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Abstract

Mechanical properties of short fiber reinforced composites manufactured with fused deposition modeling is affected by variables such as printing properties and internal structure of the composite. In this study, the relation between the tensile properties of 3D-printed short fiber reinforced composites, printing orientation and internal structure is inspected. Samples of different printing orientations are manufactured. These samples are inspected under X-ray micro computed tomography (micro-CT) and their fiber orientation distributions and fiber properties are determined. Then, these internal structure properties are applied to analytical material models to estimate the tensile properties of composites. Estimated material properties are compared with tensile test results. It turns out that analytical models that consider internal structure properties provide more accurate estimations than other analytical models that does not take these into account.

Keywords

Micro-CT scanning 3D printing composite materials fiber orientation analytical models

Introduction

3D printing of complex-shaped parts from composite materials is becoming widespread in the last decade, especially in the defense, automotive, and aerospace industries. Among various production methods, the most common type of this printing process is the fused deposition modeling (FDM) method. This method is preferred over other forms of 3D printing, such as stereolithography (SLA) or selective laser sintering (SLS), due to its ease of use, low cost, and reduced waste properties.¹ Despite these advantages, most FDM printed polymers are not preferred for end-user applications or load-bearing members of a structure due to polymers used in printing being insufficient in terms of required strength for most applications.^2–4 In the last couple of years, many studies have been performed to increase the mechanical capability of these polymers.³ Adding nano-materials, micro-particles, and short and continuous fibers are among the solutions for this purpose.^5,6 Inspection of bronze-reinforced PLA⁷ or hybrid metal-composite materials⁸ in structural applications, graphite-reinforced EVA in electrical applications,⁹ copper and iron-reinforced ABS in thermal applications,¹⁰ and carbon fiber-reinforced ABS under load-bearing applications¹¹ are some of these studies in which such additives are used to improve the mechanical properties of these materials.

Short fibers are the most widely used reinforcements for FDM-printed ABS, PLA, or nylon.^2,12,13 Isobe et al.¹⁴ concluded that using short fiber reinforcements instead of continuous fibers can maintain the ease of printing due to its structure. Ivey et al.¹⁵ found that reinforcing PLA with short-carbon fibers led to an increase in the strength of the produced samples, compared to non-reinforced PLA. Yasa and Ersoy¹⁶ inspected the mechanical properties of 3D-printed short carbon fiber-reinforced composites and found that fiber-reinforced composites have increased tensile strength and elastic modulus compared to the polymer itself. Al Abadi et al.¹⁷ developed an analytical model to predict the elastic properties and a numerical model to predict the failure and damage behavior of FDM printed carbon, Kevlar, and glass fiber-reinforced nylon material.

Apart from reinforcements, printing orientation is also essential for determining the strength of 3D-printed materials. Hanon et al.¹⁸ inspected the effect of printing and raster orientations on the tensile strength of FDM-printed PLA specimens. The study has shown that the raster orientation does not significantly affect the tensile properties. However, on-edge printing orientation provided the best performance regarding Young’s modulus and tensile strength. Chacón et al.¹⁹ found that the upright-oriented, FDM-printed PLA samples provided the lowest tensile properties compared to the flat and on-edge-oriented samples. Cantrell et al.²⁰ found that raster and printing orientations did not significantly affect the tensile behavior of ABS and PC specimens. However, they inspected a change of up to 20% in shear properties. Tanabi²¹ examined the effect of printing orientation on the mechanical properties of FDM-printed, short carbon fiber-reinforced PET materials. It was observed that printing orientation caused a significant anisotropy in the shear properties of the samples.

In addition to these aspects, a key characteristic should also be considered while working on the mechanical performance of 3D-printed short fiber-reinforced polymers, which is the internal structure of these materials. Parts manufactured with FDM have different internal structures than those manufactured with conventional methods. Deposed layers involve voids, which can affect the mechanical properties of the 3D-printed composite, such as causing an anisotropic structure.²² Also, the orientation of fibers may differ due to the printing parameters, which can also affect the mechanical behavior of the material. However, most of the classical analytical models employed for composite materials, such as rule of mixtures, do not consider the effect of essential parameters such as embedded fiber orientation, length, and void content on the mechanical behavior of 3D-printed composites.²³ Such internal properties of a 3D-printed composite can be examined and analyzed via micro-CT scanning.²⁴ Micro-CT scanning provides a stack of images belonging to the subjected samples’ cross-sections. This process allows for creating a 3D voxel model of the sample and quantifying the properties mentioned earlier.

