<table><caption>Table 1: Summary of thermoplastic polymer matrix optimization studies featuring SLS</caption><thead><tr><th>Material</th><th>Heat source</th><th>Laydown speed</th><th>Compaction force or pressure</th><th>Tool temperature</th><th>Ref.</th></tr></thead><tbody><tr><td>CF/PEEK</td><td>Laser</td><td>200 – 800 mm/s</td><td>1025 N</td><td>Unheated</td><td>Di Francesco et al. [6]</td></tr><tr><td>CF/PEEK</td><td>HGT</td><td>57 – 95 mm/s</td><td>333 – 556 N</td><td>20 – 150 °C</td><td>Qureshi et al. [7]</td></tr><tr><td>CF/LM-PAEK</td><td>Laser</td><td>125 – 250 mm/s</td><td>0.6 MPa</td><td>20 and 200 °C</td><td>Schiel et al. [8]</td></tr><tr><td>CF/PEI</td><td>HGT</td><td>0.5 – 3.5 mm/s</td><td>75 – 275 N</td><td>100 – 140 °C</td><td>Sabido [9]</td></tr></tbody></table>

Di Francesco et al. [6] indicates the increase in material laydown velocity reduces the degree of crystallinity in in-situ consolidated CF/PEEK. On the other hand, Schiel et al. [8] reported that the deposition rate did not affect crystallinity of in-situ consolidated CF/LM-PAEK.

HGT based heating is only able to achieve approximately 60% of the interlaminar strength of autoclaved parts and it decreases with deposition velocity according to Qureshi et al. [7]. Lower heating efficiency by convection lead to insufficient time to melt the PEEK polymer matrix for adequate autohesion.

## Materials and Methods

The material used in this investigation is a unidirectional thermoplastic prepreg tape consisting of Poly-ether-ether-ketone (PEEK) reinforced with standard modulus carbon fibers (whose trade name used by Cytec is APC-2).

PEEK is by far the most commonly used thermoplastic in tape placement processes. The main properties of CF/PEEK have been listed in Table 2.

<table><caption>Table 2: Material properties of unidirectional CF/PEEK</caption><thead><tr><th>Property</th><th>CFRTP</th></tr></thead><tbody><tr><td>Prepreg</td><td>APC-2</td></tr><tr><td>Fiber</td><td>AS4</td></tr><tr><td>Fiber volume fraction V<sub>f</sub></td><td>60%</td></tr><tr><td>Tape width</td><td>6.35 mm</td></tr><tr><td>Melt temperature T<sub>m</sub></td><td>343 °C</td></tr><tr><td>Glass transition temperature T<sub>g</sub></td><td>143 °C</td></tr><tr><td>Crystallization enthalpy H<sub>ref</sub></td><td>122.5 Jg<sup>-1</sup></td></tr></tbody></table>

The CFRTP AFP setup consists of a laying head based on hot gas torch (HGT) heating source, controlled pressure on a stainless steel compaction roller (30 mm diameter, 30 mm width) and IR thermal monitoring. The head is moved by a six DOF anthropomorphic arm (KUKA KR240 R2900-2). Tapes are laid down on a steel cylindrical mandrel with 300 mm diameter (see Fig. 3a). The end effector in Fig. 3b enables the placement of a single 0.25" unidirectional prepreg tow.

The heat source plays a crucial role in the key manufacturing parameter of in-situ consolidation process. Currently radiant heating using near-infrared (NIR) lasers are more commonly used in AFP. However, despite having lower thermal efficiency, HGT heating is still being used for in-situ consolidation due to its lower capital costs and ease of implementation. With HGT there is also a reduced risk of damaging the matrix, compared to methods involving CO₂ and NIR laser, which can affect the interfacial adhesion through matrix burning. As can also be seen in Table 1, usually the laydown speeds of AFP with laser heating source are higher than those equipped with HGT systems.
<figure><img src="image_572.png" /><figcaption>Figure 3: CFRTP AFP Cell (a) and details of the end effector (b) and its components (c)</figcaption></figure>

Ring shaped SLS specimen was produced according to the following approach: a first layer of CF/PEEK (inner ring) was laid down on the tooling surface, then polyimide films (Kapton) with a thickness of 50 µm was subsequently placed in two 8-mm-apart separate courses perpendicular over the ring stripes and after that one more layer (outer ring) was placed on the first track of every substrate ring (see Fig. 4a). To evaluate the bonding region (see Fig. 4b-c) the tapes were cut through on opposite lying sides, one cut on the inner ring and a second cut on the outer ring (Fig. 4a). The shear force thus takes effect in the predefined region in between the Kapton films. The purpose of polyimide films is to create delamination zones upstream and downstream of the bonding region. The area highlighted in red Fig. 4a has been detailed in Fig. 4b.

<figure><img src="image_573.png" /><figcaption>Figure 4: SLS coupon scheme (a) and detail of the bonding region of a coupon (b) and (c)</figcaption></figure>

During the tensile test the load was transferred with a split-disk approach as described in Fig. 4a and in Fig. 5. This approach, utilizing non-planar coupons instead of flat ones, was chosen for two key reasons: first, cylindrical specimens better mimic the actual behavior of the material in the presence of multiaxial stresses (i.e. in pressure vessels applications). Second, they minimize the impact of edge effects, a common issue with thin planar samples.

Tensile force F was applied to pull the split halves apart until failure. The external radius of the two half-disks had the same length of 150 mm as the mandrel used to manufacture the specimens in order not to introduce deformation of the composite rings during the test. Friction between the specimen and metal fixtures was minimized.

The average ILSS was computed according to the following equation:

$$ \overline{ILSS} = \frac{F_{max}/2}{w \cdot l} \qquad (1) $$
<figure><img src="image_583.png" /><figcaption>Figure 3: CFRTP AFP Cell (a) and details of the end effector (b) and its components (c)</figcaption></figure>

Ring shaped SLS specimen was produced according to the following approach: a first layer of CF/PEEK (inner ring) was laid down on the tooling surface, then polyimide films (Kapton) with a thickness of 50 µm was subsequently placed in two 8-mm-apart separate courses perpendicular over the ring stripes and after that one more layer (outer ring) was placed on the first track of every substrate ring (see Fig. 4a). To evaluate the bonding region (see Fig. 4b-c) the tapes were cut through on opposite lying sides, one cut on the inner ring and a second cut on the outer ring (Fig. 4a). The shear force thus takes effect in the predefined region in between the Kapton films. The purpose of polyimide films is to create delamination zones upstream and downstream of the bonding region. The area highlighted in red Fig. 4a has been detailed in Fig. 4b.

<figure><img src="image_584.png" /><figcaption>Figure 4: SLS coupon scheme (a) and detail of the bonding region of a coupon (b) and (c)</figcaption></figure>

During the tensile test the load was transferred with a split-disk approach as described in Fig. 4a and in Fig. 5. This approach, utilizing non-planar coupons instead of flat ones, was chosen for two key reasons: first, cylindrical specimens better mimic the actual behavior of the material in the presence of multiaxial stresses (i.e. in pressure vessels applications). Second, they minimize the impact of edge effects, a common issue with thin planar samples.

Tensile force F was applied to pull the split halves apart until failure. The external radius of the two half-disks had the same length of 150 mm as the mandrel used to manufacture the specimens in order not to introduce deformation of the composite rings during the test. Friction between the specimen and metal fixtures was minimized.

The average ILSS was computed according to the following equation:

$$ \overline{ILSS} = \frac{F_{max}/2}{w \cdot l} \qquad (1) $$
<figure><img src="image_574.png" /><figcaption>Figure 5: SLS test setup for average ILSS determination (a) and with coupon mounted on during test execution (b)</figcaption></figure>

The ultimate tensile load, $F_{max}$, was measured by the load cell and the width, $w$, and length, $l$, of the adhesion zone between the Kapton films were measured with a calliper. It has to be noted that the shear stress distribution is not expected to be constant. Although the followed test approach is not standardized, the results obtained can still be considered representative for the purposes of optimizing the AFP process parameters through the evaluation of consolidation quality as will be discussed further.

An amount of 60 ring coupons has been manufactured - 15 for each deposition set - and during laydown operations all relevant process parameters (temperatures, compaction pressure, laydown speed) have been in-line monitored and recorded. Process variables settings are summarized in Table 3. The compaction force was set by choosing the pressure $p_{rs}$ operating in the pneumatic actuator of the vertical suspension of the roller. It was equal to 2 bars for SET 01-03 and to 1 bar for SET 04. Laydown speeds of the outer rings were varied within the single SET assuming three different values with an increasing trend (see Table 3 for details). The tool was unheated.

<table><caption>Table 3: Process Variables Setting</caption><thead><tr><th>SET ID</th><th>Coupons Count</th><th>HGT air flow set [l/s]</th><th>HGT voltage set [V]</th><th>v<sub>ls</sub> [mm/s]</th><th>p<sub>rs</sub> [bar]</th></tr></thead><tbody><tr><td>01</td><td>5 / 5 / 5</td><td>59.9</td><td>165.8</td><td>6.3 / 13.1 / 19.7</td><td>2</td></tr><tr><td>02</td><td>5 / 5 / 5</td><td>60.0</td><td>164.2</td><td>6.3 / 13.1 / 19.7</td><td>2</td></tr><tr><td>03</td><td>5 / 5 / 5</td><td>59.0</td><td>165.3</td><td>6.3 / 13.1 / 19.7</td><td>2</td></tr><tr><td>04</td><td>5 / 5 / 5</td><td>60.6</td><td>165.3</td><td>2.8 / 6.3 / 9.8</td><td>1</td></tr></tbody></table>

Fig. 6 shows the coupons manufactured within a single deposition set with highlighted (Fig. 6b) the 5-element subsets with varying laydown speeds.

<figure><img src="image_575.png" /><figcaption>Figure 6: A typical set of in-situ consolidated ring coupons with inner layers (a) and outer layers (b)</figcaption></figure>

## Results

The results of the mechanical testing are summarized below in Fig. 7. The box plot graph shows the average interlaminar shear strength value ($\overline{ILSS}$) for each subset of 5 element across the
<figure><img src="image_585.png" /><figcaption>Figure 5: SLS test setup for average ILSS determination (a) and with coupon mounted on during test execution (b)</figcaption></figure>

The ultimate tensile load, $F_{max}$, was measured by the load cell and the width, $w$, and length, $l$, of the adhesion zone between the Kapton films were measured with a calliper. It has to be noted that the shear stress distribution is not expected to be constant. Although the followed test approach is not standardized, the results obtained can still be considered representative for the purposes of optimizing the AFP process parameters through the evaluation of consolidation quality as will be discussed further.

An amount of 60 ring coupons has been manufactured - 15 for each deposition set - and during laydown operations all relevant process parameters (temperatures, compaction pressure, laydown speed) have been in-line monitored and recorded. Process variables settings are summarized in Table 3. The compaction force was set by choosing the pressure $p_{rs}$ operating in the pneumatic actuator of the vertical suspension of the roller. It was equal to 2 bars for SET 01-03 and to 1 bar for SET 04. Laydown speeds of the outer rings were varied within the single SET assuming three different values with an increasing trend (see Table 3 for details). The tool was unheated.

<table><caption>Table 3: Process Variables Setting</caption><thead><tr><th>SET ID</th><th>Coupons Count</th><th>HGT air flow set [l/s]</th><th>HGT voltage set [V]</th><th>v<sub>ls</sub> [mm/s]</th><th>p<sub>rs</sub> [bar]</th></tr></thead><tbody><tr><td>01</td><td>5 / 5 / 5</td><td>59.9</td><td>165.8</td><td>6.3 / 13.1 / 19.7</td><td>2</td></tr><tr><td>02</td><td>5 / 5 / 5</td><td>60.0</td><td>164.2</td><td>6.3 / 13.1 / 19.7</td><td>2</td></tr><tr><td>03</td><td>5 / 5 / 5</td><td>59.0</td><td>165.3</td><td>6.3 / 13.1 / 19.7</td><td>2</td></tr><tr><td>04</td><td>5 / 5 / 5</td><td>60.6</td><td>165.3</td><td>2.8 / 6.3 / 9.8</td><td>1</td></tr></tbody></table>

Fig. 6 shows the coupons manufactured within a single deposition set with highlighted (Fig. 6b) the 5-element subsets with varying laydown speeds.

<figure><img src="image_586.png" /><figcaption>Figure 6: A typical set of in-situ consolidated ring coupons with inner layers (a) and outer layers (b)</figcaption></figure>

## Results

The results of the mechanical testing are summarized below in Fig. 7. The box plot graph shows the average interlaminar shear strength value ($\overline{ILSS}$) for each subset of 5 element across the
different laydown speeds $v_{ls}$. The median value was also highlighted by horizontal markers. Variations in the deposition speed showcase distinct influences on the $\overline{ILSS}$ values. For instance, in SET 02, as the $v_{ls}$ increases from 6.3 to 19.7 mm/s, there's a discernible decrease in the $\overline{ILSS}$ mean values, coupled with a reduction in the standard deviation. Conversely, SET 03 illustrates an upward trend in $\overline{ILSS}$ mean values with increasing deposition speed, accompanied by a minimal standard deviation at 13.1 mm/s. Maximum mean value of $\overline{ILSS}$ for SET 03 is 24.9 MPa at 19.7 mm/s laydown speed. Also SET 04 demonstrates the impact of varied deposition speeds (from 2.8 to 9.8 mm/s) on $\overline{ILSS}$, revealing fluctuations in mean values and standard deviations with a slightly increasing trend.

<figure><img src="image_576.png" /><figcaption>Figure 7: Box plot of the average ILSS over set laydown speed</figcaption></figure>

According to the graphs depicted in Fig. 8a, SET 03 and exhibits higher HGT thermocouple temperatures compared to SET 01-03. This aspect is also present in the temperature measured downstream the deposition area $IR T$ (evaluated by the pyrometer) and reported in Fig. 8b. The $IR T$ graph, however, highlights the effects of the heating of the mandrel as one proceeds with the deposition of the rings within a single set. Such aspect seems to have been the process parameter that influenced the $\overline{ILSS}$ the most.

<figure><img src="image_577.png" /><figcaption>Figure 8: Mean HGT temperature (a) and mean $IR T$ temperature (b) evaluated during laydown process of each outer ring manufactured</figcaption></figure>

Scatter plots between $\overline{ILSS}$ and other relevant parameters are reported below in Fig. 9. In particular Fig. 9a remarks the how higher temperatures – still below the degradation of the material - leads to higher $\overline{ILSS}$. Fig. 9b and Fig. 9c puts in relation respectively laydown speed $v_l$ and compaction pressure $p_r$ with $\overline{ILSS}$.
different laydown speeds $v_{ls}$. The median value was also highlighted by horizontal markers. Variations in the deposition speed showcase distinct influences on the $\overline{ILSS}$ values. For instance, in SET 02, as the $v_{ls}$ increases from 6.3 to 19.7 mm/s, there's a discernible decrease in the $\overline{ILSS}$ mean values, coupled with a reduction in the standard deviation. Conversely, SET 03 illustrates an upward trend in $\overline{ILSS}$ mean values with increasing deposition speed, accompanied by a minimal standard deviation at 13.1 mm/s. Maximum mean value of $\overline{ILSS}$ for SET 03 is 24.9 MPa at 19.7 mm/s laydown speed. Also SET 04 demonstrates the impact of varied deposition speeds (from 2.8 to 9.8 mm/s) on $\overline{ILSS}$, revealing fluctuations in mean values and standard deviations with a slightly increasing trend.

<figure><img src="image_587.png" /><figcaption>Figure 7: Box plot of the average ILSS over set laydown speed</figcaption></figure>

According to the graphs depicted in Fig. 8a, SET 03 and exhibits higher HGT thermocouple temperatures compared to SET 01-03. This aspect is also present in the temperature measured downstream the deposition area $IR T$ (evaluated by the pyrometer) and reported in Fig. 8b. The $IR T$ graph, however, highlights the effects of the heating of the mandrel as one proceeds with the deposition of the rings within a single set. Such aspect seems to have been the process parameter that influenced the $\overline{ILSS}$ the most.

<figure><img src="image_588.png" /><figcaption>Figure 8: Mean HGT temperature (a) and mean $IR T$ temperature (b) evaluated during laydown process of each outer ring manufactured</figcaption></figure>

Scatter plots between $\overline{ILSS}$ and other relevant parameters are reported below in Fig. 9. In particular Fig. 9a remarks the how higher temperatures – still below the degradation of the material - leads to higher $\overline{ILSS}$. Fig. 9b and Fig. 9c puts in relation respectively laydown speed $v_l$ and compaction pressure $p_r$ with $\overline{ILSS}$.
<figure><img src="image_578.png" /><figcaption>Figure 9: Average ILSS over HGT temperature (a) laydown speed (b) and compaction pressure (c)</figcaption></figure>

## Discussion

Although the $\overline{ILSS}$ values obtained from the data analysis may not have reached the desired level of satisfaction and also displayed a notable degree of scattering, it is essential to recognize that such variability is a common phenomenon in similar studies documented in the literature [7-8]. This scattering can be attributed to the intricate interplay among the numerous thermo-mechanical variables inherent in the processing.

In Fig. 10 a correlation matrix is proposed in order to evaluate the relationship between the different analyzed variables of the data sets. In addition to the expected correlations such as the inverse one between compaction pressure $p_r$ and overlap thickness $t$, those that seem most interesting are the already described direct correlation between $\overline{ILSS}$ and $IR T$ and the inverse one between $\overline{ILSS}$ and overlap length $l$. This aspect seems to indicate that when the overlap length is kept lower, better bonding quality is obtained (higher $\overline{ILSS}$).

<figure><img src="image_579.png" /><figcaption>Figure 10: Correlation matrix</figcaption></figure>

## Conclusions

The key findings of the research underscore that:

* the proposed split-disk testing approach has emerged as an alternative option – to those commonly used – for relate the process parameter of the TP-AFP cell with the interlaminar bonding properties of the manufactured coupons;

* such method needs further research to see if it truly captures a representative value of $ILSS$ and gives the same results as planar specimens;
<figure><img src="image_589.png" /><figcaption>Figure 9: Average ILSS over HGT temperature (a) laydown speed (b) and compaction pressure (c)</figcaption></figure>

## Discussion

Although the *ILSS* values obtained from the data analysis may not have reached the desired level of satisfaction and also displayed a notable degree of scattering, it is essential to recognize that such variability is a common phenomenon in similar studies documented in the literature [7-8]. This scattering can be attributed to the intricate interplay among the numerous thermo-mechanical variables inherent in the processing.

In Fig. 10 a correlation matrix is proposed in order to evaluate the relationship between the different analyzed variables of the data sets. In addition to the expected correlations such as the inverse one between compaction pressure *p*<sub>r</sub> and overlap thickness *t*, those that seem most interesting are the already described direct correlation between *ILSS* and *IR T* and the inverse one between *ILSS* and overlap length *l*. This aspect seems to indicate that when the overlap length is kept lower, better bonding quality is obtained (higher *ILSS*).

<figure><img src="image_590.png" /><figcaption>Figure 10: Correlation matrix</figcaption></figure>

## Conclusions

The key findings of the research underscore that:

* the proposed split-disk testing approach has emerged as an alternative option – to those commonly used – for relate the process parameter of the TP-AFP cell with the interlaminar bonding properties of the manufactured coupons;

* such method needs further research to see if it truly captures a representative value of *ILSS* and gives the same results as planar specimens;
* in the laydown speed ranges analyzed there is no decrease in *ILSS* with increasing speed;

* the parameter that most influences the quality of the bonding is the operating temperature of the hot gas torch and therefore the temperature on the mandrel in the deposition area.

## References

[1] P. Boisse, R. Akkerman, P. Carlone, L. Kärger, S.V. Lomov, J. A. Sherwood, Advances in composite forming through 25 years of ESAFORM, Int J Mater Form 15, 39 (2022). https://doi.org/10.1007/s12289-022-01682-8

[2] H. Parmar, T. Khan, F. Tucci, R. Umer, P. Carlone, Advanced robotics and additive manufacturing of composites: towards a new era in Industry 4.0, Materials and Manufacturing Processes (2021). https://doi.org/10.1080/10426914.2020.1866195

[3] I. Martin, D. Saenz del Castillo, A. Fernandez, A. Güemes, Advanced Thermoplastic Composite Manufacturing by In-Situ Consolidation: A Review, Journal of Composites Science. 4, (2020). https://doi.org/10.3390/jcs4040149

[4] F. Tucci, F. Rubino, G. Pasquino, P. Carlone, Thermoplastic Pultrusion Process of Polypropylene/Glass Tapes, Polymers 15, 10 (2023), Article 2374, https://doi.org/10.3390/polym15102374

[5] M.J. Donough, Shafaq, N.A. St John, A.W. Philips, B. Gangadhara Prusty, Process modelling of In-situ consolidated thermoplastic composite by automated fibre placement – A review, Composites Part A: Applied Science and Manufacturing. 163 (2022). https://doi.org/10.1016/j.compositesa.2022.107179

[6] M. Di Francesco, M.A. Valverde, C. Ward, P. Giddings, G. Dell'Anno, K. Potter, Influence of Layup Speed on the Quality of Thermoplastic Preforms Manufactured by Laser-Assisted Automated Fibre Placement, 2016.

[7] Z. Qureshi, T. Swait, R. Scaife, H.M. El-Dessouky, In situ consolidation of thermoplastic prepreg tape using automated tape placement technology: Potential and possibilities, Composites Part B: Engineering, 66 (2014) 255-267. https://doi.org/10.1016/j.compositesb.2014.05.025

[8] I. Schiel, L. Raps, As. R. Chadwick, I. Schmidt, M. Simone, S. Nowotny, An investigation of in-situ AFP process parameters using CF/LM-PAEK, Advanced Manufacturing: Polymer & Composites Science. 6:4 (2020) 191-197. https://doi.org/10.1080/20550340.2020.1826772

[9] A.M. Sabido, Development of an Automated Fiber Placement Process for the Fabrication of Thermoplastic Composite Laminates. Diss. University of South Carolina, (2019).
* in the laydown speed ranges analyzed there is no decrease in *ILSS* with increasing speed;

* the parameter that most influences the quality of the bonding is the operating temperature of the hot gas torch and therefore the temperature on the mandrel in the deposition area.

