# An experimental and numerical study of the mechanical response of 3D printed PLA/CB polymers

Robin Delbart¹*, Aris Papasavvas², Colin Robert², Thuy Quynh Truong Hoang³ and
Francisca Martinez – Hergueta¹*

¹ School of Engineering, Institute for Infrastructure and Environment, University of Edinburgh, UK

² School of Engineering, Institute for Materials and Processes, University of Edinburgh, UK

³ ESTACA, Pôle Mécanique des Structures Composites et Environment, Ecole d'ingénieurs, France

*francisca.mhergueta@ed.ac.uk

## Abstract

Fused Deposition Modelling is an Additive Manufacturing method that can produce bespoke components due to the high number of printing parameters available. Each of them plays a significant role in the final mechanical properties of the 3D printed device. This study aimed to characterise the mechanical and morphological properties of carbon black/PLA 3D printed samples as function of the printing parameters such as layer height, printing angle and nozzle diameter. A thermodynamic model is included to understand the influence of each parameter in the mechanical performance and decouple the role of the degree of crystallinity and the mesostructure of the 3D printed material. Specimens were mechanically tested under uniaxial tensile loads to determine the main deformation and failure mechanisms and results showed that samples were strongly influenced by the printing direction. Furthermore, the nozzle diameter played a significant role in the mesostructure and failure mechanisms, resulting in large differences in ductility. It was also found that the layer height had a strong influence on the temperature profile and the resulting crystallinity. This work provides the basic fundamentals to manufacture 3D printed components with tailored mechanical properties for specific stress solicitations.

**Keywords:** Additive Manufacturing, crystallinity, mechanical response, modelling
## 1. Introduction

Additive manufacturing (AM) is an affordable process that allows the production of complex shapes with minimal waste compared to the classic subtractive manufacturing processes [1]. The most widespread manufacturing method is Fused Filament Fabrication, also called Fused Deposition Modelling (FDM), where a solid material (usually a raw filament) is pushed through a hot nozzle at a temperature above glass transition temperature but under melting temperature. Subsequently, the quasi-melted filament is deposited on the bed sheet layer by layer building the part from the bottom to the top [2]. This method allows to print with a large range of materials which includes thermoplastic polymers [3], metal matrix composites [4, 5, 6], ceramic [7] or natural fibre-reinforced composites [6, 8, 9].

One of the main disadvantages of FDM in comparison to conventional bulk polymers is the strong anisotropy induced by the printing process. This strong anisotropy is directly related to the printing parameters of the FDM technique and their role in the mechanical response have been investigated in the past. For instance, reported analysis for 3D printed PLA include the influence of the printing angle [10, 11], layer thickness [12, 13, 14], infill percentage (also called infill density) [15, 16] or printing speed [17, 18]. All these studies explore the influence of the printing parameters on the mechanical properties by analysing the mesostructure and voids distribution, and they do not take in consideration the coupled role of the thermal history and the crystallisation rate. Crystallinity has an important impact on material properties such as stiffness and strength, and is also directly linked to those printing parameters. Further efforts to uncouple the role of thermal history and mesostructure are needed to develop a full understanding of the physical phenomena involved during the 3D printing process.

Numerical and analytical models have been employed to provide additional understanding of the physics involved, however, modelling the whole FDM process is a challenging task. As summary, the numerical/analytical studies available focus on (a) the melting of the filament in the nozzle and the prediction of the deposition temperature [19, 20, 21, 22], (b) the flow simulation of the deposited filament [23, 24], (c) the welding between filaments [25, 26, 27, 28], (d) the thermal exchange between the previous deposited layer and the deposited one [29, 30, 31], and (e) the prediction of the degree of crystallinity of semi-crystalline polymers [32]. The models available in the literature combine up to three of the previous physical mechanisms, but there are
currently no holistic approaches available in literature that cover all the mechanisms reported due to their complexity. For instance, several authors have developed models to predict the degree of crystallinity of polymers such as PLA, PAEKs or PEEK [29, 33, 30], but they considered a constant deposition temperature at the hot-end nozzle, simplifying the outcomes from previous investigations that prove the melting process results in an heterogeneous temperature profile at the hot-end of the nozzle [19]. These differences in deposition temperature can drastically modify the crystallinity of deposited polymers and affect the mechanical properties of 3D printed parts [34]. These simplifications limit the applicability of the numerical modes to specific printing setups, since they cannot fully decouple the role of the mesostructure and the crystallinity for a set of printing parameters. This has a detrimental impact in the overall design exercise of 3D printed components, and hinders the optimisation of the mechanical response for structural applications.

This paper presents an experimental and numerical approach to determine the impact of different printing parameters (printing angle, layer height and nozzle's diameter) in the final mechanical response of 3D printed carbon black particle/PLA as function of the mesostructure and the degree of crystallinity. Anisotropic mechanical properties in terms of stiffness, strength, and strain to failure are characterised for each set of parameters. Fractographies are employed to shed light into the different failure modes triggered. A numerical model is introduced to determine the role of the thermal history and predict the crystallinity of each configuration. To increase the accuracy of reported approaches, this model estimates the temperature of the filament during the melting process inside the nozzle and simulates the heat transfer process during FDM afterwards. That information is combined with the crystallisation kinetics to obtain the crystallinity degree of each material point. This investigation provides the basic fundamentals to design 3D printed components with tailored mechanical properties for different stress solicitations.