In order to inspect the internal structure of composite materials, a software called VoxTex is developed by KU Leuven Composite Materials Group. This software analyzes image stacks obtained from a micro-CT scan and creates a 3D model of the inspected material. With this 3D model, components of a composite material can be examined separately. Properties like fiber volume ratio, void content, anisotropy, and stiffness matrix can be obtained from this analysis.^25,26 In our previous study, the effect of microvascular channels on the stiffness of a composite and changes in fiber angles were studied by analyzing the component properties and the anisotropy of the material by VoxTex.²⁷

In this study, the tensile behavior of the 3D-printed composites under different raster and printing orientations was analyzed. In order to achieve that, samples of different orientations were fabricated behavior. The analytical approaches were used to estimate the tensile properties of the 3D-printed composite specimens, considering the embedded reinforcement fibers’ orientation. This aim was realized by first fabricating appropriate samples for inspection under a micro-CT device. After the inspection, the internal structure of the specimen was revealed as 3D images. These images were then processed via VoxTex software to differentiate fibers and matrix and determine the fiber orientation. The obtained orientation functions were employed in the analytical models to determine the elastic modulus and tensile strength of the FDM printed composites. Failure conditions were defined with theoretical formulations and analytical models were verified with experimental test results.

In the following sections, specimen preparation procedures, characterization of the internal morphology of these specimens, determining the composite properties and tensile testing procedures are explained. After that, micro-CT scanning procedures and their results are given. Using the images obtained from the scan, fiber orientation analysis and the estimation of the tensile behavior through analytical methods are performed, and the results are presented. Finally, conclusions obtained from the study are presented.

Material and specimen preparation

The specimens used for the mechanical characterizations are FDM-printed using ABS and XSTRAND GF30-PA6 filaments, with a diameter of 1.75 mm, with regard to ASTM D638-type V standard. XSTRAND GF30-PA6 is a Polyamide six reinforced with short glass fibers (30 wt.%). A Zortrax M200 3D printer with a 0.4 mm diameter hardened steel nozzle is used for printing the specimens. A printing speed of 40 mm/s, bed temperature of 80°C, and nozzle temperature of 255°C are used for the XSTRAND GF30-PA6 specimens. For the ABS specimens, these parameters are modified as 35 mm/s of printing speed, 80°C of bed temperature, and 275°C of nozzle temperature, respectively. Infill is set to 100%, and layer height is 0.19 mm for all specimens.

The effect of printing direction on the embedded fiber orientation and tensile properties of the 3D printed samples were investigated by printing the samples in flat, on-edge, and up-right directions at [0°/90°] and [±45°] raster orientations as shown in Figure 1(a). For the micro-CT scans, specimens of the same XSTRAND GF30-PA6 material with 10 mm × 5 mm × 8 mm dimensions are fabricated with the same printing parameters (Figure 1(b)). Altogether 156 specimens are fabricated for mechanical characterization tests and micro-CT scans (Table 1).

Figure 1.

(a) Naming of the printed specimens, which are manufactured according to the ASTM D638 standard (red-colored specimens have [0°/90°] orientation, while the black-colored specimens have [±45°] orientation). (b) Micro-CT specimens.

Table 1.

The number of specimens printed for each type of test of each material.

Specimen type and printing direction
Material	ASTM D638-type V		Micro-CT
Material	[0°/90°]	[±45°]	[0°/90°]	[±45°]
GF30-PA6	15	15	9	9
ABS	15	15	9	9

Characterization of the internal morphology of the composite

In order to determine the weight ( $w_{f}$ ) and the fiber volume ratios ( $V_{f}$ ) of the embedded glass fibers, thermogravimetric analysis (TGA) is performed in a temperature range of 25°C up to 400°C with an increment of 10°C/min under the nitrogen atmosphere. Resulting value of $w_{f}$ is combined with the densities of each component in the composite ( $ρ_{m}, ρ_{f}$ ) and the volumes of each component ( $v_{m}, v_{f}$ ) are determined (equations (1a) and (1b)). Then, the fiber volume ratio is determined through equation (2).

