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Abstract

3D-printing induced defects are intrinsic to the layer-by-layer deposition process, which results in reduced performance of materials fabricated using extrusion-based additive manufacturing (AM) techniques. In this study, the effect of porosity introduced by fused deposition modeling (FDM) AM technique on the mechanical performance of natural carbon-enhanced polymer composite (NCPC) materials was evaluated experimentally and through finite element analysis (FEA). Computed Tomography (CT) scans of 3D-printed and traditionally fabricated specimens were used to evaluate porosity and generate the mesh for the FEA model. The FEA results showed that a porosity level of 5.6% led to a reduction in ultimate tensile strength (UTS) and flexural strength (FS) by approximately 6%, compared to a non-porous FEA model. However, the experimental 3D-printed samples showed a 7% lower UTS and 39% lower FS compared to the FEA porous model. As expected, the injection-molded NCPC materials outperformed the compression-molded and 3D-printed samples for both experimental and FEA results.

Keywords

Natural carbon-enhanced polymer composite (NCPC)additive manufacturing (AM)fused deposition modelling (FDM)finite element analysis (FEA)mechanical performance

Introduction

Additive manufacturing (AM) offers a multitude of advantages, including the ability to construct complex geometries, cost effectiveness, and reduced material waste.¹ Due to their recyclability, cost efficiency, and ease of manufacturability, thermoplastic polymers have been widely used in AM applications. However, the mechanical, physical, thermal, or electrical properties of neat thermoplastics often need to be tailored to achieve the performance needed for specific applications. Furthermore, AM of certain thermoplastics, such as polyethylene (PE), has been severely limited due to challenges related to materials shrinkage and warping during printing. Several studies have delved into the incorporation of different types of fillers into thermoplastic materials, aiming to enhance both the printability and performance of the final products.^1–4 In these studies, various types of fillers such as carbon-based nanomaterials, ceramic powders, metallic powders, glassy fillers, minerals, and wood flour, have been investigated.^1,5,6 In the realm of composite fillers, coal and coal-derived carbons have recently emerged as sustainable options for polymer composites. Researchers have successfully demonstrated the technical, environmental, and economic viability of utilizing coal as a filler for structural and building materials such as composite decking and piping applications.^7–9 Compared to unfilled plastics and traditional wood plastic composite (WPC), coal filled composites have shown to possess higher oxidation resistance (i.e., longer service life), greater thermal stability and flammability resistance, lower embodied energy and emission, and lower production costs.^10–12 In addition, recent studies have shown coal to help overcome the warping issues often encountered in PE additive manufacturing.⁴ This development not only enables the utilization of the inexpensive and widely available PE in AM but also creates novel material that is a viable solution to meet the projected demand in high-volume applications like composite tooling and additive housing.

Fused deposition modeling (FDM) is an AM technique widely used to manufacture polymers and polymer composites. One of the drawbacks of FDM for polymer composites is the formation of porosities during the manufacturing process. To determine the effect of porosity on the overall performance, the porosity content needs to be quantified within the AM-manufactured parts. In recent years, many researchers have used computed tomography (CT) to quantify porosities within the various materials.^13–18 Moreover, CT has been used to report the effect of AM processing parameters, including the print direction, print orientation, extrusion temperature, nozzle diameter, layer height and width and printing speed on porosity within the 3D-printed parts.^19–27 Porosity present in the AM parts has been found to reduce mechanical performance. Several studies have stated that the presence of porosity caused the reduction of the tensile strength, flexural strength, elastic modulus, and impact resistance of the material compared to a solid structure with no porosity.^16,19,20,28 Researchers have used finite element analysis (FEA) to assess the impact of porosity on the mechanical performance of polymer composites fabricated using various manufacturing techniques. Using data from CT scans, they generated meshed models, which were then imported into FEA software to evaluate the mechanical response.^{13,15,17,19,28} Additionally, the mechanical results obtained from FEA were compared with experimental findings. These comparisons revealed that FEA generated models typically predict a higher modulus than the results observed in experimental testing.^9,19

Alafaghani et al.²⁶ developed an FEA model to assess the impact of various FDM processing parameters on the tensile behavior of the manufactured parts. Key findings indicated that build direction, extrusion temperature, and layer height were the most critical parameters influencing the tensile responses. While this study yielded compelling results, lack of true geometry-in reference to CT scans-led to structural simplification and result discrepancy. Zouaoui et al.²⁹ later studied the effect printing direction and infill pattern had on the mechanical performance and concluded the 3D-printed material to have anisotropic mechanical properties. The study developed methods for determining bonding conditions that affect the performance of a printed component. The methods include stating local material references in the mesh which allowed for anisotropic simplification. Implementation of local references depicted a quasi-isotropic response due to similar longitudinal and transverse moduli. Behseresht et al.^30,31 developed one of the most comprehensive FDM models to date, which integrates a thermal-mechanical model with user subroutines for greater control over local events during the printing process. By integrating the realistic boundary conditions, and time dependent material deposition, they successfully predicted the temperature distribution, residual stresses, and deformation of FDM parts. The only missing portion of this study would be the introduction of true geometry. There exist a handful of studies simulating the effect of porosity with true geometry on mechanical strength. Yu et al¹⁹ used the true geometry of a fiber-reinforced polymer but results showed significantly more variance in the Young’s modulus than the tensile strength. Elkolali et al.³² used CT data to conduct a 2D model with plane loading, but this was only to evaluate damage and was not compared to experimental stress and strain. Wang et al³³ created a true geometry ABAUQS model for homogenous PLA where the effect of porosity was evaluated with respect to the Young’s modulus.