## 2. Material & Methods

### 2.1. *Materials and manufacturing*

The material selected for this study is a commercial PLA filament with brand name Proto-Pasta supplied by the company Protoplant. The filament is based on the Natureworks 4043 PLA polymer reinforced with carbon black particles. The specimens were manufactured by a Prusa i3 MK3S FDM printer. A hot-end temperature of 225 °C and a printing bed temperature of 60 °C
<figure><img src="image_1.png" /><figcaption>Figure 1: *Dimensions of the coupons used for the mechanical characterisation (both samples have the same thickness of 3.2 mm). (a) Samples for the 0º and 90º printing angles (according to ASTM D3039) and (b) ±45º printing angle (according to ASTM D6387).*</figcaption></figure>

were used as recommended by the manufacturer, with a fix deposition velocity of 30 mm/s. Two different nozzle diameters were chosen (0.4 and 1 mm) at 100% extrusion ratio. Furthermore, different layer heights of 0.05, 0.1 and 0.2 mm were selected. Moreover, three different printing angles were studied, following two protocols, ASTM D638 for the printing angle ±45º with respect to the loading direction and ASTM D3039 for the 0º and 90º according to figure 1. One perimeter layer was included. All specimens had the same thickness of 3.2 mm. Additionally the samples were tabbed using epoxy glass boards according to the ASTM D3039. The porosity was characterized using an Archimedes density kit and a Denvwe SI-234 scale.

## 2.2. *Mechanical characterisation*

The quasi-static tensile characterisation was performed using a MTS Criterion 45 Series 4 screw driven frame following the ASTM D6387 standard under stroke control at cross head speed of 2 mm/min. Additionally, a 2D video extensometer was used to acquire the local longitudinal and transverse strains. The polymer specimens (black due to their carbon filler), were speckled with white paint to enable contrast and capture the local strain field using an Imetrum camera at 5 fps and 1392 x 1038 pixels resolution. The analysis was performed with the software VIC 2D provided by Correlated Solutions. Window size and distance were selected to provide at least 2600 tracking points per image. 5 specimens were tested per configuration (layer height, printing angle and nozzle diameter). The force and strain data were processed with a Python script to obtain the Young's modulus, the ultimate strength, and the elongation at break of every sample.
Post-mortem specimens were inspected using a TM4000Plus Scanning Electron Microscope (SEM) manufactured by Hitachi (Tokyo, Japan) with a 15 kV accelerating voltage and a working distance of 50 mm. The fractographies of the cracked surfaces were taken to identify the failure modes of each configuration and see the welded filament before failure.

## 2.3. Thermal characterisation

The particle content was determined by Thermal Gravimetric Analysis (TGA). TGA was conducted in nitrogen atmosphere using a Mettler Toledo TGA/DSC 1 at a heating rate of 10°C/min in the temperature range 30 to 600°C. TGA curves and derivatograms were recorded to obtain the loss of weight with the evolution of the temperature.

The thermal properties were investigated by Differential Scanning Calorimetry (DSC). The characterisation was carried out in nitrogen atmosphere using a PerkinElmer DSC 8000. Prior to testing, each specimen was weighted and placed in an aluminium pan, sealed with an aluminium cover. The specimen temperature was stabilised at 30°C for 5 min and then heated up to 220°C (above the melting temperature) at a constant rate of 10°C/min. This analysis provided the thermogram curves (heat flow as function of temperature) to identify the glass transition temperature, the cold crystallisation temperature and the melting temperature. The degree of crystallinity was calculated according to eq 1 [35]:

$$X_c = \frac{1 \Delta H_m - \Delta H_c}{w \Delta H_m^0}, \qquad (1)$$

where $\Delta H_m$ and $\Delta H_c$ are the enthalpies of fusion and cold recrystallisation of the specimen respectively and $\Delta H_m^0$ is the enthalpy of fusion for 100% crystalline PLA, taken from the literature as 93 J/g [36]. $w$ stands for the PLA mass fraction obtained from the TGA and normalises the result considering the percentage of carbon black particles in the material [37].

Moreover, the crystallisation speed has been investigated within the cold recrystallisation range. Samples extracted from the raw PLA filament were heated above the melting temperature at 220°C and hold for 5 minutes in order to delete the thermal history. Subsequently, the samples were rapidly cooled in one minute at a fix temperature $T$ (80°C, 90°C, 110°C and 120°C) to ensure they kept a full amorphous structure. Afterwards the temperature $T$ was hold for 30 minutes to determine the evolution of crystallinity over time.

The crystallisation speed $V_{X_c}(T(t))$ as a composite function of the held temperature and time
133 was determined according to:

$$V_{X_c}(T(t)) = w \frac{\partial X_c(T(t))}{\partial t}, \qquad (2)$$

134 where $X_c(T(t))$ is the relative crystallinity, calculated according to the method suggested by Su et al [38] defined as:

$$X_c(T(t)) = \frac{\int_{t}^{t+dt} H(T(t)) dt}{\int_{0}^{t_F} H(T(t)) dt}, \qquad (3)$$

136 where $H(T(t))$ stands for the enthalpies and $t_F$ is the final time.

## 3. Modelling

137 This section summarises the theoretical framework to predict the crystallinity degree of each sample as function of their unique thermal history defined by the printing temperature, the geometry of the nozzle, the printing speed and the layer height. This model aims to predict the temperature of the filament since it is melted in the nozzle, during deposition and until it reaches thermal equilibrium at the temperature of the printing bed.

### 3.1. Theoretical model

143 A theoretical model is proposed to determine the thermal history of the manufactured components and compute the crystallinity degree. It provides: (i) the deposition temperature of the filament as function of the nozzle diameter (ii) the thermal interaction between the extruded filament (hot) and those previously deposited and (iii) the time evolution of the crystallinity degree for each material point. It should be emphasised that the purpose of these analyses is not to reproduce with high fidelity all the thermodynamic interactions during the printing process, but rather to determine the physics involved and identify the role of each parameter.

