adoption of recycled polymers involves possible issues in the quality of the composite products
due to the larger deviations from the average physical and mechanical properties. Therefore, highly
stable and controllable processes are preferable [6].

Pultrusion can respond to this stability requirement. Indeed, it is a continuous process for
manufacturing constant cross-section elements in composite material [7]. Pultrusion has been
designed and developed considering thermoset matrices, nevertheless, recently, a growing number
of studies have focused on the revision of the pultrusion line for the manufacturing of fiber
reinforced thermoplastics. The most used approaches are based on the usage of low-viscosity
thermoplastics or the pultrusion of pre-impregnated reinforcement [8].

The aim of this work is the study of the pultrusion of preimpregnated tapes in glass/recycled polyethylene terephthalate. The composite profile cross-section has been analyzed by optical microscopy to assess the continuity of the matrix and the reinforcement distribution, and interlaminar shear strength testing has been carried out to evaluate its mechanical performance.

**Materials and Methods**

Preconsolidated tapes in glass fiber reinforced thermoplastic provided by CompTape BV (Delft, Netherlands) have been adopted for the present investigation. The reinforcement consists of glass fiber linear rovings having a tex number of 2400, while the matrix is composed of 95% recycled polyethylene terephthalate (PET) and 5% other polymeric components improving the compatibility with the fibrous reinforcement. The tapes have a width of 6 mm and a thickness of about 0.65 mm, with a linear mass of 4.36 ± 0.35 g/m and they appear of brownish color (Fig. 1).

<figure><img src="image_403.png" /><figcaption>Figure 1. Preconsolidated tapes in glass fiber reinforced recycled PET.</figcaption></figure>

Aiming to achieve a composite profile with a volume fraction of reinforcement of about 30%, 31 tapes have been pultruded using a laboratory-scale thermoplastic pultrusion line used to produce rectangular cross-section profiles having a width of 25 mm and thickness of 4 mm. It is worth mentioning that in the case of thermoplastic pultrusion, the fiber volume fraction is sensibly lower than the values achieved using thermoset resins. The value of 30% is comparable with the one previously achieved by other authors [9–12].

The pultrusion line adopted is moved by a continuous counter-rotating caterpillar system, moving the processed materials along with two dies, mechanically connected with each other, as represented in Fig. 2.
adoption of recycled polymers involves possible issues in the quality of the composite products due to the larger deviations from the average physical and mechanical properties. Therefore, highly stable and controllable processes are preferable [6].

Pultrusion can respond to this stability requirement. Indeed, it is a continuous process for manufacturing constant cross-section elements in composite material [7]. Pultrusion has been designed and developed considering thermoset matrices, nevertheless, recently, a growing number of studies have focused on the revision of the pultrusion line for the manufacturing of fiber reinforced thermoplastics. The most used approaches are based on the usage of low-viscosity thermoplastics or the pultrusion of pre-impregnated reinforcement [8].

The aim of this work is the study of the pultrusion of preimpregnated tapes in glass/recycled polyethylene terephthalate. The composite profile cross-section has been analyzed by optical microscopy to assess the continuity of the matrix and the reinforcement distribution, and interlaminar shear strength testing has been carried out to evaluate its mechanical performance.

## Materials and Methods

Preconsolidated tapes in glass fiber reinforced thermoplastic provided by CompTape BV (Delft, Netherlands) have been adopted for the present investigation. The reinforcement consists of glass fiber linear rovings having a tex number of 2400, while the matrix is composed of 95% recycled polyethylene terephthalate (PET) and 5% other polymeric components improving the compatibility with the fibrous reinforcement. The tapes have a width of 6 mm and a thickness of about 0.65 mm, with a linear mass of 4.36 ± 0.35 g/m and they appear of brownish color (Fig. 1).

<figure><img src="image_414.png" /><figcaption>Figure 1. Preconsolidated tapes in glass fiber reinforced recycled PET.</figcaption></figure>

Aiming to achieve a composite profile with a volume fraction of reinforcement of about 30%, 31 tapes have been pultruded using a laboratory-scale thermoplastic pultrusion line used to produce rectangular cross-section profiles having a width of 25 mm and thickness of 4 mm. It is worth mentioning that in the case of thermoplastic pultrusion, the fiber volume fraction is sensibly lower than the values achieved using thermoset resins. The value of 30% is comparable with the one previously achieved by other authors [9–12].

The pultrusion line adopted is moved by a continuous counter-rotating caterpillar system, moving the processed materials along with two dies, mechanically connected with each other, as represented in Fig. 2.
<figure><img src="image_404.png" /><figcaption>Figure 2. a) Thermoplastic pultrusion dies; b) Cavities of the pultrusion dies.</figcaption></figure>

The first die is responsible for the tapes' compaction and composite forming. It is heated by electrical platens governed by PID controllers. The temperature set point of 240°C has been chosen to overcome the melting point of the adopted matrix. The heating die is 280 mm long and, as visible in Fig. 2b, the cavity is convergent in the earliest 160 mm, with a taper angle of 4.35°, then it presents a constant cross-section having dimensions of the final profile. The increase in temperature softens and melts the thermoplastic, while the geometrical convergence compacts the tapes and promotes the matrix transversal flow. The cooling die cavity is 350 mm long and it has a constant section geometry. A chiller is responsible for the absorption of the thermal energy via the cooling fluid (a mixture of water and glycol) flowing through the copper pipes visible in Fig. 2. The temperature setpoint for the cooling fluid is 13°C. The advancing velocity of 200 mm/min is controlled by the caterpillar pulling system.

During the process, in steady state conditions, the internal temperature was measured using the traveling thermocouple method [13,14]. The thermocouple has been fixed to a central tape in order to evaluate the core temperature. Being the pultrusion line equipped with a load cell, the process has been considered in steady state conditions based on the stabilization of the pulling force, which is highly variable during the initial transient.

The cross-section of the produced composite profile has been analyzed by optical microscopy using a stereomicroscope Motic SMZ171 and an optical microscope Nikon Eclipse L150. The mechanical properties have been evaluated by interlaminar shear strength test performed in the short beam shear mode according to the ASTM D2344. Three samples having a width of 18 mm, and thickness of 4 mm were collected from the produced profile and tested using a span length of 20 mm.

## Results and Discussion

At a visual inspection, the produced profile appeared well compacted and with constant cross-section, even if the external surface presented marked irregularities, as visible in Fig. 3.
<figure><img src="image_415.png" /><figcaption>Figure 2. a) Thermoplastic pultrusion dies; b) Cavities of the pultrusion dies.</figcaption></figure>

The first die is responsible for the tapes' compaction and composite forming. It is heated by electrical platens governed by PID controllers. The temperature set point of 240°C has been chosen to overcome the melting point of the adopted matrix. The heating die is 280 mm long and, as visible in Fig. 2b, the cavity is convergent in the earliest 160 mm, with a taper angle of 4.35°, then it presents a constant cross-section having dimensions of the final profile. The increase in temperature softens and melts the thermoplastic, while the geometrical convergence compacts the tapes and promotes the matrix transversal flow. The cooling die cavity is 350 mm long and it has a constant section geometry. A chiller is responsible for the absorption of the thermal energy via the cooling fluid (a mixture of water and glycol) flowing through the copper pipes visible in Fig. 2. The temperature setpoint for the cooling fluid is 13°C. The advancing velocity of 200 mm/min is controlled by the caterpillar pulling system.