The primary objective of this study is to assess the effect of 3D-printing induced defects on the mechanical performance of novel natural carbon-enhanced polymer composite (NCPC) materials. These composites consist of coal and high-density polyethylene (HDPE), formulated to enhance performance and printability for large-volume market applications such as composite tooling and additive housing construction. Compared to traditional processes like compression-molding and injection-molding, porosity introduced during additive manufacturing significantly impacts the mechanical properties of the materials. Understanding these effects is crucial for developing solutions to minimize porosity and improve material performance. In this study, FEA models were developed to simulate NCPC materials manufactured using compression-molded, injection-molded, and additive manufacturing methods, aiming to establish the correlation between printing defects and the resulting mechanical performance. The focus of this study, and its framework, are depicted in Figure 1.

Figure 1.

Framework of the Study with the focus highlighted in green.

Methodologies

Materials

HDPE (EA55-003) obtained from ExxonMobil was utilized as the matrix material while bituminous coal (Keystone 325) sourced from Keystone Filler & Manufacturing Co. was used as the filler material in this study. Particle size distribution for the Keystone 325 coal powder can be found in Table 1. Particle size distribution was characterized by the parameters d(0.9), d(0.5), and d(0.1). The d(0.9) value indicates the size below which 90% of the particles are found, while d(0.5) and d(0.1) represent the sizes below which 50% and 10% of the particles fall, respectively.

Table 1.

Average particle size of Keystone 325 coal powder.

Filler type	d(0.9) (μm)	d(0.5) (μm)	d(0.1) (μm)
Keystone 325	29.60	14.57	3.61

To determine the composition of the Keystone 325 coal powder used in this study, proximate and ultimate analyses were conducted. The proximate analysis determines the moisture, ash, volatile matter, and fixed carbon contents in the coal, while the ultimate analysis measures the elemental composition, including carbon, hydrogen, oxygen, nitrogen, sulfur, and ash. These analyses were performed prior to the manufacturing process to evaluate the effect of moisture content on the overall carbon content. Detailed results of the proximate and ultimate analyses are presented in Table 2.

Table 2.

Proximate and ultimate analysis of the Keystone 325 coal powder.

Filler	Proximate				Ultimate
Filler	Moisture	Ash	Volatile matter	Fixed carbon	Carbon	Oxygen	Hydrogen	Nitrogen	Sulfur	Ash
Keystone 325 powder	0.26	7.69	16.02	76.03	81.98	4.19	3.94	1.20	1.00	7.69

NCPC development

Compounding

The composite formulations, consisting of 0.60 wt fraction (60 wt%) Keystone 325 coal powder, 0.39 wt fraction (39 wt%) HDPE pellets, and 0.01 wt fraction (1 wt%) lubricant, were melt-mixed using a Haake Rheocord batch mixer. Initially, the mixer was set to 195°C and operated at 50 rpm to melt the HDPE before the addition of Keystone 325 coal powder. After thoroughly incorporating the coal powder (60 wt%), the mixer speed was increased to 100 rpm for 5 minutes to finalize the compounding process. Subsequently, the resulting NCPC material was processed further by grinding it with a Retsch SM 100 cutting mill.

Filament extruding

The pelletized NCPC material, with a diameter of 2-3 mm, was extruded using a Filabot EX2 single screw extruder to produce a 1.75±0.05 mm 3D-printable filament compatible with commercially available lab-scale FDM 3D-printers. The filament extrusion was performed at a temperature of 200°C and a speed of 4 rpm. NCPC material compounding and filament extrusion processes are shown in Figure 2.

Figure 2.

NCPC compounding and filament extrusion process.

Printing trials

A Flashforge Creator Pro FDM printer was utilized to print test specimens from the NCPC filament. The test specimens included tensile samples compliant with ATSM D638 and flexural samples following ASTM D790. Both the tensile and flexural test specimens (Figure 3) were 3D-printed using the same printing parameters indicated in Table 3. To enhance adhesion and minimize warpage, each sample was printed on a polypropylene build plate.

Figure 3.

3D-printed (a) Type IV tensile and (b) Flexural samples of the NCPC material.

Table 3.

3D-printing parameters for the NCPC formulation.

Nozzle temperature (°C)	Nozzle diameter (mm)	Layer height (mm)	Extrusion speed (mm/s)	Infill (%)	Raster angle (°)
240	0.8	0.2	30	100	0 – 90

Compression-molding

For comparison with 3D-printed samples, the NCPC pellets consisting of 60 wt% Keystone 325 coal powder, 30 wt% HDPE, and 1 wt% lubricant was compression-molded into thin sheets (4 mm) using a Carver hydraulic press. The pelletized NCPC material was placed into a 254 × 254 × 4 mm aluminum mold and heated at 200°C for 20 minutes under zero pressure. Following this, the molds were compressed at a pressure of 1.0 MPa for 5 minutes. Tensile and flexural test specimens following ASTM D638 and D790, respectively, were cut using an OMAX ProtoMax abrasive waterjet. Figure 4 depicts NCPC compression-molded type IV tensile samples. The tensile and flexural samples were sized identically to the 3D-printed samples to ensure an accurate comparison between the two manufacturing methods.

