viscosity changes by orders of magnitude [4]. The surface tension of HIPS was assumed similar to that of ABS, so a surface tension of 0.029 N/m with a temperature dependence of [4] was used. Equation (12) indicates that two materials will initially wet one another rapidly, but the wetting process will slow down as the separate materials move closer to complete coalescence.
Discretizing Eq. (12) at various time increments, i, and solving for Wbond gives
Combining Eqs. (11) and (13) results in two equations and two unknowns to solve for Wbond and Wmax over the transient cooling process for each layer. Both the surface tension and viscosity terms in the wetting model are temperature dependent variables [5], calculated based on the average temperature of the most recently deposited layer, based on the previously described transient heat analysis. The supplementary material [45] describes how Eqs. (13) and (14) were validated against previous literature results [4], verifying the accuracy of the model.
Both the wetting model and the intimate contact model were applied to calculate Wbond for all 2863 interfaces analyzed in this work. The intimate contact is assumed to occur instantaneously at Tmelt, and then the wetting model is applied to the resulting Wbond, allowing it to continue to grow while the material cools.
F. Contact pressure predictions
Given the contact pressure measurements, we next explore how and why Pcontact values are critical to the quality of the final printed parts. It is, therefore, useful to develop the framework for a simplified model for providing insights into Pcontact. Considering the deposition process as the molten polymer exits the nozzle (Fig. 10), the FFF process strongly resembles common industrial processes such as slot-die coating and blade coating, which are often described using the steady-state Navier–Stokes momentum balance [39,40].
Neglecting inertial terms (very reasonable since the Reynolds number is less than 0.0001 for all the printed conditions), the influence of gravity (very reasonable since the Capillary number divided by the Bond number is greater than 4000 for all the printed conditions), surface tension effects (very reasonable since the capillary number is greater than 150 for all printing conditions in this paper), and using the lubrication approximation where the flow is assumed to be one-dimensional (not as reasonable but enables finding an analytical solution), provides the following ordinary differential equation:
Solving Eq. (15) based on the boundary conditions either for a moving build platform (V = S at z = 0 and V = 0 at z = H) or for a printer with a moving nozzle (V = 0 at z = 0 and V = V at z = H) results in an approximation of contact pressure, Pcont_approx, during the FFF printing process where the first term is always larger than the second, resulting in a positive Pcontact:
where L is the length of the outer orifice of the nozzle, S is the velocity of the nozzle or build platform, q is the volumetric flow rate divided by the unit width (y-axis) into the page (flow rate is normalized by the width because this equation is based on the assumption of a slit of near-infinite width, which is true for operations like sheet extrusion or knife coating). Equation (16) has poor accuracy as a predictive model due to a few sources of error: the nozzle is a small diameter rather than an infinite slit, so the flow and pressure profiles are multidimensional and should not be modeled as one-dimensional; polymer melts are non-Newtonian and should be modeled as such; the previous layers below the nozzle may be deformable under the contact pressures. Despite the inaccuracies and assumptions of Eq. (16), the model provides important insights into the main parameters that influence contact pressure. Therefore, Eq. (16) is useful because it indicates that layer height has a profound effect on pressure drop and that the total flow rate, print speed, viscosity, and nozzle dimensions also affect Pcontact.
IV. Results
A. Pressure curves
The pressure curve for the entire print of condition 1 (all center conditions of Tm = 250 °C, H = 0.25 mm, W = 0.5 mm, S = 2500 mm/min) is shown in Fig. 11(a) with the corresponding volumetric flow rate below it in Fig. 11(c). The pressure spike at the beginning of the process (t ∼ 80 s) is caused by feeding filament that had previously been retracted to make sure the nozzle is filled with new material. The low plateau pressure from ∼80 to 280 s corresponds to printing the brim, which is printed at a slow flow rate to aid adhesion to the build platform.