During the process, in steady state conditions, the internal temperature was measured using the traveling thermocouple method [13,14]. The thermocouple has been fixed to a central tape in order to evaluate the core temperature. Being the pultrusion line equipped with a load cell, the process has been considered in steady state conditions based on the stabilization of the pulling force, which is highly variable during the initial transient.

The cross-section of the produced composite profile has been analyzed by optical microscopy using a stereomicroscope Motic SMZ171 and an optical microscope Nikon Eclipse L150. The mechanical properties have been evaluated by interlaminar shear strength test performed in the short beam shear mode according to the ASTM D2344. Three samples having a width of 18 mm, and thickness of 4 mm were collected from the produced profile and tested using a span length of 20 mm.

## Results and Discussion

At a visual inspection, the produced profile appeared well compacted and with constant cross-section, even if the external surface presented marked irregularities, as visible in Fig. 3.
<figure><img src="image_405.png" /><figcaption>Figure 3. a) Pultruded composite at the cooling die outlet; b) Surface of the pultruded composite.</figcaption></figure>

The surface unevenness has been already detected in previous studies on thermoplastic pultrusion with different materials [15,16]. The microscope analysis of the internal structure is necessary to assess the quality of the composite.

<figure><img src="image_406.png" /><figcaption>Figure 4. a) Micrographic view of the profile cross-section acquired by stereomicroscope; b),c), and d) cross-section details acquired by optical microscope.</figcaption></figure>

Fig. 4 (a) reports the overall view of the cross-section of the produced composite acquired by stereomicroscope. On average, the profile presents good compaction, nevertheless, there are several marked transversal cracks crossing the thickness of the profile. The cracks can be analyzed in higher detail by the microscope images Fig 4 (b-c). Cracks do not appear at the boundary of the tapes, but, on the contrary, they cross the tapes. This suggests that the compaction phase in the heating die has been successfully completed, and the cracks formed and propagated successively. The cooling phase could be responsible for an excessive heat flow provoking fast internal
<figure><img src="image_416.png" /><figcaption>Figure 3. a) Pultruded composite at the cooling die outlet; b) Surface of the pultruded composite.</figcaption></figure>

The surface unevenness has been already detected in previous studies on thermoplastic pultrusion with different materials [15,16]. The microscope analysis of the internal structure is necessary to assess the quality of the composite.

<figure><img src="image_417.png" /><figcaption>Figure 4. a) Micrographic view of the profile cross-section acquired by stereomicroscope; b),c), and d) cross-section details acquired by optical microscope.</figcaption></figure>

Fig. 4 (a) reports the overall view of the cross-section of the produced composite acquired by stereomicroscope. On average, the profile presents good compaction, nevertheless, there are several marked transversal cracks crossing the thickness of the profile. The cracks can be analyzed in higher detail by the microscope images Fig 4 (b-c). Cracks do not appear at the boundary of the tapes, but, on the contrary, they cross the tapes. This suggests that the compaction phase in the heating die has been successfully completed, and the cracks formed and propagated successively. The cooling phase could be responsible for an excessive heat flow provoking fast internal
contractions of the materials and the consequent cracking. It is worth mentioning that in the zones not affected by cracks, the matrix generally appears continuous, and the reinforcement is homogeneously distributed Fig. 4 (d). The unevenness of the external surface is evident in the micrography of the whole section. In thicker zones, a concentration of tapes is visible, probably due to the uncontrolled mobility of the tapes while crossing the converging cavity of the heating die. A stiffer constraint of the tapes upstream of the entrance in the heating dies could provide a preliminary arrangement that could mitigate this effect.

<figure><img src="image_407.png" /><figcaption>Figure 5. Internal temperature during pultrusion.</figcaption></figure>

The temperature data acquired using the traveling thermocouple method are reported in Fig. 5. The tapes pass through the heating die inlet at environmental temperature, since, in this experiment, no preheating systems have been used. The temperature increases along with the convergent zone of the cavity. Considering the taper angle and the dimensions of the tapes, at 120 mm from the die inlet, the compaction of the material starts, and the sensitive bulb detects a sharp increase in temperature. The temperature is sufficient to start the matrix softening and melting. The presence of a viscous liquid phase and the tapering shape of the cavity provoke an increase in pressure and transversal flow of thermoplastic, which, in turn, generates noise in the thermal signal detected by the thermocouple. The pressure increase in tapered pultrusion cavities has been predicted and demonstrated in several literature works [17–20]. The temperature along with the straight portion of the heating die oscillates around 235°C. The decrease in temperature starts in the last millimeters of the heating die and continues along with the entire cooling die. At the crossover between the two dies, the most relevant temperature drop can be observed. Such gradient could be responsible for the formation and propagation of the cracks, nevertheless, further repetitions of the thermal measurement and deeper analyses are necessary to confirm this hypothesis.
contractions of the materials and the consequent cracking. It is worth mentioning that in the zones not affected by cracks, the matrix generally appears continuous, and the reinforcement is homogeneously distributed Fig. 4 (d). The unevenness of the external surface is evident in the micrography of the whole section. In thicker zones, a concentration of tapes is visible, probably due to the uncontrolled mobility of the tapes while crossing the converging cavity of the heating die. A stiffer constraint of the tapes upstream of the entrance in the heating dies could provide a preliminary arrangement that could mitigate this effect.

<figure><img src="image_418.png" /><figcaption>Figure 5. Internal temperature during pultrusion.</figcaption></figure>

The temperature data acquired using the traveling thermocouple method are reported in Fig. 5. The tapes pass through the heating die inlet at environmental temperature, since, in this experiment, no preheating systems have been used. The temperature increases along with the convergent zone of the cavity. Considering the taper angle and the dimensions of the tapes, at 120 mm from the die inlet, the compaction of the material starts, and the sensitive bulb detects a sharp increase in temperature. The temperature is sufficient to start the matrix softening and melting. The presence of a viscous liquid phase and the tapering shape of the cavity provoke an increase in pressure and transversal flow of thermoplastic, which, in turn, generates noise in the thermal signal detected by the thermocouple. The pressure increase in tapered pultrusion cavities has been predicted and demonstrated in several literature works [17–20]. The temperature along with the straight portion of the heating die oscillates around 235°C. The decrease in temperature starts in the last millimeters of the heating die and continues along with the entire cooling die. At the crossover between the two dies, the most relevant temperature drop can be observed. Such gradient could be responsible for the formation and propagation of the cracks, nevertheless, further repetitions of the thermal measurement and deeper analyses are necessary to confirm this hypothesis.
<figure><img src="image_408.png" /><figcaption>Figure 6. Interlaminar shear strength of the pultruded profiles.</figcaption></figure>

Fig. 6 depicts the results of the interlaminar shear strength test. The three curves present initially a linear behavior until a displacement of 1 mm. After that, the samples exhibited large plastic deformations. The maximum load observed is about 4550 N. A longitudinal crack, visible in the failed sample 1, formed during testing at a displacement of about 5.5. According to the ASTM D2344 standard, the maximum interlaminar shear strength of the pultruded composite has a value of 45 MPa.