Figure 4.

Compression-molded type IV tensile samples of the NCPC material.

NCPC characterization

Microstructure

A Keyence VHX-7000 series digital microscope, operating at a magnification of ×80, was employed to compare the microstructure of as-fractured surfaces from 3D-printed and compression-molded NCPC specimens. In addition, computed tomography (CT) scans were performed on the 3D-printed and compression-molded NCPC specimens using a TriFoil Imaging Explore CT 120 X-ray CT scanner. The CT scanner had a scan resolution of 25 μm, where pores smaller than the resolution could not be captured in the model. CT scanning was conducted at an energy level of 120 kV and a current of 32 mA while an aluminum filter was used for all scans. Microstructural features, including porosity percentage, size, and distribution, were determined to provide insights into the effect of 3D-printing process on the composite microstructure.

Tensile testing

The NCPC 3D-printed and compression-molded tensile samples were tested as per ASTM D638.³⁴ Testing was conducted using an Instron 5966 at a strain rate of 0.1 mm/mm/min. Strain values were recorded using clip-on extensometers and the load was applied until fracture occurred. A minimum of six samples were tested, and average values were reported.

Digital image correlation (DIC)

Digital image correlation (DIC) technique was utilized to obtain the Poisson’s ratio of NCPC materials for integration into the FEA models. To accomplish this, GOM 2.3-megapixel cameras were used in stereo configuration, and the acquisition software used was Aramis pro. All components were calibrated to the desired field of view of 90 mm with 75 mm lenses for this testing. Tensile testing was conducted on compression-molded samples in accordance with ASTM D638 using an Instron 5567 testing machine, with a strain rate of 5 mm/min. The DIC capture was set to 60 Hz while tensile testing was conducted with five reference frames to determine the strain floor. Using ZEISS inspect correlate, a full field surface component was applied to the gauge section with a facet size of 40 pixels and a point distance of 20 pixels. Poisson’s ratio is determined by applying the arithmetic mean of the transverse and longitudinal strain of the surface component using equation (1).

ν = \frac{ε_{x}}{ε_{y}}

(1)

where ɛ_x is the transverse strain and ɛ_y is the longitudinal strain.

Flexural testing

Flexural testing was conducted as per ASTM D790³⁵ for the NCPC 3D-printed and compression-molded samples. Flexural strength (FS) and flexural modulus (FM) for both 3D-printed and compression-molded specimens were determined. The dimensions for the flexural samples were 100 mm in length, 12.7 mm in width, and 3.2 mm in thickness. Three-point bending tests were conducted using Instron 5966. The rate of crosshead speed (R) was calculated using equation (2).

R = \frac{Z L^{2}}{6 t}

(2)

where R is the rate of the crosshead testing speed (mm/min), Z is the strain rate (mm/mm/min), L is the support span distance (mm) that was calculated by a span-to-thickness ratio of 16:1, and t is the thickness (mm) of the sample. The flexural stress (

σ_{f}

) and flexural modulus (

E_{f}

) were calculated using equations (3) and (4).

σ_{f} = \frac{3 P L}{2 w t^{2}}

(3)

\frac{E_{f} = L^{3} m}{4 w t^{3}}

(4)

where P is the load (N), w is the width of the sample (mm), and m is the slope (N/mm) of the linear region of the force-displacement graph.

Finite element analysis

Prior to creating geometry or representative models, a single-element validation model was created to verify the material model. This process involved tensile validation by incorporating the elastic modulus and Poisson’s ratio obtained from the tensile DIC testing, and plastic stress-strain data. The analysis was conducted in ABAQUS/Standard with nonlinear geometry enabled. Boundary conditions included a fixed constraint on one side and a displacement boundary condition applied to the opposite side. Once validated, the material model was translated into the NCPC geometry and porous representation.

Model geometry and meshing

The FEA models ranged from simple geometries for the creation of solid models, to complex geometries reconstructed from CT scans. CT scans were utilized to capture the intricate internal structure of 3D-printed and compression-molded tensile specimens. The CT scans were processed using Amira 3D, ensuring the generation of finite element meshes suitable for direct comparison to experimental results.³⁶ The following steps were conducted within Amira 3D to prepare the data for meshing:

1. Extract Representative Volume Element (RVE): A subvolume was isolated from the gauge section of the 3D-printed CT scan, which represents the region of interest and loading with porosity characteristics similar to those of the entire sample. Previous literature has been done that utilize RVEs for simplifying simulations.^{13,15,17,19,32,33}

2. Interactive Thresholding: Material and porosity phases were segmented based on intensity thresholds. This was done by visual inspection of the cross section of true geometry using an optical microscope and comparing it to the CT scan Ortho slices. Overlapping the threshold with the ortho slices allow for mapping the solid and porous regions.

3. Volume Fraction: The volume fraction is the ratio volume of the enclosed surface to the volume of the set bounding box set by the sub volume. The calculation is done internally in Amira 3D and is conducted on the thresholded data to determine the porosity. A verification step ensured that the extracted RVE’s pore distribution accurately represented the overall material. To ensure that the subvolume meshes were representative, the full gauge was analyzed for its porosity and scaled down to ensure compatibility between model sizes based on the porosity and its associated pore size and distribution.