v_{m} = \frac{w_{m}}{ρ_{m}}

(1a)

v_{f} = \frac{w_{f}}{ρ_{f}}

(1b)

V_{f} = \frac{v_{f}}{v_{m} + v_{f}}

(2)

As a result of the analysis, the weight ratio of the glass fibers turned out to be 27% (Figure 2). The densities of the component materials are determined as $ρ_{m}$ = 1.13 $g / c m^{3}$ ²⁸ for the matrix material and $ρ_{f}$ = 2.58 $g / c m^{3}$ ²⁹ for the glass fibers. The fiber volume ratio is calculated as $V_{f}$ = 0.14 according to these values. By comparing a printed specimen weight with a theorerical weight based on used filament length, a difference of 15% is calculated, which may indicate voids. However, this issue could not be evaluated under CT imaging due to low contrast of the material. Hence, its effects are not considered in this study.

Figure 2.

TGA results of the GF30-PA6 filament as the percent decrease of the normalized weight against temperature.

Scanning electron microscopy (SEM) was used to determine the embedded glass fiber length and diameter. The imaging was performed on representative samples using Tescan GAIA three equipped with a field emission electron gun in Hacettepe University Research and Application Center of Advanced Technologies (HUNITEK). Secondary electron (SE) imagery has been acquired under 7 kV accelerating voltage, 50 Pa beam current with 7 mm of working distance. Figure 3 shows the microstructure of the fabricated samples with PA6-G30 filament. The average diameter and length of the glass fibers were measured as 11.27 μm and 300 μm, respectively.

Figure 3.

SEM images of (a) [0°/90°]; (b) [±45°] on edge specimens.

Tensile tests

Specimens for the tensile tests were fabricated from both ABS and GF30-PA6 materials in specific printing directions at the same numbers (Table 2) so that the effect of the printing direction on the mechanical behavior of the specimens can be investigated directly. The digital image correlation (DIC) method³⁰ was used to measure the strain during tensile tests in the Atılım University Metal Forming Center of Excellence Laboratories. Obtained force and strain data are post-processed in MATLAB and converted to the stress-strain curves, which are used to determine the mechanical behavior of the specimens.

Table 2.

Types and printing directions of the tensile test specimens.

Material	On edge		Upright		Flat
GF30-PA6	[0°/90°]	[±45°]	[0°/90°]	[±45°]	[0°/90°]	[±45°]
ABS	[0°/90°]	[±45°]	[0°/90°]	[±45°]	[0°/90°]	[±45°]

Figure 4 presents the strain distribution on the specimens and the virtual measurement points. In order to increase the effectiveness and save time, only the displacements from a certain number of measurement points are processed. The measurement points are chosen to be within a 1 mm distance from each side of the fracture point. (Figure 5). Six points are determined to be within the decided area. Elastic modulus, ultimate tensile, and fracture stress-strain values are determined, as shown in Figure 6.

Figure 4.

DIC image examples of specimens.

Figure 5.

DIC image of [±45°] upright PA6 specimen and the distance scale in mm.

Figure 6.

Determination of tensile properties from the stress-strain curve (blue curve indicates the data set; orange dots indicate the polynomial curve fitted to the data set).

Results of the tensile tests are given in Table 3 and Figure 7. These results show that the elastic modulus is maximum at [±45°] on edge configuration for GF30-PA6 and at [±45°] flat configuration for ABS. Regardless of raster orientation in both flat and on-edge printing configurations, GF30-PA6 filament provides higher strength than ABS. The highest tensile strength is observed for GF30-PA6 at [0°/90°] orientation, and the lowest strength is observed for ABS at [0°/90°] on-edge configuration. The obtained values resemble the tensile behavior of each material found in the literature.^28,31 Since the upright configuration results deviate significantly, these results are excluded from this comparison. In upright printing configurations of both raster orientations, ABS has a higher strength value than GF30-PA6. However, both materials provide less elastic modulus and strength than flat and on-edge configurations. Layers of 3D-printed parts have weak interlayer bonding; thus, a force applied in the layer stacking direction leads to delamination. The delamination causes this outcome during the tensile testing of upright-printed specimens.²¹ Hence, it can be said that flat and on-edge printing configurations should be favored instead of the upright printing direction.

Table 3.

Material properties obtained from the stress-strain curves.

