1. Introduction
Large-format extrusion-based additive manufacturing is a technology that, in recent years, has become widespread in the fabrication of composite applications in the marine and construction industries, allowing for greater design flexibility while reducing lead times and costs [
1,
2,
3]. The Big Area Additive Manufacturing (BAAM) [
4] system developed at Oak Ridge National Laboratory in collaboration with Cincinnati Inc. has been successfully used to manufacture large parts with a variety of thermoplastic composites [
5,
6]. Both the BAAM system and desktop-scale Fused Filament Fabrication (FFF) extrude heated thermoplastic material along programmed tool paths to manufacture parts on a layer-by-layer basis [
6]. Unlike FFF, BAAM uses a single-screw extruder to melt polymer pellets and force the molten material through a nozzle via a pressure differential [
7] instead of resistively melting a thin filament feedstock. Single-screw extruders enable the use of thermoplastic materials at a relatively lower cost and at faster deposition rates with mass throughputs up to 50 kg/h. With regard to the architecture of manufactured parts, BAAM- and FFF-produced components are similar, although the former produces parts which are an order of magnitude larger with bead dimensions at or above 10 mm. An example of a large-format additively manufactured structure is BioHome3D, which is a 56 m
2 modular house manufactured using a recyclable biopolymer filled with wood fiber [
8].
Performance objectives for 3D-printed parts create demand for materials to exhibit functionalities [
9] including improved electrical and thermal conductivity, mechanical strength, and stiffness at relatively low cost [
5,
10]. To accommodate this demand, researchers have attempted to mix different types of fillers, such as metal [
10], glass fibers [
11], and vapor grown short carbon fibers [
11,
12] into the polymer matrix. Although the macrostructure of large 3D-printed parts alone contributes to thermal and mechanical anisotropy due to layer-wise deposition [
12,
13], this phenomenon is accentuated in short-fiber composites. Fibers with varying aspect ratios tend to align in the print direction, significantly affecting homogenized material properties [
7]. Moreover, fiber alignment has also been seen to vary within the printed bead itself [
14].
For a fiber-reinforced thermoplastic polymer, the cooling behavior of the deposited material is governed by heat transfer to the environment due to convective and radiative heat losses as well as conduction between beads and layers [
15]. The rate of cooling governs both the phase change from viscoelastic fluid to solid and inter-bead bond quality [
16]. The combination of these processes impacts the formation of residual stresses and deformations within the part [
17], affecting the shape of the extrudate [
18] and subsequent mechanical properties [
19,
20]. High-quality characterization of the associated thermal history is therefore required to ensure robust prediction of outcomes from the manufacturing process. Moreover, new additive manufacturing technologies such as 4D printing rely on the programming of different extrudate temperatures throughout printing to govern the polymer structure shape transformation over time [
21,
22].
Experimentally obtained thermal history data are often captured and reported by means of infrared (IR) radiation thermography [
14,
23,
24,
25]. The initialization of an IR camera for data capture, which is a necessary component of thermographic measurement for accurate temperature reporting, requires information about the scene and subject to correctly correlate as-measured radiance with as-reported temperatures. This requisite information includes an emissivity parameter, which varies according to the material surface roughness, the temperature dependence of the material’s emissive response, the angle of incidence between the subject surface normal and camera optical axis, and the line-of-sight distance between subject and camera. Similarly, knowledge of the scene temperature is required during initialization to accurately account for the proportion of as-measured radiance due to reflection from the subject [
26]. These factors are often neglected or simplified, as in the case of a constant emissivity value, the practice of which imposes error on the temperature data reported by IR cameras [
25]. By contrast, thermocouples are commonly used in research and industry to measure temperature with relatively simple sources of inaccuracy and across different processes. Previously, thermocouples have been embedded in small-scale additively manufactured parts for in situ temperature characterization [
27,
28].