## References

[1] P. Boisse, R. Akkerman, P. Carlone, L. Kärger, S.V. Lomov, J. A. Sherwood, Advances in composite forming through 25 years of ESAFORM, Int J Mater Form 15, 39 (2022). https://doi.org/10.1007/s12289-022-01682-8

[2] H. Parmar, T. Khan, F. Tucci, R. Umer, P. Carlone, Advanced robotics and additive manufacturing of composites: towards a new era in Industry 4.0, Materials and Manufacturing Processes (2021). https://doi.org/10.1080/10426914.2020.1866195

[3] I. Martin, D. Saenz del Castillo, A. Fernandez, A. Güemes, Advanced Thermoplastic Composite Manufacturing by In-Situ Consolidation: A Review, Journal of Composites Science. 4, (2020). https://doi.org/10.3390/jcs4040149

[4] F. Tucci, F. Rubino, G. Pasquino, P. Carlone, Thermoplastic Pultrusion Process of Polypropylene/Glass Tapes, Polymers 15, 10 (2023), Article 2374, https://doi.org/10.3390/polym15102374

[5] M.J. Donough, Shafaq, N.A. St John, A.W. Philips, B. Gangadhara Prusty, Process modelling of In-situ consolidated thermoplastic composite by automated fibre placement – A review, Composites Part A: Applied Science and Manufacturing. 163 (2022). https://doi.org/10.1016/j.compositesa.2022.107179

[6] M. Di Francesco, M.A. Valverde, C. Ward, P. Giddings, G. Dell'Anno, K. Potter, Influence of Layup Speed on the Quality of Thermoplastic Preforms Manufactured by Laser-Assisted Automated Fibre Placement, 2016.

[7] Z. Qureshi, T. Swait, R. Scaife, H.M. El-Dessouky, In situ consolidation of thermoplastic prepreg tape using automated tape placement technology: Potential and possibilities, Composites Part B: Engineering, 66 (2014) 255-267. https://doi.org/10.1016/j.compositesb.2014.05.025

[8] I. Schiel, L. Raps, As. R. Chadwick, I. Schmidt, M. Simone, S. Nowotny, An investigation of in-situ AFP process parameters using CF/LM-PAEK, Advanced Manufacturing: Polymer & Composites Science. 6:4 (2020) 191-197. https://doi.org/10.1080/20550340.2020.1826772

[9] A.M. Sabido, Development of an Automated Fiber Placement Process for the Fabrication of Thermoplastic Composite Laminates. Diss. University of South Carolina, (2019).
# Modeling time-dependent anisotropy in MEX component-scale process simulation

DI NARDO Mario Emanuele<fnref n="1" />,ª*, FRÖLICH Felix<fnref n="2" />,ᵇ, KÄRGER Luise<fnref n="2" />,ᶜ and CARLONE Pierpaolo<fnref n="1" />,ᵈ

**Keywords:** Additive Manufacturing, FFF, Process Simulation, FEM, Filament Orientation, Material Anisotropy, Homogenization

**Abstract.** In this paper, a numerical method is proposed to consider the transient anisotropic orientation state of a material extruded (MEX) part during a macroscale process simulation. To enhance computational efficiency, multiple filament strands are considered within single finite elements. The model is constructed around the utilization of 4th order orientation tensors, obtained by combining the information of the nozzle toolpath and the mesh elements in accordance with the process time. This provides a dynamic mapping of the anisotropic material orientation state within each element, in real-time to the process trajectory. Through the integration of time-dependent orientation tensors, this research provides deeper insights into filaments alignment evolution during the MEX process. This advancement not only enhances predictive capabilities in process simulation but also streamlines computational demands.

## Introduction

Material Extrusion (MEX) is a highly versatile method within additive manufacturing, enabling the fabrication of intricate components with improved qualities [1]. Nevertheless, selecting the right process parameters is crucial in determining the ultimate characteristics of these components [2]. The alignment of the filament, which is directly linked to the path taken by the nozzle tool, holds a central significance in designing both the structural robustness and operational performance of produced components [3,4,5]. The pronounced anisotropy [6] observed in additively manufactured structures significantly influences their properties, necessitating thorough consideration and investigation when designing and evaluating components. Instead of the often-used trial and error approach, which stems from the interplay between the process, material and component, process simulation offers a more strategic solution. One of the key challenges in simulating the process is to capture the material orientation determined by the strand deposition. Leveraging computation and the finite element method proves to be a potent approach not just for forecasting the mechanical characteristics at a macroscopic level but also for simulating the manufacturing process itself for the prediction of process-induced distortion and residual stresses. However, a substantial portion of studies has predominantly concentrated on modeling either unidirectional or bidirectional raster orientations by predefining the filament's alignment [7,8,9,10,11]. Moreover, several studies delve into exploring how orientation impacts the mechanical characteristics of parts produced through MEX via experimental methods [8]. Biswas et al. [12] investigated orthotropic elastic properties by crafting computational models employing a representative volume element (RVE). Additionally, classical laminate theory (CLT) has been utilized to simulate orthotropic mechanical attributes [13]. However, it is essential to note that this

<figure><img src="image_580.png" /></figure>

<footnote n="1">¹Department of Industrial Engineering, University of Salerno, 132 Via Giovanni Paolo II, 84084 Fisciano (SA), Italy</footnote>

<footnote n="2">²Institute of Vehicle System Technology (FAST), Lightweight Design Division, Karlsruhe Institute of Technology, Rintheimer Querallee 2, Building 70.04, 76131 Karlsruhe, Germany</footnote>

<footnote>ªmdinardo@unisa.it, ᵇfelix.froelich@kit.edu, ᶜluise.kaerger@kit.edu, ᵈpcarlone@unisa.it</footnote>
# Modeling time-dependent anisotropy in MEX component-scale process simulation

DI NARDO Mario Emanuele<fnref n="1" />,ᵃ*, FRÖLICH Felix<fnref n="2" />,ᵇ, KÄRGER Luise<fnref n="2" />,ᶜ and CARLONE Pierpaolo<fnref n="1" />,ᵈ

**Keywords:** Additive Manufacturing, FFF, Process Simulation, FEM, Filament Orientation, Material Anisotropy, Homogenization

**Abstract.** In this paper, a numerical method is proposed to consider the transient anisotropic orientation state of a material extruded (MEX) part during a macroscale process simulation. To enhance computational efficiency, multiple filament strands are considered within single finite elements. The model is constructed around the utilization of 4th order orientation tensors, obtained by combining the information of the nozzle toolpath and the mesh elements in accordance with the process time. This provides a dynamic mapping of the anisotropic material orientation state within each element, in real-time to the process trajectory. Through the integration of time-dependent orientation tensors, this research provides deeper insights into filaments alignment evolution during the MEX process. This advancement not only enhances predictive capabilities in process simulation but also streamlines computational demands.

## Introduction

Material Extrusion (MEX) is a highly versatile method within additive manufacturing, enabling the fabrication of intricate components with improved qualities [1]. Nevertheless, selecting the right process parameters is crucial in determining the ultimate characteristics of these components [2]. The alignment of the filament, which is directly linked to the path taken by the nozzle tool, holds a central significance in designing both the structural robustness and operational performance of produced components [3,4,5]. The pronounced anisotropy [6] observed in additively manufactured structures significantly influences their properties, necessitating thorough consideration and investigation when designing and evaluating components. Instead of the often-used trial and error approach, which stems from the interplay between the process, material and component, process simulation offers a more strategic solution. One of the key challenges in simulating the process is to capture the material orientation determined by the strand deposition. Leveraging computation and the finite element method proves to be a potent approach not just for forecasting the mechanical characteristics at a macroscopic level but also for simulating the manufacturing process itself for the prediction of process-induced distortion and residual stresses. However, a substantial portion of studies has predominantly concentrated on modeling either unidirectional or bidirectional raster orientations by predefining the filament's alignment [7,8,9,10,11]. Moreover, several studies delve into exploring how orientation impacts the mechanical characteristics of parts produced through MEX via experimental methods [8]. Biswas et al. [12] investigated orthotropic elastic properties by crafting computational models employing a representative volume element (RVE). Additionally, classical laminate theory (CLT) has been utilized to simulate orthotropic mechanical attributes [13]. However, it is essential to note that this

<figure><img src="image_591.png" /></figure>

<footnote n="1">¹Department of Industrial Engineering, University of Salerno, 132 Via Giovanni Paolo II, 84084 Fisciano (SA), Italy</footnote>

<footnote n="2">²Institute of Vehicle System Technology (FAST), Lightweight Design Division, Karlsruhe Institute of Technology, Rintheimer Querallee 2, Building 70.04, 76131 Karlsruhe, Germany</footnote>

<footnote>ᵃmdinardo@unisa.it, ᵇfelix.froelich@kit.edu, ᶜluise.kaerger@kit.edu, ᵈpcarlone@unisa.it</footnote>
study primarily focuses on process simulation, requiring precise orientation data at each process time point, rendering techniques as CLT impractical. Although numerous studies have explored orientation effects using diverse modeling techniques and experimental approaches, there has not been a dedicated investigation into depicting deposition trajectories and their evolution over time. The aim is to introduce a streamlined approach that overcomes the computational intricacies associated with filament orientation. The objective is to enhance accuracy while maintaining computational efficiency. To achieve this, orientation tensors are formulated, giving continual update of the orientation state for every element throughout the process [14,15]. This modeling approach involves the finite element software ABAQUS in conjunction with specific subroutines. The recent development involves incorporating these codes as "internal" user subroutines within an Abaqus plugin called AM Modeler. In this paper, the novel methodology is presented by first explaining the mathematical formulation of tensors and their special properties in the MEX process, followed by a general explanation of the workflow of the method. In addition, a verification scenario is presented and the resulting orientation states within an element are discussed and compared with an analytical solution.

## Methodology

### Orientation Tensors

The orientation tensor formulation was introduced by Kanatani [14] and further developed by Advani and Tucker [15] serving to map the alignment probability of fibers in composites. This tensor aids in detailing the orientation distribution function (ODF) [15], reflecting how fibers align within a composite. Their approach involves utilizing spherical harmonics to represent the distribution of fiber orientations. By employing these mathematical functions, Advani and Tucker expanded the ODF into a series, creating a representation that encapsulates the diverse orientations of fibers within the material. The resulting 4th order tensor comprises coefficients representing different spherical harmonic terms, offering insights into the distribution and intensity of fibers in various orientations within the composite.

The representation of fiber directions is denoted by unit vectors, symbolized as **p**. These unit vectors **p** correspond to the spherical coordinates defining the direction of fiber alignment in three-dimensional space as shown in Figure 1:

$$ \mathbf{p} = \begin{Bmatrix} p_x \\ p_y \\ p_z \end{Bmatrix} = \begin{Bmatrix} \sin \theta \cos \varphi \\ \sin \theta \sin \varphi \\ \cos \theta \end{Bmatrix} \qquad (1) $$

<figure><img src="image_581.png" /><figcaption>Figure 1. The unit vector **p** characterized by the angles $\theta$ and $\varphi$ in relation to Cartesian coordinate axes. (Adapted from [15]).</figcaption></figure>
study primarily focuses on process simulation, requiring precise orientation data at each process time point, rendering techniques as CLT impractical. Although numerous studies have explored orientation effects using diverse modeling techniques and experimental approaches, there has not been a dedicated investigation into depicting deposition trajectories and their evolution over time. The aim is to introduce a streamlined approach that overcomes the computational intricacies associated with filament orientation. The objective is to enhance accuracy while maintaining computational efficiency. To achieve this, orientation tensors are formulated, giving continual update of the orientation state for every element throughout the process [14,15]. This modeling approach involves the finite element software ABAQUS in conjunction with specific subroutines. The recent development involves incorporating these codes as "internal" user subroutines within an Abaqus plugin called AM Modeler. In this paper, the novel methodology is presented by first explaining the mathematical formulation of tensors and their special properties in the MEX process, followed by a general explanation of the workflow of the method. In addition, a verification scenario is presented and the resulting orientation states within an element are discussed and compared with an analytical solution.

## Methodology

### Orientation Tensors

The orientation tensor formulation was introduced by Kanatani [14] and further developed by Advani and Tucker [15] serving to map the alignment probability of fibers in composites. This tensor aids in detailing the orientation distribution function (ODF) [15], reflecting how fibers align within a composite. Their approach involves utilizing spherical harmonics to represent the distribution of fiber orientations. By employing these mathematical functions, Advani and Tucker expanded the ODF into a series, creating a representation that encapsulates the diverse orientations of fibers within the material. The resulting 4th order tensor comprises coefficients representing different spherical harmonic terms, offering insights into the distribution and intensity of fibers in various orientations within the composite.

The representation of fiber directions is denoted by unit vectors, symbolized as **p**. These unit vectors **p** correspond to the spherical coordinates defining the direction of fiber alignment in three-dimensional space as shown in Figure 1:

$$ \mathbf{p} = \begin{Bmatrix} p_x \\ p_y \\ p_z \end{Bmatrix} = \begin{Bmatrix} \sin \theta \cos \varphi \\ \sin \theta \sin \varphi \\ \cos \theta \end{Bmatrix} \qquad (1) $$

<figure><img src="image_592.png" /><figcaption>Figure 1. The unit vector **p** characterized by the angles θ and φ in relation to Cartesian coordinate axes. (Adapted from [15]).</figcaption></figure>
Due to the unitary nature, traditional scalar or cross products cannot account for a distribution, leading to results lacking comprehensive information [15]. To encapsulate the fiber orientation as a tensor, the dyadic product is employed, which consists in a mathematical operation combining vectors to create tensors by multiplying the vectors components for themselves [16]. This operation involves multiplying the vectors components four times, yielding a 4th order tensor A that characterizes how the fibers are aligned in relation to the coordinate axes. Furthermore, given the need of a distribution representation, the formulation includes an averaging of multiple orientation vectors denoted within the angle brackets:

$$A \equiv \langle \mathbf{p} \mathbf{p} \mathbf{p} \mathbf{p} \rangle \equiv \begin{bmatrix} A_{1111} & A_{1122} & A_{1133} & A_{1123} & A_{1131} & A_{1112} \\ A_{2211} & A_{2222} & A_{2233} & A_{2223} & A_{2231} & A_{2212} \\ A_{3311} & A_{3322} & A_{3333} & A_{3323} & A_{3331} & A_{3312} \\ A_{2311} & A_{2322} & A_{2333} & A_{2323} & A_{2331} & A_{2312} \\ A_{3111} & A_{3122} & A_{3133} & A_{3123} & A_{3131} & A_{3112} \\ A_{1211} & A_{1222} & A_{1233} & A_{1223} & A_{1231} & A_{1212} \end{bmatrix} \quad (2)$$

The utilization of the 4th order orientation tensor across multiple studies is rooted in its ability to provide a holistic linkage between fiber orientation and material properties. It serves as a pivotal tool to capture directional details that are necessary for comprehending the impact of fiber alignment on material behavior [17,18]. It allows for precise predictions of mechanical or thermal responses along different axes, providing a robust framework for studying material properties in diverse conditions.

## Distinctive properties of the orientation vectors and tensors within the MEX process

In the context of this research, the orientation tensor A is used to describe the distribution of orientation after deposition events at various time steps within a finite element. Consequently, the orientation vectors are describing the alignment of the filament, which are considered straight and rigid as in [15]. The tensor notation, as shown in Eq. 2, represents the visualization in the contracted notation as used in [15], which basically translates into the Voigt notation. It encapsulates information regarding the alignment distribution along the axes, providing insights into the anisotropic properties during the extrusion process.

Indeed, due to the nature of the MEX process characterized by sole deposition on the x-y plane, the angle θ within the orientation vector p remains consistently at π/2, resulting in a fixed z-component, leading to p_z = 0. Consequently, this characteristic trait shapes the 4th order distribution tensor in a distinct manner, rendering only those tensor components non-zero that arise from the multiplication without the involvement of the z-component:

$$A^{(t=n)}(NOEL) = \begin{bmatrix} A_{1111} & A_{1122} & 0 & 0 & 0 & A_{1112} \\ A_{2211} & A_{2222} & 0 & 0 & 0 & A_{2212} \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ A_{1211} & A_{1222} & 0 & 0 & 0 & A_{1212} \end{bmatrix} \quad (3)$$

In this numerical modeling, for each element of the mesh in the FE Model, an orientation tensor is formulated at every time increment defined in the simulation, leading to tensors dependent on the time increment. The NOEL parameter used in Eq. 3 represents the element numbering defined in Abaqus.
Due to the unitary nature, traditional scalar or cross products cannot account for a distribution, leading to results lacking comprehensive information [15]. To encapsulate the fiber orientation as a tensor, the dyadic product is employed, which consists in a mathematical operation combining vectors to create tensors by multiplying the vectors components for themselves [16]. This operation involves multiplying the vectors components four times, yielding a 4th order tensor A that characterizes how the fibers are aligned in relation to the coordinate axes. Furthermore, given the need of a distribution representation, the formulation includes an averaging of multiple orientation vectors denoted within the angle brackets:

$$A \equiv \langle \mathbf{p} \mathbf{p} \mathbf{p} \mathbf{p} \rangle \equiv \begin{bmatrix} A_{1111} & A_{1122} & A_{1133} & A_{1123} & A_{1131} & A_{1112} \\ A_{2211} & A_{2222} & A_{2233} & A_{2223} & A_{2231} & A_{2212} \\ A_{3311} & A_{3322} & A_{3333} & A_{3323} & A_{3331} & A_{3312} \\ A_{2311} & A_{2322} & A_{2333} & A_{2323} & A_{2331} & A_{2312} \\ A_{3111} & A_{3122} & A_{3133} & A_{3123} & A_{3131} & A_{3112} \\ A_{1211} & A_{1222} & A_{1233} & A_{1223} & A_{1231} & A_{1212} \end{bmatrix} \quad (2)$$

The utilization of the 4th order orientation tensor across multiple studies is rooted in its ability to provide a holistic linkage between fiber orientation and material properties. It serves as a pivotal tool to capture directional details that are necessary for comprehending the impact of fiber alignment on material behavior [17,18]. It allows for precise predictions of mechanical or thermal responses along different axes, providing a robust framework for studying material properties in diverse conditions.

## Distinctive properties of the orientation vectors and tensors within the MEX process

In the context of this research, the orientation tensor A is used to describe the distribution of orientation after deposition events at various time steps within a finite element. Consequently, the orientation vectors are describing the alignment of the filament, which are considered straight and rigid as in [15]. The tensor notation, as shown in Eq. 2, represents the visualization in the contracted notation as used in [15], which basically translates into the Voigt notation. It encapsulates information regarding the alignment distribution along the axes, providing insights into the anisotropic properties during the extrusion process.

Indeed, due to the nature of the MEX process characterized by sole deposition on the x-y plane, the angle θ within the orientation vector p remains consistently at π/2, resulting in a fixed z-component, leading to p_z = 0. Consequently, this characteristic trait shapes the 4th order distribution tensor in a distinct manner, rendering only those tensor components non-zero that arise from the multiplication without the involvement of the z-component:

$$A^{(t=n)}(NOEL) = \begin{bmatrix} A_{1111} & A_{1122} & 0 & 0 & 0 & A_{1112} \\ A_{2211} & A_{2222} & 0 & 0 & 0 & A_{2212} \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ A_{1211} & A_{1222} & 0 & 0 & 0 & A_{1212} \end{bmatrix} \quad (3)$$

In this numerical modeling, for each element of the mesh in the FE Model, an orientation tensor is formulated at every time increment defined in the simulation, leading to tensors dependent on the time increment. The NOEL parameter used in Eq. 3 represents the element numbering defined in Abaqus.
A generalized formula for updating $A_{ijkl}$ incorporates weighted contributions from multiple orientation vectors, as previously denoted in Eq.2 using angular brackets. Thus, the formulation of entries within the orientation tensor $A_{ijkl}$ can be expressed as follows:

$$A_{ijkl}^{(t=n)}(NOEL) = \sum_{m=1}^{N} \left( \frac{w_m}{\sum_{o=1}^{N} w_o} \right) \cdot (p_i \cdot p_j \cdot p_k \cdot p_l)_m, \quad (4)$$

where:

* $A_{ijkl}^{(t=n)}$ represents the orientation tensor entry after deposition at time $t = n$;

* N signifies the number of orientation vectors $p_m$ observed during the deposition;

* $w_m$ denotes the weight associated with each orientation vector $p_m$ reflecting its significance or occurrence frequency.

## Modeling Methodology

The method's workflow, as depicted in Figure 2, involves a combination of Python and Fortran programming. To simulate the MEX process, an FE model is generated using Abaqus, leveraging the AM Modeler plugin.

<figure><img src="image_582.png" /><figcaption>Figure 2. Workflow of the modeling methodology</figcaption></figure>

Python is instrumental in creating import files with “.inp” extension tailored for Abaqus compatibility and generating the analytical solution necessary for validation purposes.

After the slicing phase that generates the G-Code, there's a subsequent step involving extrapolation of data. This phase aims to determine the process time, the coordinates followed by the nozzle, and an ON-OFF variable called EA, indicating when the extruder is activated during the deposition process. This data is organized within a file named “EventSeries.inp”, structured as depicted in Table 1.

<table><caption>Table 1. Structure of toolpath data.</caption><thead><tr><th>Process Time</th><th>x</th><th>y</th><th>z</th><th>EA</th></tr></thead><tbody><tr><td>[s]</td><td>[mm]</td><td>[mm]</td><td>[mm]</td><td>/]</td></tr></tbody></table>
A generalized formula for updating $A_{ijkl}$ incorporates weighted contributions from multiple orientation vectors, as previously denoted in Eq.2 using angular brackets. Thus, the formulation of entries within the orientation tensor $A_{ijkl}$ can be expressed as follows:

$$A_{ijkl}^{(t=n)}(NOEL) = \sum_{m=1}^{N} \left( \frac{w_m}{\sum_{o=1}^{N} w_o} \right) \cdot (p_i \cdot p_j \cdot p_k \cdot p_l)_m, \quad (4)$$

where:

* $A_{ijkl}^{(t=n)}$ represents the orientation tensor entry after deposition at time $t = n$;

* N signifies the number of orientation vectors $p_m$ observed during the deposition;

* $w_m$ denotes the weight associated with each orientation vector $p_m$ reflecting its significance or occurrence frequency.

## Modeling Methodology

The method's workflow, as depicted in Figure 2, involves a combination of Python and Fortran programming. To simulate the MEX process, an FE model is generated using Abaqus, leveraging the AM Modeler plugin.

<figure><img src="image_593.png" /><figcaption>Figure 2. Workflow of the modeling methodology</figcaption></figure>

Python is instrumental in creating import files with “.inp” extension tailored for Abaqus compatibility and generating the analytical solution necessary for validation purposes.

After the slicing phase that generates the G-Code, there's a subsequent step involving extrapolation of data. This phase aims to determine the process time, the coordinates followed by the nozzle, and an ON-OFF variable called EA, indicating when the extruder is activated during the deposition process. This data is organized within a file named “EventSeries.inp”, structured as depicted in Table 1.

<table><caption>Table 1. Structure of toolpath data.</caption><thead><tr><th>Process Time</th><th>x</th><th>y</th><th>z</th><th>EA</th></tr></thead><tbody><tr><td>[s]</td><td>[mm]</td><td>[mm]</td><td>[mm]</td><td>/]</td></tr></tbody></table>
Simultaneously, another phase entails creating the component mesh, which it has been made by using the Meshio package [19], resulting in an import file named "Mesh.inp" containing all the necessary information that can be read by Abaqus in VTK format.

