Process-induced degradation of tensile strength in 3D-printed carbon fiber–reinforced PA6: Experimental and numerical study

Abstract

Continuous carbon fiber–reinforced composites (CCFRCs) produced by 3D printing offer design flexibility but often exhibit reduced mechanical performance due to process-induced defects. This study examines the effect of the printing process on the tensile strength of a CCFRC with polyamide 6 as the matrix using both numerical and experimental techniques. The experiment comprises two phases: 3D printing and tensile testing. The first phase is further divided into three stages, referred to as before (Stage 1), during (Stage 2), and after printing (Stage 3), with samples collected at each stage for tensile testing and analysis. Microscopic structure analysis was conducted using powerful X-ray imaging at the synchrotron radiation facility “NanoTerasu,” revealing the effects of the printing process. Based on these observations, simulations are performed using a spring element model (SEM) that incorporates process-induced initial fiber breakage and voids. For Stages 1 and 2, the simulation predicts the strength with high accuracy; however, for Stage 3, a 20% overestimation is observed. This result suggests that Stage 3 may introduce changes in the probabilistic strength distribution of the fibers and may cause degradation of the fiber/resin interface due to the presence of voids, which cannot be modeled using the current numerical approach, leading to a further reduction in the tensile strength. The findings of this study contribute to elucidating the degradation mechanisms of tensile strength induced by the 3D printing process in CCFRCs.

Keywords

3D printing tensile strength finite element analysis synchrotron radiation continuous carbon fiber–reinforced polymer composites

Introduction

Carbon fiber–reinforced plastic (CFRP) has been used in the aerospace, automotive, transport, energy, and infrastructure sectors owing to its exceptional mechanical properties and lightweight nature. In aerospace, CFRP constitutes nearly 50% of modern aircraft structures, while the space industry harnesses its potential for applications ranging from rockets to spacecraft.^1,2 Recently, additive manufacturing (AM), also known as 3D printing, has emerged as a new trend in CFRP production. AM is a process of “depositing successive thin layers of material upon each other, producing a final three-dimensional product.”³ It offers several advantages over traditional methods, primarily in its ability to create intricate geometries without the need for molds, special tools, or equipment. This process, known as rapid prototyping, significantly reduces the time required to produce prototypes.^4,5 Despite these advantages, AM products have limited applications in some industries, such as aerospace, owing to concerns about quality and the lack of standards.⁶

One widely recognized method in AM, owing to its low cost, ease of use, and ability to manufacture complex structures directly from digital designs, is fused deposition modeling (FDM).^7,8 The FDM technique involves the layer-by-layer deposition of molten polymeric materials until the designed part is complete.⁹ However, concerns about the mechanical properties of FDM parts made from conventional materials have led to the addition of short fibers, such as carbon, to the filament.¹⁰ When combined with optimized printing parameters, such as nozzle temperature and fiber alignment, this approach has demonstrated improvements in properties such as the tensile modulus.¹¹ Nevertheless, the enhanced materials still fall short of the strength requirements for high-performance applications, such as those in the aerospace industry.¹² To address this, Markforged^TM developed a 3D printer and filament in 2015 capable of printing continuous carbon fiber–reinforced composites (CCFRCs).¹³

Several studies have investigated the relationship between printing process conditions and mechanical properties.^14–16 Shirasu et al. conducted an experimental design study using short carbon fiber–reinforced PA6 filament. They reported that both Young’s modulus and strength increased with rising nozzle temperature, showing a tendency to saturate beyond 240°C.¹⁷

In addition, factors such as low fiber volume fractions (typically below 40%), warpage from residual stress, and damage incurred during the printing process further reduce its mechanical properties.^18–20 These limitations have prompted further research to explore potential solutions. Hu et al. found that the FDM process reduces the strength of individual fibers by approximately 33%, with fiber breakage leading to reductions in tensile and compressive strengths of up to 60% and 25%, respectively.¹⁹ In a separate study, He et al. identified the formation of microscopic voids as the main cause of strength degradation in FDM filaments. By applying compression molding to reduce the void content, they achieved a 22.5% increase in the tensile strength and 36.4% increase in the modulus.²¹ Another study examined the effect of nozzle pressure on fiber waviness and twisting, showing that filament stress became significant only beyond 120°C. Meanwhile, a different study reported that, at 0° fiber orientation, the breaking force did not vary significantly even when the feed rate was changed.^22,23 Other studies have combined numerical and experimental methods to investigate factors affecting the degradation of mechanical properties in FDM filaments.¹⁷ Tang et al. modeled the reduction in compressive strength caused by fiber waviness and successfully predicted the compressive strength along the fiber direction in CCFRCs.²⁴ Similarly, Hoshikawa et al. demonstrated through modeling that nozzle-induced pressure causes filament waviness, which alters elastic properties.²⁵ Some studies have combined compression molding with Finite Element–based topology optimization to assess their effects on the overall strength,²⁶ while others have focused solely on topology optimization.²⁷ These studies utilized Finite Element Analysis (FEA) to reveal degradation mechanisms impacting the elastic properties and compressive strength owing to material defects from the FDM process. However, investigations into the tensile strength along the fiber direction remain insufficient.