The high pressure duration from about 280 to 780 s occurs while printing the various layers that form the walls of the box. Looking at the 100 s window of Fig. 11(d), the volumetric flow rate (measured from the linear speed of fed filament) is typically around 5.25 mm3/s when at equilibrium, but it exhibits a series of oscillations where the flow rate steps down to 0 mm3/s. Each oscillation corresponds to a different layer because the flow rate stops momentarily while the nozzles moves up to the next layer. Likewise, the transitions in flow rate transfer to the melt pressure, causing a slightly delayed transient in the pressure curve [Fig. 11(b)]. After the start of printing each layer, the pressure quickly plateaus to the print pressure which is a superposition of open extrusion pressure, Popen, and contact pressure, Pcontact. Many more fluctuations in the plateau pressure occur during layer printing compared to printing into open space [this is seen most clearly in Fig. 4 (Multimedia view)], indicating that the plateau fluctuations are caused by changes in Pcontact. Since Pcontact is forcing the fresh material into intimate contact with the previous layer, the pressure fluctuations may be caused by changes in the shape and topology of the previous layer or by changes in the distance between the nozzle and the previous layer, which would all have a profound effect on Pcontact based on the approximation in Eq. (16). Pressure fluctuations are also caused by the accelerations around the four corners of the box, which occur when the nozzle and the flow rate slow down slightly while accelerating around corners.
Figure 11 shows a steady-state melt pressure of about 1.3 MPa. Considering all the parts from the DOE in Table II, the plateau pressures ranged from 0.38 to 2.2 MPa, which is significantly lower than the melt pressures of 28 MPa predicted in the literature [35,42]. The discrepancy occurred because the pressures predicted in the literature [35,42] were based on motor power measurements, which failed to correctly measure polymer viscosity; therefore, the accurate in-line rheometer used in our research is critical for testing the models developed for FFF and for understanding the melt flow through the nozzle.
For each new layer, there is a delay between beginning to extrude material (plateau of Q) and achieving the pressure plateau. This delay is associated with an equilibrium time to achieve steady-state flow out of the nozzle. The equilibrium time for each layer occurs while printing wall A, resulting in slightly less material at wall A, which has previously been shown to cause a lower strength at wall A [1]. The final event in the process, which occurs from about 780–820 s in Fig. 11, is the extrusion of molten polymer into open space at the same volumetric flow rate and same shear rate used to print the walls of the box. This enables accurate comparison between the extrusion pressure while printing in open space versus the pressure while printing the part, which was found to be the most accurate way to calculate Pcontact.
For the remaining results in the paper, the first 10% of all layers were removed from the analysis because the first few layers are very sensitive to small variations in the level and positioning of the build platform. For some conditions, this was evident by observing differences in the pressure curves or dimensional measurements. For example, Fig. 11(a) shows that the first 6 layers of Condition 1 had a lower pressure plateau than the rest of the part. For consistency, the first 10% of layers were removed from the statistical analysis of all conditions.
B. Contact pressure measurements
Intuitively, and as supported by the approximation in Eq. (16), Pcontact is expected to drastically increase as the layer height, H, is decreased. Conditions 17–21 were designed to validate the correlation between Pcontact and H by maintaining a constant Tm, W, Q, and nozzle shear rate, , in order to minimize the influence from all variables other than H. As shown in Fig. 12, there is a profound and expected increase in Pcontact as H decreases, particularly for small H. This finding supports that the increase in P while printing layers (compared to printing in open space) is indeed caused by the confined space created by the layer beneath the nozzle, which effectively increases the pressure at the exit of the nozzle from ambient pressure to Pcontact. Additionally, these results show that Pcontact can be successfully measured with the pressure transducer used in this work.
Pressure curves and flow rates for condition 1: [(a) and (c)] full curve and [(b) and (d)] zoomed in to 100 s range.
Pressure curves and flow rates for condition 1: [(a) and (c)] full curve and [(b) and (d)] zoomed in to 100 s range.
Average Pcontact for conditions 17–21 where H was systematically varied while maintaining a constant Q; error bars show 95% confidence interval.