At this stage, merging these datasets allows for pinpointing the exact cell activated as the nozzle progresses along its trajectory. Indeed, after the mesh and trajectory data are loaded, the Python script seeks the time step value. Using this input, the script outputs the necessary information required to formulate the 4th order orientation tensors throughout the time simulation. This results in a new import file named "OrientationData.inp," structured as in Table 2.

<table><caption>Table 2. Structure of the orientation data containing the vectors components and frequency.</caption><thead><tr><th>Total Time</th><th>NOEL</th><th>p<sub>x</sub></th><th>p<sub>y</sub></th><th>p<sub>z</sub></th><th>w<sub>m</sub></th></tr></thead><tbody><tr><td>[s]</td><td>/]</td><td>/]</td><td>/]</td><td>/]</td><td>/]</td></tr></tbody></table>

To give a clearer understanding, as shown in Figure 3, when the printhead traverses the mesh, the script recognizes the element index by manipulating its vertices coordinates and the printhead coordinates outputting the components of the orientation vectors and their corresponding weights, indicating the quantity of beads deposited. These insights hold significant importance for deriving Python results and for seamless integration into the finite element (FE) model via Subroutines.

<figure><img src="image_583.png" /><figcaption>Figure 3. Mesh portion composed of cube elements. The script operates by identifying the print head at element 1, distinguished by its specific node coordinates.</figcaption></figure>

The final step regards the creation of the FE model and the activation of the AM Modeler in Abaqus. The AM Modeler plugin is instrumental for the element activation, representing the addition of material during the simulation and ensuring accurate heat transfer analysis interactions. During activation, non-isothermal properties undergo a homogenization process, wherein the accumulated heat input through the strands is averaged over time. Subsequently, this averaged thermal energy is introduced into the component as a unified effect upon activation. In instances of partial activation, only a specific portion of the element is activated, and the corresponding thermal energy is introduced proportionally. Steps for analysis could involves a heat transfer study followed by a static analysis. This way of modelling is mainly used for aiming at predicting internal stresses and warpage resulting from thermal histories affecting the filament and, consequently, the final structure. Furthermore, a notable feature of the AM Modeler plugin is its ability to utilize the previously created "EventSeries.inp" file. This enables the display of material addition during the simulation in line with process timings. However, it is important to note that it is possible to take the orientation into account, but only as a vector where the x-direction is the extrusion direction. If there are several strands in one element, this is no longer representative. Essential to note is that
Simultaneously, another phase entails creating the component mesh, which it has been made by using the Meshio package [19], resulting in an import file named "Mesh.inp" containing all the necessary information that can be read by Abaqus in VTK format.

At this stage, merging these datasets allows for pinpointing the exact cell activated as the nozzle progresses along its trajectory. Indeed, after the mesh and trajectory data are loaded, the Python script seeks the time step value. Using this input, the script outputs the necessary information required to formulate the 4th order orientation tensors throughout the time simulation. This results in a new import file named "OrientationData.inp," structured as in Table 2.

<table><caption>Table 2. Structure of the orientation data containing the vectors components and frequency.</caption><thead><tr><th>Total Time</th><th>NOEL</th><th>p<sub>x</sub></th><th>p<sub>y</sub></th><th>p<sub>z</sub></th><th>w<sub>m</sub></th></tr></thead><tbody><tr><td>[s]</td><td>/]</td><td>/]</td><td>/]</td><td>/]</td><td>/]</td></tr></tbody></table>

To give a clearer understanding, as shown in Figure 3, when the printhead traverses the mesh, the script recognizes the element index by manipulating its vertices coordinates and the printhead coordinates outputting the components of the orientation vectors and their corresponding weights, indicating the quantity of beads deposited. These insights hold significant importance for deriving Python results and for seamless integration into the finite element (FE) model via Subroutines.

<figure><img src="image_594.png" /><figcaption>Figure 3. Mesh portion composed of cube elements. The script operates by identifying the print head at element 1, distinguished by its specific node coordinates.</figcaption></figure>

The final step regards the creation of the FE model and the activation of the AM Modeler in Abaqus. The AM Modeler plugin is instrumental for the element activation, representing the addition of material during the simulation and ensuring accurate heat transfer analysis interactions. During activation, non-isothermal properties undergo a homogenization process, wherein the accumulated heat input through the strands is averaged over time. Subsequently, this averaged thermal energy is introduced into the component as a unified effect upon activation. In instances of partial activation, only a specific portion of the element is activated, and the corresponding thermal energy is introduced proportionally. Steps for analysis could involve a heat transfer study followed by a static analysis. This way of modelling is mainly used for aiming at predicting internal stresses and warpage resulting from thermal histories affecting the filament and, consequently, the final structure. Furthermore, a notable feature of the AM Modeler plugin is its ability to utilize the previously created "EventSeries.inp" file. This enables the display of material addition during the simulation in line with process timings. However, it is important to note that it is possible to take the orientation into account, but only as a vector where the x-direction is the extrusion direction. If there are several strands in one element, this is no longer representative. Essential to note is that
this approach focuses exclusively on the orientation distribution over time, which is determined by the trajectory of the nozzle. Indeed, it is crucial to acknowledge that the changing mass of the element also plays a significant role. One effective approach to address this could be achieved by defining a time-dependent mass for each element, taking into consideration its density. The “OrientationData.inp” file is initially integrated using the UEXTERNALDB subroutine [20]. This subroutine is invoked once at the outset of the analysis and facilitates communication with other user subroutines, specifically the USDFLD [20], within ABAQUS/Standard. In this modeling, the subroutine UEXTERNALDB reads the external file with orientation data created in Python once at the beginning of the process simulation. Each column of this file is stored in so-called global arrays. This type of array can be called up for each integration point and is therefore valid for the entire domain. The data of the individual columns can thus be efficiently managed using special pointers and called up in the USDFLD subroutine for each integration point.

After storing each column’s data in a global array, the data is processed similarly to the analytical method employed in Python to generate the orientation tensors for every element within the mesh. However, the construction of the algorithm in this context is based on the variables: NOEL (element identification index), NPT (integration point), and DTIME (time increment). This design enabled the formation of orientation tensors at every time increment (DTIME) and for every integration point (NPT). Leveraging the element identification index (NOEL), iteration is made feasible for each cell of the mesh. In practical terms, all tensor entries are connected to a state-dependent variable (SDV) as specified in:

$$A^{(t=n)}(NOEL) = \begin{bmatrix} A_{1111} & A_{1122} & 0 & 0 & 0 & A_{1112} \\ A_{2211} & A_{2222} & 0 & 0 & 0 & A_{2212} \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ A_{1211} & A_{1222} & 0 & 0 & 0 & A_{1212} \end{bmatrix} = \begin{bmatrix} SDV_1 & SDV_3 & 0 & 0 & 0 & SDV_4 \\ SDV_3 & SDV_2 & 0 & 0 & 0 & SDV_5 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ SDV_4 & SDV_5 & 0 & 0 & 0 & SDV_3 \end{bmatrix} \quad (5)$$

This variable SDV is used to store and retrieve additional information about the state of each element at each integration point. It adopts a scalar value for each time increment, effectively representing the values embodied by the tensor elements.

## Verification Scenario

A verification test employed a cube as the simulation component, utilizing a model comprised of 27 elements and a trajectory alternating between deposition at 0° and 90°, according to the x-axis.

This toolpath excludes deposition on the perimeter giving the two different orientation vectors:

$$p_1 = \begin{pmatrix} 1 \\ 0 \\ 0 \end{pmatrix}; \quad p_2 = \begin{pmatrix} 0 \\ 1 \\ 0 \end{pmatrix}. \qquad (6)$$

Focusing on specific orientations streamlines the formulation of 4th orientation tensors, facilitating a clearer understanding of the final outcomes. These tensors predominantly exhibit non-zero values along the first two positions of the main diagonal, indicating alignment along the x and y axes. The computation of trajectory orientation integrates these details as per guidelines outlined in Section 2.3, based on the chosen time increment. In this MEX simulation, the time increment corresponds to the duration required for depositing a layer. Considering the geometry, trajectory, and printing speed, this time increment approximates 97.14 seconds. Consequently, every 97.14 seconds triggers the deposition of a new layer, leading to a simulation update for each element.
this approach focuses exclusively on the orientation distribution over time, which is determined by the trajectory of the nozzle. Indeed, it is crucial to acknowledge that the changing mass of the element also plays a significant role. One effective approach to address this could be achieved by defining a time-dependent mass for each element, taking into consideration its density. The “OrientationData.inp” file is initially integrated using the UEXTERNALDB subroutine [20]. This subroutine is invoked once at the outset of the analysis and facilitates communication with other user subroutines, specifically the USDFLD [20], within ABAQUS/Standard. In this modeling, the subroutine UEXTERNALDB reads the external file with orientation data created in Python once at the beginning of the process simulation. Each column of this file is stored in so-called global arrays. This type of array can be called up for each integration point and is therefore valid for the entire domain. The data of the individual columns can thus be efficiently managed using special pointers and called up in the USDFLD subroutine for each integration point.

After storing each column’s data in a global array, the data is processed similarly to the analytical method employed in Python to generate the orientation tensors for every element within the mesh. However, the construction of the algorithm in this context is based on the variables: NOEL (element identification index), NPT (integration point), and DTIME (time increment). This design enabled the formation of orientation tensors at every time increment (DTIME) and for every integration point (NPT). Leveraging the element identification index (NOEL), iteration is made feasible for each cell of the mesh. In practical terms, all tensor entries are connected to a state-dependent variable (SDV) as specified in:

$$ A^{(t=n)}(NOEL) = \begin{bmatrix} A_{1111} & A_{1122} & 0 & 0 & 0 & A_{1112} \\ A_{2211} & A_{2222} & 0 & 0 & 0 & A_{2212} \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ A_{1211} & A_{1222} & 0 & 0 & 0 & A_{1212} \end{bmatrix} = \begin{bmatrix} SDV_1 & SDV_3 & 0 & 0 & 0 & SDV_4 \\ SDV_3 & SDV_2 & 0 & 0 & 0 & SDV_5 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ SDV_4 & SDV_5 & 0 & 0 & 0 & SDV_3 \end{bmatrix} \quad (5) $$

This variable SDV is used to store and retrieve additional information about the state of each element at each integration point. It adopts a scalar value for each time increment, effectively representing the values embodied by the tensor elements.

## Verification Scenario

A verification test employed a cube as the simulation component, utilizing a model comprised of 27 elements and a trajectory alternating between deposition at 0° and 90°, according to the x-axis.

This toolpath excludes deposition on the perimeter giving the two different orientation vectors:

$$ p_1 = \begin{Bmatrix} 1 \\ 0 \\ 0 \end{Bmatrix}; \quad p_2 = \begin{Bmatrix} 0 \\ 1 \\ 0 \end{Bmatrix}. \quad (6) $$

Focusing on specific orientations streamlines the formulation of 4th orientation tensors, facilitating a clearer understanding of the final outcomes. These tensors predominantly exhibit non-zero values along the first two positions of the main diagonal, indicating alignment along the x and y axes. The computation of trajectory orientation integrates these details as per guidelines outlined in Section 2.3, based on the chosen time increment. In this MEX simulation, the time increment corresponds to the duration required for depositing a layer. Considering the geometry, trajectory, and printing speed, this time increment approximates 97.14 seconds. Consequently, every 97.14 seconds triggers the deposition of a new layer, leading to a simulation update for each element.
To simplify the representation of tensor filling, the chosen process parameters involve depositing 15 lanes per layer, distributed as 5 lanes per layer and per element, with a total of 27 layers. This designates 9 layers for each element. However, adjusting for shorter time steps may require more frequent tensor formulation and subsequent updates.

<figure><img src="image_584.png" /><figcaption>Figure 4. Visualization of the cube mesh during the initial layer deposition along the x-axis. Notably, elements 1, 4, and 7 are activated at this stage of the process.</figcaption></figure>

<table><caption>Table 3. Data snippet generated by the script at the first layer deposition.</caption><thead><tr><th>Total Time</th><th>NOEL</th><th>p<sub>x</sub></th><th>p<sub>y</sub></th><th>p<sub>z</sub></th><th>w<sub>m</sub></th></tr></thead><tbody><tr><td>97.14 [s]</td><td>1</td><td>1</td><td>0</td><td>0</td><td>5</td></tr><tr><td>97.14 [s]</td><td>4</td><td>1</td><td>0</td><td>0</td><td>5</td></tr><tr><td>97.14 [s]</td><td>7</td><td>1</td><td>0</td><td>0</td><td>5</td></tr></tbody></table>

At the first layer deposition, during the initial time step (Total Time = 97.14s), activation occurs for all the elements at the base of the cube, revealing both the count of deposited filaments ($w_m$) and the individual components of the orientation vectors ($p_x, p_y, p_z$). Specifically, let's narrow our focus solely to Elements 1, 4, and 7 as depicted in Figure 4. As the nozzle traverses these elements, they get recognized and activated. Table 3 provides a comprehensive display, showcasing the count of deposited filaments ($w_m = 5$) and the corresponding vector components that define the orientation along the x-axis. This entire process iterates for the remaining elements, updating after each new layer deposition.

## Results and discussion

To validate the method, Element 1 is analysed, which is located at the base of the cube, as shown in Figure 4. Given the simple toolpath and the time increment chosen, the tensors are the same for the other elements at the cube's bottom. Indeed, the nine elements at the cube's bottom are the initial ones to be activated. This is due to the process's inherent nature, which constructs objects beginning from the initial layer, responsible for adhesion to the building platform, and culminating in the final layer, adhering to a layer-by-layer strategy. As shown in the orientation data snippet in Table 3, at the initial time increment (97.14 s), as the first layer is laid down, the data indicates 10 lanes deposited in the x direction. At this point it is possible to visualize the orientation sensor of this element. At the first time increment, the tensor corresponds to a null matrix, with the first term on the main diagonal equal to 1. This means that 100% of the filaments are fully aligned in the x-direction. At the second time increment (198.28 s) the algorithm considers also the second layer which is oriented in the y direction. The tensor then is updated with a value of 0.5 for the first two terms on the principal diagonal, signifying that 50% of the filaments are oriented in the x
To simplify the representation of tensor filling, the chosen process parameters involve depositing 15 lanes per layer, distributed as 5 lanes per layer and per element, with a total of 27 layers. This designates 9 layers for each element. However, adjusting for shorter time steps may require more frequent tensor formulation and subsequent updates.

<figure><img src="image_595.png" /><figcaption>Figure 4. Visualization of the cube mesh during the initial layer deposition along the x-axis. Notably, elements 1, 4, and 7 are activated at this stage of the process.</figcaption></figure>

<table><caption>Table 3. Data snippet generated by the script at the first layer deposition.</caption><thead><tr><th>Total Time</th><th>NOEL</th><th>p<sub>x</sub></th><th>p<sub>y</sub></th><th>p<sub>z</sub></th><th>w<sub>m</sub></th></tr></thead><tbody><tr><td>97.14 [s]</td><td>1</td><td>1</td><td>0</td><td>0</td><td>5</td></tr><tr><td>97.14 [s]</td><td>4</td><td>1</td><td>0</td><td>0</td><td>5</td></tr><tr><td>97.14 [s]</td><td>7</td><td>1</td><td>0</td><td>0</td><td>5</td></tr></tbody></table>

At the first layer deposition, during the initial time step (Total Time = 97.14s), activation occurs for all the elements at the base of the cube, revealing both the count of deposited filaments ($w_m$) and the individual components of the orientation vectors ($p_x, p_y, p_z$). Specifically, let's narrow our focus solely to Elements 1, 4, and 7 as depicted in Figure 4. As the nozzle traverses these elements, they get recognized and activated. Table 3 provides a comprehensive display, showcasing the count of deposited filaments ($w_m = 5$) and the corresponding vector components that define the orientation along the x-axis. This entire process iterates for the remaining elements, updating after each new layer deposition.

## Results and discussion

To validate the method, Element 1 is analysed, which is located at the base of the cube, as shown in Figure 4. Given the simple toolpath and the time increment chosen, the tensors are the same for the other elements at the cube's bottom. Indeed, the nine elements at the cube's bottom are the initial ones to be activated. This is due to the process's inherent nature, which constructs objects beginning from the initial layer, responsible for adhesion to the building platform, and culminating in the final layer, adhering to a layer-by-layer strategy. As shown in the orientation data snippet in Table 3, at the initial time increment (97.14 s), as the first layer is laid down, the data indicates 10 lanes deposited in the x direction. At this point it is possible to visualize the orientation sensor of this element. At the first time increment, the tensor corresponds to a null matrix, with the first term on the main diagonal equal to 1. This means that 100% of the filaments are fully aligned in the x-direction. At the second time increment (198.28 s) the algorithm considers also the second layer which is oriented in the y direction. The tensor then is updated with a value of 0.5 for the first two terms on the principal diagonal, signifying that 50% of the filaments are oriented in the x
direction and the other 50% in the y direction. The updating goes on until the last layer is deposited. Figure 5 visualizes the tensor's updates for the Element 1 after the deposition of three layers.

<figure><img src="image_585.png" /><figcaption>Figure 5. Updates pertaining to Element 1. On the Left: Tensor states throughout the deposition phases. Middle: 2D representation of these tensors. Right: $SDV_1$ is exhibited using a color-coded scheme as implemented in Abaqus.</figcaption></figure>

The analytical results are then compared with Abaqus results. Given the straightforward deposition trajectory of 0° and 90° in this study, the sole entries undergoing value changes during the simulation are the first two elements on the primary diagonal $SDV_1$ and $SDV_2$. As shown in Figure 4, in Abaqus the individual entries of the tensors can be visualised over time in the component by associating a code color. The comparison shows that the implementation in Abaqus produces the same values and is therefore verified by the analytical solution.

## Conclusion

The presented methodology demonstrates a systematic approach to simulate the orientation state in the MEX process, considering the interplay between the nozzle toolpath and induced anisotropic material orientation. This transient anisotropic material orientation state is crucial for predicting residual stresses and distortion accurately. Utilizing 4th order orientation tensors provides a holistic perspective of weighted average orientation within each finite element. It is important to note that the verification scenario is simplistic and could be adequately addressed with 2nd rank tensors.
direction and the other 50% in the y direction. The updating goes on until the last layer is deposited. Figure 5 visualizes the tensor's updates for the Element 1 after the deposition of three layers.

<figure><img src="image_596.png" /><figcaption>Figure 5. Updates pertaining to Element 1. On the Left: Tensor states throughout the deposition phases. Middle: 2D representation of these tensors. Right: $SDV_1$ is exhibited using a color-coded scheme as implemented in Abaqus.</figcaption></figure>

The analytical results are then compared with Abaqus results. Given the straightforward deposition trajectory of 0° and 90° in this study, the sole entries undergoing value changes during the simulation are the first two elements on the primary diagonal $SDV_1$ and $SDV_2$. As shown in Figure 4, in Abaqus the individual entries of the tensors can be visualised over time in the component by associating a code color. The comparison shows that the implementation in Abaqus produces the same values and is therefore verified by the analytical solution.

## Conclusion

The presented methodology demonstrates a systematic approach to simulate the orientation state in the MEX process, considering the interplay between the nozzle toolpath and induced anisotropic material orientation. This transient anisotropic material orientation state is crucial for predicting residual stresses and distortion accurately. Utilizing 4th order orientation tensors provides a holistic perspective of weighted average orientation within each finite element. It is important to note that the verification scenario is simplistic and could be adequately addressed with 2nd rank tensors.
However, using 4th order orientation tensor permits to describe the resulting distribution on stiffness tensors and in more complex components with elaborate trajectories, more complicated orientation distributions may occur, which make the 4th order tensor necessary. This methodology, integrating Python, Fortran programming, and Abaqus subroutines, streamlines the workflow from generating import files to incorporating orientation data, ensuring a representation in the FE model. The alignment depicted in the analytical solution mirrors the orientation changes captured in Abaqus, verifying the method in tracking orientation states for each element and at each time step. Visualization of tensor updates further solidifies the congruence between the analytical and numerical results. Future enhancements could focus on integrating material properties associated with orientation for a more comprehensive predictive model. Indeed, this method stands to enhance predictive capabilities by serving of time-dependent orientation tensors as valuable inputs, enabling a nuanced correlation with material intrinsic properties by using homogenization approaches.

## Authors contribution

Conceptualization: Mario Emanuele Di Nardo, Felix Frölich, Luise Kärger; Methodology: Mario Emanuele Di Nardo, Felix Frölich; Software: Mario Emanuele Di Nardo, Felix Frölich; Visualization: Mario Emanuele Di Nardo, Felix Frölich; Writing - original draft preparation: Mario Emanuele Di Nardo, Felix Frölich; Writing - review and editing: Luise Kärger, Pierpaolo Carlone; Funding acquisition: Luise Kärger, Pierpaolo Carlone; Supervision: Felix Frölich, Luise Kärger, Pierpaolo Carlone.

## Acknowledgements

The authors thank Baden-Württemberg State Ministry of Science, Research and the Arts (MWK) for funding the project "Basics of a remanufacturing process chain for functional, hybridized polymer components to increase reusability and optimize resource utilization (Restore)" as part of the Innovation Campus Future Mobility (ICM), and the German Research Foundation (DFG) for funding the Heisenberg Professorship of Prof. Kärger.

## References

[1] Gibson, I., Rosen, D. W., Stucker, B., Khorasani, M., Rosen, D., Stucker, B., & Khorasani, M. (2021). Additive manufacturing technologies (Vol. 17, pp. 160-186). Cham, Switzerland: Springer. https://doi.org/10.1007/978-3-030-56127-7

[2] Kaur, G., Singari, R. M., & Kumar, H. (2022). A review of fused filament fabrication (FFF): Process parameters and their impact on the tribological behavior of polymers (ABS). Materials Today: Proceedings, 51, 854-860. https://doi.org/10.1016/j.matpr.2021.06.274

[3] Li, J., Yang, S., Li, D., & Chalivendra, V. (2018). Numerical and experimental studies of additively manufactured polymers for enhanced fracture properties. Engineering Fracture Mechanics, 204, 557-569. https://doi.org/10.1016/j.engfracmech.2018.11.001

[4] Rashid, A. A., & Koç, M. (2021). Fused filament fabrication process: a review of numerical simulation techniques. Polymers, 13(20), 3534. https://doi.org/10.3390/polym13203534

[5] Jin, Y. A., He, Y., Fu, J. Z., Gan, W. F., & Lin, Z. W. (2014). Optimization of tool-path generation for material extrusion-based additive manufacturing technology. Additive manufacturing, 1, 32-47. https://doi.org/10.1016/j.addma.2014.08.004

[6] Ahn, S. H., Montero, M., Odell, D., Roundy, S., & Wright, P. K. (2002). Anisotropic material properties of fused deposition modeling ABS. Rapid prototyping journal, 8(4), 248-257. https://doi.org/10.1108/13552540210441166
However, using 4th order orientation tensor permits to describe the resulting distribution on stiffness tensors and in more complex components with elaborate trajectories, more complicated orientation distributions may occur, which make the 4th order tensor necessary. This methodology, integrating Python, Fortran programming, and Abaqus subroutines, streamlines the workflow from generating import files to incorporating orientation data, ensuring a representation in the FE model. The alignment depicted in the analytical solution mirrors the orientation changes captured in Abaqus, verifying the method in tracking orientation states for each element and at each time step. Visualization of tensor updates further solidifies the congruence between the analytical and numerical results. Future enhancements could focus on integrating material properties associated with orientation for a more comprehensive predictive model. Indeed, this method stands to enhance predictive capabilities by serving of time-dependent orientation tensors as valuable inputs, enabling a nuanced correlation with material intrinsic properties by using homogenization approaches.