To incorporate new materials into designs, it is necessary to establish appropriate safety criteria based on deformation and strength predictions using FEA.^28–32 In recent years, researchers have developed numerical models to predict damage in CCFRC parts over time. For example, one study used a finite element method based on continuum damage mechanics,³³ while others focused on improving the print quality by optimizing factors such as the lattice structure.³⁴ However, in all these studies, FEA was found to be costly and time-consuming, leading to the development of alternative methods such as the shear–lag (SLM) and spring element models.^35,36 While SLM focuses on stress transfer between the fiber and matrix, the spring element model simplifies structures into spring-like elements to study phenomena such as the deformation and mechanical properties of composites. SLM performs poorly at predicting behavior at low fiber volume fractions compared with the spring element model,³⁷ making the spring element model a useful numerical approach for expressing the microscopic structure of the CCFRC while predicting its macroscopic mechanical properties.^38,39

This study introduces a micromechanics-based numerical analysis approach for predicting the tensile strength of CCFRCs produced by 3D printing. While the spring element model provides an initial prediction framework, it was insufficient to fully reproduce the experimental behavior. Therefore, process-induced voids and fiber damage observed through synchrotron micro-CT were newly incorporated to improve the model. Tensile tests were performed on specimens collected at different printing stages, and filament structural changes were characterized by high-resolution micro-CT at the NanoTerasu synchrotron radiation facility. The improved numerical model, which accounts for both voids and fiber breakage, was then compared with the universal testing machine (UTM) results across printing stages to evaluate and validate its predictive accuracy.

Experimental and numerical setups

Experimental setup

3D printing setup

The filament, with a radius of 0.375 mm, was a continuous fiber reinforcement provided by Markforged (Cambridge, MA, United States). In conjunction with Onyx as the filler material, the Markforged CFR is the most widely used commercial continuous fiber filament. The carbon fiber used was similar to that of Torayca T300, whereas the matrix material was identified as Polyamide 6 (PA6).⁴⁰ PA6 together with PA12 is the most commonly used matrix for composite additive manufacturing due to its high mechanical strength, strong fiber–matrix adhesion, and reliable melt processability. Its balance of stiffness, toughness, and thermal stability makes it especially suitable for continuous-fiber 3D-printing applications.⁴¹ The mechanical properties of the filament, as listed in Table 1, are available on the specification sheet provided by Markforged and Toray.^42,43

Table 1.

Mechanical properties of fiber and matrix materials.

Carbon Fiber – Toray T300
Tensile modulus (E_f)	230 GPa
Tensile strength (σ_S)	3530 MPa
Matrix – PA6
Tensile modulus (E_m)	1.7 GPa
Poisson’s ratio (ν_m)	0.35

A modified Prusa i3 MK3 3D printer was used, which was adjusted to better accommodate the experimental setup. Specifically, the original feed gear of the printer head was removed and replaced with a modified feed gear installed as a separate component of the unit.

As shown in Figure 1(a), these modifications were based on a previous study by Hoshikawa et al.^16,44 Consequently, the printing process was divided into three distinct stages to ensure consistency throughout the experiment. To enable a comprehensive analysis, 28 filament samples were collected at each stage, allowing for a detailed investigation of filament properties across different phases.

Figure 1.

(a) Modified Prusa i3 MK3 printer with an external feed unit and (b) schematic illustration of the three filament collection stages during the printing process.

The printing process, outlined in the three stages shown in Figure 1(b), is described as follows.

In Stage 1, the raw carbon fiber filament, which was sourced directly from Markforged, retained its original structural and material properties and served as a baseline for subsequent comparisons.

In Stage 2, the modified roller mechanism fed the filament at a controlled rate of 6 mm/s and directed it through a plastic tube toward the printer head. Upon reaching the printer head, the filament passed through a nozzle heated to 270°C, and the heating process altered its internal structure and prepared it for extrusion.

In Stage 3, the filament was deposited onto the print bed following a preprogrammed pattern. During this process, the nozzle applied pressure as the filament was extruded, flattening it to a width of 0.13 mm. The filament was fed in a straight line with consistent applied pressure to ensure a uniform thickness and density. As the process continued, the deposited layers gradually cooled and solidified, creating a stable structure. This cycle of extrusion, pressure application, and solidification was repeated several times to produce the samples required for mechanical testing and analysis.

As stated in Section 1, 3D printing is subject to complex thermal histories and pressures, which can lead to material defects such as voids, fiber waviness, and breakage. To evaluate the influence of the manufacturing process on the formation of these defects, specimens from Stages 1 to 3 were examined using X-ray micro-CT at BL10U of NanoTerasu (Sendai, Miyagi, Japan).

Tensile tests

Tensile tests were performed using an A&D tabletop tensile compression tester (MCT–1150). A total of 28 test samples per stage were prepared by mounting the samples onto cardboard⁴⁵ with a rectangular cut at the edge and securing them with an epoxy adhesive, as shown in Figure 2. The cardboard had a gauge length of 30 mm and a grip length of 30 mm on both sides. The remaining cardboard was removed prior to testing. This mounting method was used to prevent damage to the gripped portion of the filament and to ensure proper alignment with the testing machine. Specimens that failed within the grip region or at the grip–gauge transition were excluded from the analysis to ensure the accuracy of the results. The tests were conducted at a room temperature of 25°C with a vertical pulling speed of 10 mm/min. During the test, the software recorded the maximum load before failure, displacement, and the load–displacement curve.

Figure 2.

(a) Tensile test setup and (b) specimen mounted on a precut cardboard tab, showing the gauge section and grip sections.