4. Generate Surface: This step is crucial in creating the surface from the binary mask made from the interactive thresholding. For this case, the model was smoothed by a value of 1.5, which is the spatial extent in voxel units. The smoothing was done by applying a Gaussian filter on the binary mask and selecting pixels with an intensity above 0.5.^37,38

5. Scan Surface to Volume: The surface model was then converted from 2D surfaces to a volumetric 3D representation suitable for meshing. The dimension options of this module allow for the creation of a solid volume with the detail proportional to the pixel count. This study used dimensions of 1000 pixels in each direction of the bounding box to maintain high detail of the pores, whereas dimensions of 100 pixels in each direction were visualized and depicted a loss in geometry.

6. Generate Tetrahedral Mesh: The mesh is generated on the solid volume, and the mesh quality is proportional to the dimensional values used in the previous step. This model used a mesh quality of medium as it was the coarsest option to maintain pore geometry. The edge size, cell size, and facet size are set to 0.119 mm. The facet distance, or distance from the middle of the face to the edges, is 0.00597 mm. Element quality metrics will be discussed in the next section and the resulting mesh can be exported as an Abaqus input file for use.

Mesh quality

Mesh quality was evaluated to ensure numerical accuracy and solution stability. The primary quality metrics considered were:

1. Aspect Ratio: Elements with an aspect ratio close to 1 were preferred to minimize numerical errors, and values up to 10 were acceptable. However, given the geometry, a small percentage of elements exceeded the aspect ratio of 10:1 and were considered excessively elongated or distorted elements.

2. Dihedral Angles: The dihedral angles of tetrahedral elements were monitored to avoid poorly shaped elements. Angles close to 90° were ideal, while angles below 30° or above 150° were minimized to reduce numerical inaccuracies and ensure accurate element behavior under deformation.

Elements failing to meet these quality criteria were refined or adjusted during the meshing process within Amira, this ensured that the generated mesh provided an accurate representation of the geometry. There were some elements that did not meet these criteria, but due to local mesh refinement, these were almost exclusively outside of the area of interest for data collection which limited their impact on the overall response. The resulting element type was C3D6 for the unstructured mesh. Hexahedral elements, while more accurate due to their shape function, were not able to be used due to the complex geometry. A tetrahedral to hexahedral element split could be conducted, but it would result in a significant model size increase.

Material properties

Material properties were assigned based on the experimental data from the compression- and injection-molded samples, which can be considered effectively void-free due to their very low porosity levels. FEA models were not directly developed from CT scans of the 3D printed parts. Instead, the printing-induced porosity network was implemented in solid compression-molded (C.M.) and injection-molded (I.M.) models to isolate the effect of porosity on the mechanical performance. Both compression- and injection-molded data were used in this study to account for differences in material properties arising from the manufacturing process. Properties of the 3D-printed samples were not used as FEA input, since these values already reflect the effects of printing-induced porosity. All models used an elastic-plastic material model, with the input parameters for the elastic modulus, plastic stress/strain, Poisson’s ratio, and density of the material. The input parameters for compression-molded C.M. and I.M. data can be found in the Supplemental Files. Porous models used the same properties as the solid models, capturing the effects of porosity on mechanical behavior. The NCPC material was treated as homogeneous in the FEA models. This assumption was made due to the size and shape of the coal particles.⁹ Moreover, the RVE was chosen to be much larger than the coal particles, with a volume of 6.80 mm³, approximately 50 times larger than the maximum coal particle diameter, thereby satisfying the scale-separation requirement for homogenization.

Boundary conditions and loading

Boundary conditions were applied to replicate experimental setups. Fixed supports constrained the base surfaces, while loads were applied as a displacement to mimic uniaxial tension for the tensile model, and as a displacement on a pin for a three-point bending setup for the flexural model. Symmetry was not used due to the non-uniform distribution of porosities. The loading displacement magnitudes were representative of experimental testing to enable direct comparison.

Solver and analysis type

Finite element analyses were simulated using ABAQUS 2023, focusing on non-linear plastic material models. For models with complex material behavior or geometric nonlinearities, an incremental-iterative approach with the Newton-Raphson method was employed due to the inclusion of plasticity and large deformation of the non-linear solution to be solved iteratively for convergence. Both solid and porous tensile models were stable and were run with ABAQUS Standard solver, and it was set to run with an initial time step and spacing of 0.01 increments until a value of one was met. Similarly, the solid flexural model was stable and was run with the same solver settings as the tensile models. However, the porous flexural model had initial contact issues due to overpenetration of the roller to the porous surface with the ABAQUS Standard solver at an increment of 0.01 and continued even with a reduction in the initial increment. To account for overpenetration of the model, ABAQUS/Explicit was used to better handle contact for large displacements relative to the small elements to maintain pore geometry. Once initial contact was made, increment growth was allowed as it did not contain non-linearities outside of plasticity seen in the other models.

Post-processing

Primary variables of force and displacement were extracted from reference points set as kinematic couplings in the model. Secondary values of stress and strain were converted from the primary variables for comparison between geometries. Stress contours were visualized to determine stress concentrations near large pores. Results from both tensile and flexural loading were compared to the experimental results for verification. Excel and Python would both be used to process large data sets from the experimental testing and simulation results.

Computational resources

Finite element simulations were conducted on a VRLA Tech workstation with an AMD Ryzen Threadripper 5965WX 3.8 GHz 24-Core CPU, 256 GB DDR4 3200 MHz ECC RAM, and an Nvidia RTX4090 24 GB GPU.