## Authors contribution

Conceptualization: Mario Emanuele Di Nardo, Felix Frölich, Luise Kärger; Methodology: Mario Emanuele Di Nardo, Felix Frölich; Software: Mario Emanuele Di Nardo, Felix Frölich; Visualization: Mario Emanuele Di Nardo, Felix Frölich; Writing - original draft preparation: Mario Emanuele Di Nardo, Felix Frölich; Writing - review and editing: Luise Kärger, Pierpaolo Carlone; Funding acquisition: Luise Kärger, Pierpaolo Carlone; Supervision: Felix Frölich, Luise Kärger, Pierpaolo Carlone.

## Acknowledgements

The authors thank Baden-Württemberg State Ministry of Science, Research and the Arts (MWK) for funding the project "Basics of a remanufacturing process chain for functional, hybridized polymer components to increase reusability and optimize resource utilization (Restore)" as part of the Innovation Campus Future Mobility (ICM), and the German Research Foundation (DFG) for funding the Heisenberg Professorship of Prof. Kärger.

## References

[1] Gibson, I., Rosen, D. W., Stucker, B., Khorasani, M., Rosen, D., Stucker, B., & Khorasani, M. (2021). Additive manufacturing technologies (Vol. 17, pp. 160-186). Cham, Switzerland: Springer. https://doi.org/10.1007/978-3-030-56127-7

[2] Kaur, G., Singari, R. M., & Kumar, H. (2022). A review of fused filament fabrication (FFF): Process parameters and their impact on the tribological behavior of polymers (ABS). Materials Today: Proceedings, 51, 854-860. https://doi.org/10.1016/j.matpr.2021.06.274

[3] Li, J., Yang, S., Li, D., & Chalivendra, V. (2018). Numerical and experimental studies of additively manufactured polymers for enhanced fracture properties. Engineering Fracture Mechanics, 204, 557-569. https://doi.org/10.1016/j.engfracmech.2018.11.001

[4] Rashid, A. A., & Koç, M. (2021). Fused filament fabrication process: a review of numerical simulation techniques. Polymers, 13(20), 3534. https://doi.org/10.3390/polym13203534

[5] Jin, Y. A., He, Y., Fu, J. Z., Gan, W. F., & Lin, Z. W. (2014). Optimization of tool-path generation for material extrusion-based additive manufacturing technology. Additive manufacturing, 1, 32-47. https://doi.org/10.1016/j.addma.2014.08.004

[6] Ahn, S. H., Montero, M., Odell, D., Roundy, S., & Wright, P. K. (2002). Anisotropic material properties of fused deposition modeling ABS. Rapid prototyping journal, 8(4), 248-257. https://doi.org/10.1108/13552540210441166
[7] Cattenone, A., Morganti, S., Alaimo, G., & Auricchio, F. (2019). Finite element analysis of additive manufacturing based on fused deposition modeling: Distortions prediction and comparison with experimental data. Journal of Manufacturing Science and Engineering, 141(1), 011010. https://doi.org/10.1115/1.4041626

[8] Brenken, B., Favaloro, A., Barocio, E., DeNardo, N. M., & Pipes, R. B. (2016, May). Development of a model to predict temperature history and crystallization behavior of 3D printed parts made from fiber-reinforced thermoplastic polymers. In Int. SAMPE Tech. Conf (Vol. 12, p. 704).

[9] Zhou, Y., Lu, H., Wang, G., Wang, J., & Li, W. (2020). Voxelization modelling based finite element simulation and process parameter optimization for Fused Filament Fabrication. Materials & Design, 187, 108409. https://doi.org/10.1016/j.matdes.2019.108409

[10] Ahn, S. H., Baek, C., Lee, S., & Ahn, I. S. (2003). Anisotropic tensile failure model of rapid prototyping parts-fused deposition modeling (FDM). International Journal of Modern Physics B, 17(08n09), 1510-1516. https://doi.org/10.1142/S0217979203019241

[11] Domingo-Espin, M., Puigoriol-Forcada, J. M., Garcia-Granada, A. A., Llumà, J., Borros, S., & Reyes, G. (2015). Mechanical property characterization and simulation of fused deposition modeling Polycarbonate parts. Materials & Design, 83, 670-677. https://doi.org/10.1016/j.matdes.2015.06.074

[12] Biswas, P., Guessasma, S., & Li, J. (2020). Numerical prediction of orthotropic elastic properties of 3D-printed materials using micro-CT and representative volume element. Acta Mechanica, 231(2), 503-516. https://doi.org/10.1007/s00707-019-02544-2

[13] Zhao, Y., Chen, Y., & Zhou, Y. (2019). Novel mechanical models of tensile strength and elastic property of FDM AM PLA materials: Experimental and theoretical analyses. Materials & Design, 181, 108089. https://doi.org/10.1016/j.matdes.2019.108089

[14] Kanatani, K. (1984). Distribution of directional data and fabric tensors. International journal of engineering science, 22(2), 149-164. https://doi.org/10.1016/0020-7225(84)90090-9

[15] Advani, S. G., & Tucker III, C. L. (1987). The use of tensors to describe and predict fiber orientation in short fiber composites. Journal of rheology, 31(8), 751-784. https://doi.org/10.1122/1.549945

[16] Lebedev, L. P., Cloud, M. J., & Eremeyev, V. A. (2010). Tensor analysis with applications in mechanics. World Scientific. https://doi.org/10.1142/7826

[17] Heller, B. P., Smith, D. E., & Jack, D. A. (2017). Simulation of planar deposition polymer melt flow and fiber orientation in fused filament fabrication. In 2017 International Solid Freeform Fabrication Symposium. University of Texas at Austin.

[18] Lupone, F., Padovano, E., Venezia, C., & Badini, C. (2022). Experimental Characterization and Modeling of 3D Printed Continuous Carbon Fibers Composites with Different Fiber Orientation Produced by FFF Process. Polymers, 14(3), 426. https://doi.org/10.3390/polym14030426

[19] Python Documentation, Meshio Package, Available on 08/12/2023, Information on: https://pypi.org/project/meshio/

[20] Abaqus 6.14 documentation, User Subroutines Reference Guide, Available on 08/12/2023, Information on: http://130.149.89.49:2080/v6.14/
[7] Cattenone, A., Morganti, S., Alaimo, G., & Auricchio, F. (2019). Finite element analysis of additive manufacturing based on fused deposition modeling: Distortions prediction and comparison with experimental data. Journal of Manufacturing Science and Engineering, 141(1), 011010. https://doi.org/10.1115/1.4041626

[8] Brenken, B., Favaloro, A., Barocio, E., DeNardo, N. M., & Pipes, R. B. (2016, May). Development of a model to predict temperature history and crystallization behavior of 3D printed parts made from fiber-reinforced thermoplastic polymers. In Int. SAMPE Tech. Conf (Vol. 12, p. 704).

[9] Zhou, Y., Lu, H., Wang, G., Wang, J., & Li, W. (2020). Voxelization modelling based finite element simulation and process parameter optimization for Fused Filament Fabrication. Materials & Design, 187, 108409. https://doi.org/10.1016/j.matdes.2019.108409

[10] Ahn, S. H., Baek, C., Lee, S., & Ahn, I. S. (2003). Anisotropic tensile failure model of rapid prototyping parts-fused deposition modeling (FDM). International Journal of Modern Physics B, 17(08n09), 1510-1516. https://doi.org/10.1142/S0217979203019241

[11] Domingo-Espin, M., Puigoriol-Forcada, J. M., Garcia-Granada, A. A., Llumà, J., Borros, S., & Reyes, G. (2015). Mechanical property characterization and simulation of fused deposition modeling Polycarbonate parts. Materials & Design, 83, 670-677. https://doi.org/10.1016/j.matdes.2015.06.074

[12] Biswas, P., Guessasma, S., & Li, J. (2020). Numerical prediction of orthotropic elastic properties of 3D-printed materials using micro-CT and representative volume element. Acta Mechanica, 231(2), 503-516. https://doi.org/10.1007/s00707-019-02544-2

[13] Zhao, Y., Chen, Y., & Zhou, Y. (2019). Novel mechanical models of tensile strength and elastic property of FDM AM PLA materials: Experimental and theoretical analyses. Materials & Design, 181, 108089. https://doi.org/10.1016/j.matdes.2019.108089

[14] Kanatani, K. (1984). Distribution of directional data and fabric tensors. International journal of engineering science, 22(2), 149-164. https://doi.org/10.1016/0020-7225(84)90090-9

[15] Advani, S. G., & Tucker III, C. L. (1987). The use of tensors to describe and predict fiber orientation in short fiber composites. Journal of rheology, 31(8), 751-784. https://doi.org/10.1122/1.549945

[16] Lebedev, L. P., Cloud, M. J., & Eremeyev, V. A. (2010). Tensor analysis with applications in mechanics. World Scientific. https://doi.org/10.1142/7826

[17] Heller, B. P., Smith, D. E., & Jack, D. A. (2017). Simulation of planar deposition polymer melt flow and fiber orientation in fused filament fabrication. In 2017 International Solid Freeform Fabrication Symposium. University of Texas at Austin.

[18] Lupone, F., Padovano, E., Venezia, C., & Badini, C. (2022). Experimental Characterization and Modeling of 3D Printed Continuous Carbon Fibers Composites with Different Fiber Orientation Produced by FFF Process. Polymers, 14(3), 426. https://doi.org/10.3390/polym14030426

[19] Python Documentation, Meshio Package, Available on 08/12/2023, Information on: https://pypi.org/project/meshio/

[20] Abaqus 6.14 documentation, User Subroutines Reference Guide, Available on 08/12/2023, Information on: http://130.149.89.49:2080/v6.14/
# Multi-scale characterization of carbon-fibre reinforced PEEK composites manufactured by laser-assisted tape placement

RESTIF Noé<fnref n="1" />,<fnref n="2" />,a*, LAIK Suzanne<fnref n="1" />, PERON Mael<fnref n="2" />, DAGHIA Federica<fnref n="3" />, JACQUEMIN Frederic<fnref n="2" />

**Keywords:** Thermoplastic Composites, PEEK, Tape Placement, Experimental Characterization

**Abstract.** The Laser-Assisted Tape Placement forming process of thermoplastic composites enables the rapid production of laminates. However, it requires the tuning of the processing parameters, which is currently limited by a misunderstanding of the consolidation phenomena occurring during process and the interlaminar properties related with strong welded interfaces. This study aims at establishing correlations between physical properties and mechanical strength of welded thermoplastic composites, by using several methods and characterizations at different scales. Carbon-fibre reinforced PEEK (CF/PEEK) composites produced by a LATP process were investigated by varying the Laser Setpoint Temperature (LST) and Tool Temperature (TT). The results show that laminates manufactured at a LST of 350 °C have high void content, with the location of the voids depending on the TT: at a TT of 25 °C (unheated tool), interply and intraply voids are present while for a TT of 250 °C they are mainly intraply. Laminates produced at a LST of 450 °C also have mainly intraply voids, although their void content is significantly lower than that of laminates produced at an LST of 350 °C. For laminates having mainly intraply voids, ILSS testing demonstrates failure by an intralaminar failure mode. An increase in intralaminar shear strength is observed as the intraply void content decreases and the degree of crystallinity increases, related to the LST and the TT. The combination of experimental techniques thus allowed to provide understanding on the influence of local physical properties of the composites manufactured by LATP on specific interface-related mechanical properties, and demonstrate that, despite variations of mechanical performances with processing conditions, interfaces are no longer a weak point within the laminates when the processing conditions allow for sufficient intimate contact to occur during the consolidation phase.

**Introduction**

Thermoplastic matrix composites are increasingly used in the aeronautic and automotive industries due to their many advantages over thermoset matrix composites. These advantages include their better impact resistance and toughness and their potential for being reused or even recycled. Also, the forming of laminates by « out of autoclave » fusion bonding processes is more environmentally sustainable. The LATP was identified as an efficient and versatile process to manufacture high performance and complex-shaped parts. However, this process involves several complex and interdependent consolidation and deconsolidation phenomena within very short times [1]. At first, increasing the temperature and then the pressure allows the establishment of intimate contact [2]. Then, healing of the material takes place [2], [3]. It corresponds to the inter-diffusion

<figure><img src="image_586.png" /></figure>

<footnote n="1">¹CETIM, Technocampus Composites, Chemin du Chaffault, 44340 Bouguenais, France</footnote>

<footnote n="2">²Nantes Université, Ecole Centrale de Nantes, CNRS, GeM, UMR CNRS 6183, 44600 Saint-Nazaire, France</footnote>

<footnote n="3">³Université Paris-Saclay, CentraleSupélec, ENS Paris-Saclay, CNRS, LMPS - Laboratoire de Mécanique Paris-Saclay, 91190, Gif-sur-Yvette, France</footnote>

<footnote>a noe.restif@cetim.fr</footnote>
# Multi-scale characterization of carbon-fibre reinforced PEEK composites manufactured by laser-assisted tape placement

RESTIF Noé<fnref n="1" />,<fnref n="2" />,a*, LAIK Suzanne<fnref n="1" />, PERON Mael<fnref n="2" />, DAGHIA Federica<fnref n="3" />, JACQUEMIN Frederic<fnref n="2" />

**Keywords:** Thermoplastic Composites, PEEK, Tape Placement, Experimental
Characterization

**Abstract.** The Laser-Assisted Tape Placement forming process of thermoplastic composites enables the rapid production of laminates. However, it requires the tuning of the processing parameters, which is currently limited by a misunderstanding of the consolidation phenomena occurring during process and the interlaminar properties related with strong welded interfaces. This study aims at establishing correlations between physical properties and mechanical strength of welded thermoplastic composites, by using several methods and characterizations at different scales. Carbon-fibre reinforced PEEK (CF/PEEK) composites produced by a LATP process were investigated by varying the Laser Setpoint Temperature (LST) and Tool Temperature (TT). The results show that laminates manufactured at a LST of 350 °C have high void content, with the location of the voids depending on the TT: at a TT of 25 °C (unheated tool), interply and intraply voids are present while for a TT of 250 °C they are mainly intraply. Laminates produced at a LST of 450 °C also have mainly intraply voids, although their void content is significantly lower than that of laminates produced at an LST of 350 °C. For laminates having mainly intraply voids, ILSS testing demonstrates failure by an intralaminar failure mode. An increase in intralaminar shear strength is observed as the intraply void content decreases and the degree of crystallinity increases, related to the LST and the TT. The combination of experimental techniques thus allowed to provide understanding on the influence of local physical properties of the composites manufactured by LATP on specific interface-related mechanical properties, and demonstrate that, despite variations of mechanical performances with processing conditions, interfaces are no longer a weak point within the laminates when the processing conditions allow for sufficient intimate contact to occur during the consolidation phase.

**Introduction**

Thermoplastic matrix composites are increasingly used in the aeronautic and automotive industries due to their many advantages over thermoset matrix composites. These advantages include their better impact resistance and toughness and their potential for being reused or even recycled. Also, the forming of laminates by « out of autoclave » fusion bonding processes is more environmentally sustainable. The LATP was identified as an efficient and versatile process to manufacture high performance and complex-shaped parts. However, this process involves several complex and interdependent consolidation and deconsolidation phenomena within very short times [1]. At first, increasing the temperature and then the pressure allows the establishment of intimate contact [2]. Then, healing of the material takes place [2], [3]. It corresponds to the inter-diffusion

<figure><img src="image_597.png" /></figure>

<footnote n="1">¹CETIM, Technocampus Composites, Chemin du Chaffault, 44340 Bouguenais, France</footnote>

<footnote n="2">²Nantes Université, Ecole Centrale de Nantes, CNRS, GeM, UMR CNRS 6183, 44600 Saint-Nazaire, France</footnote>

<footnote n="3">³Université Paris-Saclay, CentraleSupélec, ENS Paris-Saclay, CNRS, LMPS - Laboratoire de Mécanique Paris-Saclay, 91190, Gif-sur-Yvette, France</footnote>

<footnote>a noe.reతIf@cetim.fr</footnote>
of molecular chains from one surface to another [4] and it strongly depends on time and temperature[2], [3], [5]. During cooling, crystallization can occur and is promoted by a low cooling rate. Moreover, deconsolidation mechanisms of the incoming tape and the previously consolidated laminate (substrate) can occur during layup. The deconsolidation mechanisms which affect the void content are the void growth into rich resin area and confined fibers area [6], [7], [8]. Recent work on hot pressed laminates [8] showed that a significant growth of voids requires melting of the matrix, while a preliminary phase of voids nucleation can take place above the glass-transition temperature (Tg).

Current knowledge is not sufficient to establish the interaction between these phenomena, and their effect on laminate mechanical properties. Many authors are establishing the link between the processing parameters and the laminate mechanical properties, showing an increase in shear strength with an increase of the TT or the LST [9]. However, there are only a few studies relating an increase in shear strength to the consolidation phenomena, by characterizing physical properties at the welded interface [10], [11]. Most studies investigating physicochemical characterization have correlated the increase in shear strength as a result of the change in the processing parameters with a void content decrease [12], [13], [14]; however, only a few investigations on the failure mode were described, and when it was described it is often interlaminar, even for autoclaved manufactured laminates [14]. It means that even for optimal manufacturing conditions, the interply remains the weakest area of the laminate, which raises many questions about the material and process quality. However, Comer et al. [15] show the major presence of intraply voids within ATP laminates, together with a decrease of the ILSS performance, though they did not relate the failure mode to the presence of these intraply voids.

This study aims at establishing links among the processing parameters, the physical properties associated with the consolidation phenomena and the shear strength and corresponding failure mode of PEEK/CF laminates. The experimental method consists of two steps: (i) investigate the influence of the manufacturing conditions over the mechanical properties by ILSS testing with a critical investigation of the failure mode (interply or intraply); and (ii) characterize the relationship between physical properties and the aforementioned mechanical properties.

## Materials and Method

Materials. Laminates were produced using unidirectional carbon fibre reinforced PEEK tape of 0.23-mm thick and 18-mm wide. PEEK's glass transition temperature ($T_g$) and melting temperature ($T_m$) were measured by Differential Scanning Calorimetry (DSC) on the as-received material leading to 143.3 °C and 344.6 °C, respectively, for a degree of crystallinity of $25.2 \pm 0.2 \%$. The void content was measured on micrographs of embedded and micron-polished tape section and was concluded to be $0.49 \pm 0.4 \%$. Due to confidentiality matters, further information about the material cannot be disclosed.

Process. The production of laminates (containing two flat sides) was performed at CETIM using SPIDE TP®. It is a LATP and filament winding process (Fig. 1). During processing, the LATP head (from AFPT GmbH) winds the tape around the oblong tool in the y direction shifting of one tape width along its course on one flat side over each lap, allowing for continuous deposition of the layers. Meanwhile, the tool is rotated in the opposite direction to the layup direction of the tape. For all manufactured parts, a number of 30 layers was laid up, resulting in approximately 6-mm thick laminates. The two processing parameters that were varied in this study were the LST (350 and 450 °C), and the TT (25 and 250 °C). The laser power and tilt were continuously regulated through a feedback temperature loop set on the LST and based on the measurement of the illuminated tape and substrate area by an embedded infrared camera. All processing parameters are given in Table 1, including the average laser power for each LST and corresponding average standard deviation between the plies. Because of limited space, more detailed data (e.g. variation of power within plies or evolution between the first and the last ply) are not provided in this paper.
of molecular chains from one surface to another [4] and it strongly depends on time and temperature[2], [3], [5]. During cooling, crystallization can occur and is promoted by a low cooling rate. Moreover, deconsolidation mechanisms of the incoming tape and the previously consolidated laminate (substrate) can occur during layup. The deconsolidation mechanisms which affect the void content are the void growth into rich resin area and confined fibers area [6], [7], [8]. Recent work on hot pressed laminates [8] showed that a significant growth of voids requires melting of the matrix, while a preliminary phase of voids nucleation can take place above the glass-transition temperature (Tg).

Current knowledge is not sufficient to establish the interaction between these phenomena, and their effect on laminate mechanical properties. Many authors are establishing the link between the processing parameters and the laminate mechanical properties, showing an increase in shear strength with an increase of the TT or the LST [9]. However, there are only a few studies relating an increase in shear strength to the consolidation phenomena, by characterizing physical properties at the welded interface [10], [11]. Most studies investigating physicochemical characterization have correlated the increase in shear strength as a result of the change in the processing parameters with a void content decrease [12], [13], [14]; however, only a few investigations on the failure mode were described, and when it was described it is often interlaminar, even for autoclaved manufactured laminates [14]. It means that even for optimal manufacturing conditions, the interply remains the weakest area of the laminate, which raises many questions about the material and process quality. However, Comer et al. [15] show the major presence of intraply voids within ATP laminates, together with a decrease of the ILSS performance, though they did not relate the failure mode to the presence of these intraply voids.

This study aims at establishing links among the processing parameters, the physical properties associated with the consolidation phenomena and the shear strength and corresponding failure mode of PEEK/CF laminates. The experimental method consists of two steps: (i) investigate the influence of the manufacturing conditions over the mechanical properties by ILSS testing with a critical investigation of the failure mode (interply or intraply); and (ii) characterize the relationship between physical properties and the aforementioned mechanical properties.

## Materials and Method

Materials. Laminates were produced using unidirectional carbon fibre reinforced PEEK tape of 0.23-mm thick and 18-mm wide. PEEK's glass transition temperature ($T_g$) and melting temperature ($T_m$) were measured by Differential Scanning Calorimetry (DSC) on the as-received material leading to 143.3 °C and 344.6 °C, respectively, for a degree of crystallinity of 25.2 ± 0.2 %. The void content was measured on micrographs of embedded and micron-polished tape section and was concluded to be 0.49 ± 0.4 %. Due to confidentiality matters, further information about the material cannot be disclosed.