X-ray analysis

The internal structure of the printed CCFRC was investigated via X-ray micro-CT installed in Experimental Hutch 2 of BL10U at the 3 GeV synchrotron radiation facility NanoTerasu, Japan. The X-ray micro-CT system was equipped with a CMOS camera (Orca-Flash 4.0 V3, Hamamatsu Photonics K. K., Japan), scintillator, and an optical lens unit with ×10 magnification (AA–51, Hamamatsu Photonics K. K., Japan), yielding a field-of-view and pixel size of 1.3 mm and 0.65 µm/pixel, respectively. To transmit the X-ray beam, approximately damaged areas of 0.3 × 0.3 × 0.5 (X × Y × Z) mm³ of the samples were cropped, and X-rays with a photon energy of 15 keV (corresponding to a wavelength of 0.0827 nm) were used.⁴⁶ For each CT scan, 1800 projection images were acquired with a rotation increment of 0.1° and an exposure time of 30 ms, where the exposure time was set to achieve the maximum irradiation intensity of approximately 60,000 counts per pixel. CT sections were reconstructed using the convolutional back-projection method implemented in the software developed in SPring-8.⁴⁷

Numerical method

Spring element model

The spring element model was introduced by Okabe et al. as an efficient and accurate alternative to SLM, particularly for cases with low fiber to matrix volume fractions. Unlike the SLM, the spring element model employs linear equations for analytical problem solving, significantly reducing computational costs.⁴⁸

The spring element model shown in Figure 3 was developed by building a network of spring elements to simulate the behavior of fiber-reinforced composites. In this framework, fibers were represented by longitudinal spring elements, whereas the matrix was modeled using transverse spring elements. The effect of broken fibers was incorporated by introducing a stress recovery region resulting from the fiber slip. Together, these components accounted for the internal work, which was balanced against the external work applied to the system to achieve equilibrium. Consequently, the stiffness equation for the spring element model is expressed as follows:

δ u^{T} (\sum_{e = 1}^{N_{L} - N_{B} - N_{S L}} K_{L}^{e} + \sum_{e = 1}^{N_{T}} K_{T}^{e}) u + δ u^{T} (\sum_{e = 1}^{N_{S L}} π R^{2} \int_{0}^{l_{s}} B_{L}^{T} σ_{S L} d z) = δ u^{t} f,

(1)

where f and u are the load and displacements, respectively; δ represents the virtual component of the system; and N denotes the number of elements. The subscripts L and T indicate elements in the longitudinal and transverse directions, respectively, and B and SL represent broken and slipping fibers.

Figure 3.

Schematic of the spring element model: (a) unit cell showing the longitudinal fiber element and surrounding matrix element and (b) assembly showing fiber breakage and the slip region.

The first half of the equation represents the contributions of the longitudinal (fiber) and transverse (matrix) elements, which are further expanded as follows:

K_{L}^{e} = π R^{2} \int_{0}^{l} B_{L}^{e^{T}} E B_{L}^{e} d z,

(2)

K_{T}^{e} = \frac{π R l}{3} \int_{0}^{d} B_{T}^{e^{T}} G B_{T}^{e} d r,

(3)

where E and G represent the elastic modulus of the fiber and shear modulus of the matrix, respectively; R is the fiber radius; and B is the strain–displacement transformation matrix given by

B_{L}^{e} = [\frac{1}{l} - \frac{1}{l}],

(4)

B_{T}^{e} = [\frac{1}{d} - \frac{1}{d}]

(5)

Here, l and d correspond to the lengths of the longitudinal and transverse elements, respectively, with d given by the following equation:

d = R (\sqrt{\frac{2 π}{\sqrt{3} V_{f}}} - 2),

(6)

where V_f is the fiber volume fraction. It is assumed that the distances between fibers are equal. The second part of the equation, shown in Figure 3(b), represents the stress recovery region caused by broken fibers. The stress within this region is expressed as

σ_{S L} = \frac{2 τ_{s} z}{R},

(7)

and the stress recovery length, l_s, is modeled after the Kelly–Tyson equation as³⁶:

l_{s} = \frac{R E ε}{2 τ_{s}},

where τ_s is the constant shear stress and z is the distance from the break point. Although the stress-recovery behavior is influenced by matrix deformation through τ_s, the present model assumes a constant interfacial shear stress and neglects the effect of temperature-dependent viscoelasticity of the matrix. In the present analysis, a model with length L (=3 mm) was considered, and the analysis was performed using a material principal coordinate system in which the fiber direction was defined as the z-axis. Displacement boundary conditions were imposed such that the displacement in the fiber direction was fixed to u = 0 at z = 0, while a prescribed displacement of u = ɛL was applied at z = L (as shown in Figure 3(b)). The parameter ɛ was employed as a control parameter, and the displacement field was incrementally increased. The numerical analysis was carried out until the onset of fracture.

Fiber breakage and stress concentration factor

In the spring element model, the quantities of broken fibers and fibers in the stress recovery region were probabilistically determined based on fiber fracture. While broken fibers can form during printing, initial breakage may also occur owing to fiber defects, with its probability expressed by the following equation:

P_{f} = 1 - \exp [- \frac{S_{f}}{S_{f, 0}} {(\frac{σ}{σ_{1}})}^{m 1} - \frac{S_{f}}{S_{f, 0}} {(\frac{σ}{σ_{2}})}^{m 2}],

(8)

where the above equation follows a bimodal Weibull distribution; m₁ and m₂ are shape parameters, σ₁ and σ₂ are scale parameters, and S_f and S_f,0 represent the lateral surface area of the broken fiber and lateral arc area of the adjacent fiber, respectively.