Material	ABS	GF30-PA6	ABS	GF30-PA6
	[0°/90°] flat		[±45°] flat
Elastic modulus (MPa)	1700 ± 27	4060 ± 103	1859 ± 34	3738 ± 158
Tensile strength (MPa)	21	52	20.7	50.5
Tensile strain	0.0234 ± 0.0205	0.0274 ± 0.0052	0.0226 ± 0.0063	0.0332 ± 0.0120
Fracture strength (MPa)	11.9	51	20.0	48.7
Fracture strain	0.0400 ± 0.0211	0.0278 ± 0.0051	0.0236 ± 0.0064	0.0410 ± 0.0126
	[0°/90°] on edge		[±45°] on edge
Elastic modulus (MPa)	1516 ± 2	3182 ± 290	1633 ± 38	4469 ± 153
Tensile strength (MPa)	19.7	49.4	21.9	49.7
Tensile strain	0.0219 ± 0.0061	0.0332 ± 0.0172	0.0226 ± 0.0140	0.0202 ± 0.0032
Fracture strength (MPa)	18.0	48.0	19.6	49.3
Fracture strain	0.0257 ± 0.0070	0.0365 ± 0.0172	0.0430 ± 0.0147	0.0205 ± 0.0032
	[0°/90°] upright		[±45°] upright
Elastic modulus (MPa)	1542 ± 87	94 ± 6	1169 ± 452	482 ± 3
Tensile strength (MPa)	10.1	3.6	11.9	8.8
Tensile strain	0.0219 ± 0.0089	0.0609 ± 0.2277	0.0127 ± 0.0051	0.0262 ± 0.0070
Fracture strength (MPa)	10.0	2.8	11.9	4.7
Fracture strain	0.0082 ± 0.0086	0.1143 ± 0.2277	0.0127 ± 0.0051	0.0298 ± 0.0070

Figure 7.

Stress-strain curves per printing configuration. (a) [0°/90°] flat; (b) [±45°] flat; (c) [0°/90°] on edge; (d) [±45°] on edge; (e) [0°/90°] upright; (f) [±45°] upright.

The SEM images of the fractured surfaces in Figure 8 show that the dominant failure mode at GF30-PA6 samples is fiber pull-out in different specimens, even though their printing directions and fiber orientations are different. The red circles on the images indicate that the fibers are pulled out of the matrix as a whole, meaning that fiber pull-out has occurred in the sample.

Figure 8.

Fracture surface images of (a) [0°/90°] upright; (b) [0°/90°] flat; (c) [±45°] on edge; (d) [±45°] flat specimens. Red circles indicate the fiber pull-out regions.

Micro-CT scanning procedure

Representative samples (Figure 10) have been chosen for computerized microtomography (µCT) analyses in order to reveal the three-dimensional distribution of components. The samples have been scanned using Bruker 1272 scanner installed in Hacettepe University Research and Application Center of Advanced Technologies (HUNITEK). Samples have been scanned under 75 kV source voltage and 100 µA source current with 0.18° rotation step generating 2450 × 2450 pixel raw images having 4 µm/pixel resolution. This resolution is selected such that it is about 1/3 of the average fiber diameter, which is determined through experience from prior studies. Raw images were reconstructed into a virtual stack of virtual slices with the same resolution using InstaRecon algorithm. Image processing was then employed on reconstructed image stacks using VoxTex software platform.

Fiber orientation analysis

Images of the internal structure are obtained using micro-CT scans. The fiber orientation distribution is extracted from these images to estimate the mechanical behavior with analytical methods. For the micro-CT scans, smaller samples are manufactured in [0/90°] and [±45°] orientations (Figure 9).

Figure 9.

(a), (b) Micro-CT scan samples (scale = 10 mm).