Results

NCPC microstructure

The microstructure of the as-fractured specimens of both 3D-printed and compression-molded NCPC was examined using a Keyence VHX digital microscope. Microscopy images of 3D-printed, and compression-molded specimens are shown in Figure 5(a) and (b), respectively. As seen in Figure 5(a), the 3D-printed specimen exhibited a higher degree of porosity compared to the compression-molded specimen as shown in Figure 5(b). Additionally, delamination between the deposited layers was observed in the microstructure of the 3D-printed specimen, as a result of the layer-by-layer deposition process (indicated in Figure 5(a)). The porosities within the 3D-printed NCPC specimen may negatively impact the material’s mechanical properties and overall performance. Furthermore, the microstructural differences between the two fabrication methods underscore the importance of optimizing the 3D-printing process to improve interlayer bonding and minimize porosity formation.

Figure 5.

Representative microscopy images of the 3D-printed (a) and compression-molded (b) NCPC specimens.

CT scans were conducted to assess the porosity levels within the NCPC specimens, including the filament, injection-molded, compression-molded, and 3D-printed specimens. The porosity volume fraction is reported in Table 5.

Table 5.

Porosity volume fraction of NCPC specimens.

Specimen	Porosity volume fraction (%)
Filament	0.51
Injection molded (I.M.)	0.05
Compression molded (C.M.)	0.04
3D-printed	5.60

The analysis of the CT data provided detailed insights into the internal structures, porosity distributions, and pore network or connectivity of the pores within the 3D-printed specimens. Figure 6 displays the analyzed CT scan of the 3D-printed NCPC specimen, along with the corresponding pore network model. The CT scan results revealed that the 3D-printed NCPC formulation with 60 wt% coal exhibited a porosity level of 5.6%, and the pore network model showed the presence of approximately 4,000 pores. In contrast, the same NCPC formulation, fabricated using compression molding and injection molding, demonstrated significantly lower porosity levels of 0.04% and 0.05%, respectively, and can therefore be considered void-free. Another study also reported higher porosity in 3D-printed samples compared to compression-molded samples.^24,33 Figure 7 illustrates the pore size distribution, depicting the number of pores corresponding to each size.

Figure 6.

(a) Representative 3D volume rendering of 3D-printed NCPC specimen, (b) 3D volume rendering of the porosity, and (c) The pore network model.

Figure 7.

Pore network model histogram.

Both CT scan analysis and optical microscopy show the size of each 3D-printed porosity is smaller than 0.5 mm. The pore network model determined that most of the pores are around 0.05 – 0.15 mm which can be verified from the optical microscopy image. The majority of the porosity lies along the edges of the sample where the printing path changes from printing the infill to the perimeter layers which can be shown in both the CT scan analysis and optical microscopy image. The type of porosity shown in the 3D-printed NCPC sample is inter-layer porosity which is the space between the printed layers. Stress concentrations can form around the inter-layer porosity and cause premature failure due to the weak bonding between the printed layers. The existence of both intra-layer porosity and inter-layer porosities (which reduce the bonding between the layers) are the main contributors to the reduction in the mechanical performance of the FDM-manufactured samples compared to traditional manufacturing methods. Previous studies have presented a detailed analysis of both inter-layer and intra-layer porosities within the 3D-printed polymer composites.^{13,20,21,25,28,33,38}

Tensile testing

Figure 8 illustrates the representative stress-strain curves for NCPC samples with identical composition, highlighting the mechanical performance differences between the three fabrication methods: 3D-printing, compression-molding, and injection-molding. The 3D-printed and compression-molded samples were created and experimentally tested while the injection-molded data was taken from literature.⁹ The 3D-printed samples demonstrated an ultimate tensile strength (UTS) of 13.4 MPa and an elastic modulus of 0.96 GPa. In comparison, the compression-molded NCPC exhibited improved mechanical properties, with a UTS of 15.3 MPa and an elastic modulus of 2.51 GPa. The difference in tensile strength between the 3D-printed and compression-molded samples was 13%. The injection-molded samples outperformed both, achieving the highest UTS of 29.3 MPa and an elastic modulus of 2.57 GPa, highlighting significant differences in mechanical performance across fabrication methods.⁹ The comparison of the microstructures of the CT-scanned injection-molded and compression-molded samples indicated porosity contents of 0.05% and 0.04%, respectively. Despite using the same base material (NCPC), the two manufacturing techniques differ, which can affect the final part’s overall properties. Specifically, the injection molding process produces a more uniform distribution of reinforcement within the polymer matrix compared to compression molding, resulting in greater homogeneity and improved mechanical performance in the injection-molded samples.^39,40 Moreover, despite the very low porosity in both cases, a significant difference was observed in the ultimate tensile strength (UTS) and elastic modulus between specimens prepared by the two methods. Although the overall porosity is slightly higher in the injection-molded sample, very few pores were detected within the part. In contrast, the compression-molded sample contains a larger number of micro-pores distributed throughout the part. These micro-pores can act as stress concentrators and crack initiation sites, leading to lower UTS. This effect is also evident in Figure 8, where the compression-molded sample exhibits a larger brittle region and lower elongation, while the injection-molded sample demonstrates greater ductility. Similar trends were reported by Angulo et al.⁴¹ in their comparison of the mechanical properties of injection- and compression-molded carbon fiber-reinforced polymer composites.

Figure 8.

Experimentally obtained tensile data for 3D-printed, compression-molded, and injection-molded NCPC samples.