144 First the melting of the filament in the nozzle is reproduced. The main boundary conditions assume the entering filament is at room temperature (e.g. 20°C), the material in contact with the walls of the nozzle is at the pre-selected printing temperature (e.g. 225°C), and the material at the center of the nozzle is at its coldest temperature, as suggested in [19]. The heat transfer is assumed radially through conduction, i.e. the filament is heated from its external surface to its center and no heat transfer along the Z axis of a nozzle is considered. Therefore, on each section of the nozzle, the thermal exchange is described by the partial differential equation (PDE):

$$\frac{\partial^2 T(r,t)}{\partial r^2} + \frac{1}{r} \frac{\partial T(r,t)}{\partial r} = \frac{1}{a} \frac{\partial T(r,t)}{\partial t}, \qquad (4)$$
where $T(r,t)$ is the temperature in [K] of the filament at the distance $r$ in [m] from its center and at the time $t$ in [s], and $a$ is the thermal diffusion coefficient of the filament in [$m^2/s$], constant along the length of the nozzle and independent on the solid or fluid state of the polymer.

If the movement of the melted filament is considered laminar and friction between the polymer and the walls of the nozzle is negligible, all points on an horizontal section of the filament move at the same speed towards the exit of the nozzle. This assumption implies that one can link the time $t$ and the location $z$ of a given section of the filament in the nozzle with the following equation:

$$z = t \frac{F}{\pi R(z)^2}, \qquad (5)$$

where $R(z)$ is the radius [m] of the nozzle with respect to the location $z$, and $F$ is the volume flow rate [$m^3/s$].

Then, by combining equations (4) and (5) with the initial boundary conditions, the temperature of the filament, $T$, with respect to its location in the nozzle, $(r, z)$, can be obtained. The temperature of the filament at the end of the nozzle is used afterwards as input of the interlayer heat transfer model. If the thermal exchange with the atmosphere due to convection is neglected, and the heat transfer is assumed to be performed vertically through the layers due to conduction, it can be modeled by the following PDE:

$$\frac{\partial^2 T(z, t)}{\partial z^2} = \frac{1}{a} \frac{\partial T(z, t)}{\partial t}, \qquad (6)$$

where this time $T(z,t)$ is the temperature in [K] at the level $z$ in [m] of the printed material point at time $t$ in [s]. If the printing velocity is slow enough to ensure thermal equilibrium has been reached in the previously deposited layers, the main boundary condition is imposed by the temperature of the warm printing plate, i.e. previous layers are initially at a constant temperature of $T_\infty = 60^\circ C$. The transient heat transfer as function of the filament geometry can be introduced through the Newton's law of cooling [39, 40]:

$$\frac{T(z,t) - T_\infty}{T(z,0) - T_\infty} = e^{-bt} \qquad (7)$$

where $b$ represents the cooling rate:

$$b = \frac{h_T A}{\rho V C_p} \qquad (8)$$

where $h_T$ is the heat transfer coefficient, $A$ is the heat transfer surface area, $V$ is the volume of the filament and $C_p$ is the specific heat capacity. Finally, the evolution of the temperature over time
<table><caption>Table 1: Value of the initial volume flow rate as function of the layer height and the nozzle diameter.</caption><thead><tr><th>F (mm³/s)</th><th colspan="3">Layer height (mm)</th></tr><tr><th>Nozzle diameter (mm)</th><th>0.2</th><th>0.1</th><th>0.05</th></tr></thead><tbody><tr><td>0.4</td><td>3.95</td><td>1.97</td><td>0.98</td></tr><tr><td>1.0</td><td>10.41</td><td>5.20</td><td>2.60</td></tr></tbody></table>

of each material point, $T(z, t)$, can be combined with the crystallisation speed curves obtained experimentally by DSC to calculate the crystallisation degree of the 3D printed polymer according to the expression:

$$X_C(z) = \int_0^{t_F} V_{X_c}(T(z, t)) dt \qquad (9)$$

## 3.2. Implementation

The previous model has been implemented in the software Python. The complete source code is available for download on GitHub<fnref n="1" />. All the simulations have been run over 4 s, except the worst case scenario (1 mm nozzle and 0.2 mm layer height) that has been run for a longer period of time (10 s) to ensure thermal equilibrium is reached to prove the assumptions of the model are reasonable. The PDEs have been solved using the *pdepe* function solved with the ode15s solver with a relative error tolerance of $10^{-5}$ [41, 42] in combination with the boundary conditions aforementioned and the following geometrical dimensions and material properties.

The value of the thermal diffusion coefficient, $a = 0.105 \cdot 10^{-6} m^2/s$ in equations 4 and 6 has been taken from the literature [43] considering the carbon black particles have a negligible influence in thermal diffusion [44]. The initial volume flow rate, $F$ in equation 5, depends on the nozzle diameter and the layer height and the values are summarised in Table 1. The nozzle has been divided in 3 sections with different diameters as illustrated in Figure 2. The intermediate section has been idealised by a cylindrical section where the diameter is the mean of the top and bottom diameters. Dimensions are provided in Table 2.