Average Pcontact for conditions 17–21 where H was systematically varied while maintaining a constant Q; error bars show 95% confidence interval.
Contact pressures are expected to be related to how the polymer flows upon exiting the nozzle, and they are expected to cause the intimate contact with the previous layer. This theory is supported by the results in both Figs. 13 and 14. Figure 13 shows an overlay of both the measured bond width, Wbond, and measured Pcontact for the 90 layers at the center (approximately halfway up the 25.4 mm tall box) of the parts printed in Condition 1 where H was 0.25 mm and Condition 5 where H was 0.1 mm. There is a visually obvious pattern identified by matching the peaks and valleys of the Pcontact and Wbond curves where layers printed with a higher Pcontact also have a larger Wbond, supporting the theory that pressure is driving the two layers together. On a more quantitative basis, Fig. 14 shows a regression of Wbond and Pcontact raised to the 1/5 power [the 1/5 relationship is predicted by Eq. (8)] for Conditions 17–21 after removing the outliers with residual errors greater than two times the standard deviation of the residuals (this resulted in 5% of the data being removed). Again, there is a strong relationship between Pcontact and Wbond, supporting the hypothesis that pressure is driving interlayer contact.
Bond width for 90 of the center layers for (a) condition 1 (H = 0.25 mm, Tm = 250 °C, W = 0.5 mm, S = 2500 mm/min) and (b) condition 5 (H = 0.1 mm, Tm = 250 °C, W = 0.5 mm, S = 2500 mm/min).
Bond width for 90 of the center layers for (a) condition 1 (H = 0.25 mm, Tm = 250 °C, W = 0.5 mm, S = 2500 mm/min) and (b) condition 5 (H = 0.1 mm, Tm = 250 °C, W = 0.5 mm, S = 2500 mm/min).
Regression of bond width and contact pressure raised to the 1/5 power for the layers printed in conditions 17–21 where layer height was systematically varied.
Regression of bond width and contact pressure raised to the 1/5 power for the layers printed in conditions 17–21 where layer height was systematically varied.
Observing Figs. 13 and 14, the correlation between Wbond and Pcontact is stronger for higher Pcontact values. For example, parts printed with H equal to 0.25, 0.175, or 0.1 mm have high Pcontact measurements, and the Wbond and Pcontact correlation is visually detectable like in Fig. 13; however, the measured Pcontact is small (close to the resolution limit of the in-line rheometer) for layer heights of 0.4 and 0.55 mm, so an obvious trend is not visible for these large layer heights. Nonetheless, as later discussed in more detail, the smaller pressures for larger H conditions result in smaller Wbond values, confirming the strong trend between Wbond and Pcontact. Figures 13 and 14 also show that there is significant variation in both Wbond and Pcontact. Some of this variation is likely caused by the variation in the filament diameter, but as shown in the supplementary material [45], the correlation between Pcontact, Wbond, and printed area is poor, indicating that filament diameter does not completely describe these variations. The variations are believed to be induced by the dynamics of the transient printing process; for example, any change in the topography of the underlying layer or any change in the distance between the nozzle and the previously deposited layer will locally affect H, which will drastically affect Pcontact and Wbond. Regardless, increasing the filament diameter or decreasing the local H generally results in an increase in Wbond, which would also be detected by an increase in Pcontact.
An important outcome from this work is that process variations like changes in local layer height or changes in filament diameter can be monitored by observing P and Pcontact with the in-line rheometer to better understand part consistency and to develop real-time predictions of the resulting Wbond. Pcontact could also have important implications on the print processing window and part quality because the increase in printing pressure due to the Pcontact could limit print speed by causing filament slippage or motor torque limitations.