In the spring element model, assuming a hexagonal shape as shown in Figure 4(a), the failure of a single fiber causes stress concentration in adjacent fibers via the matrix interface. To account for this, the stress concentration factor α is introduced, expressed in equation (9):

α = 1 + γ_{1} (1 - \frac{D_{s}}{l_{s}}),

(9)

where D_S is the distance between broken fibers, and γ₁ varies depending on whether the segment faces a broken or intact fiber.

Figure 4.

Schematic illustration of the effect of a broken fiber on adjacent fibers in the spring element model: (a) top view and (b) side view.

By incorporating the stress concentration factor into the original equation, the updated probability of fiber fracture becomes

P_{f} = 1 - \exp [- \frac{S_{f}}{S_{f, 0}} {(\frac{α σ}{σ_{1}})}^{m_{1}} - \frac{S_{f}}{S_{f, 0}} {(\frac{α σ}{σ_{2}})}^{m_{2}}],

(10)

The values of this factor were determined from previous studies and are summarized in Table 2.⁴⁹ The fiber Weibull parameters were assumed to remain constant throughout the process, as it is difficult to determine their values once fiber breakage occurs. This assumption is consistent with several previous studies that have successfully adopted the same approach.^49,50

Table 2.

Bimodal Weibull parameters used in the analysis.

Bimodal Weibull parameters
Representative length (l)	10 mm
Failure stress 1 (σ₁)	4.10 GPa
Failure stress 2 (σ₂)	4.20 GPa
Weibull modulus 1 (m₁)	4.00
Weibull modulus 2 (m₂)	15.00

Consideration of voids

The spring element model is intended for laminates with little to no void content.³⁶ However, significant void formation is frequently observed in 3D-printed filaments during the various printing stages, thereby reducing the effective load-bearing cross-sectional area. Voids and fiber breakage, which are now considered, are process-induced defects inherent to filament fabrication. Although these defects incorporate the effects of printing conditions, they are only considered indirectly in the present model.

To evaluate how these defects influence tensile behavior within the spring element model, it is important to note that the model calculates only the true stress acting on the fiber. Therefore, when comparing spring element model results with experimental tensile strength, the fiber stress must be converted to the filament level stress using its total cross-sectional area. Because the presence of voids reduces this effective area, the measured void fraction V_p,void is incorporated into this geometric conversion to obtain the effective fiber volume fraction:

V_{f, eff} = V_{f} (1 - V_{p, void}),

(11)

where V_f is the initial volume fraction and V_f,eff denotes the effective volume fraction. The effective bundle strength at each stage can also be calculated using the following equation:

T_{2,3} = T_{0} (1 - V_{p, void}),

(12)

where T_2,3 is the effective bundle strength at Stage 2 or 3, and T₀ is the bundle strength without the void effect.

Results and discussions

Observation of the micro-scale structure

Figure 5 shows an X-ray cross-sectional image of the raw filament, which corresponds to the filament at Stage 1, revealing an uneven fiber distribution and noticeable voids between fiber groups. Based on digital microscope measurements, the average cross-sectional area and radius were 0.111 mm² and 0.375 mm, respectively. The average fiber volume fraction was 35%.

Figure 5.

Synchrotron X-ray micro-CT cross-sectional image of the raw filament (Stage 1), showing the non-uniform fiber distribution and voids between fiber groups.

Figure 6(a) and (b) shows X-ray cross-sectional views of the filaments at Stages 2 and 3, corresponding to sections perpendicular and parallel to the filament axis, respectively. In the first stage, the filament exhibits uneven distribution, with small voids primarily situated between the fibers. However, in the second stage, these air voids or cavitations increase markedly, forming small and large pockets mainly at the center of the filament. Some parts of the fibers were also separated from the matrix and located in the void region. By the third stage, the air-void pockets became smaller yet more irregular, accompanied by minor fiber waviness. In addition, the number of fibers in the void region increased significantly. This is mainly due to the printing process, where the pressure from the nozzle and the build platform induces a lateral flow within the filament, known as squeeze flow. This flow causes part of the fibers to migrate laterally while entraining the matrix resin, resulting in the formation of fiber bundles that are partially separated from the surrounding resin.

Figure 6.

Synchrotron X-ray micro-CT cross-sectional images of the filament at (a) Stage 2 and (b) Stage 3, showing large voids in Stage 2 and fibers located in a void region in Stage 3.

Detecting fiber breakage proved difficult. Nonetheless, after multiple examinations, it was found that most fiber breakages were located within the cavitations, implying that the lack of matrix material may have reduced fiber protection during the process, thereby increasing its vulnerability to damage (Figure 7).

Figure 7.

Synchrotron X-ray micro-CT images along the filament axis at each stage of the printing process: (a) Stage 1, (b) Stage 2, and (c) Stage 3, showing fiber breakages (red circles) and voids. Most fiber breakages were observed in void regions.

Void formation expanded across both stages, leading to a reduction in the effective cross-section and a decrease in the actual volume fraction. These variations were assessed by averaging the void percentages of five samples using phase-contrast imaging in ImageJ. Submicron voids were excluded from the analysis, as they are too small to influence fracture initiation compared with the numerous micron-sized voids present in the material. These results are summarized in Table 3. In Stage 1, the void percentage was less than 1%, but it increased significantly to 32% in Stage 2. A substantial reduction occurred in Stage 3, likely owing to the compaction effect of the nozzle as the filament was placed on the print bed. However, the void percentage remained high, suggesting that the pressure exerted by the nozzle was insufficient to eliminate most of the voids.