A slower cooling rate was implemented in the interlayer welding model for the smallest nozzle

<footnote n="1">¹ https://github.com/RobinDelbart</footnote>
<figure><img src="image_2.png" /><figcaption>Figure 2: Nozzle dimensions used for the analytical model.</figcaption></figure>

<table><caption>Table 2: Numerical value of the nozzle dimensions.</caption><thead><tr><th>Cylinder</th><th>Nozzle</th><th>0.4 mm</th><th>1 mm</th></tr></thead><tbody><tr><td rowspan="2">1</td><td>R<sub>1</sub> [mm]</td><td>0.875</td><td>0.875</td></tr><tr><td>Z<sub>1</sub> [mm]</td><td>3.825</td><td>4.125</td></tr><tr><td rowspan="2">2</td><td>R<sub>2</sub> [mm]</td><td>0.5375</td><td>0.6875</td></tr><tr><td>Z<sub>2</sub> [mm]</td><td>0.675</td><td>0.375</td></tr><tr><td rowspan="2">3</td><td>R<sub>3</sub> [mm]</td><td>0.2</td><td>0.5</td></tr><tr><td>Z<sub>3</sub> [mm]</td><td>1.5</td><td>1.5</td></tr></tbody></table>
diameter (0.4 mm) according to:

$$ \frac{T_{0.4mm}(z,t) - T_{\infty}}{T_{0.4mm}(z,0) - T_{\infty}} = \frac{T_{1mm}(z,t) - T_{\infty}}{T_{1mm}(z,0) - T_{\infty}}e^{bt} \quad (10) $$

with

$$ b = \frac{h_T}{\rho C_p} \left( \frac{A_{1mm}}{V_{1mm}} - \frac{A_{0.4mm}}{V_{0.4mm}} \right) \quad (11) $$

where $A_{1mm}$, $V_{1mm}$, $A_{0.4mm}$ & $V_{0.4mm}$ stand for the area and the volume for the 1 mm nozzle and 0.4 mm nozzle respectively measured by SEM, resulting in a final coefficient $b = 0.0517s^{-1}$.

To calculate the crystallinity as defined in equation 9, the continuous temperature function $T(z,t)$ obtained from the thermal model has been transformed into a discontinuous step function $T_m(z,t)$ where the mean temperature of the filament at the end of the nozzle has have been rounded to the nearest crystallisation speed curve experimentally characterised by DSC. The integral of the composite function over time has been solved numerically using a trapezoidal rule.

## 4. Results and Discussion

### 4.1. Morphological characterisation

The 3D printed parts present a characteristic periodic mesostructure defined by the filaments, their interfaces (inter- and intra-layer) and voids, see Fig. 3(a). Voids are systematically located between the interfaces parallel to the printing direction. As the nozzle deposits the melted polymer, it reheats and welds the filaments, consolidating the interfaces. The SEM micrographics show a total melting of the inter-layer interface, but only a partial melting of the intra-layer contact, eventually presenting no consolidation between adjacent filaments for low layer heights, see Fig. 3(b).

Figure 4 shows the void content of the specimens as function of the layer height, printing direction and the nozzle diameter. When printed with the 1 mm nozzle, large differences are appreciated as function of the printing angle, with significant lower porosity when printing along the 0° direction. The porosity decreased with the layer height, however, negligible differences were found for the samples printed at 90°. The smaller nozzle exhibits an overall lower porosity overall. At lower diameter, the polymer undergoes more compaction, due to the shear stress gradient from the nozzle to the bed, resulting in lower porosity. It can also be seen that the layer height also has an influence on porosity for all 0 degrees sample, with the lower layer height leading to lower
<figure><img src="image_3.png" /><figcaption>Figure 3: Difference between inter-layer contact and intra-layer contact.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>Figure 4: Porosity according to the layer height & printing angle for the 1 mm nozzle (left) and 0.4 mm nozzle (right)</figcaption></figure>

porosity. This behavior can also be explained by the nozzle to bed shear stress gradient, being more severe for lower layer height, albeit the influence of layer height is smaller than the nozzle diameter.

## 4.2. *Mechanical properties*

The mechanical response of the 3D printed carbon reinforced PLA material was characterised as function of the layer height, printing direction and nozzle diameter. The average values of the Young's Modulus, ultimate tensile strength (UTS) and elongation at break are shown in Table 3.

Figure 5 compares the stiffness of all the configurations against the theoretical value provided by the manufacturer (2.639 GPa). The largest nozzle diameter (1 mm) provides a consistent stiffness regardless of the printing angle and the layer height, close to the theoretical value. The difference between the highest average (layer height of 1 mm printed at 45°) and the lowest (layer height of 0.2
<table><caption>Table 3: In-plane tensile mechanical properties of the Protopasta filament as function of the printing angle, the nozzle diameter and the layer height.</caption><thead><tr><th rowspan="3"></th><th rowspan="3"></th><th colspan="6">Printing angle</th></tr><tr><th colspan="2">0°</th><th colspan="2">45°</th><th colspan="2">90°</th></tr><tr><th colspan="6">Nozzle diameter</th></tr><tr><th></th><th></th><th>1 mm</th><th>0.4 mm</th><th>1 mm</th><th>0.4 mm</th><th>1 mm</th><th>0.4 mm</th></tr></thead><tbody><tr><td rowspan="3">Ultimate<br>Strength<br>(MPa)</td><td>0.2 mm</td><td>30.02</td><td>29.61</td><td>30.35</td><td>19.68</td><td>17.07</td><td>11.89</td></tr><tr><td>0.1 mm</td><td>32.21</td><td>30.29</td><td>31.50</td><td>21.07</td><td>16.29</td><td>7.34</td></tr><tr><td>0.05 mm</td><td>36.56</td><td>34.38</td><td>36.23</td><td>29.54</td><td>9.38</td><td>3.46</td></tr><tr><td rowspan="3">Elongation<br>at break</td><td>0.2 mm</td><td>0.0229</td><td>0.0204</td><td>0.0231</td><td>0.0307</td><td>0.0092</td><td>0.0071</td></tr><tr><td>0.1 mm</td><td>0.0216</td><td>0.0236</td><td>0.0236</td><td>0.0391</td><td>0.0084</td><td>0.0061</td></tr><tr><td>0.05 mm</td><td>0.0369</td><td>0.0373</td><td>0.0265</td><td>0.0337</td><td>0.0072</td><td>0.0053</td></tr><tr><td rowspan="3">Young's<br>Modulus<br>(GPa)</td><td>0.2 mm</td><td>2.301</td><td>2.474</td><td>2.468</td><td>1.593</td><td>2.433</td><td>2.07</td></tr><tr><td>0.1 mm</td><td>2.600</td><td>2.543</td><td>2.682</td><td>1.437</td><td>2.494</td><td>1.869</td></tr><tr><td>0.05 mm</td><td>2.490</td><td>2.274</td><td>2.543</td><td>1.973</td><td>1.170</td><td>2.433</td></tr></tbody></table>