Scanned images from the high-resolution scan of the samples are imported to the VoxTEX software and processed to get anisotropy and orientation distribution data. The anisotropy and density values are used to determine the fibers, where high anisotropy and high-density values indicate the presence of fibers in the scanned region. The orientation of the fibers is defined in the spherical coordinate system, where the phi angle defines the in-plane angle, which is also the angle in the plane of stacks. Obtained anisotropy–density histogram, in-plane ( $y - z$ ), and out-of-plane ( $x - y$ ) orientation distributions for the [0/90] configuration sample are given in Figure 10. The anisotropy of the sample can be seen clearly, and peaks for the orientation distribution are distinct, indicating that the scan is successful and the orientation distribution can be used in the analytical calculations. The same procedure is applied for the [±45°] sample, and its results are given in Figure 11. There is an apparent irregularity in this sample’s fiber orientation distribution, which can be seen from the anisotropy plot, where the peak is at a smaller anisotropy value. Also, the $y - z$ orientation distribution plot indicates that the peak at +45° is much more pronounced than the peak at −45°. To check whether it was a problem caused by a scanning mistake, scans were repeated in different regions of the part. However, the results were similar, showing that the printer distributes fibers in a specific direction while not being as successful in the opposite direction. Nevertheless, this orientation difference is considered insignificant in terms of mechanical behavior. Thus, these results from the scans are used in analytical calculations.

Figure 10.

(a) Anisotropy - density; (b) in-plane orientation distribution; (c) out-of-plane orientation distribution of the [0°/90°] sample.

Figure 11.

(a) Anisotropy - density; (b) in-plane orientation distribution of the [±45°] sample.

Estimation of tensile behavior

Once the micro-CT imaging and the orientation analysis are done, the data obtained from these processes are used with analytical models to estimate the tensile behavior of the specimens. The fiber orientation distributions obtained through micro-CT imaging analysis in VoxTex, are extracted into MATLAB for a further process. They are determined for [0°/90°] and [±45°] oriented flat specimens and given in Figure 12, which are represented in gauss distribution functions (equation (3)). Their corresponding coefficients are shown in Table 4. In addition to the obtained data, fiber length distribution data is needed to employ the analytical models correctly. As these data were unavailable, the fiber length distribution present in a previous study³² was assumed to be similar to the one in the current study.

g (θ) = a_{1} \exp [- {(\frac{θ - b_{1}}{c_{1}})}^{2}] + a_{2} \exp [- {(\frac{θ - b_{2}}{c_{2}})}^{2}]

(3)

Figure 12.

Fiber orientation probability distributions.

Table 4.

Fiber orientation distribution coefficients corresponding to the orientation.

	[0°/90°] specimen	[±45°] specimen
$a_{1}$	0.01012	0.008802
$a_{2}$	0.009386	0.008386
$b_{1}$	5.375	41.63
$b_{2}$	87.84	−39.03
$c_{1}$	30.55	28.59
$c_{2}$	26.47	37.21

In this study, various analytical models for elastic modulus and tensile strength estimation are employed. Halpin-Tsai, laminate analogy and modified linear rule of mixtures are used to estimate the elastic modulus of the FDM printed composites. Halpin – Tsai model³³ estimates longitudinal and transverse stiffnesses by only using the properties of the constituent materials (equations (4) and (5)). This model does not take fiber orientation or fiber length distributions. However, average fiber length and diameter are used as variables obtained through the SEM imaging process.

E_{L} = E_{m} \frac{1 + (\frac{2 l}{d}) η_{L} V_{f}}{1 - η_{L} V_{f}} η_{L} = \frac{\frac{E_{f}}{E_{m}} - 1}{\frac{E_{f}}{E_{m}} + \frac{2 l}{d}}

(4)

E_{T} = E_{f} \frac{1 + 2 η_{T} V_{f}}{1 - η_{T} V_{f}} η_{L} = \frac{\frac{E_{f}}{E_{m}} - 1}{\frac{E_{f}}{E_{m}} + \frac{2 l}{d}}

(5)

The second model is the laminate analogy model, which models a composite with a random fiber distribution as a laminate composite such that each lamina has different orientations.³⁴ The equation of this model is given in equation (6):

E = \frac{{\bar{A}}_{11} {\bar{A}}_{22} - {\bar{A}}_{12}^{2}}{{\bar{A}}_{22}}

(6)

Here,

{\bar{A}}_{i j}

variables correspond to a variation of the transformed stiffness matrix,

{\bar{Q}}_{i j}

, which gets integrated with the fiber orientation,

g (θ)

and fiber length distributions,

f (l)

. The integration formula is given in equation (7).

{\bar{A}}_{i j} = \int_{l_{\min}}^{l_{\max}} \int_{θ_{\min}}^{θ_{\max}} {\bar{Q}}_{i j} * f (l) * g (θ) d θ d l

(7)

In that formula,

l_{\max}

and

l_{\min}

correspond the maximum and minimum fiber lengths and used as 588 μm and 118 μm, taken from the literature.³²

θ_{\max}

and

θ_{\min}

correspond to the limits of the fiber orientation distribution plots of [0°/90°] and [±45°] oriented specimens, which are 135°, −45° and 90°, −90° respectively.