## Conclusions

Tapes in fiber reinforced recycled PET have been pultruded using a laboratory-scale thermoplastic pultrusion line. The composite profile produced appeared continuous and well-compacted, but the external surface appeared irregular at a visual inspection, evidencing the necessity for a stiffer pre-tensioning of the tapes. The microscope observation of the cross-section revealed a good consolidation of the tapes but the presence of through-the-thickness cracks. This undesired effect could be mitigated by setting a slower cooling process, which will be investigated in future research. Despite the defects detected, the samples collected from the pultruded profile exhibited a relevant value of interlaminar shear strength.

## References

[1] Y. Gong, Z. Song, H. Ning, N. Hu, X. Peng, X. Wu, R. Zou, F. Liu, S. Weng, Q. Liu, A comprehensive review of characterization and simulation methods for thermo-stamping of 2D woven fabric reinforced thermoplastics, Compos. Part B Eng. 203 (2020) 108462. https://doi.org/10.1016/j.compositesb.2020.108462

[2] 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 (2022) 39. https://doi.org/10.1007/s12289-022-01682-8

[3] M. Péron, F. Jacquemin, P. Casari, G. Orange, J.L. Bailleul, N. Boyard, Thermomechanical characterization of a low viscosity PA66 thermoplastic matrix and associated continuous glass
<figure><img src="image_419.png" /><figcaption>Figure 6. Interlaminar shear strength of the pultruded profiles.</figcaption></figure>

Fig. 6 depicts the results of the interlaminar shear strength test. The three curves present initially a linear behavior until a displacement of 1 mm. After that, the samples exhibited large plastic deformations. The maximum load observed is about 4550 N. A longitudinal crack, visible in the failed sample 1, formed during testing at a displacement of about 5.5. According to the ASTM D2344 standard, the maximum interlaminar shear strength of the pultruded composite has a value of 45 MPa.

## Conclusions

Tapes in fiber reinforced recycled PET have been pultruded using a laboratory-scale thermoplastic pultrusion line. The composite profile produced appeared continuous and well-compacted, but the external surface appeared irregular at a visual inspection, evidencing the necessity for a stiffer pre-tensioning of the tapes. The microscope observation of the cross-section revealed a good consolidation of the tapes but the presence of through-the-thickness cracks. This undesired effect could be mitigated by setting a slower cooling process, which will be investigated in future research. Despite the defects detected, the samples collected from the pultruded profile exhibited a relevant value of interlaminar shear strength.

## References

[1] Y. Gong, Z. Song, H. Ning, N. Hu, X. Peng, X. Wu, R. Zou, F. Liu, S. Weng, Q. Liu, A comprehensive review of characterization and simulation methods for thermo-stamping of 2D woven fabric reinforced thermoplastics, Compos. Part B Eng. 203 (2020) 108462. https://doi.org/10.1016/j.compositesb.2020.108462

[2] 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 (2022) 39. https://doi.org/10.1007/s12289-022-01682-8

[3] M. Péron, F. Jacquemin, P. Casari, G. Orange, J.L. Bailleul, N. Boyard, Thermomechanical characterization of a low viscosity PA66 thermoplastic matrix and associated continuous glass
fibre composite under processing conditions, J. Compos. Mater. 53 (2019) 3169-3186.
https://doi.org/10.1177/0021998319862344

[4] M. Liu, L. Wang, X. Peng, Testing, characterizing, and forming of glass twill fabric/polypropylene prepregs, J. Compos. Mater. 53 (2019) 3939-3950.
https://doi.org/10.1177/0021998319851215

[5] L. Scelsi, A. Hodzic, C. Soutis, S.A. Hayes, S. Rajendran, M.A. AlMa'adeed, R. Kahraman, A review on composite materials based on recycled thermoplastics and glass fibres, Plast. Rubber Compos. 40 (2011) 1-10. https://doi.org/10.1179/174328911X12940139029121

[6] G.W. de Kort, S. Saidi, D. Hermida-Merino, N. Leone, V. Srinivas, S. Rastogi, C.H.R.M. Wilsens, Importance of viscosity control for recyclable reinforced thermoplastic composites, Macromolecules. 53 (2020) 6690-6702. https://doi.org/10.1021/acs.macromol.9b02689

[7] T.F. Starr, Pultrusion for engineers, Abington Hall, Abington Cambridge CB1 6AH, England, 2000. https://doi.org/10.1533/9781855738881.97

[8] K. Minchenkov, A. Vedernikov, A. Safonov, I. Akhatov, Thermoplastic pultrusion: A review, Polymers (Basel). 13 (2021) 1-36. https://doi.org/10.3390/polym13020180

[9] P. Zhou, C. Li, Y. Bai, S. Dong, G. Xian, A. Vedernikov, I. Akhatov, A. Safonov, Q. Yue, Durability study on the interlaminar shear behavior of glass-fibre reinforced polypropylene (GFRPP) bars for marine applications, Constr. Build. Mater. 349 (2022) 128694.
https://doi.org/10.1016/j.conbuildmat.2022.128694

[10] K. Minchenkov, A. Vedernikov, Y. Kuzminova, S. Gusev, A. Sulimov, A. Gulyaev, A. Kreslavskaya, I. Prosyanoy, G. Xian, I. Akhatov, A. Safonov, Effects of the quality of pre-consolidated materials on the mechanical properties and morphology of thermoplastic pultruded flat laminates, Compos. Commun. 35 (2022) 101281. https://doi.org/10.1016/j.coco.2022.101281

[11] P.J. Novo, J.F. Silva, J.P. Nunes, A.T. Marques, Pultrusion of fibre reinforced thermoplastic pre-impregnated materials, Compos. Part B Eng. 89 (2016) 328-339.
https://doi.org/10.1016/j.compositesb.2015.12.026

[12] A. Vedernikov, K. Minchenkov, S. Gusev, A. Sulimov, P. Zhou, C. Li, G. Xian, I. Akhatov, A. Safonov, Effects of the Pre-Consolidated Materials Manufacturing Method on the Mechanical Properties of Pultruded Thermoplastic Composites, Polymers (Basel). 14 (2022) 1-15.
https://doi.org/10.3390/polym14112246

[13] F. Tucci, D. Larrea-Wachtendorff, G. Ferrari, P. Carlone, Pulling force analysis in injection pultrusion of glass/epoxy composites, Mater. Manuf. Process. 00 (2022) 1-12.
https://doi.org/10.1080/10426914.2022.2049296