<figure><img src="image_5.png" /><figcaption>Figure 5: Young's modulus (GPa) as function of the printing direction and the layer height for (left) the 0.4 mm nozzle diameter and (right) the 1 mm nozzle diameter.</figcaption></figure>

mm printed at 0°) is only 0.3 GPa. Nevertheless, the smallest nozzle diameter (0.4 mm) provides an heterogeneous result, with higher stiffness for the 0° printing angle. The authors suspect that the higher temperature allowed more reagglomeration of the carbon black powder leading to this increased heterogeneity. Overall, the stiffness increases when increasing the layer height although the deformation mechanisms of the samples printed at 45° will be further analysed in Section 4.3.3.
<figure><img src="image_6.png" /><figcaption>Figure 6: Ultimate tensile stress (MPa) as function of the printing direction and the layer height. (left) 1 mm nozzle size and (right) 0.4 mm nozzle.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Figure 7: Ultimate strain (%) as function of the printing direction and the layer height. (left) 1 mm nozzle size and (right) 0.4 mm nozzle.</figcaption></figure>

Figure 6 displays the average UTS and the standard deviation. Similar trends are observed for both nozzle diameters, nevertheless, the layer height influences the UTS differently according to the printing angle. At 0º and 45º, the ultimate strength increases when decreasing the layer height. In contrast, the opposite trend is observed with the samples printed at 90º. Overall, a superior strength is obtained for the specimens printed at 0º, replicated by the samples printed at 45º only when manufactured with the biggest nozzle diameter (1 mm).

Figure 7 shows the elongation at break. Similar trends are found for both nozzle diameters, comparable to the trends of the ultimate strength. The samples printed at 90º present a modest increment of ultimate strain when increasing the layer height, and the opposite trend is appreciated for samples printed at 0º, with a remarkable increment of the ductility in the case of 0.05 mm layer height. The highest elongation at break is registered for the 45º specimens when printed with the smallest nozzle (0.4 mm) and a layer height of 0.1 mm.
<figure><img src="image_8.png" /><figcaption>Figure 8: Representative stress-strain curves for the samples printed at 0º with different nozzle diameters: (a) 1 mm and (b) 0.4 mm.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Figure 9: Fractographies of samples printed at 0º and 0.2 mm (a), & 0.05 mm (b) layer heights.</figcaption></figure>

## 4.3. Failure analysis and fractography

The response of the samples printed at 0º are consistent for both nozzle diameters. The mechanical properties are inversely proportional to the porosity of the material, so the lower the porosity, the higher the stiffness, strength and ultimate strain, see Fig. 8. Filament tensile failure is the intrinsic failure mode of this printing direction, although depending on the layer height it results in a brittle or a ductile fracture. Fig. 9 compares the brittle fracture surface of the 0.1 and 0.2 mm layer heights specimens, and the ductile fracture surface of the thinnest layer height, 0.05 mm. The difference in ductility can not be justified by the 3D printed mesostructure and, therefore, subsequent crystallinity analysis will be conducted in Section 4.4.

The specimens printed at 90º present a poor mechanical response. The stiffness, strength and strain to failure are directly proportional to the thickness of the layer height and best performance
<figure><img src="image_10.png" /><figcaption>Figure 10: Representative stress-strain curves for samples printed at 90° with different nozzle diameters: (right) 1 mm and (left) 0.4 mm.</figcaption></figure>

is found when printing with the biggest nozzle diameter of 1 mm despite the higher porosity, see Fig. 10.

The fracture surfaces have been inspected by SEM and the fractography analysis shows all the specimens fail due to intra-layer debonding, resulting in a brittle failure mode. The intra-layer is the weakest interface of the 3D printed component due to the systematic location of the voids and the eventual lack of welding between adjacent filaments, in agreement with previous findings [27]. Fig. 11 and 12 analyse the fracture surfaces (highlighted in red colour) for the biggest nozzle diameter (1 mm) and the different layer heights (0.2 and 0.05 mm respectively). The mechanical properties are directly proportional to the extension of the fractured area, which increases with the layer height and nozzle diameter. In the case of the thickest layer height (0.2 mm, see Fig. 11), weldlines are consistently formed at each layer, resulting in the best mechanical performance. Nevertheless, for thinner layer heights, the experimental width of printing is lower than the theoretical value, hence weldlines are not formed on each layer. As a result, large voids appear in the intra-layer and samples exhibit premature failure, with particularly poor mechanical properties in the case of the thinnest layer height, 0.05 mm, see Fig. 12.