The third model is called the modified linear rule of mixtures, a modified version of the classical rule of mixtures.³⁵ The model includes the effects of the fiber orientation and the fiber length distributions (equation (8)).

E = C D E_{f} V_{f} + E_{m} (1 - V_{f})

(8)

Here,

C

represents the fiber orientation, and

D

represents fiber length distributions. Formulas of these variables are presented in equations (9) and (10):

C = \int_{θ_{\min}}^{θ_{\max}} g (θ) \cos θ \int_{θ_{\min}}^{θ_{\max}} g (θ) {(\cos}^{3} θ - ν_{12} \sin^{2} θ \cos θ)

(9)

D = \int_{0}^{\infty} ϕ f (l) d l

(10)

In equation (9),

ν_{12}

represents the Poisson’s ratio of the composite, which is obtained through the tensile tests and determined as 0.34. In equation (10),

ϕ

is a variable that represents the load transfer mechanism between the fibers and the matrix. It is calculated as presented in Jayaraman and Kortschot.³⁶

For estimating the tensile strength, the aforementioned rule of mixtures and Tsai-Hill models have been modified differently to be used in tensile strength estimations. The first model for this case, the modified rule of mixtures model, includes the effects of fiber orientation and length distributions to achieve a more accurate representation of the mechanical behavior (equation (11)).

σ = C V_{f} σ_{f} [\int_{l_{c r}}^{\infty} f (l) (1 - \frac{l_{c r}}{2 l}) d l + \int_{0}^{l_{c r}} f (l) \frac{l}{2 l_{c r}} d l] + σ_{m} (1 - V_{f})

(11)

l_{c r} = \frac{σ_{f} d}{2 τ_{m}}

(12)

Here, the

C

variable is the same as in equation (9).

σ_{f}

represents the fiber tensile strength and

τ_{m}

represents the shear strength of the matrix material. The matrix material’s shear strength is assumed to be half of the matrix material’s tensile strength.³² In addition to that, for the determination of the effect of the fiber length distribution, critical fiber length (

l_{c r}

) is also used (equation (12)).³² The critical fiber length is a variable that indicates the smallest fiber length that provides the highest fiber strength.³⁷

The second model used for the estimation of the tensile strength is the modified Tsai–Hill model.³⁷ This model is a modified version of the Tsai-Hill model to account for the fiber orientation distribution. The equation used in this model is given in equation (13).

σ = \int_{θ_{\min}}^{θ_{\max}} g (θ) σ (θ) d θ

(13)

σ (θ) = {[\frac{\cos^{4} (θ)}{σ_{L}^{2}} + (\frac{1}{τ_{L T}^{2}} - \frac{1}{σ_{L}^{2}}) \sin^{2} (θ) \cos^{2} (θ) + \frac{\sin^{4} (θ)}{σ_{T}^{2}}]}^{- \frac{1}{2}}

(14)

Here, the estimated tensile strength is denoted by

σ,

and the variable of the modified Tsai-Hill method is indicated by

σ (θ)

, which is given in the expanded form in equation (14). The variable of

σ_{L}

is taken as the

σ

value found in the previous method. The fibers are distributed equally in longitudinal and transverse directions for the present material. Hence, there should be no difference between

σ_{L}

and

σ_{T}

in our case and they are taken as equal values. These values are found to be 57.7 MPa for [±45°] and 54.6 MPa for [0°/90°] orientations. The

τ_{L T}

value denote the shear strength of the composite, and it is assumed as half of the tensile strength of the matrix material.

According to these analytical models, calculations are performed and compared with the results of the tensile tests. In order to investigate the effect of the printing orientation, results of [0°/90°] and [±45°] oriented specimens are presented. The tensile test results belong to the flat-printed samples. Since the constituent materials’ exact property values are unknown, needed values are taken from the literature. These values are presented with their references in Table 5. All models estimate the elastic properties within a range, indicating that the developed regression models have acceptable robustness and accuracy within the explored experimental parameters. Halpin–Tsai model estimates the farthest values from the tensile test results (Figure 13). The other two methods, laminate analogy and modified rule of mixtures, provide closer results as they take into account the fiber orientations and fiber lengths. However, since the laminate analogy model uses values from the Halpin–Tsai model, its accuracy is less than the modified rule of mixtures model.