Process. The production of laminates (containing two flat sides) was performed at CETIM using SPIDE TP®. It is a LATP and filament winding process (Fig. 1). During processing, the LATP head (from AFPT GmbH) winds the tape around the oblong tool in the y direction shifting of one tape width along its course on one flat side over each lap, allowing for continuous deposition of the layers. Meanwhile, the tool is rotated in the opposite direction to the layup direction of the tape. For all manufactured parts, a number of 30 layers was laid up, resulting in approximately 6-mm thick laminates. The two processing parameters that were varied in this study were the LST (350 and 450 °C), and the TT (25 and 250 °C). The laser power and tilt were continuously regulated through a feedback temperature loop set on the LST and based on the measurement of the illuminated tape and substrate area by an embedded infrared camera. All processing parameters are given in Table 1, including the average laser power for each LST and corresponding average standard deviation between the plies. Because of limited space, more detailed data (e.g. variation of power within plies or evolution between the first and the last ply) are not provided in this paper.
Laminates are identified through both parameters with the following reference code type “TT/LST”. For all laminates, the layup speed was set to 5 m/min and a consolidation force of 250 N was applied by a 60-shore silicon compaction roller.

<figure><img src="image_587.png" /><figcaption>Table 1 – Manufacturing conditions of laminates with all processing parameters programmed by SPIDE TP®</figcaption></figure>

<table><caption>Figure 1 – SPIDE TP® Process</caption><thead><tr><th>Reference</th><th>Tool Temperature (TT) [°C]</th><th>Laser Setpoint Temperature (LST) [°C]; Laser average power [W]</th></tr></thead><tbody><tr><td>25/350</td><td>25</td><td>350; 924 ± 32</td></tr><tr><td>250/350</td><td>250</td><td>350; 653 ± 53</td></tr><tr><td>25/450</td><td>25</td><td>450; 1271 ± 65</td></tr><tr><td>250/450</td><td>250</td><td>450; 1012 ± 43</td></tr></tbody></table>

Optical Microscopy (OM). All images of laminate cross-sections were produced with an optical microscope ZEISS AXIOSCOPE 5. The samples were prepared by being embedded in a resin and polished using sandpapers from P500 down to 1 µm grit size. An area of approximately 10-mm wide over the entire thickness of each laminate was analysed. The void content was calculated in both intralaminar and interlaminar regions using ImageJ software.

Ultrasonic (US) testing. All the laminates were controlled by US nondestructive testing through C-Scan and A-Scan to check for local defect indications and/or obtain relative attenuation levels. In the absence of local defects, global attenuation as compared to a healthy laminate of the same material could be attributed to diffuse porosity. Results are given in %SH (screen height) which is a relative unit based on a signal gain set on a reference material of the same nature with known good material health level.

Scanning Electronic Microscopy (SEM). A ZEISS SUPRA 25 scanning Electron Microscope was used at an acceleration voltage of 15 kV to analyze the fracture surfaces of mechanically tested specimens. Specimens were metallized with Platinum prior to observation.

Differential scanning calorimetry (DSC). DSC analyses were performed using a Mettler TOLEDO DSC 3. To obtain results over the entire thickness of the laminates, sampling consisted of cutting a thin cross-section using a microtome. Samples of approximately 10 mg were placed in 40 µl aluminum pans, with non-hermetically sealed lids. Two temperature ramp-ups and -downs were performed at heating rates of 10 °C/min between room temperature and 380 °C. Three sample were analysed for each laminate in a nitrogen environment (to avoid any sample oxidation) at a flow rate of 50 ml/min. The degree of crystallinity of a sample was estimated by using Eq.1:

$$X = \frac{\Delta H_m - \Delta H_{cc}}{(1 - \omega) \times \Delta H_{m\infty}} \quad (1)$$

where $\Delta H_m$ is the melting enthalpy, $\Delta H_{cc}$ is the cold crystallization enthalpy, $\omega$ is the weight fraction of matrix content, and $\Delta H_{m\infty}$ is the theoretical melting enthalpy of 100% crystalline PEEK which has been calculated to be 130 J/g by Blundell et al. [16].

Interlaminar shear strength (ILSS) testing. The interlaminar shear behavior of laminates was assessed by following the ASTM D2344 Standard, using a span-to-thickness ratio of 4:1. Five specimens measuring 40 x 12 x t mm (t is the thickness, being approximately 6 mm) were tested
Laminates are identified through both parameters with the following reference code type "TT/LST". For all laminates, the layup speed was set to 5 m/min and a consolidation force of 250 N was applied by a 60-shore silicon compaction roller.

<figure><img src="image_598.png" /><figcaption>Table 1 – Manufacturing conditions of laminates with all processing parameters programmed by SPIDE TP®</figcaption></figure>

<table><caption>Figure 1 – SPIDE TP® Process</caption><thead><tr><th>Reference</th><th>Tool Temperature (TT) [°C]</th><th>Laser Setpoint Temperature (LST) [°C]; Laser average power [W]</th></tr></thead><tbody><tr><td>25/350</td><td>25</td><td>350; 924 ± 32</td></tr><tr><td>250/350</td><td>250</td><td>350; 653 ± 53</td></tr><tr><td>25/450</td><td>25</td><td>450; 1271 ± 65</td></tr><tr><td>250/450</td><td>250</td><td>450; 1012 ± 43</td></tr></tbody></table>

Optical Microscopy (OM). All images of laminate cross-sections were produced with an optical microscope ZEISS AXIOSCOPE 5. The samples were prepared by being embedded in a resin and polished using sandpapers from P500 down to 1 µm grit size. An area of approximately 10-mm wide over the entire thickness of each laminate was analysed. The void content was calculated in both intralaminar and interlaminar regions using ImageJ software.

Ultrasonic (US) testing. All the laminates were controlled by US nondestructive testing through C-Scan and A-Scan to check for local defect indications and/or obtain relative attenuation levels. In the absence of local defects, global attenuation as compared to a healthy laminate of the same material could be attributed to diffuse porosity. Results are given in %SH (screen height) which is a relative unit based on a signal gain set on a reference material of the same nature with known good material health level.

Scanning Electronic Microscopy (SEM). A ZEISS SUPRA 25 scanning Electron Microscope was used at an acceleration voltage of 15 kV to analyze the fracture surfaces of mechanically tested specimens. Specimens were metallized with Platinum prior to observation.

Differential scanning calorimetry (DSC). DSC analyses were performed using a Mettler TOLEDO DSC 3. To obtain results over the entire thickness of the laminates, sampling consisted of cutting a thin cross-section using a microtome. Samples of approximately 10 mg were placed in 40 µl aluminum pans, with non-hermetically sealed lids. Two temperature ramp-ups and -downs were performed at heating rates of 10 °C/min between room temperature and 380 °C. Three sample were analysed for each laminate in a nitrogen environment (to avoid any sample oxidation) at a flow rate of 50 ml/min. The degree of crystallinity of a sample was estimated by using Eq.1:

$$X = \frac{\Delta H_m - \Delta H_{cc}}{(1 - \omega) \times \Delta H_{m\infty}} \quad (1)$$

where $\Delta H_m$ is the melting enthalpy, $\Delta H_{cc}$ is the cold crystallization enthalpy, $\omega$ is the weight fraction of matrix content, and $\Delta H_{m\infty}$ is the theoretical melting enthalpy of 100% crystalline PEEK which has been calculated to be 130 J/g by Blundell et al. [16].

Interlaminar shear strength (ILSS) testing. The interlaminar shear behavior of laminates was assessed by following the ASTM D2344 Standard, using a span-to-thickness ratio of 4:1. Five specimens measuring 40 x 12 x t mm (t is the thickness, being approximately 6 mm) were tested
for each laminate. Testing was performed at 1 mm/min on an INSTRON 3369 tensile testing machine with a maximum load capacity of 10 kN. The apparent interlaminar shear strength is calculated using Eq.2:

$$ \tau_{max} = \frac{3 \times F_{max}}{4 \times w \times t} \qquad (2) $$

where $F_{max}$ is the maximum force in N, $w$ is the specimen width (mm) and $t$ is the specimen thickness (mm).

Dynamic Mechanical Analysis (DMA). Mechanical testing by DMA assesses the mechanical response of the laminates according to the temperature. The tests consist of a three-point bending in the transverse-to-fibre direction. For each manufacturing conditions investigated, two samples were tested on a Mettler TOLEDO DMA 1. The scans were performed from room temperature to 250°C at a scanning speed of 2 °C/min. A frequency of 1 Hz and a displacement amplitude of 3 µm were used. The peak value of the loss factor tan δ was obtained by a mathematical treatment in Matlab, which consisted of fitting the baseline and smoothing the curve to extract the maximum value of tan δ.

## Results and discussion

Overall laminate quality. The results of the mean signal amplitude measured by ultrasonic nondestructive control of plates are shown in Table 2. Through C-Scan measurement, a global material health difference between 25/350 and 250/350 is observed with an increase of the transmitted US signal amplitude from 30 to 35 %SH respectively. An equivalent increase in amplitude of 5%SH between 25/450 and 250/450 is also observed, showing a better material quality of the plates produced on a heated tool. However, the effect of the TT is small compared to the effect of the LST, as there is approximately a 45 %SH rise in amplitude with an increase of LST from 350 to 450 °C.

Microscopy observations of manufactured panels are presented in Fig. 2. Void contents were measured for all laminates, and the interply and intraply void contents are listed in Table 2. Such information allow to discriminate porosities resulting from the lack of intimate contact and those generated by deconsolidation phenomena. The former is visible by a high interply void content, while the latter can be associated with a higher intraply void content as compared to the initial tape [6], [14]. At first glance, the evolution of void content with the changing of the LST and the TT follows the same trend as the evolution of the US signal amplitude discussed previously. However, when considering the location of voids, three different cases can be highlighted: the 25/350 contains both interply and intraply voids, the 250/350 rather contains intraply voids and almost no interply voids, and the 25/450 and 250/350 show only a small amount of intraply voids, slightly higher than the initial void content of the tape. Through these observations, we can conclude that only the laminate 25/350 presents a lack of intimate contact at the welded interface, indicating that its establishment is promoted by increasing the TT or the LST.

Indeed, the observations of Celik et al. [17] on a PEEK/CF demonstrated the establishment of the intimate contact at a TT of 155 °C (and a LST of 380-400 °C), as compared to similar lay-up on an unheated tool. However, it is important to remember that in this latter study and all others referenced in this article, comparison with literature data is limited by differences in material composition. The favourable conditions for the establishment of intimate contact and healing when the tool is heated over the $T_g$ can be explained by an increased time above $T_g$ and by a lower cooling rate [1], [18], [19]. Hence, for the 25/350 condition, even if the $T_m$ is reached, there might not be enough time left to activate these consolidation mechanisms.

If we one focus now on intraply void related to deconsolidation, one could notice that laminates welded at 350 °C are much more concerned by this phenomenon. A proposed assumption to
for each laminate. Testing was performed at 1 mm/min on an INSTRON 3369 tensile testing machine with a maximum load capacity of 10 kN. The apparent interlaminar shear strength is calculated using Eq.2:

$$ \tau_{max} = \frac{3 \times F_{max}}{4 \times w \times t} \qquad (2) $$

where $F_{max}$ is the maximum force in N, w is the specimen width (mm) and t is the specimen thickness (mm).

Dynamic Mechanical Analysis (DMA). Mechanical testing by DMA assesses the mechanical response of the laminates according to the temperature. The tests consist of a three-point bending in the transverse-to-fibre direction. For each manufacturing conditions investigated, two samples were tested on a Mettler TOLEDO DMA 1. The scans were performed from room temperature to 250°C at a scanning speed of 2 °C/min. A frequency of 1 Hz and a displacement amplitude of 3 µm were used. The peak value of the loss factor tan δ was obtained by a mathematical treatment in Matlab, which consisted of fitting the baseline and smoothing the curve to extract the maximum value of tan δ.

## Results and discussion

Overall laminate quality. The results of the mean signal amplitude measured by ultrasonic nondestructive control of plates are shown in Table 2. Through C-Scan measurement, a global material health difference between 25/350 and 250/350 is observed with an increase of the transmitted US signal amplitude from 30 to 35 %SH respectively. An equivalent increase in amplitude of 5%SH between 25/450 and 250/450 is also observed, showing a better material quality of the plates produced on a heated tool. However, the effect of the TT is small compared to the effect of the LST, as there is approximately a 45 %SH rise in amplitude with an increase of LST from 350 to 450 °C.

Microscopy observations of manufactured panels are presented in Fig. 2. Void contents were measured for all laminates, and the interply and intraply void contents are listed in Table 2. Such information allow to discriminate porosities resulting from the lack of intimate contact and those generated by deconsolidation phenomena. The former is visible by a high interply void content, while the latter can be associated with a higher intraply void content as compared to the initial tape [6], [14]. At first glance, the evolution of void content with the changing of the LST and the TT follows the same trend as the evolution of the US signal amplitude discussed previously. However, when considering the location of voids, three different cases can be highlighted: the 25/350 contains both interply and intraply voids, the 250/350 rather contains intraply voids and almost no interply voids, and the 25/450 and 250/350 show only a small amount of intraply voids, slightly higher than the initial void content of the tape. Through these observations, we can conclude that only the laminate 25/350 presents a lack of intimate contact at the welded interface, indicating that its establishment is promoted by increasing the TT or the LST.

Indeed, the observations of Celik et al. [17] on a PEEK/CF demonstrated the establishment of the intimate contact at a TT of 155 °C (and a LST of 380-400 °C), as compared to similar lay-up on an unheated tool. However, it is important to remember that in this latter study and all others referenced in this article, comparison with literature data is limited by differences in material composition. The favourable conditions for the establishment of intimate contact and healing when the tool is heated over the $T_g$ can be explained by an increased time above $T_g$ and by a lower cooling rate [1], [18], [19]. Hence, for the 25/350 condition, even if the $T_m$ is reached, there might not be enough time left to activate these consolidation mechanisms.

If we one focus now on intraply void related to deconsolidation, one could notice that laminates welded at 350 °C are much more concerned by this phenomenon. A proposed assumption to
explain deconsolidation by increasing intraply void content is sufficient time for void growth and frozen-in-fibre stress release during the heating phase prior to consolidation under the roller, combined with a too short time under pressure for allowing the squeeze flow mechanisms to fill the voids with matrix. Hence, the difference between the 250/350 and the laminates welded at 450 °C could be explained by the material viscosity which affect the establishment of the consolidation by squeeze flow: the matrix of the laminate 250/350 could have a sufficiently low viscosity to deconsolidate, but a too high viscosity to fill in all the voids during the application of pressure. This assumption is based on an almost 10-fold difference in viscosity of PEEK between 350 °C and 450 °C [20].

Finally, the intraply void content of laminates welded at 450 °C is slightly higher than the void content of the as-received tape, reflecting a little deconsolidation for these manufacturing conditions. The void content of an autoclaved manufactured laminate from literature ([15]₀ CF/PEEK consolidated in autoclave at 370 °C during 20 min under a pressure of 7 bar, and cooled at 2 °C/min) is presented in Table 2 and in Fig. 4[15]. While a void content respecting the standard criterion for most aerospace applications (lower than 1 % [1]) is reached for a LST at 450 °C with our material system and processing conditions, we notice that it is possible to reach lower void content by autoclave, when maximum consolidation is achieved.

<table><caption>Table 2 – Void content results</caption><thead><tr><th></th><th>25/350</th><th>250/350</th><th>25/450</th><th>250/450</th><th>autoclaved-manufactured reference [15]</th><th>as-received tape</th></tr></thead><tbody><tr><th>US amplitude [%SH]</th><td>30</td><td>35</td><td>75</td><td>80</td><td>-</td><td>-</td></tr><tr><th>Interply void content [%]</th><td>3.12 ± 0.7</td><td>0.11 ± 0.02</td><td>0.06 ± 0.02</td><td>0.02 ± 0.01</td><td rowspan="2">0.08</td><td rowspan="2">-</td></tr><tr><th>Intraply void content [%]</th><td>2.35 ± 0.3</td><td>2.71 ± 0.2</td><td>0.75 ± 0.2</td><td>0.69 ± 0.2</td></tr></tbody></table>

<figure><img src="image_588.png" /><figcaption>Figure 2 – Images of cross-section laminates (a) 25/350, (b) 250/350, (c) 25/450 and (d) 250/450 with the associated void content</figcaption></figure>
explain deconsolidation by increasing intraply void content is sufficient time for void growth and frozen-in-fibre stress release during the heating phase prior to consolidation under the roller, combined with a too short time under pressure for allowing the squeeze flow mechanisms to fill the voids with matrix. Hence, the difference between the 250/350 and the laminates welded at 450 °C could be explained by the material viscosity which affect the establishment of the consolidation by squeeze flow: the matrix of the laminate 250/350 could have a sufficiently low viscosity to deconsolidate, but a too high viscosity to fill in all the voids during the application of pressure. This assumption is based on an almost 10-fold difference in viscosity of PEEK between 350 °C and 450 °C [20].

Finally, the intraply void content of laminates welded at 450 °C is slightly higher than the void content of the as-received tape, reflecting a little deconsolidation for these manufacturing conditions. The void content of an autoclaved manufactured laminate from literature ([15]₀ CF/PEEK consolidated in autoclave at 370 °C during 20 min under a pressure of 7 bar, and cooled at 2 °C/min) is presented in Table 2 and in Fig. 4[15]. While a void content respecting the standard criterion for most aerospace applications (lower than 1 % [1]) is reached for a LST at 450 °C with our material system and processing conditions, we notice that it is possible to reach lower void content by autoclave, when maximum consolidation is achieved.

<table><caption>Table 2 – Void content results</caption><thead><tr><th></th><th>25/350</th><th>250/350</th><th>25/450</th><th>250/450</th><th>autoclaved-manufactured reference [15]</th><th>as-received tape</th></tr></thead><tbody><tr><th>US amplitude [%SH]</th><td>30</td><td>35</td><td>75</td><td>80</td><td>-</td><td>-</td></tr><tr><th>Interply void content [%]</th><td>3.12 ± 0.7</td><td>0.11 ± 0.02</td><td>0.06 ± 0.02</td><td>0.02 ± 0.01</td><td rowspan="2">0.08</td><td>-</td></tr><tr><th>Intraply void content [%]</th><td>2.35 ± 0.3</td><td>2.71 ± 0.2</td><td>0.75 ± 0.2</td><td>0.69 ± 0.2</td><td>0.49 ± 0.4</td></tr></tbody></table>

<figure><img src="image_599.png" /><figcaption>Figure 2 – Images of cross-section laminates (a) 25/350, (b) 250/350, (c) 25/450 and (d) 250/450 with the associated void content</figcaption></figure>
ILSS mechanical performances. On the load-displacement curves presented in Fig. 3a., we can clearly see a different mechanical behavior in sample 25/350, which drops significantly at a low load, compared to the other specimens presenting nonlinear response and higher values for load and displacement at failure. The combined observations of cross-section of fracture (Fig. 3b and c.) and fracture surfaces on SEM (Fig. 3d and e) confirm a different behavior of 25/350 specimens. This laminate, which have a high interply void content, failed at a welded interface due to an interlaminar shear mechanism. Fracture surfaces of the specimens are comprised of a smooth resin layer with few bare fibres. For the three other laminates, having mainly intraply voids, the maximum load varies (Fig. 3a) but they all break by an intralaminar shear mode, and especially at the fibre-matrix interfaces, as shown in Fig. 3e. on the 250/350 condition. This result means that when processing parameters are favorable for intimate contact and healing establishment (even if healing is not complete), the welded interface is no longer the weakest area of the laminate when subjected to out-of-plane shear loading. It explains why the ILSS values of these laminates are close among each other compared to the ILSS value of the 25/350 laminates (Fig. 3a).

Furthermore, the difference of behavior between all the specimens correlates with the void content, which decreases when the apparent ILSS strength increases (Fig.4a). A correlation is found between the intraply void content and the ILSS values when the failure mode is intralaminar. It would be interesting to know the failure mode of the autoclave laminate from literature [15] (previously presented) to confirm the relation established in the well-consolidated laminates of this study. However, even if these results highlight an obvious effect of intraply void content on ILSS, the understanding of fracture mechanisms during ILSS testing is necessary to confirm that state. Also, Gao & Kim [21] showed that fast cooling of semi-crystalline thermoplastic reduces the thickness of the transcrystalline region around the fibres, leading to a weaker fibre-matrix interface. Hence, for low intraply void contents (at a LST of 450 °C), the increase in ILSS by increasing the TT at 250 °C may be in agreement with this latter statement, because these conditions may promote the crystallization of PEEK [18]. To explain the different ILSS values between 25/450 and 250/450 presenting no significant differences in intraply void content, the characterization of the crystallinity of PEEK is then required.

Also, Fig. 4a shows that the ILSS value of the PEEK/CF autoclave reference is significantly higher than the ILSS values of the LATP laminate obtained in this study. However, the authors specified that this high ILSS value of autoclave reference is due to a high crystallinity (40%).

<figure><img src="image_589.png" /><figcaption>Figure 3 – a) Load curves for the different manufacturing conditions; post-mortem cross-section images of ILSS laminates (b) 25/350 and(c) 250/350 where red arrows indicate the inter-ply position; fracture surfaces (by SEM) of ILSS laminates (d) 25/350 and (e) 250/350</figcaption></figure>
ILSS mechanical performances. On the load-displacement curves presented in Fig. 3a., we can clearly see a different mechanical behavior in sample 25/350, which drops significantly at a low load, compared to the other specimens presenting nonlinear response and higher values for load and displacement at failure. The combined observations of cross-section of fracture (Fig. 3b and c.) and fracture surfaces on SEM (Fig. 3d and e) confirm a different behavior of 25/350 specimens. This laminate, which have a high interply void content, failed at a welded interface due to an interlaminar shear mechanism. Fracture surfaces of the specimens are comprised of a smooth resin layer with few bare fibres. For the three other laminates, having mainly intraply voids, the maximum load varies (Fig. 3a) but they all break by an intralaminar shear mode, and especially at the fibre-matrix interfaces, as shown in Fig. 3e. on the 250/350 condition. This result means that when processing parameters are favorable for intimate contact and healing establishment (even if healing is not complete), the welded interface is no longer the weakest area of the laminate when subjected to out-of-plane shear loading. It explains why the ILSS values of these laminates are close among each other compared to the ILSS value of the 25/350 laminates (Fig. 3a).

Furthermore, the difference of behavior between all the specimens correlates with the void content, which decreases when the apparent ILSS strength increases (Fig.4a). A correlation is found between the intraply void content and the ILSS values when the failure mode is intralaminar. It would be interesting to know the failure mode of the autoclave laminate from literature [15] (previously presented) to confirm the relation established in the well-consolidated laminates of this study. However, even if these results highlight an obvious effect of intraply void content on ILSS, the understanding of fracture mechanisms during ILSS testing is necessary to confirm that state. Also, Gao & Kim [21] showed that fast cooling of semi-crystalline thermoplastic reduces the thickness of the transcrystalline region around the fibres, leading to a weaker fibre-matrix interface. Hence, for low intraply void contents (at a LST of 450 °C), the increase in ILSS by increasing the TT at 250 °C may be in agreement with this latter statement, because these conditions may promote the crystallization of PEEK [18]. To explain the different ILSS values between 25/450 and 250/450 presenting no significant differences in intraply void content, the characterization of the crystallinity of PEEK is then required.