The samples printed at 45° present a different response depending on the nozzle size. Figure 13 shows the representative stress vs strain curves. The specimens printed with the biggest nozzle (1 mm diameter) present a brittle fracture surface, see Fig 13(a). As per samples printed at 0°, the thinner layer heights result in lower porosity and higher mechanical properties (stiffness, strength and strain to failure). In comparison, the specimens printed with the smallest nozzle (0.4 mm
<figure><img src="image_11.png" /><figcaption>Figure 11: Fractography for the samples printed at 90° with a layer height of 0.2 mm and 1 mm nozzle size.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>Figure 12: Fractography for the samples printed at 90° with a layer height of 0.05 mm and 1 mm nozzle size.</figcaption></figure>

diameter) show an elasto-plastic response with a higher elastic compliance. The highest stiffness and strength are registered for the thinnest layer height of 0.05 mm.

The differences in mechanical response are a result of the deformation and failure mechanisms triggered during the loading process for each configuration. In the case of the specimens printed with the biggest nozzle diameter (1 mm) the behaviour is driven by two main failure mechanisms: (i) intra-layer debonding and (ii) filament brittle tensile failure. An homogeneous strain distribution is exhibited until 2% of deformation, when intra-layer debonding is triggered, see Fig 14.

As the elongation progresses, the tensile strength of PLA is overtaken resulting in the final failure of the specimen. Fig. 15 shows the SEM fractography and the crack path, formed by a succession of filament debonding and tensile rupture. The relatively large width of the filaments
<figure><img src="image_13.png" /><figcaption>Figure 13: Representative stress-strain curves for the samples printed at 45° with different nozzle diameters: (left) 0.4 mm and (right) 1 mm.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>Figure 14: Contour plots of the evolution of engineering strain in the loading direction at different applied strains for the specimens printed at 45° with the 1 mm nozzle diameter & 0.1 mm layer height. (a) 1.12% deformation, (b) 1.61% deformation and (c) 1.99% deformation.</figcaption></figure>

(1.2 mm) promotes through-thickness crack propagation, minimising the fracture surface.

In the case of the specimens printed with the smallest nozzle diameter (0.4 mm), there is one additional failure mechanism to consider: through-thickness inter-layer debonding. The large compliance appreciated in the stress-strain curves, see Fig. 13(b), is a result of the higher number
<figure><img src="image_15.png" /><figcaption>Figure 15: Failure analysis of the specimens printed at 45° with the 1 mm nozzle diameter & 0.1 mm layer height. (a) SEM fractography. (b) Frontal and (c) side schematics views of the crack path.</figcaption></figure>

of interfaces and the lower welding capacity of these printing parameters. Fig. 16 shows the DIC full-field of the strain along the loading axis. The first failure mechanisms, intra-layer and inter-layer debonding, are triggered at 2.18% of deformation. As a result, detached filaments tend to rotate and align towards the loading direction without increasing the external force applied. The final failure of the specimen happens due to filament brittle tensile failure. A longer crack path is generated for this configuration as a result of the interlayer debonding, see Fig. 17.

### 4.4. *Thermal properties, history and crystallinity*

Figure 18 shows the DSC thermograms of the 3D printed samples and the as-received raw filament. Three characteristic temperatures can be distinguished: (i) the transition temperature, $T_g$ (57.54°C and 60.89°C for the samples printed with the 1 mm nozzle and the 0.4 mm nozzle respectively regardless of the layer height), (ii) the cold crystallisation exotherm peak, $T_c$ (103.33°C and 105.86°C for the 1 mm and 0.4 mm nozzle respectively) and (iii) the melting peak, $T_m$ (153.65°C and 154.57°C for the 1 mm and 0.4 mm nozzle respectively). The crystallisation rate has been calculated considering a weight percentage of PLA $w = 0.56$ determined by TGA. Table 4 resumes all the crystallisation rate as function of the layer height and nozzle diameter.

The peak temperatures are quite homogeneous for all the layer heights. The cold recrystallisation and melting temperatures are in agreement with the conventional values reported for PLA, within the 100-130°C and 120-180°C ranges respectively [45]. The as-received raw filament presents a fully amorphous structure characteristic of PLA samples cold down homogeneously [46]. The heating cycles imposed by the 3D printing process increase the degree of crystallinity of the PLA,
<figure><img src="image_16.png" /><figcaption>Figure 16: Contour plots of the evolution of engineering strain in the loading direction at different applied strains for the specimens printed at 45º with the 0.4 mm nozzle diameter & 0.1 mm layer height. (a) 2.18% deformation, (b) 2.78% deformation and (c) 3.58% deformation.</figcaption></figure>

<figure><img src="image_17.png" /><figcaption>Figure 17: Failure analysis of the specimens printed at 45º with the 0.4 mm nozzle diameter & 0.1 mm layer height. (a) SEM fractography. (b) Frontal and (c) side schematics views of the crack path.</figcaption></figure>

up to a maximum of ≈ 15%, however, the 0.05 mm layer height configuration still results in a fully amorphous polymer. These values are in agreement with previous findings which report that overall crystallisation rates of PLA in homogeneous conditions are relatively low [45]. When printed with the smallest nozzle the crystallisation is globally lower with a bigger difference between the
<figure><img src="image_18.png" /><figcaption>Figure 18: DSC for sample printed with the 1 mm nozzle(a) & 0.4 mm nozzle (b).</figcaption></figure>

<table><caption>Table 4: *Crystallinity behavior for 1mm and 0.4mm nozzle diameter samples at different layer height at 0°*</caption><thead><tr><th>Layer height (mm)</th><th>0.05</th><th>0.1</th><th>0.2</th><th>Raw filament</th></tr></thead><tbody><tr><td>X<sub>c</sub> 1mm nozzle (%)</td><td>2.80</td><td>10.32</td><td>15.78</td><td rowspan="2">0.21</td></tr><tr><td>X<sub>c</sub> 0.4 mm nozzle (%)</td><td>1.48</td><td>5.41</td><td>13.31</td></tr></tbody></table>

0.2 mm layer height and the 0.1 mm layer height. The degree of crystallinity correlates with the ductility of the filaments. The higher percentage of amorphous chains in the specimens with a 0.05 mm layer height justify the increment of ultimate strain as reported in Figure 7 and explain why the mechanical properties of 0.4mm are lower, despite the lower porosity, see Figure 4.