C. Bond width predictions
Wbond was predicted based on the average in-line measurements for each of the 2863 printed interfaces to compare to the 2863 interlayer measurements. Wbond was predicted initially with the intimate contact model [Eq. (8)] in combination with the Pcontact and Tmelt measurements, and the and η calculations for each layer; the predicted Wbond after the intimate contact step is referred to as Wbond_IC. Wbond_IC is then predicted to grow during the cooling process based on the wetting model [Eqs. (13) and (14)] and transient heat analysis. The final predicted Wbond after combining intimate contact and wetting is referred to as Wbond_pred. The results of the final model predictions (Wbond_pred) are compared to the Wbond measurements in Figs. 15 and 16, and Table IV. Table IV also includes the average P and Pcontact for each condition.
Average measured bond width and model predicted bond width for the main effects: (a) conditions 1–3, (b) conditions 17–21, (c) conditions 1, 6, 7, and (d) conditions 1, 8, 9; error bars show 95% confidence intervals.
Average measured bond width and model predicted bond width for the main effects: (a) conditions 1–3, (b) conditions 17–21, (c) conditions 1, 6, 7, and (d) conditions 1, 8, 9; error bars show 95% confidence intervals.
Regression of bond width and predicted bond width for all conditions from Table II.
Regression of bond width and predicted bond width for all conditions from Table II.
Figure 15 shows how changing each of the processing parameters independently affects both the measured and predicted Wbond values. Other than the conditions that resulted in very low Pcontact measurements that may have been outside the resolution of the custom pressure transducer, such as Condition 3 where W = 0.35 mm and Condition 7 where S = 1000 mm/min, the measured and predicted values show good agreement. Additionally, the model shows the appropriate trends. For example, increasing W or decreasing H both cause large increases in Pcontact, resulting in greater interlayer contact. The effect of S is minimal because there are many competing factors when considering Eq. (8). As S increases, Q increases which causes Pcontact to increase, but tP also decreases due to the faster speed, and viscosity slightly decreases due to an increase in . Likewise, increases in Tm only cause marginal increases in Wbond because the decrease in viscosity favors intimate contact and wetting but will also decreases in Pcontact.
The measurements and model results in this work match those in the literature where Abbott et al., who experimentally explored interlayer strength and contact in ABS, also found that parts made with the smallest layer heights had the largest interlayer contact and that increasing Tmelt slightly increased interlayer contact [30]. Similarly, the model presented here supports previous findings that have shown an increase in Wbond due to increases in-print speed [43]. In contrast, the Wbond measurements from our work show that increases in-print speed have negligible to slightly negative influence on Wbond, which could be due to a couple factors: Flow rates have previously been found to decrease at higher print speeds due to either filament slip or motor torque limitations [1], but the flow rates measured by the filament encoder during this DOE indicate that flow rates only decreased by 1% when going from a print speed of 1000 to 4000 mm/min, indicating that flow rate does not completely explain the decrease in Wbond with print speed. Errors in estimating the shear rate between the nozzle and previous layer as well as the model assumption of a Newtonian viscosity may also contribute to the discrepancy between the trend of Wbond as a function of print speed.
The results presented in Table IV and Fig. 16 further confirm the agreement between the interlayer contact measurements and predictions. Figure 16 shows the regression for all conditions included in the study. The bottom 10% of layers were removed as previously discussed, and all layers printed with Pcontact < 0.04 MPa were removed from Fig. 16 due to the lack of resolution of the in-line rheometer at these low pressures [34]. Finally, the outliers with residual errors greater than two times the standard deviation of the residuals were removed (the outliers totaled under 5% of the data).
V. Discussion
A. Intimate contact and wetting
An interesting finding from Table IV is that the effect of wetting was negligible for all the printed conditions, since Wbond_IC ≈ Wbond_pred. Intimate contact is, therefore, the main contributor to interlayer contact with minimal influence from wetting. Additional results are shown in the supplementary material [45] where the wetting model is applied to materials in an isothermal molten state, showing that wetting can theoretically contribute to Wbond growth; however, the rapid cooling during practical FFF printing conditions causes viscosity to increase very rapidly and limit the wetting growth. The transient wetting growth during the first one second of cooling is shown in Fig. 17 for conditions 1 and 10. Condition 1, which was printed at the center points of all the parameters, shows representative wetting growth while condition 10 shows the results for the condition with the greatest amount of wetting growth due to the high Tm and low Wbond_IC. Additional results in the supplementary material [45] show that wetting growth is very minor even if intimate contact is neglected such that wetting starts with only one point of contact between the two layers.