Also, Fig. 4a shows that the ILSS value of the PEEK/CF autoclave reference is significantly higher than the ILSS values of the LATP laminate obtained in this study. However, the authors specified that this high ILSS value of autoclave reference is due to a high crystallinity (40%).

<figure><img src="image_600.png" /><figcaption>Figure 3 – a) Load curves for the different manufacturing conditions; post-mortem cross-section images of ILSS laminates (b) 25/350 and(c) 250/350 where red arrows indicate the inter-ply position; fracture surfaces (by SEM) of ILSS laminates (d) 25/350 and (e) 250/350</figcaption></figure>
Crystallinity. Results of degree of crystallinity obtained by DSC analysis are presented in Fig. 4b and they show a higher effect of the LST on the degree of crystallinity than the TT. However, due to the size of sampling in DSC and the sensitivity limiting detection of low variation of heat flux (especially for the cold crystallization) and measured enthalpies to experimental repetitiveness and presence of carbon fibers, we obtained more accurate (through indirect) and repetitive information by DMA analysis to assess an evolution of the crystallinity with the manufacturing conditions.

DMA. A correlation between the viscoelastic behavior of the laminates and their degree of crystallinity was performed by DMA analysis. The goal was to assess the variation of the tan δ loss factor peak and its corresponding temperature (Fig. 4b), which is considered as the glass transition temperature Tg, with LST and TT. Only the variation of tan δ will be discussed in this paper. This value is defined by the ratio between the loss and the storage modulus, explaining the reverse link between tan δ and the degree of crystallinity because increasing the crystallinity is equivalent to decreasing the amorphous chain mobility, even if this latter also depends on the morphology (type and size of the crystals).

By comparing LATP and autoclave PEEK/CF laminates, Ray et al. [22] showed an increase of T<sub>g</sub> from 140 °C to 153 °C and a decrease in tan δ from 0,075 to 0,03 related to an increase in crystallinity from 17,6% to 42%. Also, the effect of TT on the T<sub>g</sub> has been already observed in a PEEK/CF laminate manufactured by SPIDE TP® by El Bayssari [23] : a variation of T<sub>g</sub> from 140 °C to 148 °C when the tool is heated at 180 °C was noted.

As shown in Fig. 4b, our results confirmed this trend. There is a significant drop of tan δ when increasing the TT. This drop takes place from values of tan δ of 0,18 to 0,10 in the laminates manufactured with a LST of 350 °C and from 0,15 to 0,1 in the laminates manufactured at 450°C. However, there is probably an effect of the void content on the Tg and tan δ values measured by DMA [24]. In order to decorrelate these effects, one can comparatively evaluate the tan δ and Tg from cooling curves, assuming all cold crystallization was completed during the temperature ramp until 250°C (crystallization occurs in a few seconds at this temperature according to Tardif et al. [25]) and that this ramp do not affect the porosity content. In this way, it can be assumed that all specimens are all fully crystallized during the cooling down phase, and that differences in Tg and tan δ between the laminates can only be attributed to differences in porosity contents. Hence, the differences between laminates observed during the ramp-up can then be analyzed to evaluate qualitatively the influence of crystallinity variations between laminates. This evaluation is not presented here as it is still in progress, however the comparison of tan δ and Tg remains valid for the 25/450 and 250/450, for which the void contents are similar. Considering these laminates, it is clearly seen that the drop in tan δ could be related to a rise in the crystallinity of the material. This observation could reveal that for laminates containing similar void content, any small variation of the degree of crystallinity may has an influence on the intralaminar resistance. Particularly, a drop of 33 % of the tan δ value is responsible of a rise of 6 % of the ILSS value (i.e Fig. 4a and b). An effect of the crystallinity of the material on its ILSS value has already been emphasized by the observations of Gao and Kim [26]. They showed variation in ILSS values from approximately 80 to 55 MPa when the degree of crystallinity varied from approximately 38 to 13 %. However, no investigation was performed about void content and laminates were manufactured by hot press in this study.

Finally, the higher degree of crystallinity for laminates manufactured on a heated tool at 250 °C or at a Laser Setpoint temperature of 450 °C is in accordance with thermal modelling predicting longer time above T<sub>g</sub> under these conditions, and consequently a longer time to crystallize [18], [19].
Crystallinity. Results of degree of crystallinity obtained by DSC analysis are presented in Fig. 4b and they show a higher effect of the LST on the degree of crystallinity than the TT. However, due to the size of sampling in DSC and the sensitivity limiting detection of low variation of heat flux (especially for the cold crystallization) and measured enthalpies to experimental repetitiveness and presence of carbon fibers, we obtained more accurate (through indirect) and repetitive information by DMA analysis to assess an evolution of the crystallinity with the manufacturing conditions.

DMA. A correlation between the viscoelastic behavior of the laminates and their degree of crystallinity was performed by DMA analysis. The goal was to assess the variation of the tan δ loss factor peak and its corresponding temperature (Fig. 4b), which is considered as the glass transition temperature Tg, with LST and TT. Only the variation of tan δ will be discussed in this paper. This value is defined by the ratio between the loss and the storage modulus, explaining the reverse link between tan δ and the degree of crystallinity because increasing the crystallinity is equivalent to decreasing the amorphous chain mobility, even if this latter also depends on the morphology (type and size of the crystals).

By comparing LATP and autoclave PEEK/CF laminates, Ray et al. [22] showed an increase of T<sub>g</sub> from 140 °C to 153 °C and a decrease in tan δ from 0,075 to 0,03 related to an increase in crystallinity from 17,6% to 42%. Also, the effect of TT on the T<sub>g</sub> has been already observed in a PEEK/CF laminate manufactured by SPIDE TP® by El Bayssari [23] : a variation of T<sub>g</sub> from 140 °C to 148 °C when the tool is heated at 180 °C was noted.

As shown in Fig. 4b, our results confirmed this trend. There is a significant drop of tan δ when increasing the TT. This drop takes place from values of tan δ of 0,18 to 0,10 in the laminates manufactured with a LST of 350 °C and from 0,15 to 0,1 in the laminates manufactured at 450°C. However, there is probably an effect of the void content on the Tg and tan δ values measured by DMA [24]. In order to decorrelate these effects, one can comparatively evaluate the tan δ and Tg from cooling curves, assuming all cold crystallization was completed during the temperature ramp until 250°C (crystallization occurs in a few seconds at this temperature according to Tardif et al. [25]) and that this ramp do not affect the porosity content. In this way, it can be assumed that all specimens are all fully crystallized during the cooling down phase, and that differences in Tg and tan δ between the laminates can only be attributed to differences in porosity contents. Hence, the differences between laminates observed during the ramp-up can then be analyzed to evaluate qualitatively the influence of crystallinity variations between laminates. This evaluation is not presented here as it is still in progress, however the comparison of tan δ and Tg remains valid for the 25/450 and 250/450, for which the void contents are similar. Considering these laminates, it is clearly seen that the drop in tan δ could be related to a rise in the crystallinity of the material. This observation could reveal that for laminates containing similar void content, any small variation of the degree of crystallinity may has an influence on the intralaminar resistance. Particularly, a drop of 33 % of the tan δ value is responsible of a rise of 6 % of the ILSS value (i.e Fig. 4a and b). An effect of the crystallinity of the material on its ILSS value has already been emphasized by the observations of Gao and Kim [26]. They showed variation in ILSS values from approximately 80 to 55 MPa when the degree of crystallinity varied from approximately 38 to 13 %. However, no investigation was performed about void content and laminates were manufactured by hot press in this study.

Finally, the higher degree of crystallinity for laminates manufactured on a heated tool at 250 °C or at a Laser Setpoint temperature of 450 °C is in accordance with thermal modelling predicting longer time above T<sub>g</sub> under these conditions, and consequently a longer time to crystallize [18], [19].
<figure><img src="image_590.png" /><figcaption>Figure 4 – For all manufacturing conditions investigated: a) ILSS data according to the void content, with black dashed lines representing the as-received tape void content b) ILSS data according to the degree of crystallinity measured by DSC and the loss factor tan δ assessed by DMA. Grey dashed lines corresponding to the as-received tape degree of crystallinity</figcaption></figure>

## Conclusion

In this work, the characterization of PEEK/CF laminates processed using several LATP manufacturing conditions was performed.

To observe the effect of the process temperature and the cooling rate inside the material, the two processing parameters that were varied are the laser setpoint temperature (LST) (350 and 450 °C), and the tool temperature (TT) (25 and 250 °C). Then the laminates void content and distribution, crystallinity, viscoelastic and shear behaviors were investigated.

Firstly, it was shown that the LST and the TT affect the overall laminate qualities. The ultrasonic signal amplitude was much high for laminates manufactured at 450 °C compared to laminates manufactured at 350°C. This trend was confirmed by microscopy observations of the cross-section of the laminates showing a higher void content for the latter.

In order to determine the voids repartition, the measurement of interply and intraply void content was carried out. Results highlighted the lack of intimate contact for the laminate processed at 350 °C on an unheated tool, resulting in interply void content of 4%. Although the laminate welded at 350 °C on a tool heated at 250 °C has a lower interply void content (0,8 %), it contains much more intraply voids (3 %) than the laminates manufactured at 450 °C (about 0,7 %), whatever the TT. It has been speculated that the deconsolidation by increasing the intraply void content is due to a growth of initial void content and the development of cavities around fiber due to relaxation of stress at the fiber-matrix interfaces during the heating phase.

Secondly, a correlation between void distribution, ILSS results and failure mode was demonstrated. For laminates processed at 350 °C on an unheated tool, showing a lack of intimate contact, the interlaminar failure mode is obviously governed by the presence of interply voids Unsurprisingly, this laminate has the lowest ILSS value.

Finally, the characterization of the degree of crystallinity by DSC and DMA allowed to link this property to the ILSS of the laminates. For well-consolidated laminate having mainly intralaminar voids, both the intraply void content and the crystallinity of the laminate seem to be related to the apparent ILSS performances and further investigation are in progress in order to clearly decorrelate both effects.

## References

[1] R. Arquier, I. Iliopoulos, G. Régnier, and G. Miquelard-Garnier, “Consolidation of continuous-carbon-fiber-reinforced PAEK composites: a review,” *Mater Today Commun*, vol. 32, p. 104036, 2022. https://doi.org/10.1016/j.mtcomm.2022.104036i
<figure><img src="image_601.png" /><figcaption>Figure 4 – For all manufacturing conditions investigated: a) ILSS data according to the void content, with black dashed lines representing the as-received tape void content b) ILSS data according to the degree of crystallinity measured by DSC and the loss factor tan δ assessed by DMA. Grey dashed lines corresponding to the as-received tape degree of crystallinity</figcaption></figure>

## Conclusion

In this work, the characterization of PEEK/CF laminates processed using several LATP manufacturing conditions was performed.

To observe the effect of the process temperature and the cooling rate inside the material, the two processing parameters that were varied are the laser setpoint temperature (LST) (350 and 450 °C), and the tool temperature (TT) (25 and 250 °C). Then the laminates void content and distribution, crystallinity, viscoelastic and shear behaviors were investigated.

Firstly, it was shown that the LST and the TT affect the overall laminate qualities. The ultrasonic signal amplitude was much high for laminates manufactured at 450 °C compared to laminates manufactured at 350°C. This trend was confirmed by microscopy observations of the cross-section of the laminates showing a higher void content for the latter.

In order to determine the voids repartition, the measurement of interply and intraply void content was carried out. Results highlighted the lack of intimate contact for the laminate processed at 350 °C on an unheated tool, resulting in interply void content of 4%. Although the laminate welded at 350 °C on a tool heated at 250 °C has a lower interply void content (0,8 %), it contains much more intraply voids (3 %) than the laminates manufactured at 450 °C (about 0,7 %), whatever the TT. It has been speculated that the deconsolidation by increasing the intraply void content is due to a growth of initial void content and the development of cavities around fiber due to relaxation of stress at the fiber-matrix interfaces during the heating phase.

Secondly, a correlation between void distribution, ILSS results and failure mode was demonstrated. For laminates processed at 350 °C on an unheated tool, showing a lack of intimate contact, the interlaminar failure mode is obviously governed by the presence of interply voids Unsurprisingly, this laminate has the lowest ILSS value.

Finally, the characterization of the degree of crystallinity by DSC and DMA allowed to link this property to the ILSS of the laminates. For well-consolidated laminate having mainly intralaminar voids, both the intraply void content and the crystallinity of the laminate seem to be related to the apparent ILSS performances and further investigation are in progress in order to clearly decorrelate both effects.

## References

[1] R. Arquier, I. Iliopoulos, G. Régnier, and G. Miquelard-Garnier, “Consolidation of continuous-carbon-fiber-reinforced PAEK composites: a review,” *Mater Today Commun*, vol. 32, p. 104036, 2022. https://doi.org/10.1016/j.mtcomm.2022.104036i
[2] W. Il Lee and G. S. Springer, "A Model of the Manufacturing Process of Thermoplastic Matrix Composites," *J Compos Mater*, vol. 21, no. 11, pp. 1017-1055, 1987. https://doi.org/10.1177/002199838702101103

[3] F. Yang and R. Pitchumani, "Healing of thermoplastic polymers at an interface under nonisothermal conditions," *Macromolecules*, vol. 35, no. 8, pp. 3213-3224, Apr. 2002. https://doi.org/10.1021/ma010858o

[4] F. Dave, M. M. Ali, R. Sherlock, A. Kandasami, and D. Tormey, "Laser transmission welding of semi-crystalline polymers and their composites: A critical review," *Polymers*, vol. 13, no. 5. MDPI AG, pp. 1-52, Mar. 01, 2021. https://doi.org/10.3390/polym13050675

[5] A. Yousefpour, M. Hojjati, and J. P. Immarigeon, "Fusion bonding/welding of thermoplastic composites," *Journal of Thermoplastic Composite Materials*, vol. 17, no. 4. pp. 303-341, Jul. 2004. https://doi.org/10.1177/0892705704045187

[6] T. K. Slange, L. L. Warnet, W. J. B. Grouve, and R. Akkerman, "Deconsolidation of C/PEEK blanks: on the role of prepreg, blank manufacturing method and conditioning," *Compos Part A Appl Sci Manuf*, vol. 113, pp. 189-199, Oct. 2018. https://doi.org/10.1016/j.compositesa.2018.06.034

[7] O. Çelik, A. Choudhary, D. Peeters, J. Teuwen, and C. Dransfeld, "Deconsolidation of thermoplastic prepreg tapes during rapid laser heating," *Compos Part A Appl Sci Manuf*, vol. 149, Oct. 2021. https://doi.org/10.1016/j.compositesa.2021.106575

[8] L. Amedewovo, L. Orgéas, B. de Parscau du Plessix, N. Lefevre, A. Levy, and S. Le Corre, "Deconsolidation of carbon fiber-reinforced PEKK laminates: 3D real-time in situ observation with synchrotron X-ray microtomography," *Compos Part A Appl Sci Manuf*, vol. 177, Feb. 2024. https://doi.org/10.1016/j.compositesa.2023.107917

[9] K. Yassin and M. Hojjati, "Processing of thermoplastic matrix composites through automated fiber placement and tape laying methods: A review," *Journal of Thermoplastic Composite Materials*, vol. 31, no. 12. SAGE Publications Ltd, pp. 1676-1725, Dec. 01, 2018. https://doi.org/10.1177/0892705717738305

[10] R. Arquier, H. Sabatier, I. Iliopoulos, G. Régnier, and G. Miquelard-Garnier, "Role of the inter-ply microstructure in the consolidation quality of high-performance thermoplastic composites," *Polym Compos*, 2023. https://doi.org/10.1002/pc.27847

[11] M. Bonmatin, F. Chabert, G. Bernhart, T. Cutard, and T. Djilali, "Ultrasonic welding of CF/PEEK composites: Influence of welding parameters on interfacial temperature profiles and mechanical properties," *Compos Part A Appl Sci Manuf*, vol. 162, Nov. 2022. https://doi.org/10.1016/j.compositesa.2022.107074

[12] C. Zhang et al., "Effect of porosity and crystallinity on mechanical properties of laser in-situ consolidation thermoplastic composites," *Polymer (Guildf)*, vol. 242, Mar. 2022. https://doi.org/10.1016/j.polymer.2022.124573

[13] J. Chen, K. Fu, and Y. Li, "Understanding processing parameter effects for carbon fibre reinforced thermoplastic composites manufactured by laser-assisted automated fibre placement (AFP)," *Compos Part A Appl Sci Manuf*, vol. 140, Jan. 2021. https://doi.org/10.1016/j.compositesa.2020.106160

[14] Z. Qureshi, T. Swait, R. Scaife, and H. M. El-Dessouky, "In situ consolidation of thermoplastic prepreg tape using automated tape placement technology: Potential and
[2] W. Il Lee and G. S. Springer, "A Model of the Manufacturing Process of Thermoplastic Matrix Composites," *J Compos Mater*, vol. 21, no. 11, pp. 1017-1055, 1987. https://doi.org/10.1177/002199838702101103

[3] F. Yang and R. Pitchumani, "Healing of thermoplastic polymers at an interface under nonisothermal conditions," *Macromolecules*, vol. 35, no. 8, pp. 3213-3224, Apr. 2002. https://doi.org/10.1021/ma010858o

[4] F. Dave, M. M. Ali, R. Sherlock, A. Kandasami, and D. Tormey, "Laser transmission welding of semi-crystalline polymers and their composites: A critical review," *Polymers*, vol. 13, no. 5. MDPI AG, pp. 1-52, Mar. 01, 2021. https://doi.org/10.3390/polym13050675

[5] A. Yousefpour, M. Hojjati, and J. P. Immarigeon, "Fusion bonding/welding of thermoplastic composites," *Journal of Thermoplastic Composite Materials*, vol. 17, no. 4. pp. 303-341, Jul. 2004. https://doi.org/10.1177/0892705704045187

[6] T. K. Slange, L. L. Warnet, W. J. B. Grouve, and R. Akkerman, "Deconsolidation of C/PEEK blanks: on the role of prepreg, blank manufacturing method and conditioning," *Compos Part A Appl Sci Manuf*, vol. 113, pp. 189-199, Oct. 2018. https://doi.org/10.1016/j.compositesa.2018.06.034

[7] O. Çelik, A. Choudhary, D. Peeters, J. Teuwen, and C. Dransfeld, "Deconsolidation of thermoplastic prepreg tapes during rapid laser heating," *Compos Part A Appl Sci Manuf*, vol. 149, Oct. 2021. https://doi.org/10.1016/j.compositesa.2021.106575

[8] L. Amedewovo, L. Orgéas, B. de Parscau du Plessix, N. Lefevre, A. Levy, and S. Le Corre, "Deconsolidation of carbon fiber-reinforced PEKK laminates: 3D real-time in situ observation with synchrotron X-ray microtomography," *Compos Part A Appl Sci Manuf*, vol. 177, Feb. 2024. https://doi.org/10.1016/j.compositesa.2023.107917

[9] K. Yassin and M. Hojjati, "Processing of thermoplastic matrix composites through automated fiber placement and tape laying methods: A review," *Journal of Thermoplastic Composite Materials*, vol. 31, no. 12. SAGE Publications Ltd, pp. 1676-1725, Dec. 01, 2018. https://doi.org/10.1177/0892705717738305

[10] R. Arquier, H. Sabatier, I. Iliopoulos, G. Régnier, and G. Miquelard-Garnier, "Role of the inter-ply microstructure in the consolidation quality of high-performance thermoplastic composites," *Polym Compos*, 2023. https://doi.org/10.1002/pc.27847

[11] M. Bonmatin, F. Chabert, G. Bernhart, T. Cutard, and T. Djilali, "Ultrasonic welding of CF/PEEK composites: Influence of welding parameters on interfacial temperature profiles and mechanical properties," *Compos Part A Appl Sci Manuf*, vol. 162, Nov. 2022. https://doi.org/10.1016/j.compositesa.2022.107074

[12] C. Zhang et al., "Effect of porosity and crystallinity on mechanical properties of laser in-situ consolidation thermoplastic composites," *Polymer (Guildf)*, vol. 242, Mar. 2022. https://doi.org/10.1016/j.polymer.2022.124573

[13] J. Chen, K. Fu, and Y. Li, "Understanding processing parameter effects for carbon fibre reinforced thermoplastic composites manufactured by laser-assisted automated fibre placement (AFP)," *Compos Part A Appl Sci Manuf*, vol. 140, Jan. 2021. https://doi.org/10.1016/j.compositesa.2020.106160

[14] Z. Qureshi, T. Swait, R. Scaife, and H. M. El-Dessouky, "In situ consolidation of thermoplastic prepreg tape using automated tape placement technology: Potential and
possibilities,” *Compos B Eng*, vol. 66, pp. 255-267, 2014.
https://doi.org/10.1016/j.compositesb.2014.05.025

[15] A. J. Comer et al., "Mechanical characterisation of carbon fibre-PEEK manufactured by laser-assisted automated-tape-placement and autoclave," *Compos Part A Appl Sci Manuf*, vol. 69, pp. 10-20, Feb. 2015. https://doi.org/10.1016/j.compositesa.2014.10.003

[16] D. J. Blundell and B. N. Osborn, "The morphology of poly(aryl-ether-ether-ketone)."