Table 3.

Void percentage and effective volume fraction at different stages.

Stage	Cross-Sectional Area [mm2]	Void Percentage (%)	Effective Volume Fraction (%)
1	0.111 ± 0.002	0.9	34.7
2	0.146 ± 0.007	31.8 ± 1.8	23.9
3	0.143 ± 0.002	25.1 ± 1.1	26.2

Results of the tensile test

The tensile test results are presented in Figure 8(a). Between Stage 1 (raw filament) and Stage 2, there was a 32% reduction in tensile strength. At Stage 3, this reduction increased to 38%, confirming previous studies’ findings that the printing process affects the strength of the filament.

Figure 8.

Experimental results showing (a) tensile strength and (b) stress–displacement curves at different filament stages.

Figure 8(b) shows the stress–displacement curves at the different filament stages. A decrease in stiffness from Stage 1 to Stages 2 and 3 is observed, which is consistent with the introduction of defects such as voids and fiber waviness, as reported in a previous study.⁴⁴ In addition to the reduction in stiffness, the displacement at failure also decreased during the 3D printing process, indicating increased sensitivity to defects such as voids and fiber misalignment.

In addition to assessing the average tensile strength, a Weibull analysis was performed to evaluate the impact of the printing process on the consistency of the filament tensile strength. The results shown in Figure 9 indicate that the Weibull modulus (m) decreased in Stage 3, reflecting a greater spread in the tensile strength distribution. This suggests that the printing process may reduce the tensile strength reliability of the filament to some extent.

Figure 9.

Weibull plot of filament tensile strength at Stages 1 and 3.

Figure 10 illustrates the probability distribution of filament tensile strength at Stages 1 and 3. Stage 1 (blue) exhibits a relatively broad strength distribution, indicating moderate variability across the entire range. In contrast, Stage 3 (orange) shows a pronounced concentration of failures in the 800–900 MPa range, followed by a rapid decrease in probability at higher strength levels. This shift indicates an increased susceptibility to failure in Stage 3, which can be attributed to the influence of the printing process.

Figure 10.

Probability distribution of filament tensile strength at Stages 1 and 3.

Results of the spring element model simulations

The SEM grid was discretized into a 32 × 32 configuration, corresponding to approximately 1000 fibers within the filament, while the number of partitions along the z-axis was set to 300. Previous studies by Okabe et al.³⁶ have shown that variations in the number of longitudinal partitions have a negligible influence on the predicted tensile strength, indicating that the present discretization is sufficient. To evaluate the total fiber breakage in the model, the filament dimensions at each printing stage were multiplied by the experimentally measured surface density of fiber breakage. Based on the aforementioned micro-CT observations, there was less than 0.1 % breakage observed in Stage 1, so we assumed no breakage in the spring element model. However, as the printing process progressed, fiber breakage increased, with Stage 2 exhibiting six broken fibers and Stage 3 reaching 34. This increase in the number of fiber breaks is expected to affect the material strength and reliability (Table 4).

Table 4.

Number of fiber breakages at each stage.

Filament stage	Observed [breakage/mm³]	Model
1	None	None
2	18.0	6
3	99.1	34

Using this observational data, spring element model simulations were conducted for each printing stage. The original spring element models described in Sections 2.2.2 and 2.2.3 were used, incorporating the initial fiber breakage corresponding to each printing stage. The number of initial fiber breakages introduced into the model was determined to match the number of broken fibers observed in the micro-CT analysis. For each stage, simulations were performed using the spring element method without considering voids, and the resulting strengths were adjusted using equation (12) to account for the knockdown caused by the void volume fraction V_void. A summary of these results is presented in Table 5.

Table 5.

Results of the spring element model simulations at different filament stages.

Filament stage	Experiment [MPa]	Simulation T₀ [MPa]	Simulation T_1,2,3 [MPa]
1	1199.1 ± 157.1	1212.9	1212.9
2	812.0 ± 155.6	1210.3	826.3
3	743.0 ± 119.0	1199.2	903.4

During the filament analysis in the first stage, calibration of the stress concentration factor was performed. This enabled SEM strength predictions to represent experimental values with 99% accuracy. The predicted strength T₀, which accounts only for the initial fiber breakage, showed a minimal reduction of less than 1% across all printing stages, indicating that the introduced initial breakage has only a limited influence on the overall strength. In contrast, increases in void content had a pronounced effect. A void percentage of approximately 32% resulted in a corresponding 32% reduction in strength for both the simulation and tensile test in Stage 2. However, despite the reduction in void content in Stage 3, the tensile test exhibited a greater strength reduction than Stage 2, whereas the simulation showed the opposite trend with a much smaller reduction. This discrepancy suggests that the assumptions of the proposed model do not fully capture the strength degradation behavior, particularly in Stage 3. In this study, process-induced voids and fiber breakage were taken into account while maintaining the high computational efficiency of the SEM; however, particularly in Stage 3, the results suggest that resin degradation, which is not explicitly considered in the present model, may have played a big role in the observed strength reduction. Such degradation can lead to changes in the fiber/resin interface and/or reductions in interfacial shear stress effects. These factors may also alter the local stress concentration factor and the extent of the stress-recovery region. In particular, the assumption that broken fibers form stress-recovery regions following the Kelly–Tyson framework may no longer be valid once the matrix has degraded during the printing process. Therefore, further validation, including fracture morphology analysis, may be required in future work.