[14] F. Tucci, F. Rubino, P. Carlone, Strain and temperature measurement in pultrusion processes by fiber Bragg grating sensors, AIP Conf. Proc. 1960 (2018). https://doi.org/10.1063/1.5034837

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

[16] F. Tucci, F. Rubino, V. Esperto, G. Pasquino, P. Carlone, Investigation on the pultrusion of thermoplastic preimpregnated polypropylene-glass tapes, Mater. Res. Proc. 28 (2023) 393-398.
https://doi.org/10.21741/9781644902479-43

[17] S. Ranjit, J.A. Roux, A.L. Jeswani, Impact of injection slot width and final composite thickness for attached-die and detached-die tapered resin injection pultrusion, Appl. Compos. Mater. 20 (2013) 431-448. https://doi.org/10.1007/s10443-012-9280-9
fibre composite under processing conditions, J. Compos. Mater. 53 (2019) 3169-3186.
https://doi.org/10.1177/0021998319862344

[4] M. Liu, L. Wang, X. Peng, Testing, characterizing, and forming of glass twill fabric/polypropylene prepregs, J. Compos. Mater. 53 (2019) 3939-3950.
https://doi.org/10.1177/0021998319851215

[5] L. Scelsi, A. Hodzic, C. Soutis, S.A. Hayes, S. Rajendran, M.A. AlMa'adeed, R. Kahraman, A review on composite materials based on recycled thermoplastics and glass fibres, Plast. Rubber Compos. 40 (2011) 1-10. https://doi.org/10.1179/174328911X12940139029121

[6] G.W. de Kort, S. Saidi, D. Hermida-Merino, N. Leone, V. Srinivas, S. Rastogi, C.H.R.M. Wilsens, Importance of viscosity control for recyclable reinforced thermoplastic composites, Macromolecules. 53 (2020) 6690-6702. https://doi.org/10.1021/acs.macromol.9b02689

[7] T.F. Starr, Pultrusion for engineers, Abington Hall, Abington Cambridge CB1 6AH, England, 2000. https://doi.org/10.1533/9781855738881.97

[8] K. Minchenkov, A. Vedernikov, A. Safonov, I. Akhatov, Thermoplastic pultrusion: A review, Polymers (Basel). 13 (2021) 1-36. https://doi.org/10.3390/polym13020180

[9] P. Zhou, C. Li, Y. Bai, S. Dong, G. Xian, A. Vedernikov, I. Akhatov, A. Safonov, Q. Yue, Durability study on the interlaminar shear behavior of glass-fibre reinforced polypropylene (GFRPP) bars for marine applications, Constr. Build. Mater. 349 (2022) 128694.
https://doi.org/10.1016/j.conbuildmat.2022.128694

[10] K. Minchenkov, A. Vedernikov, Y. Kuzminova, S. Gusev, A. Sulimov, A. Gulyaev, A. Kreslavskaya, I. Prosyanoy, G. Xian, I. Akhatov, A. Safonov, Effects of the quality of pre-consolidated materials on the mechanical properties and morphology of thermoplastic pultruded flat laminates, Compos. Commun. 35 (2022) 101281. https://doi.org/10.1016/j.coco.2022.101281

[11] P.J. Novo, J.F. Silva, J.P. Nunes, A.T. Marques, Pultrusion of fibre reinforced thermoplastic pre-impregnated materials, Compos. Part B Eng. 89 (2016) 328-339.
https://doi.org/10.1016/j.compositesb.2015.12.026

[12] A. Vedernikov, K. Minchenkov, S. Gusev, A. Sulimov, P. Zhou, C. Li, G. Xian, I. Akhatov, A. Safonov, Effects of the Pre-Consolidated Materials Manufacturing Method on the Mechanical Properties of Pultruded Thermoplastic Composites, Polymers (Basel). 14 (2022) 1-15.
https://doi.org/10.3390/polym14112246

[13] F. Tucci, D. Larrea-Wachtendorff, G. Ferrari, P. Carlone, Pulling force analysis in injection pultrusion of glass/epoxy composites, Mater. Manuf. Process. 00 (2022) 1-12.
https://doi.org/10.1080/10426914.2022.2049296

[14] F. Tucci, F. Rubino, P. Carlone, Strain and temperature measurement in pultrusion processes by fiber Bragg grating sensors, AIP Conf. Proc. 1960 (2018). https://doi.org/10.1063/1.5034837

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

[16] F. Tucci, F. Rubino, V. Esperto, G. Pasquino, P. Carlone, Investigation on the pultrusion of thermoplastic preimpregnated polypropylene-glass tapes, Mater. Res. Proc. 28 (2023) 393-398.
https://doi.org/10.21741/9781644902479-43

[17] S. Ranjit, J.A. Roux, A.L. Jeswani, Impact of injection slot width and final composite thickness for attached-die and detached-die tapered resin injection pultrusion, Appl. Compos. Mater. 20 (2013) 431-448. https://doi.org/10.1007/s10443-012-9280-9
[18] D.R. Palikhel, J.A. Roux, A.L. Jeswani, Die-attached versus die-detached resin injection chamber for pultrusion, Appl. Compos. Mater. 20 (2013) 55-72. https://doi.org/10.1007/s10443-012-9251-1

[19] A.L. Jeswani, J.A. Roux, Manufacturing modeling of three-dimensional resin injection pultrusion process control parameters for polyester/glass rovings composites, J. Manuf. Sci. Eng. 129 (2007) 143-156. https://doi.org/10.1115/1.2383148

[20] F. Tucci, R. Bezerra, F. Rubino, P. Carlone, Multiphase flow simulation in injection pultrusion with variable properties, Mater. Manuf. Process. 35 (2020) 152-162. https://doi.org/10.1080/10426914.2020.1711928
[18] D.R. Palikhel, J.A. Roux, A.L. Jeswani, Die-attached versus die-detached resin injection chamber for pultrusion, Appl. Compos. Mater. 20 (2013) 55-72. https://doi.org/10.1007/s10443-012-9251-1

[19] A.L. Jeswani, J.A. Roux, Manufacturing modeling of three-dimensional resin injection pultrusion process control parameters for polyester/glass rovings composites, J. Manuf. Sci. Eng. 129 (2007) 143-156. https://doi.org/10.1115/1.2383148

[20] F. Tucci, R. Bezerra, F. Rubino, P. Carlone, Multiphase flow simulation in injection pultrusion with variable properties, Mater. Manuf. Process. 35 (2020) 152-162. https://doi.org/10.1080/10426914.2020.1711928
# Estimation of intimate contact of the fusion-bonded fiber reinforced thermoplastic composites

ZHOU Jiakuan¹, a*, DESPLENTERE Frederik², b and IVENS Jan¹, c

¹KU Leuven, Department of Materials Engineering, Campus De Nayer, Jan Pieter de Nayerlaan 5, 2860 Sint-Katelijne-Waver, Belgium

²KU Leuven, Department of Materials Engineering, Campus Bruges, Spoorwegstraat 12, 8200 Bruges, Belgium

ajiakuan.zhou@kuleuven.be, bfrederik.desplentere@kuleuven.be, cjan.ivens@kuleuven.be

**Keywords:** Intimate Contact, Fusion Bonding, Fiber Reinforced Thermoplastic Composites, Surface Roughness, Viscosity

**Abstract.** The quality of fusion-bonded parts relies on the development of intimate contact at first and followed by healing, where the former as a prerequisite highly dominates the consolidation and the mechanical performance of final parts. In this paper, the degree of intimate contact of continuously welded unidirectional glass fiber reinforced polypropylene tapes was investigated. Classic Lee & Springer model for theoretical estimation of intimate contact was considered in the present study. For this purpose, a relatively robust regime to extract the data inputs like surface parameters, viscosity, etc. was proposed and demonstrated clearly. Consequently, the degree of intimate contact can be plotted as a function of time. Furthermore, the degree of intimate contact was also characterized by cross-sectional microscopy, ultrasonic C-scan, and optical analysis on the delaminated surfaces. The experimentally measured results show good agreement with the theoretically predicted counterparts.