Fig 19 plots the isothermal DSC curves at different temperatures. Fig 19 (a) illustrates the change of the heat flow, fig 19 (b) shows the relative crystallinity according to equation 3 and fig 19 (c) plots the crystallisation speed obtained from equation 2. Lower temperatures (e.g. 80 and 90 °C) require additional time to activate the crystallisation process, but result in a higher crystallisation degree and speed afterwards in comparison to higher temperatures, in agreement to the findings by Balazs et al [47].

The degree of crystallinity of the 3D printed samples depends on the thermal history of each specimen, defined by the analytical model described in Section 3. The left hand side of Figure 20 provides the warming process of the center of the filament while crossing the nozzle for the three layer heights, and the right hand side of Figure 20 shows the estimated temperature profile of the
<figure><img src="image_19.png" /><figcaption>Figure 19: Isothermal DSC curves, Heat flow (a), relative crystallisation (b) & crystallisation speed (c)</figcaption></figure>
filaments while exiting the nozzle for each configuration. The lowest temperature in the center of the filament is predicted for the largest layer height, 0.2 mm, and the biggest nozzle diameter, 1 mm. The temperature gradient on the extruded filament varies for each layer height as a result of the different volume flow rate to ensure a constant printing speed for all the configurations. Hence, the largest layer height (0.2 mm) requires the fastest volume flow rate, so the processing time (the period of time that takes the filament to cross through the nozzle) is not sufficiently long to warm up the center of the filament, which barely reaches 140°C for the biggest nozzle size. In the same way, the smallest layer height (0.05 mm) requires a volume flow rate slow enough to heat the filament homogeneously for both nozzle diameters, with a negligible drop in temperature in the center of the filament, from the original 225°C to 224°C for the biggest nozzle size. The nozzle diameter also has an impact in the temperature gradient achieved in the filament. The heat transfer is more efficient for smaller nozzle sizes as the processing time is longer and the volume of material is lower. As a result, the 0.4 mm nozzle achieves relatively homogeneous filament temperatures meanwhile large gradients are appreciated for the highest nozzle size and large layer height.

The mean temperature at the end of the nozzle, $T_m$, is used as input of the interlayer heat transfer model to analyse the thermal history of the 3D printed specimens. Figure 21 compares the temperature distribution and cooling time for all the configurations once a new filament (at level 0 mm in height) is deposited over the previous layers measured in the center axis of the nozzle. As the hot filament contacts the previous layer it induces a superficial melt, welding both layers together. The thermal inertia determines the thermal history of the previous deposited layers, therefore, the thicker the layer height and the higher the deposition temperature, the higher the temperature achieved by the adjacent layers. The thinnest layer height (0.05 mm) offers a limited capacity to reheat the previous layers above the cold recrystallisation temperature. Figure 21 shows that temperatures higher 100°C are only achieved at a maximum depth of 0.05 mm, and for a period of time lower than 0.2 s. On the other hand, the configuration with the highest thermal inertia (0.2 mm layer height and 0.4 mm nozzle diameter) is able to increase the temperature of the previous layers well beyond the cold crystallisation temperature up to 0.15 mm depth for a period of time longer than 1 s. These results are in agreement with the study presented by Xia et al [31], who found that the volume of material involved in the heat exchange process was proportional to
<figure><img src="image_20.png" /><figcaption>Figure 20: Predicted filament temperature during processing as function of the nozzle diameter and the layer height. Left hand side shows the evolution of the temperature at the centre of the filament vs the position Z within the nozzle. Right hand side shows the temperature gradient of the filament at Z = 6 mm, when exiting the nozzle.</figcaption></figure>

the thermal inertia.

To predict the degree of crystallinity of the 3D printed component, the thermal history was combined with the crystallisation speeds according to equation 9. The heating cycles were replicated simulating the deposition of a reference filament and 4 additional layers on top every four seconds. Fig. 22 illustrates the time evolution of the average temperature and crystallinity of the reference filament for 0.05 mm and 0.2 mm layer heights respectively, printed with the 1 mm diameter nozzle. The two horizontal lines represent the cold crystallisation regime. As defined in the theoretical model, crystallinity only increases if the cold crystallisation temperature is reached, and it is directly proportional to the period of time within that region. Thinner layer heights (e.g. 0.05 mm) impose high input temperatures but very fast cooling rates. As a result, cold crystallisation is activated 3 times (the deposition of the reference filament plus two additional layers on top),
<figure><img src="image_21.png" /><figcaption>Figure 21: Time evolution of the temperature distribution through the layers for different layer heights and nozzle diameters.</figcaption></figure>

but its capacity to increase is limited, resulting in an amorphous polymer, see Fig. 22(a). On the other hand, thicker layer heights (e.g. 0.2 mm) exhibit large increments of crystallinity due to the higher thermal inertia and the slower cooling rates, despite the reduced number of crystallisation cycles, see Fig. 22(b). The same trends are observed for the samples printed with the 0.4 mm nozzle.