[17] O. Çelik, D. Peeters, C. Dransfeld, and J. Teuwen, "Intimate contact development during laser assisted fiber placement: Microstructure and effect of process parameters," *Compos Part A Appl Sci Manuf*, vol. 134, Jul. 2020. https://doi.org/10.1016/j.compositesa.2020.105888

[18] F. O. Sonmez and H. T. Hahn, "Analysis of the on-line consolidation process in thermoplastic composite tape placement," *Journal of Thermoplastic Composite Materials*, vol. 10, no. 6, pp. 543-572, 1997. https://doi.org/10.1177/089270579701000604

[19] C. M. Stokes-Griffin and P. Compston, "Investigation of sub-melt temperature bonding of carbon-fibre/PEEK in an automated laser tape placement process," *Compos Part A Appl Sci Manuf*, vol. 84, pp. 17-25, May 2016. https://doi.org/10.1016/j.compositesa.2015.12.019

[20] M. A. Khan, P. Mitschang, and R. Schledjewski, "Identification of some optimal parameters to achieve higher laminate quality through tape placement process," in *Advances in Polymer Technology*, Jun. 2010, pp. 98-111. https://doi.org/10.1002/adv.20177

[21] S. L. Gao and J. K. Kim, "Correlation among crystalline morphology of PEEK, interface bond strength, and in-plane mechanical properties of carbon/PEEK composites," *J Appl Polym Sci*, vol. 84, no. 6, pp. 1155-1167, Feb. 2002. https://doi.org/10.1002/app.10406

[22] D. Ray et al., "Fracture toughness of carbon fiber/polyether ether ketone composites manufactured by autoclave and laser-assisted automated tape placement," *J Appl Polym Sci*, vol. 132, no. 11, Mar. 2015. https://doi.org/10.1002/app.41643

[23] A. Maria El Bayssari, "Study and comprehension of the residual stresses and strains state in thermoplastic composite materials manufactured by tape placement." [Online]. Available: https://theses.hal.science/tel-03888045

[24] P. A. Rodriguez and D. W. Radford, "A DMA-Based Approach to Quality Evaluation of Digitally Manufactured Continuous Fiber-Reinforced Composites from Thermoplastic Commingled Tow," *Journal of Composites Science*, vol. 6, no. 2, Feb. 2022. https://doi.org/10.3390/jcs6020061

[25] X. Tardif et al., "Experimental study of crystallization of PolyEtherEtherKetone (PEEK) over a large temperature range using a nano-calorimeter," *Polym Test*, vol. 36, pp. 10-19, 2014. https://doi.org/10.1016/j.polymtesting.2014.03.013

[26] S. L. Gao and J. K. Kim, "Correlation among crystalline morphology of PEEK, interface bond strength, and in-plane mechanical properties of carbon/PEEK composites," *J Appl Polym Sci*, vol. 84, no. 6, pp. 1155-1167, Feb. 2002. https://doi.org/10.1002/app.10406
possibilities,” *Compos B Eng*, vol. 66, pp. 255-267, 2014.
https://doi.org/10.1016/j.compositesb.2014.05.025

[15] A. J. Comer et al., "Mechanical characterisation of carbon fibre-PEEK manufactured by laser-assisted automated-tape-placement and autoclave," *Compos Part A Appl Sci Manuf*, vol. 69, pp. 10-20, Feb. 2015. https://doi.org/10.1016/j.compositesa.2014.10.003

[16] D. J. Blundell and B. N. Osborn, "The morphology of poly(aryl-ether-ether-ketone)."

[17] O. Çelik, D. Peeters, C. Dransfeld, and J. Teuwen, "Intimate contact development during laser assisted fiber placement: Microstructure and effect of process parameters," *Compos Part A Appl Sci Manuf*, vol. 134, Jul. 2020. https://doi.org/10.1016/j.compositesa.2020.105888

[18] F. O. Sonmez and H. T. Hahn, "Analysis of the on-line consolidation process in thermoplastic composite tape placement," *Journal of Thermoplastic Composite Materials*, vol. 10, no. 6, pp. 543-572, 1997. https://doi.org/10.1177/089270579701000604

[19] C. M. Stokes-Griffin and P. Compston, "Investigation of sub-melt temperature bonding of carbon-fibre/PEEK in an automated laser tape placement process," *Compos Part A Appl Sci Manuf*, vol. 84, pp. 17-25, May 2016. https://doi.org/10.1016/j.compositesa.2015.12.019

[20] M. A. Khan, P. Mitschang, and R. Schledjewski, "Identification of some optimal parameters to achieve higher laminate quality through tape placement process," in *Advances in Polymer Technology*, Jun. 2010, pp. 98-111. https://doi.org/10.1002/adv.20177

[21] S. L. Gao and J. K. Kim, "Correlation among crystalline morphology of PEEK, interface bond strength, and in-plane mechanical properties of carbon/PEEK composites," *J Appl Polym Sci*, vol. 84, no. 6, pp. 1155-1167, Feb. 2002. https://doi.org/10.1002/app.10406

[22] D. Ray et al., "Fracture toughness of carbon fiber/polyether ether ketone composites manufactured by autoclave and laser-assisted automated tape placement," *J Appl Polym Sci*, vol. 132, no. 11, Mar. 2015. https://doi.org/10.1002/app.41643

[23] A. Maria El Bayssari, "Study and comprehension of the residual stresses and strains state in thermoplastic composite materials manufactured by tape placement." [Online]. Available: https://theses.hal.science/tel-03888045

[24] P. A. Rodriguez and D. W. Radford, "A DMA-Based Approach to Quality Evaluation of Digitally Manufactured Continuous Fiber-Reinforced Composites from Thermoplastic Commingled Tow," *Journal of Composites Science*, vol. 6, no. 2, Feb. 2022. https://doi.org/10.3390/jcs6020061

[25] X. Tardif et al., "Experimental study of crystallization of PolyEtherEtherKetone (PEEK) over a large temperature range using a nano-calorimeter," *Polym Test*, vol. 36, pp. 10-19, 2014. https://doi.org/10.1016/j.polymtesting.2014.03.013

[26] S. L. Gao and J. K. Kim, "Correlation among crystalline morphology of PEEK, interface bond strength, and in-plane mechanical properties of carbon/PEEK composites," *J Appl Polym Sci*, vol. 84, no. 6, pp. 1155-1167, Feb. 2002. https://doi.org/10.1002/app.10406
# Draping of biaxial non-crimp fabric on hemispherical shape

ZHENG Ruochen¹, NAOUAR Naim¹, a *, SCHÄFER Bastian², PLATZER Auriane¹, COLMARS Julien¹, KÄRGER Luise², BOISSE Philippe¹

¹Univ Lyon, INSA-Lyon, CNRS UMR5259, LaMCoS, F-69621, France

²Karlsruhe Institute of Technology (KIT), Institute of Vehicle System Technology (FAST), Karlsruhe, Germany

a naim.naouar@insa-lyon.fr

**Keywords:** Biaxial NCF, Hyperelastic, Meso-Scale Model, Composite Forming

**Abstract.** The experiment and simulation of biaxial non-crimp fabric draping process is investigated. The finite element model is formulated employing a mesoscopic approach, wherein each individual fiber yarn and stitch is treated as a continuous medium, modeled separately for a more nuanced representation. The hemispherical punch shape for the draping is selected as it is the most commonly used academic shape with a rather simple double-curved geometry. The deformed shape, material draw-in and local shear angle between the experimental and numerical results are compared and discussed.

**Introduction**

Non-crimp-fabric (NCF) composite reinforcements are one of the most promising types of reinforcements for the manufacturing of composite parts in both the automotive and aeronautical industries [1,2,3]. They consist of multiple layers of unidirectional plies bound together by stitches that pass through their thickness. Fibers in NCFs are straight, without weakening undulations like in woven fabrics [4]. This type of reinforcement offers a significant advantage in achieving mechanical stiffness greater than that of a fabric with the same thickness.

The need for higher production rates and parts with better-controlled and optimized characteristics increase the difficulty of using NCFs for large-series production and give reasons for an improved virtual validation and process design. Their forming process involves shaping flat 2D fabric plies into complex 3D shapes using an external force through the punch [5]. Blank holders are generally used during this step to tension the fabric and delay the appearance of wrinkles [6]. A simulation code allows for numerical optimization of molds and reinforcements, thus avoiding a costly trial-and-error phase during the design of composite parts [7].

Significant research efforts are devoted to the behavior of NCF and the simulation of its deformation. Its deformation mechanisms involved are specific and are studied in [8,10]. The through thickness compaction behavior of uni- and bidirectional NCF are investigated in [9]. Macroscopic approach is commonly used to simulate NCF forming process [11,12,13,14]. However, this approach may face challenges in identifying certain local defects, particularly gapping, where adjacent yarns separate, leaving an empty zone without fibers. Detection of these gapping defects is typically achieved through numerical analysis of the in-plane transverse strain for unidirectional NCF at the macroscale [13,14]. An alternative approach involves employing mesoscopic simulation approach, wherein each fiber yarn is considered as solid medium and the surrounded stitches are modelled by finite beam or bar elements [15,16,17].

A mesoscopic approach for biaxial NCF is introduced and validated using a unit cell model [17]. Subsequently, this approach is applied to larger sample sizes comprising multiple unit cells for forming simulations in this study. The selection of the hemispherical punch shape is based on its simplicity as a double-curved geometry with a smooth curvature, suitable for fabric draping.

<figure><img src="image_591.png" /></figure>
# Draping of biaxial non-crimp fabric on hemispherical shape

ZHENG Ruochen¹, NAOUAR Naim¹, a *, SCHÄFER Bastian², PLATZER Auriane¹, COLMARS Julien¹, KÄRGER Luise², BOISSE Philippe¹

¹Univ Lyon, INSA-Lyon, CNRS UMR5259, LaMCoS, F-69621, France

²Karlsruhe Institute of Technology (KIT), Institute of Vehicle System Technology (FAST), Karlsruhe, Germany

a.naim.naouar@insa-lyon.fr

**Keywords:** Biaxial NCF, Hyperelastic, Meso-Scale Model, Composite Forming

**Abstract.** The experiment and simulation of biaxial non-crimp fabric draping process is investigated. The finite element model is formulated employing a mesoscopic approach, wherein each individual fiber yarn and stitch is treated as a continuous medium, modeled separately for a more nuanced representation. The hemispherical punch shape for the draping is selected as it is the most commonly used academic shape with a rather simple double-curved geometry. The deformed shape, material draw-in and local shear angle between the experimental and numerical results are compared and discussed.

**Introduction**

Non-crimp-fabric (NCF) composite reinforcements are one of the most promising types of reinforcements for the manufacturing of composite parts in both the automotive and aeronautical industries [1,2,3]. They consist of multiple layers of unidirectional plies bound together by stitches that pass through their thickness. Fibers in NCFs are straight, without weakening undulations like in woven fabrics [4]. This type of reinforcement offers a significant advantage in achieving mechanical stiffness greater than that of a fabric with the same thickness.

The need for higher production rates and parts with better-controlled and optimized characteristics increase the difficulty of using NCFs for large-series production and give reasons for an improved virtual validation and process design. Their forming process involves shaping flat 2D fabric plies into complex 3D shapes using an external force through the punch [5]. Blank holders are generally used during this step to tension the fabric and delay the appearance of wrinkles [6]. A simulation code allows for numerical optimization of molds and reinforcements, thus avoiding a costly trial-and-error phase during the design of composite parts [7].

Significant research efforts are devoted to the behavior of NCF and the simulation of its deformation. Its deformation mechanisms involved are specific and are studied in [8,10]. The through thickness compaction behavior of uni- and bidirectional NCF are investigated in [9]. Macroscopic approach is commonly used to simulate NCF forming process [11,12,13,14]. However, this approach may face challenges in identifying certain local defects, particularly gapping, where adjacent yarns separate, leaving an empty zone without fibers. Detection of these gapping defects is typically achieved through numerical analysis of the in-plane transverse strain for unidirectional NCF at the macroscale [13,14]. An alternative approach involves employing mesoscopic simulation approach, wherein each fiber yarn is considered as solid medium and the surrounded stitches are modelled by finite beam or bar elements [15,16,17].

A mesoscopic approach for biaxial NCF is introduced and validated using a unit cell model [17]. Subsequently, this approach is applied to larger sample sizes comprising multiple unit cells for forming simulations in this study. The selection of the hemispherical punch shape is based on its simplicity as a double-curved geometry with a smooth curvature, suitable for fabric draping.

<figure><img src="image_602.png" /></figure>
Despite the simplicity, in-plane shear deformation and potential defects like gapping or wrinkles can still occur. The experimental and numerical simulation results of draping of biaxial NCF are subsequently compared and discussed.

## Materials

The material used in this study is a warp-knitted 0°/90° carbon fiber biaxial NCF with polyester tricot stitches produced by Zoltek. The two layers are bound together during the production process with loop formation in the warp direction. The photographs of bi-axial NCF on both sides are shown in Fig. 1.

<figure><img src="image_592.png" /><figcaption>Fig. 1. 0°/90° tricot-stitch biaxial non-crimp fabric architecture (a) warp fiber yarn view with a tricot stitch pattern (b) weft fiber yarn view with a chain stitch pattern</figcaption></figure>

## Mesoscopic simulation approach

**Geometrical model.** At the mesoscopic scale, the geometric modeling of biaxial NCF involves the independent representation of stitches and fiber yarns. Prior studies have assumed various cross-sectional shapes for fiber yarns, such as circular, flat, elliptic, or biconvex [18, 19]. In this study, fiber yarns are initially modeled with oval cross-sections and assumed to be straight along the fiber orientation. Node positions are determined using a 3D elliptic cylinder equation in Matlab, accounting for mesh size, and eight nodes form a solid element. The nodes along a single loop of stitch are calculated using the equilibrium equation of the elliptical fiber yarn. Following the assembly of fiber yarns and stitches, a simulation of stitch shrinkage is conducted to tighten the initially loose structure and establish effective interaction between yarn systems. The mesoscopic geometrical model of biaxial NCF is presented in Figure 2a and b.

<figure><img src="image_593.png" /><figcaption>Fig. 2. Geometrical model of biaxial NCF (a) warp yarn view (b) weft yarn view</figcaption></figure>

**Constitutive model.** The polyester stitch is modeled as a linear elastic material, its Young's modulus is characterized through tensioning one single stitch and its bending stiffness is determined using a cantilever bending test, a well-established method utilized in previous studies [20,21,22].

The constitutive law utilized for the carbon fiber yarn is a hyperelastic model developed by A. Charmetant [23]. The stresses are derived from a strain energy potential that describes the mechanical behaviour of a single carbon fibre yarn. This model accounts for four deformation modes based on the assumption that the fibre yarn is transversely isotropic: elongation along the
Despite the simplicity, in-plane shear deformation and potential defects like gapping or wrinkles can still occur. The experimental and numerical simulation results of draping of biaxial NCF are subsequently compared and discussed.

## Materials

The material used in this study is a warp-knitted 0°/90° carbon fiber biaxial NCF with polyester tricot stitches produced by Zoltek. The two layers are bound together during the production process with loop formation in the warp direction. The photographs of bi-axial NCF on both sides are shown in Fig. 1.

<figure><img src="image_603.png" /><figcaption>Fig. 1. 0°/90° tricot-stitch biaxial non-crimp fabric architecture (a) warp fiber yarn view with a tricot stitch pattern (b) weft fiber yarn view with a chain stitch pattern</figcaption></figure>

## Mesoscopic simulation approach

**Geometrical model.** At the mesoscopic scale, the geometric modeling of biaxial NCF involves the independent representation of stitches and fiber yarns. Prior studies have assumed various cross-sectional shapes for fiber yarns, such as circular, flat, elliptic, or biconvex [18, 19]. In this study, fiber yarns are initially modeled with oval cross-sections and assumed to be straight along the fiber orientation. Node positions are determined using a 3D elliptic cylinder equation in Matlab, accounting for mesh size, and eight nodes form a solid element. The nodes along a single loop of stitch are calculated using the equilibrium equation of the elliptical fiber yarn. Following the assembly of fiber yarns and stitches, a simulation of stitch shrinkage is conducted to tighten the initially loose structure and establish effective interaction between yarn systems. The mesoscopic geometrical model of biaxial NCF is presented in Figure 2a and b.

<figure><img src="image_604.png" /><figcaption>Fig. 2. Geometrical model of biaxial NCF (a) warp yarn view (b) weft yarn view</figcaption></figure>

**Constitutive model.** The polyester stitch is modeled as a linear elastic material, its Young's modulus is characterized through tensioning one single stitch and its bending stiffness is determined using a cantilever bending test, a well-established method utilized in previous studies [20,21,22].

The constitutive law utilized for the carbon fiber yarn is a hyperelastic model developed by A. Charmetant [23]. The stresses are derived from a strain energy potential that describes the mechanical behaviour of a single carbon fibre yarn. This model accounts for four deformation modes based on the assumption that the fibre yarn is transversely isotropic: elongation along the
fiber direction, cross-sectional compaction, transverse shear (cross-sectional distortion), and longitudinal shear along the fiber direction.

<figure><img src="image_594.png" /><figcaption>Fig. 3. Four deformation modes of fiber yarn (a) elongation (b) compaction of cross section (c) transverse shear (d) longitudinal shear</figcaption></figure>

The hyperelastic equation defines the stress-strain relation for the solid by specifying its strain energy density w as a function of deformation gradient tensor:

$$w = w(\underline{F}) \qquad (1)$$

The four deformation modes are translated in the form of combinations of physical invariants, $I_{elong}$, $I_{comp}$, $I_{dist}$, $I_{sh}$, linked to the invariants of the right Cauchy-Green tensor $\underline{C}$.

These physically based invariants are introduced in [23] and are expressed as:

$$I_{elong} = \frac{1}{2} \ln I_4, \quad I_{comp} = \frac{1}{4} \ln(\frac{l_3}{l_4}), \quad I_{dist} = \frac{1}{2} \ln(\frac{l_1 l_4 - l_5}{2\sqrt{l_3 l_4}} + \sqrt{(\frac{l_1 l_4 - l_5}{2\sqrt{l_3 l_4}})^2 - 1}), \quad I_{sh} = \frac{\sqrt{l_5}}{l_4^2} - 1 \quad (2)$$

Where $I_1$ to $I_5$ are classical invariants expressed by the right Cauchy Green strain tensor $\underline{C}$:

$$I_1 = \text{trace}(\underline{C}), \quad I_2 = \frac{1}{2}(\text{trace}(\underline{C})^2 - \text{trace}(\underline{C}^2)), \quad I_3 = \det(\underline{C}), \\ I_4 = \underline{C} : \underline{M}, \quad I_5 = \underline{C}^2 : \underline{M} \qquad (3)$$

Where $\underline{M}$ is a structural tensor defined by a unit vector of fiber direction $\underline{M}$:

$$\underline{M} = \underline{M} \otimes \underline{M} \qquad (4)$$

Then the deformation energy is assumed to be the sum of the energies of these four deformation modes:

$$w(\underline{F}) = w_{elong}(I_{elong}) + w_{comp}(I_{comp}) + w_{dist}(I_{dist}) + w_{sh}(I_{sh}) \qquad (5)$$

The second Piola-Kirchhoff stress tensor is defined as:

$$\underline{S} = 2 \frac{\partial w}{\partial \underline{C}} = 2 \left( \frac{\partial w_{elong}}{\partial I_{elong}} \frac{\partial I_{elong}}{\partial \underline{C}} + \frac{\partial w_{comp}}{\partial I_{comp}} \frac{\partial I_{comp}}{\partial \underline{C}} + \frac{\partial w_{dis}}{\partial I_{dis}} \frac{\partial I_{dis}}{\partial \underline{C}} + \frac{\partial w_{sh}}{\partial I_{sh}} \frac{\partial I_{sh}}{\partial \underline{C}} \right) \qquad (6)$$

The material parameters used for the stitches and yarns are shown in Table 1:
fiber direction, cross-sectional compaction, transverse shear (cross-sectional distortion), and longitudinal shear along the fiber direction.

<figure><img src="image_605.png" /><figcaption>Fig. 3. Four deformation modes of fiber yarn (a) elongation (b) compaction of cross section (c) transverse shear (d) longitudinal shear</figcaption></figure>

The hyperelastic equation defines the stress-strain relation for the solid by specifying its strain energy density w as a function of deformation gradient tensor:

$$w = w(\underline{F}) \qquad (1)$$

The four deformation modes are translated in the form of combinations of physical invariants, $I_{elong}$, $I_{comp}$, $I_{dist}$, $I_{sh}$, linked to the invariants of the right Cauchy-Green tensor $\underline{C}$.

These physically based invariants are introduced in [23] and are expressed as:

$$I_{elong} = \frac{1}{2} \ln I_4, \quad I_{comp} = \frac{1}{4} \ln(\frac{I_3}{I_4}), \quad I_{dist} = \frac{1}{2} \ln(\frac{I_1 I_4 - I_5}{2\sqrt{I_3 I_4}} + \sqrt{(\frac{I_1 I_4 - I_5}{2\sqrt{I_3 I_4}})^2 - 1}), \quad I_{sh} = \frac{\sqrt{I_5}}{I_4^2 - 1} \quad (2)$$

Where $I_1$ to $I_5$ are classical invariants expressed by the right Cauchy Green strain tensor $\underline{C}$:

$$I_1 = \text{trace}(\underline{C}), \quad I_2 = \frac{1}{2}(\text{trace}(\underline{C})^2 - \text{trace}(\underline{C}^2)), \quad I_3 = \det(\underline{C}), \\ I_4 = \underline{C} : \underline{M}, \quad I_5 = \underline{C}^2 : \underline{M} \qquad (3)$$

Where $\underline{M}$ is a structural tensor defined by a unit vector of fiber direction $\underline{M}$:

$$\underline{M} = \underline{M} \otimes \underline{M} \qquad (4)$$

Then the deformation energy is assumed to be the sum of the energies of these four deformation modes:

$$w(\underline{F}) = w_{elong}(I_{elong}) + w_{comp}(I_{comp}) + w_{dist}(I_{dist}) + w_{sh}(I_{sh}) \qquad (5)$$

The second Piola-Kirchhoff stress tensor is defined as:

$$\underline{S} = 2 \frac{\partial w}{\partial \underline{C}} = 2 \left( \frac{\partial w_{elong}}{\partial I_{elong}} \frac{\partial I_{elong}}{\partial \underline{C}} + \frac{\partial w_{comp}}{\partial I_{comp}} \frac{\partial I_{comp}}{\partial \underline{C}} + \frac{\partial w_{dis}}{\partial I_{dis}} \frac{\partial I_{dis}}{\partial \underline{C}} + \frac{\partial w_{sh}}{\partial I_{sh}} \frac{\partial I_{sh}}{\partial \underline{C}} \right) \qquad (6)$$

The material parameters used for the stitches and yarns are shown in Table 1:
<table><caption>Table 1. Parameters of the constitutive model for yarn and stitch</caption><thead><tr><td>Symbol</td><td>Physical interpretation</td><td>Value</td></tr></thead><tbody><tr><td>K<sub>elong</sub></td><td>Tensile stiffness of fiber yarn</td><td>108500N</td></tr><tr><td>K<sub>comp</sub></td><td>Compaction stiffness of fiber yarn</td><td>1.25MPa</td></tr><tr><td>p</td><td>Compaction exponent</td><td>1.84</td></tr><tr><td>K<sub>dist</sub></td><td>Transverse shear stiffness of fiber yarn</td><td>0.6MPa</td></tr><tr><td>K<sub>sh</sub></td><td>Longitudinal shear stiffness of fiber yarn</td><td>2.2MPa</td></tr><tr><td>E<sub>s</sub></td><td>Tensile stiffness of stitch</td><td>350MPa</td></tr><tr><td>G<sub>s</sub></td><td>Bending stiffness of stitch</td><td>0.00056N mm<sup>2</sup></td></tr></tbody></table>

## Experiments on hemispherical forming

The hemispherical forming experiments are completed in LaMCoS laboratory. The experimental platform is shown in Fig. 4a. It mainly consists of the motion control system, camera, mirror, punch, blank holder, and die. The blank holder and die are made transparent to observe the material deformation during the draping process. The diameter of the punch is 150 mm and of the hole in the blank holder and die is 160 mm. Two cameras are used: one is positioned above the machine, capturing half of the sample (fixed with the machine bar, which does not move); the other camera is placed at a distance from the machine and in a horizontal orientation, allowing it to capture photos of the lower surface of the specimen using a mirror arranged at a 45° angle under the transparent tooling. The Zwick 100KN traction machine controls the punch displacement (75 mm), with a motion speed 25 mm · min<sup>-1</sup>.