## Introduction

Fiber reinforced thermoplastic composites (FRTPCs) have attracted more and more attention, as well as increasing applications in numerous industries, like automotive, aerospace and aeronautics. This is attributed to their nature of being lightweight but high-performance on the one hand, and more importantly, the flexibility and high efficiency in processing. With the thermoplastic matrix, FRTPCs are capable of being heated and solidified repeatedly, without losing mechanical performance itself. This enables FRTPCs to be recycled easily and eco-friendly, and be welded as well as repaired over and over. On this basis, lots of fusion-bonding-based processing techniques have been developed. However, the performance and quality of the fusion bonded parts at the end, heavily rely on the consolidation process.

The consolidation in the processing of FRTPCs, is attained by intimate contact between two substrates (can be tapes, prepregs, parts, etc.) at first, to eliminate asperities and voids at the interface. Afterward, the healing of the polymer-polymer interface can be achieved through interdiffusion and entanglement of polymer chains, driven by Brownian motion[1]. Importantly, the healing starts only at the interface where the intimate contact has been developed, and it cannot be activated if the intimate contact is not built. Therefore, intimate contact is a prerequisite of the following healing process, and also a foundation of the consolidation as well as bond strength building. This fact makes it highly dominates the integrity, durability and mechanical performance of final parts. In order to achieve good intimate contact, heating is necessary to soften and melt the polymer matrix, and pressure should also be applied to deform the asperities of FRTPCs by plastic deformation, squeeze flow and percolation flow. However, difficulties always exist. The resin-rich surface layer is always thought to be a merit for fusion bonding, but this is not always the case.

<figure><img src="image_409.png" /></figure>
# Estimation of intimate contact of the fusion-bonded fiber reinforced thermoplastic composites

ZHOU Jiakuan¹, a*, DESPLENTERE Frederik², b and IVENS Jan¹, c

¹KU Leuven, Department of Materials Engineering, Campus De Nayer, Jan Pieter de Nayerlaan 5, 2860 Sint-Katelijne-Waver, Belgium

²KU Leuven, Department of Materials Engineering, Campus Bruges, Spoorwegstraat 12, 8200 Bruges, Belgium

ajiakuan.zhou@kuleuven.be, bfrederik.desplentere@kuleuven.be, cjan.ivens@kuleuven.be

**Keywords:** Intimate Contact, Fusion Bonding, Fiber Reinforced Thermoplastic Composites, Surface Roughness, Viscosity

**Abstract.** The quality of fusion-bonded parts relies on the development of intimate contact at first and followed by healing, where the former as a prerequisite highly dominates the consolidation and the mechanical performance of final parts. In this paper, the degree of intimate contact of continuously welded unidirectional glass fiber reinforced polypropylene tapes was investigated. Classic Lee & Springer model for theoretical estimation of intimate contact was considered in the present study. For this purpose, a relatively robust regime to extract the data inputs like surface parameters, viscosity, etc. was proposed and demonstrated clearly. Consequently, the degree of intimate contact can be plotted as a function of time. Furthermore, the degree of intimate contact was also characterized by cross-sectional microscopy, ultrasonic C-scan, and optical analysis on the delaminated surfaces. The experimentally measured results show good agreement with the theoretically predicted counterparts.

## Introduction

Fiber reinforced thermoplastic composites (FRTPCs) have attracted more and more attention, as well as increasing applications in numerous industries, like automotive, aerospace and aeronautics. This is attributed to their nature of being lightweight but high-performance on the one hand, and more importantly, the flexibility and high efficiency in processing. With the thermoplastic matrix, FRTPCs are capable of being heated and solidified repeatedly, without losing mechanical performance itself. This enables FRTPCs to be recycled easily and eco-friendly, and be welded as well as repaired over and over. On this basis, lots of fusion-bonding-based processing techniques have been developed. However, the performance and quality of the fusion bonded parts at the end, heavily rely on the consolidation process.

The consolidation in the processing of FRTPCs, is attained by intimate contact between two substrates (can be tapes, prepregs, parts, etc.) at first, to eliminate asperities and voids at the interface. Afterward, the healing of the polymer-polymer interface can be achieved through interdiffusion and entanglement of polymer chains, driven by Brownian motion[1]. Importantly, the healing starts only at the interface where the intimate contact has been developed, and it cannot be activated if the intimate contact is not built. Therefore, intimate contact is a prerequisite of the following healing process, and also a foundation of the consolidation as well as bond strength building. This fact makes it highly dominates the integrity, durability and mechanical performance of final parts. In order to achieve good intimate contact, heating is necessary to soften and melt the polymer matrix, and pressure should also be applied to deform the asperities of FRTPCs by plastic deformation, squeeze flow and percolation flow. However, difficulties always exist. The resin-rich surface layer is always thought to be a merit for fusion bonding, but this is not always the case.

<figure><img src="image_420.png" /></figure>
And, therefore, the polymer flow in the resin-poor regions is insufficient, making effective intimate contact challenging[2]. Moreover, thermoplastic polymers normally have a high viscosity, which means lower flowability and thus takes more time to spread and fill the interface. It wouldn't affect too much for techniques like autoclave molding or compression molding which has enough holding time, but more concern goes to fast processing techniques like automated fiber/tape placement, overextrusion, continuous welding (with hot gas torch), etc., which should achieve consolidation for a short duration, even within milliseconds[3].

Given the challenges in the achievement of intimate contact, a robust prediction model on the degree of intimate contact, as well as the regime for obtaining reliable data input should be well established. The essence of intimate contact processing makes it a function of temperature, pressure, and time. Furthermore, the nature of intimate contact development indicates that it is highly influenced by surface roughness, as well as the rheological behavior of melts. On this basis, there are already several different models for the estimation of degree of intimate contact, among which the Lee and Springer model[4], and the Yang and Pitchumani model[5, 6] are the most intensively used ones. Lee and Springer introduced the term "degree of intimate contact" for the first time, and their model follows the homogenizing ideology, by assuming a series of identical rectangles to represent the rough surface. Yang and Pitchumani model is more sophisticated, by describing the surface roughness as a Cantor set fractal morphology, which has a series of asperity generation with decreasing height. However, such a model is established with the assumption that the tape surface roughness behaviors fractal morphology, which is not always the case and limits the application of the Yang and Pitchumani model[7]. Moreover, it should be pointed out that intimate contact development is significantly influenced by the data inputs. Therefore, the acquisition of crucial parameters - surface parameters and viscosity, is decisive while has always been non-consensual and controversial. From the literature, there are prominent divergences in the model parameters, as well as the viscosity value to be used[8].