Finally, a sensitivity analysis was conducted on the material properties used in the analysis, and the detailed results are presented in Appendix B. The results indicated that the prediction accuracy at Stage 3 improved as the interfacial shear strength and the characteristic strength, σ₂, of the high-strength fiber population decreased. These findings suggest that, in addition to a reduction in interfacial shear strength, changes in the strength characteristics of the high-strength fiber population caused by the 3D printing process may also contribute to the observed strength reduction. For practical process optimization, the present results suggest that attention should be paid not only to reducing defect formation, but also to preserving the strength characteristics of the high-strength fiber population during printing. In particular, process parameters related to the contact pressure between the printed filament and the print bed, as well as the printing speed, may need to be carefully controlled. However, these parameters are likely to involve a trade-off, because conditions favorable for suppressing defects may simultaneously affect other aspects of mechanical performance. In addition, in the present model, voids were treated only indirectly through effective material parameters, and the local stress concentration associated with individual voids was not explicitly represented. Therefore, the absence of explicit void modeling may also be one of the causes of the remaining discrepancy at Stage 3.

Conclusion

This study combined both experimental and numerical analyses to explore the impact of the 3D printing process on the dimensions and internal structure of filaments. The experimental setup involved a three-stage 3D printing process, during which filament samples were collected at each stage for tensile testing and X-ray analysis. In addition, spring element model simulations were conducted, with the results compared with the tensile test outcomes. The printing process caused the formation of voids within the filament, with some fibers separating from the matrix, and limited fiber breakage was observed, most of which occurred in the void regions.

The tensile strength decreased significantly, by 32% in Stage 2 and 38% in Stage 3, highlighting the substantial impact of the printing process on the filament strength. For Stages 1 and 2, the spring element model, accounting for initial fiber breakage and void effects, predicted the strength with high accuracy within a 2% error; however, for Stage 3, the model overestimated the strength by 20%.

In conclusion, this study validates earlier research by demonstrating the considerable influence of the 3D printing process on filament properties, identifying the formation of significant voids during Stages 2 and 3 as the primary contributor to strength reduction. While the proposed spring element model effectively predicts the strength for Stages 1 and 2, the results suggest that additional strength degradation factors, such as changes in the probabilistic strength distribution of fibers and degradation of fiber/resin interface properties, partly due to the presence of voids, are not considered in the model for Stage 3. Thus, future research will focus more on explicit void modeling in closer integration with CT data, as well as investigating the synergistic effects with stress redistribution to better understand the process-induced microscopic degradation in 3D-CCFRCs.

Footnotes

ORCID iDs

Yamato Hoshikawa

Yoshiaki Kawagoe

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This study was supported by JST K-program Grant Number JPMJKP24W1, and the Japan Society for the Promotion of Science (JSPS) KAKENHI 24KJ0354.

Declaration of conflicting interests

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

Data Availability Statement

Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.

Appendix

References

Zhang

Lin

Vaidya

et al. Past, present and future prospective of global carbon fibre composite developments and applications. Compos B Eng 2023; 250: 110463. https://doi.org/10.1016/j.compositesb.2022.110463.

Ghidini

Grasso

Gumpinger

et al. Additive manufacturing in the new space economy: current achievements and future perspectives. Prog Aero Sci 2023; 142: 100959. https://doi.org/10.1016/j.paerosci.2023.100959.

Attaran

. The rise of 3-d printing: the advantages of additive manufacturing over traditional manufacturing. Bus Horiz 2017; 60(5): 677–688. https://doi.org/10.1016/j.bushor.2017.05.011.

Chen

Zhang

Cao

et al. Process evaluation, tensile properties, mathematical models, and fracture behavior of 3d printed continuous fiber reinforced thermoplastic composites. J Reinforc Plast Compos 2021; 40(21-22): 845–863. https://doi.org/10.1177/07316844211016091.

Kanishka

Acherjee

. Revolutionizing manufacturing: a comprehensive overview of additive manufacturing processes, materials, developments, and challenges. J Manuf Process 2023; 107: 574–619. https://doi.org/10.1016/j.jmapro.2023.10.024.

Shanmugam

Ramoni

et al. A review on additive manufacturing for aerospace application. Mater Res Express 2024; 11(2): 022001. https://doi.org/10.1088/2053-1591/ad21ad.

Alagumalai

Shanmugam

, et al. Effect of infill structures on compressive properties of additively manufactured nylon carbon fibre composite cylinders. J Reinforc Plast Compos. 2025; 45: 1641–1655. https://doi.org/10.1177/07316844251332323

Zhao

Chen

Zhang

et al. The mirror additive manufacturing process for tool-less fabrication of continuous carbon fiber reinforced thermoplastic resin matrix composite. Addit Manuf 2025; 99: 104680. https://doi.org/10.1016/j.addma.2025.104680.

Cano-Vicent

Tambuwala

Hassan

et al. Fused deposition modelling: current status, methodology, applications and future prospects. Addit Manuf 2021; 47: 102378. https://doi.org/10.1016/j.addma.2021.102378.

10.

Naranjo-Lozada

Ahuett-Garza

Orta-Castañón

et al. Tensile properties and failure behavior of chopped and continuous carbon fiber composites produced by additive manufacturing. Addit Manuf 2019; 26: 227–241. https://doi.org/10.1016/j.addma.2018.12.020.

11.

Hofstätter

Pedersen

Tosello

et al. State-of-the-art of fiber-reinforced polymers in additive manufacturing technologies. J Reinforc Plast Compos 2017; 36(15): 1061–1073. https://doi.org/10.1177/0731684417695648.