<figure><img src="image_595.png" /><figcaption>Fig. 4. Hemispherical forming experiments (a) Schema of Forming experimental platform (b) White marker painting</figcaption></figure>

The sample used consists of one layer of biaxial NCF with dimensions of 300 mm by 300 mm, corresponding to a thickness of 0.8 mm. The specimen is initially in a square shape and placed on the die. The fiber yarn is oriented parallel to the edge of the square die. Three experimental forming
<table><caption>Table 1. Parameters of the constitutive model for yarn and stitch</caption><thead><tr><td>Symbol</td><td>Physical interpretation</td><td>Value</td></tr></thead><tbody><tr><td>K<sub>elong</sub></td><td>Tensile stiffness of fiber yarn</td><td>108500N</td></tr><tr><td>K<sub>comp</sub></td><td>Compaction stiffness of fiber yarn</td><td>1.25MPa</td></tr><tr><td>p</td><td>Compaction exponent</td><td>1.84</td></tr><tr><td>K<sub>dist</sub></td><td>Transverse shear stiffness of fiber yarn</td><td>0.6MPa</td></tr><tr><td>K<sub>sh</sub></td><td>Longitudinal shear stiffness of fiber yarn</td><td>2.2MPa</td></tr><tr><td>E<sub>s</sub></td><td>Tensile stiffness of stitch</td><td>350MPa</td></tr><tr><td>G<sub>s</sub></td><td>Bending stiffness of stitch</td><td>0.00056N mm<sup>2</sup></td></tr></tbody></table>

## Experiments on hemispherical forming

The hemispherical forming experiments are completed in LaMCoS laboratory. The experimental platform is shown in Fig. 4a. It mainly consists of the motion control system, camera, mirror, punch, blank holder, and die. The blank holder and die are made transparent to observe the material deformation during the draping process. The diameter of the punch is 150 mm and of the hole in the blank holder and die is 160 mm. Two cameras are used: one is positioned above the machine, capturing half of the sample (fixed with the machine bar, which does not move); the other camera is placed at a distance from the machine and in a horizontal orientation, allowing it to capture photos of the lower surface of the specimen using a mirror arranged at a 45° angle under the transparent tooling. The Zwick 100KN traction machine controls the punch displacement (75 mm), with a motion speed 25 mm · min<sup>-1</sup>.

<figure><img src="image_606.png" /><figcaption>Fig. 4. Hemispherical forming experiments (a) Schema of Forming experimental platform (b) White marker painting</figcaption></figure>

The sample used consists of one layer of biaxial NCF with dimensions of 300 mm by 300 mm, corresponding to a thickness of 0.8 mm. The specimen is initially in a square shape and placed on the die. The fiber yarn is oriented parallel to the edge of the square die. Three experimental forming
tests were carried out, two with white marker points and one without white marker points. White marker points are drawn on the bottom layers, as shown in Fig. 4b. They are in equal interval at 10 mm, and are 10 mm away from the sample boundary. This marker-based tracking approach is used to get the material deformation in different positions and calculate the shear angle when the material is deformed.

Simulation on hemispherical forming

The forming tests are numerically simulated using ABAQUS/Explicit. Due to the symmetry of the hemispherical punch, the biaxial NCF are modeled using a quarter-sized sample to minimize computation costs. The quarter-sized model consists of 57,840 solid elements for warp and weft fiber yarns and 58,441 beam elements for stitches. The model for the punch, die and blank holder have the same dimensions as those used in the experimental tests. In the forming tests, these tools experience minimal deformations; therefore, they are modeled as rigid bodies (ABAQUS R3D4 elements). General friction law in ABAQUS is used for all the contact surfaces with coefficient 0.2. The die and blank holder are fixed in their positions throughout the simulation, while a draping displacement is prescribed for the punch. Coulomb friction contact is employed for the interaction between the tools and the fabric. The draping displacement is also set as 75 mm. The simulation is launched on the cluster with 20 CPU cores. The computation takes 6 days. Fig. 5a and b show the final deformed shape of biaxial NCF hemispherical forming simulation.

<figure><img src="image_596.png" /><figcaption>Fig. 5. Draping of biaxial NCF on hemispherical shape. Simulation results of (a) weft fiber yarn view and (b) warp fiber yarn view; Experimental results of (c) weft fiber yarn view and (d) warp fiber yarn view.</figcaption></figure>

A comparison of the deformations reveals that the simulation produces an edge shape of the reinforcement resembling the one obtained experimentally. The outer contour of the simulation results can be drawn through the image processing on this 2D view and it can be observed that the simulation exhibits a similar material draw-in as the experimental result, as shown in Fig. 6.
tests were carried out, two with white marker points and one without white marker points. White marker points are drawn on the bottom layers, as shown in Fig. 4b. They are in equal interval at 10 mm, and are 10 mm away from the sample boundary. This marker-based tracking approach is used to get the material deformation in different positions and calculate the shear angle when the material is deformed.

## Simulation on hemispherical forming

The forming tests are numerically simulated using ABAQUS/Explicit. Due to the symmetry of the hemispherical punch, the biaxial NCF are modeled using a quarter-sized sample to minimize computation costs. The quarter-sized model consists of 57,840 solid elements for warp and weft fiber yarns and 58,441 beam elements for stitches. The model for the punch, die and blank holder have the same dimensions as those used in the experimental tests. In the forming tests, these tools experience minimal deformations; therefore, they are modeled as rigid bodies (ABAQUS R3D4 elements). General friction law in ABAQUS is used for all the contact surfaces with coefficient 0.2. The die and blank holder are fixed in their positions throughout the simulation, while a draping displacement is prescribed for the punch. Coulomb friction contact is employed for the interaction between the tools and the fabric. The draping displacement is also set as 75 mm. The simulation is launched on the cluster with 20 CPU cores. The computation takes 6 days. Fig. 5a and b show the final deformed shape of biaxial NCF hemispherical forming simulation.

<figure><img src="image_607.png" /><figcaption>Fig. 5. Draping of biaxial NCF on hemispherical shape. Simulation results of (a) weft fiber yarn view and (b) warp fiber yarn view; Experimental results of (c) weft fiber yarn view and (d) warp fiber yarn view.</figcaption></figure>

A comparison of the deformations reveals that the simulation produces an edge shape of the reinforcement resembling the one obtained experimentally. The outer contour of the simulation results can be drawn through the image processing on this 2D view and it can be observed that the simulation exhibits a similar material draw-in as the experimental result, as shown in Fig. 6.
<figure><img src="image_597.png" /><figcaption>Fig. 6. Comparison of material drawn-in between experiments (red line) and simulation (blue line)</figcaption></figure>

Another requirement for the simulation is its ability to accurately trace the yarn direction in the final composite part. The advantage of the mesoscopic model is that the two fiber orientations can be directly visualized and extracted from the numerical results. These directions are then employed to calculate the shear angles, which are subsequently compared with the experimental results. Since the structural integrity of biaxial NCF is enhanced through two fiber orientations and is further secured by stitches, only minimal gapping is noticeable on a smooth hemisphere shape and no gapping is observed in the simulation results.

## Conclusion

This study explores experimental forming tests on biaxial NCF utilizing a hemispherical punch shape. Subsequently, numerical simulations of the forming process are conducted employing a mesoscopic finite element model for biaxial NCF. The comparison of deformed shapes, material draw-in, and local shear angles between experimental and numerical results serves to validate the model's accuracy. No gapping defects are detected since hemispherical shape is a rather simple double-curved geometry with a smooth curvature. Further investigations into challenging shapes, such as the square box or tetrahedron, using the mesoscopic simulation approach can shed light on the occurrence of gapping defects.

## References

[1] S. Lomov, 4 - understanding and modelling the effect of stitching on the geometry of non-crimp fabrics, in: S. V. Lomov (Eds.), Non-Crimp Fabric Composites, Woodhead Publishing Series in Composites Science and Engineering, Woodhead Publishing, 2011, pp. 84–102.
https://doi.org/10.1533/9780857092533.1.84

[2] S. Advani, E. Sozer, L. Mishnaevsky Jr, Pocess modeling in composite manufacturing, pplied Mechanics Reviews. 56 (2003) B69-B70. https://doi.org/10.1115/1.1584418

[3] S. Sihn, R. Y. Kim, K. Kawabe, S. W. Tsai, Eerimental studies of thin-ply laminated composites, Composites Science and Technology. 67 (2007) 996-1008.
https://doi.org/10.1016/j.compscitech.2006.06.008

[4] A. Schnabel, T. Gries, Production of non-crimp fabrics for composites, in: Stepan V. Lomov (Eds.), Non-Crimp Fabric Composites, Woodhead Publishing, 2011, pp. 3-41.
https://doi.org/10.1533/9780857092533.1.3
<figure><img src="image_608.png" /><figcaption>Fig. 6. Comparison of material drawn-in between experiments (red line) and simulation (blue line)</figcaption></figure>

Another requirement for the simulation is its ability to accurately trace the yarn direction in the final composite part. The advantage of the mesoscopic model is that the two fiber orientations can be directly visualized and extracted from the numerical results. These directions are then employed to calculate the shear angles, which are subsequently compared with the experimental results. Since the structural integrity of biaxial NCF is enhanced through two fiber orientations and is further secured by stitches, only minimal gapping is noticeable on a smooth hemisphere shape and no gapping is observed in the simulation results.

## Conclusion

This study explores experimental forming tests on biaxial NCF utilizing a hemispherical punch shape. Subsequently, numerical simulations of the forming process are conducted employing a mesoscopic finite element model for biaxial NCF. The comparison of deformed shapes, material draw-in, and local shear angles between experimental and numerical results serves to validate the model's accuracy. No gapping defects are detected since hemispherical shape is a rather simple double-curved geometry with a smooth curvature. Further investigations into challenging shapes, such as the square box or tetrahedron, using the mesoscopic simulation approach can shed light on the occurrence of gapping defects.

## References

[1] S. Lomov, 4 - understanding and modelling the effect of stitching on the geometry of non-crimp fabrics, in: S. V. Lomov (Eds.), Non-Crimp Fabric Composites, Woodhead Publishing Series in Composites Science and Engineering, Woodhead Publishing, 2011, pp. 84–102.
https://doi.org/10.1533/9780857092533.1.84

[2] S. Advani, E. Sozer, L. Mishnaevsky Jr, Pocess modeling in composite manufacturing, pplied Mechanics Reviews. 56 (2003) B69-B70. https://doi.org/10.1115/1.1584418

[3] S. Sihn, R. Y. Kim, K. Kawabe, S. W. Tsai, Eerimental studies of thin-ply laminated composites, Composites Science and Technology. 67 (2007) 996-1008.
https://doi.org/10.1016/j.compscitech.2006.06.008

[4] A. Schnabel, T. Gries, Production of non-crimp fabrics for composites, in: Stepan V. Lomov (Eds.), Non-Crimp Fabric Composites, Woodhead Publishing, 2011, pp. 3-41.
https://doi.org/10.1533/9780857092533.1.3
[5] M. Ashir, L. Hahn, A. Kluge, A. Nocke, C. Cherif, Development of innovative adaptive 3d fiber reinforced plastics based on shape memory alloys, Composites Science and Technolog. 126 (2016) 43-51. https://doi.org/10.1016/j.compscitech.2016.02.009

[6] P. Boisse, N. Hamila, E. Vidal-Sallé, F. Dumont, Simulation of wrinkling during textile composite reinforcement forming. Influence of tensile, in-plane shear and bending stiffnesses. Composites Science and Technology, 2011, 71 (5), pp.683. https://doi.org/10.1016/j.compscitech.2011.01.011

[7] P. Boisse, B. Zouari, A. Gasser, A mesoscopic approach for the simulation of woven fibre composite forming, Composites Science and Technolog. 65 (2005) 429-436. https://doi.org/10.1016/j.compscitech.2004.09.024

[8] H. Kong and A.P. Mouritz and R. Paton, Tensile extension properties and deformation mechanisms of multiaxial non-crimp fabrics, Composite Structures. 66 (2004) 249-259. https://doi.org/10.1016/j.compstruct.2004.04.046

[9] B. Schäfer, R. Zheng, P. Boisse, L. Kärger, Investigation of the compaction behavior of uni- and bidirectional non-crimp fabrics, Materials Research Proceedings 28 (2023) 331–338. https://doi.org/10.21741/9781644902479-36

[10] F.J. Schirmaier and K.A. Weidenmann and L. Kärger and F. Henning, Characterisation of the draping behaviour of unidirectional non-crimp fabrics (UD-NCF). Composites Part A: Applied Science and Manufacturing. 80 (2016) 28-38. https://doi.org/10.1016/j.compositesa.2015.10.004

[11] L. Kärger, S. Galkin, E. Kunze, M. Gude, B. Schäfer, Prediction of forming effects in UD-NCF by macroscopic forming simulation – Capabilities and limitations. Proceedings of the 24th international conference on material forming. (2021). https://doi.org/10.25518/esaform21.355

[12] S. Bel and N. Hamila and P. Boisse and F. Dumont, Finite element model for NCF composite reinforcement preforming: Importance of inter-ply sliding, Composites Part A: Applied Science and Manufacturing. 43 (2012) 2269-2277. https://doi.org/10.1016/j.compositesa.2012.08.005

[13] J. Schirmaier, D. Dörr, F. Henning, and L. Kärger, A macroscopic approach to simulate the forming behaviour of stitched unidirectional non-crimp fabrics (UD-NCF), Composites: Part A 102 (2017) 322–335. http://dx.doi.org/10.1016/j.compositesa.2017.08.009

[14] S. Galkin, E. Kunze, L. Kärger, R. Böhm, M. Gude, Experimental and Numerical Determination of the Local Fiber Volume Content of Unidirectional Non-Crimp Fabrics with Forming Effects, J. Compos. Sci. 2019, 3(1), 19. https://doi.org/10.3390/jcs3010019

[15] L. Li, Y. Zhao, H. Vuong, Y. Chen, J. Yang, Y. Duan, In-plane shear investigation of biaxial carbon non-crimp fabrics with experimental tests and finite element modeling, Materials & Design. 63 (2014) 757-765. https://doi.org/10.1016/j.matdes.2014.07.007

[16] G. Creech, A. K. Pickett, Meso-modelling of Non-Crimp Fabric composites for coupled drape and failure analysis. Journal of Materials Science. 41 (2006) 6725-6736. https://doi.org/10.1007/s10853-006-0213-6

[17] R. Zheng, B. Schäfer, A. Platzer, J. Colmars, N. Naouar, P. Boisse, A unit-cell mesoscale modelling of biaxial non-crimp-fabric based on a hyperelastic approach, Materials Research Proceedings 28 (2023) 285-292. https://doi.org/10.21741/9781644902479-3.1

[18] S.V. Lomov, G. Huysmans, Y. Luo, R.S. Parnas, A. Prodromou, I. Verpoest, F.R. Phelan, Textile composites: modelling strategies, Composites Part A: Applied Science and Manufacturing. 32 (2001) 1379-1394. https://doi.org/10.1016/S1359-835X(01)00038-0
[5] M. Ashir, L. Hahn, A. Kluge, A. Nocke, C. Cherif, Development of innovative adaptive 3d fiber reinforced plastics based on shape memory alloys, Composites Science and Technolog. 126 (2016) 43-51. https://doi.org/10.1016/j.compscitech.2016.02.009

[6] P. Boisse, N. Hamila, E. Vidal-Sallé, F. Dumont, Simulation of wrinkling during textile composite reinforcement forming. Influence of tensile, in-plane shear and bending stiffnesses. Composites Science and Technology, 2011, 71 (5), pp.683. https://doi.org/10.1016/j.compscitech.2011.01.011

[7] P. Boisse, B. Zouari, A. Gasser, A mesoscopic approach for the simulation of woven fibre composite forming, Composites Science and Technolog. 65 (2005) 429-436. https://doi.org/10.1016/j.compscitech.2004.09.024

[8] H. Kong and A.P. Mouritz and R. Paton, Tensile extension properties and deformation mechanisms of multiaxial non-crimp fabrics, Composite Structures. 66 (2004) 249-259. https://doi.org/10.1016/j.compstruct.2004.04.046

[9] B. Schäfer, R. Zheng, P. Boisse, L. Kärger, Investigation of the compaction behavior of uni- and bidirectional non-crimp fabrics, Materials Research Proceedings 28 (2023) 331-338. https://doi.org/10.21741/9781644902479-36

[10] F.J. Schirmaier and K.A. Weidenmann and L. Kärger and F. Henning, Characterisation of the draping behaviour of unidirectional non-crimp fabrics (UD-NCF). Composites Part A: Applied Science and Manufacturing. 80 (2016) 28-38. https://doi.org/10.1016/j.compositesa.2015.10.004

[11] L. Kärger, S. Galkin, E. Kunze, M. Gude, B. Schäfer, Prediction of forming effects in UD-NCF by macroscopic forming simulation – Capabilities and limitations. Proceedings of the 24th international conference on material forming. (2021). https://doi.org/10.25518/esaform21.355

[12] S. Bel and N. Hamila and P. Boisse and F. Dumont, Finite element model for NCF composite reinforcement preforming: Importance of inter-ply sliding, Composites Part A: Applied Science and Manufacturing. 43 (2012) 2269-2277. https://doi.org/10.1016/j.compositesa.2012.08.005

[13] J. Schirmaier, D. Dörr, F. Henning, and L. Kärger, A macroscopic approach to simulate the forming behaviour of stitched unidirectional non-crimp fabrics (UD-NCF), Composites: Part A 102 (2017) 322-335. http://dx.doi.org/10.1016/j.compositesa.2017.08.009

[14] S. Galkin, E. Kunze, L. Kärger, R. Böhm, M. Gude, Experimental and Numerical Determination of the Local Fiber Volume Content of Unidirectional Non-Crimp Fabrics with Forming Effects, J. Compos. Sci. 2019, 3(1), 19. https://doi.org/10.3390/jcs3010019

[15] L. Li, Y. Zhao, H. Vuong, Y. Chen, J. Yang, Y. Duan, In-plane shear investigation of biaxial carbon non-crimp fabrics with experimental tests and finite element modeling, Materials & Design. 63 (2014) 757-765. https://doi.org/10.1016/j.matdes.2014.07.007

[16] G. Creech, A. K. Pickett, Meso-modelling of Non-Crimp Fabric composites for coupled drape and failure analysis. Journal of Materials Science. 41 (2006) 6725-6736. https://doi.org/10.1007/s10853-006-0213-6

[17] R. Zheng, B. Schäfer, A. Platzer, J. Colmars, N. Naouar, P. Boisse, A unit-cell mesoscale modelling of biaxial non-crimp-fabric based on a hyperelastic approach, Materials Research Proceedings 28 (2023) 285-292. https://doi.org/10.21741/9781644902479-3.1

[18] S.V. Lomov, G. Huysmans, Y. Luo, R.S. Parnas, A. Prodromou, I. Verpoest, F.R. Phelan, Textile composites: modelling strategies, Composites Part A: Applied Science and Manufacturing. 32 (2001) 1379-1394. https://doi.org/10.1016/S1359-835X(01)00038-0
[19] W. Wu, W. Li, Parametric modeling based on the real geometry of glass fiber unidirectional non-crimp fabric, Textile Research Journal. 89(2019). https://doi.org/10.1177/0040517518824846

[20] P. Boisse, J. Colmars, N. Hamila, N. Naouar, Q. Steer, Bending and wrinkling of composite fiber preforms and prepregs. a review and new developments in the draping simulations, Composites Part B: Engineering. 141 (2018) 234-249.
https://doi.org/10.1016/j.compositesb.2017.12.061

[21] M. Ghazimoradi, E. A. Trejo, C. Butcher, J. Montesano, Characterizing the macroscopic response and local deformation mechanisms of a uni-directional non-crimp fabric, Composites Part A: Applied Science and Manufacturing. 156 (2022) 106857.
https://doi.org/10.1016/j.compositesa.2022.106857

[22] F. F. T. Peirce B.Sc., F.Inst.P., 26—the “handle” of cloth as a measurable quantity, Journal of the Textile Institute Transactions. 21 (1930) T377-T416.
https://doi.org/10.1080/19447023008661529

[23] A. Charmetant, E. Vidal-Sallé, P. Boisse, Hyperelastic modelling for mesoscopic analyses of composite reinforcements, Composites Science and Technology 71 (2011) 1623-1631.
https://doi.org/10.1016/j.compscitech.2011.07.004

[24] A. Iwata, T. Inoue, N. Naouar, P. Boisse, S. V. Lomov, Coupled meso-macro simulation of woven fabric local deformation during draping, Compos. Part A 118 (2019) 267-280.
https://doi.org/10.1016/j.compositesa.2019.01.004
[19] W. Wu, W. Li, Parametric modeling based on the real geometry of glass fiber unidirectional non-crimp fabric, Textile Research Journal. 89(2019). https://doi.org/10.1177/0040517518824846

[20] P. Boisse, J. Colmars, N. Hamila, N. Naouar, Q. Steer, Bending and wrinkling of composite fiber preforms and prepregs. a review and new developments in the draping simulations, Composites Part B: Engineering. 141 (2018) 234-249.
https://doi.org/10.1016/j.compositesb.2017.12.061

[21] M. Ghazimoradi, E. A. Trejo, C. Butcher, J. Montesano, Characterizing the macroscopic response and local deformation mechanisms of a uni-directional non-crimp fabric, Composites Part A: Applied Science and Manufacturing. 156 (2022) 106857.
https://doi.org/10.1016/j.compositesa.2022.106857

[22] F. F. T. Peirce B.Sc., F.Inst.P., 26—the “handle” of cloth as a measurable quantity, Journal of the Textile Institute Transactions. 21 (1930) T377-T416.
https://doi.org/10.1080/19447023008661529

[23] A. Charmetant, E. Vidal-Sallé, P. Boisse, Hyperelastic modelling for mesoscopic analyses of composite reinforcements, Composites Science and Technology 71 (2011) 1623-1631.
https://doi.org/10.1016/j.compscitech.2011.07.004

[24] A. Iwata, T. Inoue, N. Naouar, P. Boisse, S. V. Lomov, Coupled meso-macro simulation of woven fabric local deformation during draping, Compos. Part A 118 (2019) 267-280.
https://doi.org/10.1016/j.compositesa.2019.01.004