In summary, a robust model of intimate contact development is important, which is beneficial to the processing parameter optimization, and can be further used for the bond strength estimation. Therefore, in the present paper, we will contribute to a deeper understanding of intimate contact development and consolidation process, by investigating the degree of intimate contact ($D_{ic}$) mathematically and experimentally, and by proposing more universal and robust criteria for the acquisition of modeling data inputs. To do so, non-isothermal in-situ consolidation, more specifically the continuous welding in the present study, was performed on unidirectional (UD) FRTPC tapes; Characterization on the used tapes was done to obtain the modeling data inputs; And the continuously welded FRTPCs were also inspected to reckon the $D_{ic}$ for model validation. The attention is paid to the determination of mathematical model and corresponding parameters at first, based on the nature of used materials and the real processing conditions. Secondly, experimental works for the acquisition of data inputs were completed and discussed, giving the authors' opinions on the selection of experimental programs, and post-processing of the raw data. In particular, we will emphasize a solution to obtain surface parameters that are representative enough, and the determination of the viscosity value according to specific material nature and processing technique. Finally, several experimental investigations on the $D_{ic}$ were performed, and a convenient method - optical analysis on the delaminated surfaces, was proposed.

## Material and consolidation

The FRTPC used in the present study is a commercial UD glass fiber reinforced polypropylene (GF/PP) tape from FRT tapes, with 0.25 mm thickness and 25 mm width. The matrix is a polypropylene homopolymer and has a melting point of around 166 °C. The fiber volume fraction is around 45%. The tape cross-section, as shown in the µCT slice in Fig. 1, reveals a smooth surface quality and nice resin-rich surface layers. Normally, those are desired merits for decent consolidation.
And, therefore, the polymer flow in the resin-poor regions is insufficient, making effective intimate contact challenging[2]. Moreover, thermoplastic polymers normally have a high viscosity, which means lower flowability and thus takes more time to spread and fill the interface. It wouldn't affect too much for techniques like autoclave molding or compression molding which has enough holding time, but more concern goes to fast processing techniques like automated fiber/tape placement, overextrusion, continuous welding (with hot gas torch), etc., which should achieve consolidation for a short duration, even within milliseconds[3].

Given the challenges in the achievement of intimate contact, a robust prediction model on the degree of intimate contact, as well as the regime for obtaining reliable data input should be well established. The essence of intimate contact processing makes it a function of temperature, pressure, and time. Furthermore, the nature of intimate contact development indicates that it is highly influenced by surface roughness, as well as the rheological behavior of melts. On this basis, there are already several different models for the estimation of degree of intimate contact, among which the Lee and Springer model[4], and the Yang and Pitchumani model[5, 6] are the most intensively used ones. Lee and Springer introduced the term "degree of intimate contact" for the first time, and their model follows the homogenizing ideology, by assuming a series of identical rectangles to represent the rough surface. Yang and Pitchumani model is more sophisticated, by describing the surface roughness as a Cantor set fractal morphology, which has a series of asperity generation with decreasing height. However, such a model is established with the assumption that the tape surface roughness behaviors fractal morphology, which is not always the case and limits the application of the Yang and Pitchumani model[7]. Moreover, it should be pointed out that intimate contact development is significantly influenced by the data inputs. Therefore, the acquisition of crucial parameters - surface parameters and viscosity, is decisive while has always been non-consensual and controversial. From the literature, there are prominent divergences in the model parameters, as well as the viscosity value to be used[8].

In summary, a robust model of intimate contact development is important, which is beneficial to the processing parameter optimization, and can be further used for the bond strength estimation. Therefore, in the present paper, we will contribute to a deeper understanding of intimate contact development and consolidation process, by investigating the degree of intimate contact ($D_{ic}$) mathematically and experimentally, and by proposing more universal and robust criteria for the acquisition of modeling data inputs. To do so, non-isothermal in-situ consolidation, more specifically the continuous welding in the present study, was performed on unidirectional (UD) FRTPC tapes; Characterization on the used tapes was done to obtain the modeling data inputs; And the continuously welded FRTPCs were also inspected to reckon the $D_{ic}$ for model validation. The attention is paid to the determination of mathematical model and corresponding parameters at first, based on the nature of used materials and the real processing conditions. Secondly, experimental works for the acquisition of data inputs were completed and discussed, giving the authors' opinions on the selection of experimental programs, and post-processing of the raw data. In particular, we will emphasize a solution to obtain surface parameters that are representative enough, and the determination of the viscosity value according to specific material nature and processing technique. Finally, several experimental investigations on the $D_{ic}$ were performed, and a convenient method - optical analysis on the delaminated surfaces, was proposed.

## Material and consolidation

The FRTPC used in the present study is a commercial UD glass fiber reinforced polypropylene (GF/PP) tape from FRT tapes, with 0.25 mm thickness and 25 mm width. The matrix is a polypropylene homopolymer and has a melting point of around 166 °C. The fiber volume fraction is around 45%. The tape cross-section, as shown in the µCT slice in Fig. 1, reveals a smooth surface quality and nice resin-rich surface layers. Normally, those are desired merits for decent consolidation.
<figure><img src="image_410.png" /><figcaption>Fig. 1. A µCT slice of the raw GF/PP tape</figcaption></figure>

The consolidation experiments were performed on a lab-scale continuous welding setup, as shown in Fig. 2. The setup is symmetrically assembled, consisting of two tape feedings, a heat source which is a hot gas torch in this study, a pair of stainless steel compaction roller which were set at a constant temperature of 5 °C (with the help of cooling units inside), and a pulling unit. This is the most fundamental unit for the manufacturing of 2-ply laminates, and it can be further assembled and upgraded for the manufacturing of multi-ply laminates.

<figure><img src="image_411.png" /><figcaption>Fig. 2. A schematic of the continuous welding setup</figcaption></figure>

For such kind of continuous welding process, a relatively high production speed is expected. For the sake of energy-saving and less impact on the internal structure of raw tape, an appropriate welding temperature is also desired together with line speed, to melt merely the resin-rich surface layer. Taking this into consideration, a series of 2-ply laminate consolidation experiments were done with the processing parameters given in Table 1. Please note that the set parameters may differ from the actual case, for example, the line speed in the table. The measurement of compaction pressure will be given in the corresponding section. As for the nip point temperature, there is a long-lasting difficulty in its measurement with the infrared camera. In this study, we will still treat what we measured as the nip point temperature, though it is not that but the tape inlet temperature. Furthermore, due to the hot gas torch in between the tapes and thus limited space for an infrared camera, we can only measure it from the side and give a rough temperature.