The 3D-printed samples had a 74% decrease in strength compared to the injection-molded samples. The thermal stresses in the experimental 3D-printed sample greatly decrease the material properties compared to traditional manufacturing methods. Previous studies reported similar findings, attributing the superior mechanical properties of compression-molded or injection-molded samples to their reduced porosity, enhanced material homogeneity, or improved interfacial bonding between polymer chains and filler or fiber materials.^{2,9,20,24,33,42} Compared to 3D-printed wood plastic composites (WPCs), the 3D-printed NCPC materials demonstrated comparable tensile strength and higher stiffness compared to the WPC at respective filler weight loadings.⁴³ 3D-printed carbon fiber composites (CFCs) had superior tensile performance compared to 3D-printed NCPC materials at high filler weight loadings.⁴³ Additionally, superior tensile properties of injection-molding compared to compression-molding were found in literature that compared different manufacturing methods of thermoplastic and thermoplastic composite samples.^44,45

Flexural testing

Flexural testing was performed on both 3D-printed and compression-molded samples, with the average flexural response for each samples type presented in Figure 9. Injection-molded NCPC material for 60 wt% bituminous coal was captured from literature and compared to experimental results of the 3D-printed and compression-molded NCPC samples.⁹ The 3D-printed NCPC samples demonstrated an average flexural strength of 16.9 MPa and a flexural modulus of 1.01 GPa. In comparison, the compression-molded NCPC samples exhibited superior mechanical performance, with an average flexural strength of 23.7 MPa and a flexural modulus of 2.50 GPa. The comparison between 3D-printed and compression-molded samples lead to a difference in flexural strength by 33% and flexural modulus by 85%. Similar trends have been reported in other studies for coal-filled composites with various types of thermoplastics, including HDPE, PETG, PLA, and PA12.^2,4 The experimental injection-molded samples had an average flexural strength of 42.9 MPa and a flexural modulus of 1.94 GPa.⁹ This data, compared to the 3D-printed NCPC material showed a decrease in flexural strength of 87% and a difference in flexural modulus of 63%. The difference in strength between the 3D-printed sample and traditional manufactured samples can be due to the thermal stresses while printing and the weak bonds between the printed layers. Consistent with the tensile properties, the enhanced mechanical performance of compression- and injection-molded material was attributed to its lower porosity, improved material homogeneity, and stronger interfacial bonding between the polymer chains and filler particles.^{2,9,20,24,33,40} Compared to other 3D-printed composites, including WPCs and CFCs, NCPC materials exhibited comparable or superior flexural performance compared to WPC materials and lower flexural properties compared to CFC materials.⁴³ Additionally, superior flexural strength was found for injection-molded HDPE-based composites compared to compression-molded samples which validates the experimental results below that injection-molding will have superior mechanical properties.³⁹

Figure 9.

Flexural data for 3D-printed, compression-molded, and injection-molded NCPC.

Finite element analysis model response

The resulting meshes for both tensile and flexural provided a high-fidelity representation of both solid and porous microstructures. Complete recreation of the 3D-printed pore network model as depicted in Figure 6 was created as a reference for the representative models but yielded models too large for simulation. Representative models were developed for the porous tensile and flexural simulations to match the porosity content (5.6%) measured from the CT data of the 3D-printed sample. A mesh convergence study was conducted on both porous models to ensure numerical accuracy and stability to minimize model size while representing accurate porosity. The flexural model generated using CT scans are shown in Figures 10 and 11, representing the geometric retention of pores, where the tensile model was made in a similar way. The generated mesh information for all models is shown in Table 6.

Figure 10.

Generation of sub volume to surface generation from CT data.

Figure 11.

Mesh generation from surface generated CT data.

Table 6.

Tensile and flexural model mesh summary.

	Tensile		Flexural
	Porous	Solid	Porous	Solid
Elements	352,376	22,176	325,991	12,536/39,363
Nodes	71,677	27,324	90,032	24,264
Element type	C3D4	C3D8	C3D4	C3D8R/C3D4
Porosity	5.5%	N/A	5.4%	N/A

Both tensile and flexural models contained porosities close to the reference model of 5.6% to allow for comparison to experimentally 3D-printed NCPC sample. Figure 12 depicts the representative porous model that will simulate tensile loading. A solid validation model with the same dimensions as the representative porous model was created to justify using a smaller structure for the porous model. The solid validation was tested in accordance with ASTM D638 and provided equivalent results as the full type IV tensile specimen. The reasoning behind using a representative porous model was due to computation time and storage space of the resulting output database file. Both representative models of the gauge section are assumed to be in a uniform stress state within the gauge, conforming to Saint-Venant’s principle. Reference points are depicted as RP-1 and RP-2 for loading and fixing the sample, respectively, in each tensile model. Both loading and fixed reference points are kinematically coupled in all six degrees of freedom to the surfaces in which the grip section is defined by ASTM D638. The loading reference point was limited to only moving in the +Z axis for uniaxial displacement and the fixed reference point was on the −Z axis surface and encastre to mimic the fixed grip. Data was extracted from the fixed reference point to generate a force versus displacement dataset which in turn was converted to stress and strain to allow for comparison between geometries.

Figure 12.

FEA porous model for tensile loading.