Predictive tools that incorporate the coupled impacts of bed temperature, ambient temperature, and material properties on thermal history are also necessary. Layer-by-layer deposition models have been developed ranging from simple axisymmetric 1D transient heat transfer models [
14,
29] to 3D finite element models (FE) [
30,
31]. The finite difference method has also been used to numerically model temperature variation for the FFF processes, including large-format additive manufacturing, due to reduced computation costs when compared against FE implementations [
32,
33,
34]. Recently, a coupled thermo-mechanical numerical model to determine a suitable combination of the parameters that avoids the collapse of the deposited layer under self-weight was developed [
35]. FE-based methods have represented the thermal history of 3D-printed parts based on element activation [
36], accounting for temperature-dependent material properties [
37] and presented features that allow modeling heat transfer at time scales small enough to capture rapid cooling events [
38]. In particular, the commercial FE software Abaqus (
https://www.3ds.com/products-services/simulia/products/abaqus/, accessed on 1 August 2023) with additive manufacturing capabilities has been used to model complex 3D-printed parts, such as cellular structures with homogenized material properties [
39] and thin-walled tubular structures [
40]. Abaqus has also been applied to model the thermal history, final deformed shape, and residual stresses in additively manufactured parts comprised of acrylonitrile butadiene styrene (ABS) polymer [
41], ABS with short carbon fibers [
15,
42], polyphenylene sulfide (PPS) polymer with carbon fibers [
43,
44], and metals [
45]. The majority of published research on the topic of thermal modeling for FFF rely on the use of a constant convection coefficient.
This work combines in situ temperature measurements obtained from an additively manufactured part with candidate FE models of the manufacturing process. Candidate models were compared against experimental data, and the FE implementation that minimized error was found to require a non-constant convection coefficient in order to accurately capture the thermal history of the part. Finite element analysis was used to model the complete thermal history of a large-format 3D printed vertical wall made of poly(ethylene terephthalate) glycol (PETG) with short carbon fiber (CF) reinforcement. PETG is recognized for its manufacturability with glass transition and melting temperatures of 85 °C and 260 °C, respectively [
46,
47], qualifying the material as a good candidate for thermal and structural characterization. The accuracy of the thermal model was enhanced by real-time temperature data gathered by thermocouples embedded in the part during the manufacturing process. The temperature correlation between experimentally obtained and numerically generated data facilitated the characterization of conductance between the part and print bed, as well as convective heat transfer between the part and the environment, comprising process model features which were found to substantially impact the development of residual stresses. Finally, a correlation equation was derived based on the analysis of the wall manufactured with PETG/CF material and tested on a separate wall manufactured with ABS/CF. The necessity of this study is driven by the tendency for large-scale additively manufactured parts to fracture and/or develop significant distortion during manufacturing due to the accumulation of residual stresses [
48,
49,
50,
51]. Hence, the objective of this work is to improve the accuracy of FE models intended to capture the thermal behavior of large-scale polymer AM during fabrication via in situ temperature measurements.
2. Materials and Methods
2.1. Printing Process Information
Part manufacturing was executed on the BAAM machine stationed in the Advanced Structures and Composites Center at the University of Maine campus in Orono, Maine. A prismatic vertical wall was chosen for geometric simplicity and to facilitate parametric convection studies via the measurement of temperature variations along the height. The wall was manufactured with Techmer Electrafil 1711 PETG, which is compounded with 18% carbon fiber volume fraction. The magnitude of fiber volume fraction was not chosen to satisfy any specific criteria, but it is typical for materials provided by the supplier, and prior studies have used products with similar amounts [
14,
25]. The average carbon fiber length and diameter were 163 µm and 7 µm, respectively. The wall consisted of a single bead with the first layer extended laterally to form a brim for improved stability. The initial manufacturing process parameters were based on the layer time utilized in a prior publication with similar geometry [
14] and modified to mitigate the overall deformation and debonding between layers. The wall dimensions and manufacturing process parameters are given in
Table 1.
Type K thermocouples were manually installed between layers of the wall to capture the temperature at the interfaces. Thermal history was obtained below the first layer at the part/bed interface and at layers 38, 77, 116, 155, and 194. A plywood scaffolding structure was designed to hold the thermocouple leads and utilized to prevent forces due to gravity from pulling thermocouples out of position during solidification of the extrudate.