Wbond growth due to wetting during the first 1 s after deposition for (a) condition 1 (Tm = 250 °C, H = 0.1 mm, W = 0.5 mm, S = 2500 mm/min) and (b) condition 10 (Tm = 275 °C, H = 0.4 mm, W = 0.35 mm, S = 4000 mm/min); Wbond at t = 0 indicates the initial state due to pressure-driven intimate contact, Wbond_IC.
Wbond growth due to wetting during the first 1 s after deposition for (a) condition 1 (Tm = 250 °C, H = 0.1 mm, W = 0.5 mm, S = 2500 mm/min) and (b) condition 10 (Tm = 275 °C, H = 0.4 mm, W = 0.35 mm, S = 4000 mm/min); Wbond at t = 0 indicates the initial state due to pressure-driven intimate contact, Wbond_IC.
The drastic increase in viscosity during the cooling process quickly causes the wetting process to come to a halt. Sun et al. had similar findings, indicating that the wetting process for ABS is only significant at temperatures greater than 200 °C. Because they did not consider pressure-driven intimate contact, they found the wetting equation to greatly underestimate Wbond [5]. When comparing intimate contact and wetting, Butler et al. state that if pressure is required for the surfaces to flow, then intimate contact becomes important and wetting becomes negligible [31]. Both intimate contact and wetting may be important for certain materials and FFF conditions, but the wetting process is typically expected to play a minor role in the growth of Wbond. Interlayer contact is primarily a pressure-driven process that can be described by the intimate contact model.
B. Contact pressure predictions
The average Pcontact values for the main effects are shown in Fig. 18. Qualitatively, these trends are supported by the estimate provided in Eq. (16). The analysis indicates that layer height causes the greatest change in Pcontact with nonlinear growth particularly as H becomes small. Print speed is proportional to flow rate [q in Eq. (16)], so Pcontact is linearly proportional to S as expected. Increasing melt temperature decreases viscosity, so Pcontact decreases with Tm as expected.
Mean Pcontact for (a) conditions 1–3, (b) conditions 17–21, (c) conditions 1, 6, 7, and (d) conditions 1, 8, 9; error bars show 95% confidence interval.
Mean Pcontact for (a) conditions 1–3, (b) conditions 17–21, (c) conditions 1, 6, 7, and (d) conditions 1, 8, 9; error bars show 95% confidence interval.
Although Eq. (16) offers qualitative understanding of Pcontact, it fails to accurately predict Pcontact. The predicted values from Eq. (16) are not presented here because they overpredict Pcontact by about 2–5 times, depending on the condition. The predictive power of Eq. (16) suffers primarily because it is a one-dimensional solution. The effect of W on Pcontact in Fig. 18(a) clearly shows that the flow of melt exiting the nozzle is multidimensional. Additionally, Xia et al. have shown that previous layers deform while new layers are printed on top of them [44], which could affect the value of H in Eq. (16) and therefore the Pcontact. An improved model of the three-dimensional, non-Newtonian flow is needed to gain better theoretical understanding and predictive power of the contact pressures developed during printing.