12.

Wang

Ning

et al. Fiber–matrix impregnation behavior during additive manufacturing of continuous carbon fiber reinforced polylactic acid composites. Addit Manuf 2021; 37: 101661. https://doi.org/10.1016/j.addma.2020.101661.

13.

Tian

Todoroki

Liu

et al. 3d printing of continuous fiber reinforced polymer composites: development, application, and prospective. Chin J Mech Eng: Additive Manufacturing Frontiers 2022; 1(1): 100016. https://doi.org/10.1016/j.cjmeam.2022.100016.

14.

Muhamedagic

Berus

Potočnik

et al. Effect of process parameters on tensile strength of fdm printed carbon fiber reinforced polyamide parts. Applied Sciences 2022; 12, 6028(12). https://doi.org/10.3390/app12126028.

15.

Farashi

Vafaee

. Effect of printing parameters on the tensile strength of fdm 3d samples: a meta-analysis focusing on layer thickness and sample orientation. Progr Addit Manuf 2022; 7: 565–582. https://doi.org/10.1007/s40964-021-00247-6

16.

Hoshikawa

Shirasu

Tsuyuki

, et al. Experimental and numerical evaluation of open hole tensile properties of 3d printed continuous carbon fiber reinforced thermoplastics. Materials System 2021; 38: 49–54. https://doi.org/10.34401/materialssystem.38.0_49

17.

Shirasu

Yamaguchi

Hoshikawa

, et al. Micromechanics study of short carbon fiber-reinforced thermoplastics fabricated via 3d printing using design of experiments. Materials Science and Engineering: A 2024; 891: 145971. https://doi.org/10.1016/j.msea.2023.145971

18.

Awasthi

Banerjee

. Fused deposition modeling of thermoplastic elastomeric materials: challenges and opportunities. Addit Manuf 2021; 46: 102177. https://doi.org/10.1016/j.addma.2021.102177.

19.

Ladani

Brandt

et al. Carbon fibre damage during 3d printing of polymer matrix laminates using the fdm process. Mater Des 2021; 205: 109679. https://doi.org/10.1016/j.matdes.2021.109679.

20.

Akhoundi

Behravesh

Saed

. Improving mechanical properties of continuous fiber-reinforced thermoplastic composites produced by fdm 3d printer. J Reinforc Plast Compos 2019; 38(3): 99–116. https://doi.org/10.1177/0731684418807300.

21.

Wang

et al. 3d printed continuous cf/pa6 composites: effect of microscopic voids on mechanical performance. Compos Sci Technol 2020; 191: 108077. https://doi.org/10.1016/j.compscitech.2020.108077.

22.

Zhang

Chen

Yang

. Fibre misalignment and breakage in 3d printing of continuous carbon fibre reinforced thermoplastic composites. Addit Manuf 2021; 38: 101775. https://doi.org/10.1016/j.addma.2020.101775.

23.

Sandford

HJC

Tang

Dong

. Investigation of fiber waviness in fused deposition modeling printed continuous fiber-reinforced polymers. Int J Adv Manuf Technol 2024; 130(2): 3771–3780. https://doi.org/10.1007/s00170-023-12896-8.

24.

Tang

Sun

et al. Longitudinal compression failure of 3d printed continuous carbon fiber reinforced composites: an experimental and computational study. Compos Appl Sci Manuf 2021; 146: 106416. https://doi.org/10.1016/j.compositesa.2021.106416.

25.

Hoshikawa

Shirasu

Higuchi

et al. Experimental and numerical investigation of the relationship between material defects and elastoplasticity behavior of 3d-printed carbon-fiber-reinforced thermoplastics under compressive loading. Compos Sci Technol 2023; 241: 110116. https://doi.org/10.1016/j.compscitech.2023.110116.

26.

Yap

Wang

et al. Experimental investigation and validation of strength-based topology and fiber path optimization in additively manufactured continuous fiber reinforced composites. Addit Manuf 2024; 89: 104274. https://doi.org/10.1016/j.addma.2024.104274.

27.

Fernandes

van de Werken

Koirala

et al. Experimental investigation of additively manufactured continuous fiber reinforced composite parts with optimized topology and fiber paths. Addit Manuf 2021; 44: 102056. https://doi.org/10.1016/j.addma.2021.102056.

28.

Hoshikawa

Ryuzono

Onodera

et al. Finite element modeling of viscoelastic creep behavior and transverse cracking in fiber-reinforced composite materials. Int J Damage Mech 2025; 34(9): 1365–1387. https://doi.org/10.1177/10567895241302543.

29.

Hoshikawa

Kawagoe

Ryuzono

et al. Finite element modeling for cohesive/adhesive failure of adhesive structures with a thermosetting resin. Eng Fract Mech 2024; 311: 110552. https://doi.org/10.1016/j.engfracmech.2024.110552.

30.

Ryuzono

Koo

Hoshikawa

et al. Mechanism investigation and comparison of long-term deformations caused by process-induced residual stresses in thermosetting cf/epoxy and thermoplastic cf/paek composite laminates. Compos Appl Sci Manuf 2025; 196: 108963. https://doi.org/10.1016/j.compositesa.2025.108963.

31.

Oine

Ryuzono

Kawagoe

, et al. Comparative study of thermosetting cf/epoxy and thermoplastic cf/paek composite laminates: effects of stacking sequences on open-hole strength. J Thermoplast Compos Mater. 2026; 39: 259–291. https://doi.org/10.1177/08927057251344271

32.