Table 5.

Material properties used in analytical models their values. $m$ subscript denotes the matrix, and $f$ subscript denotes the fibers.

Material property	Value	Reference
$E_{m}$	2500 $MPa$	³²
$E_{f}$	70000 $MPa$	³⁸
$σ_{f}$	3000 $MPa$	²⁹
$σ_{m}$	45 $MPa$	³¹
$ρ_{m}$	1.13 $g / c m^{3}$	²⁸
$ρ_{f}$	2.58 $g / c m^{3}$	²⁹
d(avg. fiber diameter)	11.27 μm	Study outcome
L(avg. fiber length)	300 μm	Study outcome
$V_{f}$	0.14	Study outcome
Fiber aspect ratio	26.6	Study outcome

Figure 13.

Comparison of elastic modulus between experimental results and analytical estimations.

Estimations of the failure behavior produced with analytical models are compared in Figure 14. It can be seen that both analytical models provide close results when compared to the experimental results. The modified rule of mixtures model estimates the tensile strength almost the same as experimental results. The success of these models is related to the inclusion of the effects of the fiber orientations and fiber lengths inside the composite. In order to investigate the impact of material properties on the outcomes shown in Figures 13 and 14, specific material properties are applied in different values on a range (Table 6). The range of results is indicated with the black bars on the figures. It turned out that matrix elastic modulus and tensile strength significantly affect the obtained results. In contrast, the change in fiber elastic modulus affected the elastic modulus estimations just a little, and the change in fiber tensile strength did not affect the tensile strength estimations.

Figure 14.

Comparison of tensile strength between experimental results and analytical estimations.

Table 6.

Highest and lowest values of used material properties.

Material property	Lowest value (MPa)	Highest value (MPa)
$E_{m}$	2300	2700
$E_{f}$	69,000	72,000
$σ_{f}$	1700	3445
$σ_{m}$	40	60

Conclusion

In this study, the internal structure of 3D-printed composite materials is inspected through micro-CT scanning to determine the effect of fiber orientation on tensile behavior. In addition to that, the impact of printing properties on tensile behavior is also examined. After characterizing the materials through experimental methods, analytical models are employed to estimate these tensile properties, and their results are compared with the experimental results. The results indicate that the effect of the fiber orientation should be considered while using these models since the fiber orientation significantly affects the mechanical behavior of 3D-printed composites. The outputs of this study can be summarized as follows:

• Regardless of the material type, parts printed with flat and on-edge orientations have much more strength than the upright-oriented ones. Its main reason is that the layer adhesion in 3D-printed parts is weak, and layer separation occurs much earlier than other failure modes in upright-oriented samples.

• There is no significant difference in mechanical performance between flat and on-edge-oriented parts. Both printing orientations are suitable for the best mechanical performance.

• Regardless of printing direction and fiber orientation, the dominant failure mode of 3D-printed parts occurred as fiber pull-out.

• Further microstructural defects, such as voids, caused by 3D-printing process could not be evaluated under imaging procedures due to the low contrast of the material. Hence, their possible effects on failure are neglected for the scope of this study.

• Analytical models, such as Halpin-Tsai, which do not consider the fiber orientation and length distributions, may not reflect the correct mechanical performance for the 3D-printed composites. A more accurate prediction of the tensile properties of a 3D-printed composite is possible when fiber orientation and length distributions are considered.

• Used analytical models do not consider non-linear material behavior of materials, thus only linear elastic properties are considered in the scope of this study. Future studies may include different analytical models for this case.

• Among the analytical models used in this study, the modified linear rule of mixtures turned out to be the most successful one in terms of elastic modulus and tensile strength estimations.

Footnotes

Acknowledgements

The authors would like to thank the Research Fund of Hacettepe University for supporting this study. This study is a part of first author’s Ph.D. Thesis.

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 work was supported by Hacettepe University Coordination Unit of Scientific Research Projects [grant number FHD-2020-18699].

ORCID iDs

Alp Şık

Hamed Tanabi

H. Evren Çubukçu

Baris Sabuncuoglu

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Experimental and analytical investigation of the tensile behavior of 3D-printed composites based on micro-CT analysis