Figure 13 depicts FEA porous model for flexural loading. The boundary conditions were representative of flexural testing by keeping the same span and roller ratios as ASTM D790 for both solid and porous models. Although, the porous model did not have the full length as the solid model due to computational time and storage space. The bottom rollers were fixed in their displacement and X and Z axis rotation, whereas the Y axis was allowed to rotate. The top roller was similar but moved along the +Z axis for loading. Initial simulations resulted in a premature simulation due to element penetration at the simulation start, therefore, the rollers required an initial 0.01 mm gap of the contact surfaces to resolve this issue. General contact boundary conditions were applied with a tangential friction coefficient of 0.2 to minimize sliding and contact of the roller and porous structure surface. Similarly to the roller gap, initial simulations had premature model failure due to the porous model wanting to slide out during initial contact. To resolve this, a single node was in the center with a boundary condition set to limit motion in the X and Y axis to the porous flexure model. The data was extracted by collecting the force out of both bottom rollers to create the force versus displacement datasets which were converted to stress and strain for direct comparison between varying flexure model size.

Figure 13.

FEA porous model for flexural loading.

The solid tensile, solid flexural, and porous tensile models were simulated in ABAQUS 2023 standard. ABAQUS 2023 explicit was used for the simulation of the porous flexural model due to unconnected regions at the simulation start from the contact gap. Each model was simulated with experimental compression- and injection-molded tensile data as the ABAQUS input. It is worth reiterating that the C.M. and I.M. input data had porosity values of 0.04% and 0.05%, respectively. These represent the lowest achievable porosities during fabrication and were selected to ensure the FEA simulations capture the influence of 3D-printing induced porosity. Figure 14 presents the tensile data for both the experimental results and the FEA of NCPC materials.

Figure 14.

Tensile data for the experimental and FEA results for the NCPC material.

Tensile results

Figure 15 indicates a comparison of the results from the FEA simulations and experimental testing. Datasets of both C.M. and I.M. were input to determine if there would be a superior response to the porous model compared to the experimental 3D-printed sample. The experimental 3D-printed sample had a 7% difference in UTS compared to the FEA porous model with C.M. data as the input and a 69% difference in UTS compared to the FEA porous model with I.M. input data. The FEA porous models had an approximate 88% difference in elastic modulus compared to the 3D-printed samples. The significant difference between the experimental 3D-printed sample and FEA porous models are due to thermal effects and weak inter-layer bonding that are not considered in the simulation. The FEA simulations indicated a slightly higher elastic modulus compared to the experimental compression results which was also found in literature where experimental and simulation data were compared.^9,19

Figure 15.

(a) Solid type IV, (b) Solid representative, and (c) Porous representative NCPC tensile models under tensile loading.

This over stiffening is attributed to the tetrahedral deformation response in the elastic region due to default kinematic hardening in ABAQUS. The porous and solid FEA simulations with injection-molded data as the ABAQUS input did produce different mechanical results. A 6% reduction in UTS was observed when comparing the solid model to the porous model with compression-molded data as the FEA input. The UTS of the solid FEA model and experimental results were the same. The FEA models showed a slightly higher elastic modulus compared to the injection-molded experimental results. Tables 7 and 8 report the tensile and flexural performance, respectively, for both the experimental results and FEA predictions.

Table 7.

Tensile performance for the experimental and FEA results.

	3D-printed	Compression-molded	Injection-molded	Porous FEA (C.M.)	Solid FEA (C.M.)	Porous FEA (I.M.)	Solid FEA (I.M.)
UTS (MPa)	13.40 ± 1.10	15.30 ± 1.40	29.30 ± 0.70	14.4	14.6	27.6	29.4
EM (GPa)	0.96 ± 0.09	2.51 ± 0.07	2.57 ± 0.04	2.72	2.78	2.21	2.37

Table 8.

Flexural performance for the experimental and FEA results.

	3D-printed	Compression-molded	Injection-molded	Porous FEA (C.M.)	Solid FEA (C.M.)	Porous FEA (I.M.)	Solid FEA (I.M.)
FS (MPa)	16.90 ± 1.10	23.70 ± 0.50	42.90 ± 0.80	25.2	26.5	51.1	54.2
FM (GPa)	1.01 ± 0.09	2.50 ± 0.02	1.94 ± 0.03	2.79	2.97	2.89	3.07

Figure 15 depicts the full type IV solid (a), representative solid (b), and porous (c) NCPC model with compression-molded data as the FEA input under tension to show the effect of pores on stress concentrations in the gauge section. The type IV and representative solid models had equivalent tensile data, so it was concluded that the representative porous model can be used. The stress concentrations found around pores in the FEA porous models induced more plasticity under lower loads leading to lower overall strength than compared to the solid FEA models due to reduced cross-sectional area. These microstructural defects play a significant role depending on their distribution and size where large pores distributed more stress to the surrounding material, whereas smaller pores would have higher stress concentrations but much less local plasticity.

Flexural results

Figure 16 provides a comparative analysis of the results from the FEA simulations and experimental testing of the NCPC materials under flexural loading. The experimental 3D-printed samples had a 39% difference and 100% difference in FS compared to the FEA porous models with compression- and injection-molded input data, respectively. The FEA porous models had an approximate 95% difference in flexural modulus compared to the 3D-printed sample. The large difference between the experimental 3D-printed NCPC sample and FEA porous models can be attributed to thermal effects which lead to poor inter-layer bonding that are not considered in the simulations. The FEA simulations indicated a higher FS and flexural modulus compared to the experimental compression- and injection-molded results. Similar trends were found in Al-Majali et. al⁹ where the FEA model performed stiffer (i.e., higher modulus) than the experimental coal-plastic composite material. The porous and solid FEA simulations with injection-molded data as the ABAQUS input did produce different mechanical results. Approximately 5% and 6% reduction in FS was observed when comparing the solid model to the porous model with compression- and injection-molded material properties, respectively.