2.2. Interlayer Thermocouples—Final Position Measurement
Although the approximate locations of embedded thermocouples were known from visual inspection, accurate positional measurements were taken to verify the quality of contact with the extrudate. A Quantum Max FaroArm® (Faro Technologies, Lake Mary, FL, USA) was used to provide a detailed 3D scan of each wall for X–Z (length, height) location determination. A coordinate system was chosen to denote the locations of the thermocouples, and the planar geometry of the walls was leveraged accordingly. The coordinate system origin in X, Y and Z was chosen to be the first identifiable point where extrusion begins, the midpoint of the wall thickness, and the center point at the part/bed interface, respectively. Thermocouple locations are reported in reference to this coordinate system and were used for comparison with model data.
End-mill removal of the as-manufactured material revealed bond quality with the surrounding polymer as well as the relative location of the thermocouple within the bead. Overall, 30% of the thermocouples embedded in the PETG/CF wall exhibited some aspect of poor-quality bonds (C3, AI0, and AI3) as determined by visual inspection of the contact between the thermocouple lead wires and the extrudate. The set of thermocouples observed to have good bonds with their surrounding polymer was used as sources for comparison with model data.
Figure 1 shows the position coordinates together with their calculated uncertainty values and labels for each interlayer thermocouple in the PETG/CF wall with respect to the direction that material was deposited in a given layer. Location uncertainty was characterized by disruptions in the external surface of the extrudate, which created regions of scan data devoid of information due to occlusion. Positions were determined by averaging the extreme values of the disruption in X, Y, and Z orientations. Finally, the average was then subtracted from the maximum value to determine the associated uncertainty. Thermocouples labeled as C0 and C1 were placed at the part/bed interface and are not included in
Figure 1. The letter difference in thermocouple labels (C and AI) denotes sampling rates of 1 and 2 Hz, respectively.
2.3. PETG/CF Material Characterization
The material characterization procedures utilized in this work were based on a proposed roadmap for testing the same type of additively manufactured short-fiber composite materials [
52]. Thermomechanical and mechanical property data were obtained as inputs to the FE models. Material property data were generated from test specimens exercised from a different part manufactured in PETG/CF with the same deposition temperature profile, deposition speed, and nominal bead dimensions as the wall print. Aligning the processing conditions in parts manufactured for material property characterization with the processing conditions employed for experimental prints is intended to control for uncharacterized process effects.
Density measurements were performed with the Specific Gravity Method according to the ASTM D792-20 [
53]. In total, there were 54 samples (18 samples cut in each X, Y, and Z orientation). Each sample was 17 × 17 × 7 mm
3 with the short axis parallel to the orientation of interest. The final density parameter utilized in the FE model was the sample set average value of
ρ = 1271.185 kg/m
3.
Specific heat (
Cp) measurements were performed with a TA Differential Scanning Calorimeter instrument (DSC2500—TA Instruments, New Castle, DE, USA) according to ASTM D3418-21 [
54]. Five samples weighing at least 5 mg were tested to verify consistency in the measured response.
Table 2 shows a subset of the values utilized in the FE model, which was an average of the five samples from 25 to 225 °C.
Thermal conductivity at room temperature was determined using the transient plane source (TPS) method according to ISO 22007-2 [
55] which utilizes direct thermal diffusivity measurement. In total, 81 paired combinations out of 54 samples (18 samples for each X, Y, and Z orientations) were tested at room temperature of approximately 25 °C. Each sample was cut with the dimensions of 17 × 17 × 7 mm
3. Capturing the temperature dependence of the conductivity response for the same range of temperatures adopted for specific heat characterization is ideal, however, limitations to equipment functionality prevented this level of fidelity. After averaging the measurement data among all samples for each orientation, the orthotropic thermal conductivity values at room temperature adopted in the FE model were 0.59, 0.48. and 0.35 W/m
2K for the X, Y, and Z directions, respectively.
Coefficient of thermal expansion (CTE) values were obtained by using a TA Thermomechanical Analyzer (TMA Q400—TA Instruments, New Castle, DE, USA) according to ASTM E831-19 [
56]. In total, 5 samples for each orientation, X (4.9 × 4.9 × 8.2 mm
3), Y (4.9 × 4.9 × 6.9 mm
3), and Z (4.9 × 4.9 × 4.1 mm
3), were tested. Strain measurements from the test were preserved for temperatures below the glass transition temperature (T
g = 74.4 °C) of the material, which was determined according to ASTM D7028-07 [
57]. At temperatures above T
g, thermally-induced strains were assumed to be constant. The CTE for each orientation was obtained by dividing the strain measurement values by the difference between a temperature of interest and the reference temperature of T
ref = 20 °C. The average strain curves and their derived CTE curves for each orientation are shown in
Figure 2.