Fig. 23 compares the predicted and experimental degrees of crystallinity as function of the layer height and nozzle diameter. The model captures the main trend; an increment of crystallinity with the layer height. It also captures the lower crystallinity degree exhibited by the samples printed with the 0.4 mm nozzle as a result of the fastest cooling rate of that set of printing parameters.
<figure><img src="image_22.png" /><figcaption>Figure 22: Time evolution of the temperature and crystallinity of the samples printed with the 1 mm nozzle. (a) 0.05 mm and (b) 0.2 mm layer height. The two horizontal lines represent the cold crystallisation regime.</figcaption></figure>

<figure><img src="image_23.png" /><figcaption>Figure 23: Experimental vs Analytical results of the crystallisation for the 1 mm nozzle specimens</figcaption></figure>

Worst predictions are obtained for higher layer heights (0.2 mm). This can be explained by the assumption taken for the thermodynamic simulation, indeed taking into account a laminar flow of the melted filament into the nozzle will provide a better accuracy of the temperature profile and a more precise prediction of the crystallisation.

## 5. Conclusion

The mechanical response of 3D printed components manufactured in carbon particle reinforced PLA has been characterised. The influence of different printing parameters (the layer height, the nozzle diameter and the printing direction) has been analysed experimentally. Furthermore, a theoretical model has been developed to study the thermal history, predict the crystallinity of the polymer and understand the influence of each printing parameter in the final mechanical per-
formance. It was found that the mechanical response was driven by the regular filament/void
mesostructure and the degree of crystallinity of the 3D printed material. As a result, each config-
uration exhibited different deformation and failure mechanisms.

Best mechanical properties in terms of stiffness and strength were obtained for the configu-
rations printed at 0º direction with the biggest nozzle (1 mm diameter) and the smallest layer
height (0.05 mm). These samples exhibited the lowest porosity, showing the relevance of the
mesostructure in the mechanical performance. On the other hand, the samples printed at 90º
showed very poor mechanical properties as a result of the inefficient welding of the intra-layer
interface, eventually showing no contact between filaments for low layer heights.

Damage tolerance of the 3D printed components was dictated by the deformation and failure
mechanisms, which differed for each configuration. Samples printed at 90º failed due to intra-layer
debonding, resulting in a brittle failure mode. Samples printed at 45º presented different failure
mechanisms depending on the number of interfaces. Configurations with lower number of inter-
faces (e.g. 1 mm nozzle diameter) exhibited filament brittle tensile failure and intra-layer filament
debonding, leading to an overall brittle response. On the other hand, samples with higher number
of interfaces (e.g. 0.4 mm nozzle diameter) presented an additional failure mode; through-thickness
inter-layer filament debonding. This additional mechanism promoted filament rotation and realign-
ment towards the loading direction, showing improved damage tolerance. Samples printed at 0º
failed due to filament tensile failure and intra-layer filament debonding, however, depending on
the layer height, brittle or ductile fashions were found due to differences in crystallinity of the 3D
printed polymers.

The theoretical model provided valuable insight into the thermal history of the manufactured
components. First the deposition temperatures for different layer heights and nozzle diameters
were analysed. It was found the smallest nozzle (0.4 mm) presented an homogeneous heating of
the filament. Larger nozzle diameters and flow rates (to print higher layer heights) resulted in
heterogeneous temperature gradients of the filament profile at the end of the nozzle. Afterwards
the thermal interaction between deposited filaments was studied. The 3D printing process induced
thermal cycles on the previously deposited layers. The heat exchange process was driven by the
thermal inertia, as function of the deposition temperature, the volume and the surface area of the
filament. All thermal cycles that induced temperatures above the cold crystallisation temperature
promoted the growth of crystalline molecular structures. The configurations with higher thermal inertia (e.g. 0.2 mm layer height) presented a slow cooling rate and a substantial increment of the degree of crystallinity. On the other hand, a lower thermal inertia (e.g. 0.05 mm layer height and 0.4 mm nozzle diameter) resulted in a rapid cooling rate and amorphous structures. The higher percentage of amorphous chains led to the ductile failure of the filaments under tension.

This investigation provides the necessary engineering fundamentals to design 3D printed components with tailored mechanical properties for different applications. Stiffness and strength can be enhanced by reducing the void content and by aligning the filaments towards the loading direction. Superior ductility can be also reached by minimising the thermal inertia of the deposition process to retain a higher percentage of amorphous molecular chains of the semicrystalline polymer. Furthermore, improved damage tolerance can be achieved when printing along the $\pm45^\circ$ directions with smaller layer heights and nozzle diameters to promote longer crack paths and higher energy dissipation. Printing perpendicularly to the loading direction does not offer any advantage in terms of mechanical performance and should be avoided, and substituted by a non linear infill. These findings will be applied in subsequent publications to design 3D components for low-velocity impact applications.

## 6. Acknowledgements

This research is sponsored by the Defense Science and Technology Laboratory (DSTL) (grant number DSTLX1000144021R). The collaboration of Mr. Bence Toth is gratefully acknowledged.

## 7. Data Availability

The data to reproduce these graphs and the numerical model are available in GitHub. https://github.com/RobinDelbart.

## 8. Competing Interest

The authors have no conflicts of interest to declare. All co-authors have seen and agree with the contents of the manuscript and there are no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
454

# 9. Author Contributions

455

**Robin Delbart**: Investigation, methodology, formal analysis, software, visualisation, data curation, validation, writing - Original draft preparation. **Aris Papasavvas**: software, writing-review editing. **Colin Robert**: Investigation, methodology, supervision, writing-review editing. **Quyhn Truong Hoang**: supervision, conceptualisation, funding acquisition, writing-review editing. **Francisca Martinez Hergueta**: supervision, conceptualisation, funding acquisition, formal analysis, writing - Original draft preparation.

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