<table><caption>Table 1. Processing parameters for the continuous welding experiments</caption><thead><tr><th>Sample index</th><th>set line speed [m/min]</th><th>actual line speed [m/min]</th><th>set compaction pressure [MPa]</th><th>gas temperature [°C]</th><th>nip point temperature [°C]</th></tr></thead><tbody><tr><td>S1</td><td>3.5</td><td>3.15</td><td>0.1</td><td>540</td><td>190</td></tr><tr><td>S2</td><td>3.5</td><td>3.15</td><td>0.1</td><td>580</td><td>210</td></tr><tr><td>S3</td><td>3.5</td><td>3.15</td><td>0.1</td><td>500</td><td>175</td></tr><tr><td>S4</td><td>2.5</td><td>2.19</td><td>0.1</td><td>540</td><td>215</td></tr><tr><td>S5</td><td>2.5</td><td>2.19</td><td>0.1</td><td>580</td><td>235</td></tr><tr><td>S6</td><td>2.5</td><td>2.19</td><td>0.1</td><td>500</td><td>200</td></tr></tbody></table>

## Mathematical model of intimate contact

Mathematical model. As mentioned before, basically all the existing models have been proven effective, once the corresponding assumptions meet with the actual material properties and processing conditions. In the present study, we use a smooth UD GF/PP tape as shown in Fig. 1. Such tape is supposed to be produced by extrusion/pultrusion, and therefore the surface roughness
<figure><img src="image_421.png" /><figcaption>Fig. 1. A µCT slice of the raw GF/PP tape</figcaption></figure>

The consolidation experiments were performed on a lab-scale continuous welding setup, as shown in Fig. 2. The setup is symmetrically assembled, consisting of two tape feedings, a heat source which is a hot gas torch in this study, a pair of stainless steel compaction roller which were set at a constant temperature of 5 °C (with the help of cooling units inside), and a pulling unit. This is the most fundamental unit for the manufacturing of 2-ply laminates, and it can be further assembled and upgraded for the manufacturing of multi-ply laminates.

<figure><img src="image_422.png" /><figcaption>Fig. 2. A schematic of the continuous welding setup</figcaption></figure>

For such kind of continuous welding process, a relatively high production speed is expected. For the sake of energy-saving and less impact on the internal structure of raw tape, an appropriate welding temperature is also desired together with line speed, to melt merely the resin-rich surface layer. Taking this into consideration, a series of 2-ply laminate consolidation experiments were done with the processing parameters given in Table 1. Please note that the set parameters may differ from the actual case, for example, the line speed in the table. The measurement of compaction pressure will be given in the corresponding section. As for the nip point temperature, there is a long-lasting difficulty in its measurement with the infrared camera. In this study, we will still treat what we measured as the nip point temperature, though it is not that but the tape inlet temperature. Furthermore, due to the hot gas torch in between the tapes and thus limited space for an infrared camera, we can only measure it from the side and give a rough temperature.

<table><caption>Table 1. Processing parameters for the continuous welding experiments</caption><thead><tr><th>Sample index</th><th>set line speed [m/min]</th><th>actual line speed [m/min]</th><th>set compaction pressure [MPa]</th><th>gas temperature [°C]</th><th>nip point temperature [°C]</th></tr></thead><tbody><tr><td>S1</td><td>3.5</td><td>3.15</td><td>0.1</td><td>540</td><td>190</td></tr><tr><td>S2</td><td>3.5</td><td>3.15</td><td>0.1</td><td>580</td><td>210</td></tr><tr><td>S3</td><td>3.5</td><td>3.15</td><td>0.1</td><td>500</td><td>175</td></tr><tr><td>S4</td><td>2.5</td><td>2.19</td><td>0.1</td><td>540</td><td>215</td></tr><tr><td>S5</td><td>2.5</td><td>2.19</td><td>0.1</td><td>580</td><td>235</td></tr><tr><td>S6</td><td>2.5</td><td>2.19</td><td>0.1</td><td>500</td><td>200</td></tr></tbody></table>

## Mathematical model of intimate contact

Mathematical model. As mentioned before, basically all the existing models have been proven effective, once the corresponding assumptions meet with the actual material properties and processing conditions. In the present study, we use a smooth UD GF/PP tape as shown in Fig. 1. Such tape is supposed to be produced by extrusion/pultrusion, and therefore the surface roughness
should exhibit an extruded characteristic along the fiber direction, and the asperities are highly dependent on the spreading of the raw glass yarns. This possibly indicates that the surface roughness of GF/PP tape may not have a fractal nature. Taking this into consideration, and also for the sake of simplicity, the Lee and Springer model was used in this study.

Lee and Springer[4] treated the surface roughness as a succession of identical rectangles as shown in Fig. 3. The surface parameters are defined as identical rectangle height $a_0$, width $b_0$, and the gap width $w_0$ initially. Moreover, a one-dimensional Newtonian flow was assumed, with the heat and compaction pressure applied. Consequently, the asperities, the rectangles in their model, can deform and flow, and get in contact with their counterparts gradually, as shown by the dashed rectangles in Fig. 3. Therefore, the $D_{ic}$ was defined as the ratio between the surface area in physical contact and the projected tape surface area, and given as

$$D_{ic} = \frac{1}{\frac{1+w_0}{b_0}} \times \left[ 1 + \frac{5P_{app}}{\mu(T)} \left(1 + \frac{w_0}{b_0}\right) \left(\frac{a_0}{b_0}\right)^2 t \right]^{\frac{1}{5}} \quad (1)$$

with related to time $t$, where $P_{app}$ is the applied compaction pressure, $\mu(T)$ is the temperature-dependent viscosity of the asperities/rectangles. A reliable description of surface roughness, asperity viscosity and compaction pressure is essential for a reasonable $D_{ic}$ prediction.

<figure><img src="image_412.png" /><figcaption>Fig. 3. A schematic of Lee and Springer's identical rectangle model</figcaption></figure>

Surface parameter extraction. Surface parameters of the Lee and Springer model can be extracted from tape surface profiles, which are measured by a Sensofar S Neox 3D optical profiler in the present study. It is worth mentioning that in most literature the authors just gave their measurement with corresponding settings, and directly used it for surface parameter extraction. Moreover, it was also pointed out that the extraction of surface parameters can be tunable to fit with the experimental data[3]. Therefore, detailed procedures to do the measurements and post-processing should be clarified, and robust criteria should be established accordingly. A small-scale parametric study was done for this purpose (here due to the space limitation, we will not present too many details), giving the authors' remarks and suggestions at the end. The first important point, the raw data of the scanned profile always indicates the existence of form, resulting from the curved shape of the tape itself, or the unflattened posture. As shown in Fig. 4(a), the lower left is the lowest of the scanned surface while the upper right is the highest, due to the form (the warpage and mounting angle of the tape). To remove the form, a polynomial function can be applied, while it is key to select an appropriate order. We suggest trying different order values, and using the value that is capable of minimizing the difference between the maximum height and the arithmetical mean height of the surface profile. In this study, a polynomial function of order 12 was used, which revealed the extruded characteristic of asperities along the fiber direction, as can be seen from the striped pattern in Fig. 4(b). Moreover, the scanned area size should be large enough to ensure the representative of the extracted surface parameters. Meanwhile, a larger scanned area is normally stitched from multiple small scans, and this decreases the spatial resolution. To achieve balance between them, it is important to find the fundamental structure related to asperities. For the used GF/PP tape, the asperities exist in two spatial scales, first the
should exhibit an extruded characteristic along the fiber direction, and the asperities are highly dependent on the spreading of the raw glass yarns. This possibly indicates that the surface roughness of GF/PP tape may not have a fractal nature. Taking this into consideration, and also for the sake of simplicity, the Lee and Springer model was used in this study.