Elastic response in X and Z orientations as a function of temperature was measured by a TA Dynamic Mechanical Analyzer (DMA850—TA Instruments, New Castle, DE, USA) according to ASTM D5023-15 [
58]. Three rectangular specimens (49 × 2 × 10.6 mm
3) for X and Z orientations were tested in flexure as a beam. The elastic response in Y orientation was assumed to be the same as the Z orientation response for simplification. Values for shear moduli and Poisson’s ratios were obtained from published tensile and compressive test data [
59,
60]. The subsequent room temperature orthotropic elastic response was used as a reference definition for the multi-factor approach [
61] in order to represent the temperature dependence of the elastic stiffness, as shown in
Table 3. The elastic stiffness values were assumed to be constant for temperatures at and above 74.2 °C.
2.4. Thermal FE Model of the PETG/CF Wall
Thermal models of the single-bead PETG/CF wall manufactured on the BAAM were implemented in Abaqus/CAE 2021.HF8. The models utilized the Additive Manufacturing (AM) module of Abaqus that drives sequential element activation by means of an event series. An in-house MATLAB code was used to generate the event series from the G-Code-based definition of the toolpath given to the BAAM numerical controller. While the cross-section of the extruded layers is approximately elliptical, for simplicity, the models assume a rectangular bead cross-section.
The wall was meshed with linear hexahedral heat transfer elements (DC3D8) with a seed interval set equal to the layer height of 5.076 mm. The same interval was used for element length and width, producing a mesh comprised of cubic elements. Mesh convergence studies were performed separately to ensure the mesh density chosen for this analysis was acceptable. The bed was modeled using the same DC3D8 heat transfer element in direct contact with the brim. The thickness for the bed geometry was 1.6 mm corresponding to the thickness of the ABS sheet placed on the bed for printing. A density of 1140 kg/m
3, a thermal conductivity of 0.17 W/m
2K, and a specific heat of 1640 J/kg-K [
62] were used for the ABS/CF sheet.
Figure 3 shows the FE model including the wall and bed along with an image of the wall mesh.
Thermal analysis used a heat transfer step with a fixed time increment of 10 s. This time-step value was tested separately and selected because it provides a balance between computation time and solution accuracy. The top surface of the bed was assigned a convection coefficient of 2.55 W/m
2K, which was estimated for a horizontal planar surface [
63], and an emissivity value of 0.92 [
64]. Ambient temperature for the convective coefficient applied to the ABS/CF bed was captured from thermocouple data at the steady-state regime. A fixed temperature boundary condition of 74.5 °C, as measured by thermocouples installed at the part/bed interface, was set for the bottom and side surfaces of the bed, and the same temperature was used as an initial condition for the entire bed.
The thermal history data from FE models were extracted at selected nodes which correspond to the measured locations of the thermocouples. Synchronization in time was necessary to accurately compare the experimental and model-generated values. Data obtained from thermocouples exhibit a “ramp onset” feature, which is defined as the moment in time when the extrudate is deposited over the thermocouple and a sharp rise in temperature is observed. This feature of the thermocouple time series was aligned with its equivalent nodal activation feature in the FE model. After synchronization, the interpolation of FE data was conducted such that the number of sample points was equal in preparation for root-mean-square (RMS) analysis. Conductance was initially varied in the FE models, and the temperature results were compared to the thermocouple (TC) data obtained at the part/bed interface (C0 and C1). The convection study was then carried out by comparing FE model temperature data with temperature data for all subsequent thermocouples that exhibited good quality contact with the extrudate (C2, C4, C5, C6, C7, AI1, and AI2).
In the following section, results are presented on how conductance and convection values in the FE model were found from fitting the model with experimental data. Each fitting was assessed based on RMS analysis; final conductance and convection values minimized the error between experimentally obtained thermal histories and their model-predicted equivalents. Several RMS time window sizes from 5 to 300 s were tested, issuing similar results. A visualization of the study progression is shown in
Figure 4.