Koo

Hoshikawa

Kawagoe

et al. Process-induced residual stress in non-crimp fabric composites: experimental and numerical evaluation considering viscoelasticity. Mech Mater 2025; 209: 105423. https://doi.org/10.1016/j.mechmat.2025.105423.

33.

Ichihara

Ueda

Urushiyama

et al. Progressive damage simulation for a 3d-printed curvilinear continuous carbon fiber-reinforced thermoplastic based on continuum damage mechanics. Adv Compos Mater 2020; 29(5): 459–474. https://doi.org/10.1080/09243046.2020.1724430.

34.

Kayacan

. Mechanical investigation of compositing by resin filling in lattice structures manufactured with fused deposition modelling. J Reinforc Plast Compos 2024; 43(17-18): 961–979. https://doi.org/10.1177/07316844241243149.

35.

Xia

Okabe

Curtin

. Shear-lag versus finite element models for stress transfer in fiber-reinforced composites. Compos Sci Technol 2002; 62(9): 1141–1149. https://doi.org/10.1016/S0266-3538(02)00072-6.

36.

Okabe

Sekine

Ishii

et al. Numerical method for failure simulation of unidirectional fiber-reinforced composites with spring element model. Compos Sci Technol 2005; 65(6): 921–933. https://doi.org/10.1016/j.compscitech.2004.10.030.

37.

Mishnaevsky

Brøndsted

. Micromechanical modeling of damage and fracture of unidirectional fiber reinforced composites: a review. Comput Mater Sci 2009; 44(4): 1351–1359. https://doi.org/10.1016/j.commatsci.2008.09.004.

38.

Yamamoto

Onodera

Koizumi

et al. Considering the stress concentration of fiber surfaces in the prediction of the tensile strength of unidirectional carbon fiber-reinforced plastic composites. Compos Appl Sci Manuf 2019; 121: 499–509. https://doi.org/10.1016/j.compositesa.2019.04.011.

39.

Watanabe

Kawagoe

Hoshikawa

et al. Multiscale model for bottom-up prediction of failure parameters of unidirectional carbon-fiber-reinforced composite lamina from the atomic to filament-scales, and its application to failure modeling of open-hole quasi-isotropic composite laminates. Int J Solid Struct 2025; 308: 113130. https://doi.org/10.1016/j.ijsolstr.2024.113130.

40.

Chabaud

Castro

Denoual

et al. Hygromechanical properties of 3d printed continuous carbon and glass fibre reinforced polyamide composite for outdoor structural applications. Addit Manuf 2019; 26: 94–105. https://doi.org/10.1016/j.addma.2019.01.005.

41.

Kohutiar

Kakošová

Krbata

et al. Comprehensive review: technological approaches, properties, and applications of pure and reinforced polyamide 6 (pa6) and polyamide 12 (pa12) composite materials. Polymers 2025; 17(4). https://doi.org/10.3390/polym17040442. URL. https://www.mdpi.com/2073-4360/17/4/442

42.

Markforged . Composites material data sheet, 2023. URL. https://s3.us-east-1.amazonaws.com/mf.product.doc.images/Datasheets/Material+Datasheets/CompositesMaterialDatasheet.pdf (Accessed 15 October 2024).

43.

Toray . Toray t300 technical data sheet, 2018., (Accessed 15 October 2024).

44.

Hoshikawa

Shirasu

Yamamoto

et al. Open-hole tensile properties of 3d-printed continuous carbon-fiber-reinforced thermoplastic laminates: experimental study and multiscale analysis. J Thermoplast Compos Mater 2023; 36(7): 2836–2861. https://doi.org/10.1177/08927057221110791.

45.

Tokumitsu

Shimamura

Fujii

, et al. Effect of annealing and diameter on tensile property of spinnable carbon nanotube and unidirectional carbon nanotube reinforced epoxy composite. J Compos Sci 2022; 6(12): 389. https://doi.org/10.3390/jcs6120389

46.

of Quantum Science NI and Technology . Overview of the beamline at the next generation synchrotron radiation facility. (2025), (Accessed 24 April 2025).

47.

Computed tomography in spring-8 (sp-μct). Web page. URL. https://www-bl20.spring8.or.jp/xct/index-e.html

48.

Okabe

Sasayama

Koyanagi

. Micromechanical simulation of tensile failure of discontinuous fiber-reinforced polymer matrix composites using spring element model. Compos Appl Sci Manuf 2014; 56: 64–71. https://doi.org/10.1016/j.compositesa.2013.09.012.

49.

Yamamoto

Oshima

Ramadhan

et al. Tensile strength prediction of unidirectional polyacrylonitrile (pan)-based carbon fiber reinforced plastic composites considering stress distribution around fiber break points. Compos Appl Sci Manuf 2024; 183: 108234. https://doi.org/10.1016/j.compositesa.2024.108234.

50.

Watanabe

Tanaka

Okabe

. Accurate tensile strength distribution of pan-based carbon fibers. Journal of the Japan Society for Composite Materials 2021; 47(2): 51–64. https://doi.org/10.6089/jscm.47.51

51.

Christ

Gumbsch

Hohe

. Single fiber pull-out investigation at different temperature and humidity conditions: experimental characterization of the fiber-matrix interface in carbon fiber reinforced polyamide 6. J Thermoplast Compos Mater 2025; 38(8): 2894–2921. https://doi.org/10.1177/08927057251314436