Figure 16.

Flexural data for the experimental and FEA results for the NCPC material.

Figure 17(a) depicts the full sample geometry as a solid under flexural loading. Similarly to the tensile porous model, stress concentrations are present around pores in the FEA flexural porous model, shown in Figure 17(b), which lead to lower flexural strength values. The stress gradient shows a magnitude of the Von Mises stress where under flexural loading, both tensile and compressive areas show high stresses. The significance for this model is the relation between tensile and compressive stresses on the local plasticity around the pores. The local plasticity due to the pore driven stress concentrations become more apparent the further from the neutral axis. Consequently, although the material exhibits high initial stiffness, the early onset of localized plasticity leads to significant strain accumulation, ultimately reducing its load-carrying capacity. This is best shown in the comparison between both Figure 17(a) and (b) in which the solid model has a higher strength, but lower peak stresses.

Figure 17.

(a) Solid and (b) Porous NCPC models under flexural loading.

Conclusion

This research successfully developed a novel composite material for AM of NCPC, consisting of 60 wt% bituminous Keystone 325 coal powder and 39 wt% HDPE. Given that the NCPC material is intended for high-volume AM applications, such as composite tooling and additive housing/construction, understanding its failure mechanisms is critical. To this end, a modeling approach was established to investigate the mechanical performance of 3D-printed NCPC structures under both tensile and flexural loading. Moreover, the microstructure of the 3D-printed and compression-molded NCPC samples was analyzed to determine their porosity content. Results indicate a porosity of 5.6% in the 3D-printed, 0.04% in the compression-molded, and 0.05% in the injection-molded samples.

FEA models were developed to determine the difference in the mechanical performance of the 3D-printed and traditionally manufactured parts by modeling the porous and solid NCPC structures under tensile and flexural loading. Under tensile loading, the experimental 3D-printed samples exhibited a 7% lower UTS and a 96% lower elastic modulus compared to the FEA porous model with C.M. input data. However, under flexural loading, the experimental samples showed a 39% difference in FS and a 94% difference in FM compared to the FEA porous model with C.M input data. The comparison between the FEA solid and porous models demonstrated that incorporating approximately 6% porosity led to a 6% reduction in strength compared to the solid model. Stress concentrations around voids in the porous model cause the part to fail earlier and explain the 6% decrease in strength values. However, compared to the experimental 3D-printed sample, the porous FEA models had higher mechanical performance. The difference in mechanical performance between the 3D-printed and porous FEA models can be explained by the model’s inability to accurately account for thermal stresses and interlayer bonding in the 3D-printed part.

Evaluating the effect of 3D-printing defects on the performance of NCPC materials will provide insight into the structural integrity of these materials. The findings from this research will enable the optimization of 3D-printing process parameters to enhance the performance of NCPC materials for various engineering applications such as composite tooling and additive housing construction. In future work, the FEA model could be enhanced to account for inter-layer adhesion and deformation caused by thermal stresses throughout the entire structure. Accurately simulating the 3D-printed NCPC structure is theorized to provide more accurate results as to their failure mechanisms. Moreover, varying the coal weight loading in the NCPC formulation can be explored to assess its impact on porosity content and the resulting mechanical performance of 3D-printed NCPC parts.

Supplemental Material

Supplemental Material - Modeling the effect of 3D-printed induced defects on mechanical performance of natural carbon-enhanced polymer composite

Supplemental Material for Modeling the effect of 3D-printed induced defects on mechanical performance of natural carbon-enhanced polymer composite by William T. Downs, Grace S. Baranack, Neshat Sayah, Muhammad Ali, Jason Trembly, Yahya T. Al-Majali in Journal of Thermoplastic Composite Materials.

Supplemental Material

Supplemental Material - Modeling the effect of 3D-printed induced defects on mechanical performance of natural carbon-enhanced polymer composite

Footnotes

Acknowledgements

The authors would like to thank the undergraduate researchers at the Institute for Sustainable Energy and the Environment at Ohio University for helping with the NCPC material processing. The authors would like to thank Dr Brian Wisner and Cheosung O’Brien for providing access to the digital microscope and DIC system.

Author contributions

Conceptualization, W.T.D., G.S.B, and Y.T.A.; data curation, W.T.D. and G.S.B.; formal analysis, W.T.D. and G.S.B.; funding acquisition, Y.T.A.; investigation, W.T.D. and G.S.B.; methodology, W.T.D., G.S.B., and Y.T.A.; project administration, Y.T.A.; software, W.T.D.; resources, W.T.D., G.S.B., and Y.T.A.; supervision, Y.T.A.; validation, W.T.D. and G.S.B.; visualization, W.T.D. and G.S.B.; writing – review & editing, W.T.D., G.S.B., N.S., M.A., J.T., and Y.T.A.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: this material is based upon work supported by the US Department of Energy under Award Number DE-FE0032143.

Disclaimer

This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

ORCID iDs

William T. Downs

Neshat Sayah

Supplemental Material

Supplemental material for this article is available online.

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