C. Comparison to geometrical model
The subject of this paper focuses on using Pcontact to predict Wbond, but to be completely thorough, another method for predicting interlayer contact is proposed and discussed. An alternative, intuitive, and simple model could also be used to estimate Wbond based on geometrical considerations. Considering the sketch in Fig. 8(b), the two half-ellipses on both sides of the cross section can be assumed to be two half-circles, since surface tension will act to minimize surface area. The diameter of each of these half-circles would be equal to the layer height, H. Applying these assumptions to Eq. (11) and solving for Wbond provides the following equation:
The results of the geometrically predicted model are compared to the intimate contact model and the measured values in Fig. 19. The model in Eq. (17) provides a reasonable starting point for guessing Wbond, but the intimate contact model [Eq. (8)] is consistently more accurate. More importantly, the intimate contact model accounts for the real-time variations in the process. As shown in Fig. 13, the actual Wbond measurements significantly vary from one layer to the next. By using an in-line rheometer [34] to monitor the pressure variations, the intimate contact model can predict the layers of a single part with the best and worst interlayer contact, which is crucial for predicting interlayer bond strength, since parts are expected to fail at the weakest link. This work shows that the variability in Wbond can be determined from the real-time pressure measurements, so any dynamic model for interlayer contact should include the Pcontact term. Additionally, the model in Eq. (8) is simple enough to be used for real-time analysis, prediction, and control, so the in-line rheometer plus the intimate contact model can be implemented into FFF microcontrollers to provide users with immediate feedback regarding the quality of their parts.
Mean bond width and geometrically predicted bond width for (a) conditions 1–3, (b) conditions 17–21, (c) conditions 1, 6, 7, and (d) conditions 1, 8, 9; error bars show 95% confidence interval.
Mean bond width and geometrically predicted bond width for (a) conditions 1–3, (b) conditions 17–21, (c) conditions 1, 6, 7, and (d) conditions 1, 8, 9; error bars show 95% confidence interval.
Another alternative for including Pcontact into an interlayer contact model is to combine Eqs. (16) and (17) to solve for Wbond as a function of Pcontact. However, such a model would only be relevant if a multidimensional analysis were applied to improve the fidelity of Eq. (16). Future work is, therefore, recommended for predicting Pcontact through a multidimensional analysis, which could then be used as an alternative method for predicting interlayer contact.
VI. CONCLUSIONS
While printing FFF parts, the confined space created between the nozzle tip and the previous layer causes the pressure of the melt at the exit of the nozzle (Pcontact) to increase with increasing melt viscosity, volumetric flow rate, road width, and layer height. Small layer heights contribute most significantly to increasing the exit contact pressure, which is responsible for forcing the new layer into intimate contact with the previous layer. Contact pressure was found to directly correlate with interlayer contact, so contact pressure is expected to be a critical determinant of the final part strength as will be explored in the future work. A model was introduced for combining both intimate contact and wetting, and the model has proven successful for predicting the interlayer contact of FFF parts. This is the first interlayer contact model capable of accurately predicting contact length, providing a crucial missing piece toward a comprehensive FFF strength model by outperforming bond width predictions based purely on conservation of volume given by the printing geometry.
For the wide range of processing conditions explored in this work, pressure-driven intimate contact was a critical contributor for interlayer contact while wetting growth had a nearly negligible influence. The authors strongly recommend that future FFF strength models consider contact pressure and its influence on interlayer contact. All the results in this paper were enabled by the in-line pressure transducer, thermocouples, and filament encoder; future researchers should incorporate similar sensors into their printers to better understand the printing process and to monitor print consistency and part quality. The simplicity of both the in-line rheometer for measuring contact pressure and the model for predicting intimate contact allow them to be implemented into FFF microcontrollers to provide immediate feedback about part quality. Measuring in-line pressure provides the critical benefit of monitoring pressure variations to estimate the resulting variations of interlayer contact. Future work should aim at discovering the cause(s) of these variations, which would be aided by both the use of an in-line pressure measurement and a more comprehensive and accurate model for predicting contact pressure.
ACKNOWLEDGMENTS
This work was funded jointly by Saint-Gobain Research North America and the University of Massachusetts, Lowell. The authors would like to give special thanks to J. Alex Lee of Saint-Gobain for the excellent discussions related to the lubrication approximation, geometrical calculations of Wbond, and tips for programming in matlab. The authors also thank Mosaic (Toronto, Canada) for the provision of the filament velocity instrumentation.