Lee and Springer[4] treated the surface roughness as a succession of identical rectangles as shown in Fig. 3. The surface parameters are defined as identical rectangle height $a_0$, width $b_0$, and the gap width $w_0$ initially. Moreover, a one-dimensional Newtonian flow was assumed, with the heat and compaction pressure applied. Consequently, the asperities, the rectangles in their model, can deform and flow, and get in contact with their counterparts gradually, as shown by the dashed rectangles in Fig. 3. Therefore, the $D_{ic}$ was defined as the ratio between the surface area in physical contact and the projected tape surface area, and given as

$$D_{ic} = \frac{1}{1+\frac{w_0}{b_0}} \times \left[ 1 + \frac{5P_{app}}{\mu(T)} \left(1+\frac{w_0}{b_0}\right) \left(\frac{a_0}{b_0}\right)^2 t \right]^{\frac{1}{5}} \quad (1)$$

with related to time $t$, where $P_{app}$ is the applied compaction pressure, $\mu(T)$ is the temperature-dependent viscosity of the asperities/rectangles. A reliable description of surface roughness, asperity viscosity and compaction pressure is essential for a reasonable $D_{ic}$ prediction.

<figure><img src="image_423.png" /><figcaption>Fig. 3. A schematic of Lee and Springer's identical rectangle model</figcaption></figure>

Surface parameter extraction. Surface parameters of the Lee and Springer model can be extracted from tape surface profiles, which are measured by a Sensofar S Neox 3D optical profiler in the present study. It is worth mentioning that in most literature the authors just gave their measurement with corresponding settings, and directly used it for surface parameter extraction. Moreover, it was also pointed out that the extraction of surface parameters can be tunable to fit with the experimental data[3]. Therefore, detailed procedures to do the measurements and post-processing should be clarified, and robust criteria should be established accordingly. A small-scale parametric study was done for this purpose (here due to the space limitation, we will not present too many details), giving the authors' remarks and suggestions at the end. The first important point, the raw data of the scanned profile always indicates the existence of form, resulting from the curved shape of the tape itself, or the unflattened posture. As shown in Fig. 4(a), the lower left is the lowest of the scanned surface while the upper right is the highest, due to the form (the warpage and mounting angle of the tape). To remove the form, a polynomial function can be applied, while it is key to select an appropriate order. We suggest trying different order values, and using the value that is capable of minimizing the difference between the maximum height and the arithmetical mean height of the surface profile. In this study, a polynomial function of order 12 was used, which revealed the extruded characteristic of asperities along the fiber direction, as can be seen from the striped pattern in Fig. 4(b). Moreover, the scanned area size should be large enough to ensure the representative of the extracted surface parameters. Meanwhile, a larger scanned area is normally stitched from multiple small scans, and this decreases the spatial resolution. To achieve balance between them, it is important to find the fundamental structure related to asperities. For the used GF/PP tape, the asperities exist in two spatial scales, first the
extruded ones and second the irregular micro hills on the extruded asperities. Thus the extruded asperities, normally around hundreds of microns, were regarded as the fundamental structure, and 5 to 10 times that scale should be determined as the dimension perpendicular to the fiber direction.

<figure><img src="image_413.png" /><figcaption>Fig. 4. (a) A pseudo-color view of the raw scanned surface; (b) After the form removal.</figcaption></figure>

Following the remarks abovementioned, a 3D topography of GF/PP tape was obtained, and we started with extracting surface profiles that are perpendicular to the fiber direction, as the Lee and Springer model is a 2D squeeze flow model. A MATLAB script was developed to automatically extract the surface parameters, from the surface profiles. The script algorithm, see Fig. 5(a), follows similar steps from the literature[9], and several further modifications including the definition of the region of interest (ROI), width of asperities at the boundary, etc. Again, for the surface profile like Fig. 5(b), the surface parameter extraction is achieved by homogenizing the irregular asperities into identical rectangles with the same gap distance, like Fig. 5(c). It starts with doing interpolation but this is not mandatory, as this would benefit the accuracy more only when the asperities are extremely sharp. Second, the identical rectangle height $a_0$ represents the mean height of all asperities, and therefore can be approximated as $2\sigma$, with $\sigma$ the standard deviation of the surface profile. Third, the homogenization of irregular asperity width, should be done within a ROI, and it was defined as the whole region in between the highest and lowest profile point, across the whole length $l$. A series of horizontal reference lines (30 lines in this study) were assumed to be vertically distributed in the ROI with equal intervals. Thus, there were lots of intersections - the green dots in Fig. 5(b), which can be used to calculate each $b_i$ as a corresponding asperity width at a specific vertical position. And the identical rectangle width $b_0$ is the average of all $b_i$ values. Lastly, as the area of the ROI, as well as that of asperities and of gaps should be equivalent before and after homogenization, we have

$$ \frac{A_{gap}}{A_{asperity}} = \frac{k a_0 w_0}{k a_0 b_0} = \frac{w_0}{b_0} \qquad (2) $$

with $k$ the repeat numbers of identical rectangles. As the area of asperities and gaps can be calculated with numerical integration, the gap width $w_0$ can be obtained. For the GF/PP tape, three surface profiles were analyzed and the corresponding surface parameters showed small deviation, thus the average of them was finally used, given as $a_0 = 0.7693$, $b_0 = 9.5965$, and $w_0 = 10.2441$. These parameters also reflect the smooth nature of the GF/PP tape.
extruded ones and second the irregular micro hills on the extruded asperities. Thus the extruded asperities, normally around hundreds of microns, were regarded as the fundamental structure, and 5 to 10 times that scale should be determined as the dimension perpendicular to the fiber direction.

<figure><img src="image_424.png" /><figcaption>Fig. 4. (a) A pseudo-color view of the raw scanned surface; (b) After the form removal.</figcaption></figure>

Following the remarks abovementioned, a 3D topography of GF/PP tape was obtained, and we started with extracting surface profiles that are perpendicular to the fiber direction, as the Lee and Springer model is a 2D squeeze flow model. A MATLAB script was developed to automatically extract the surface parameters, from the surface profiles. The script algorithm, see Fig. 5(a), follows similar steps from the literature[9], and several further modifications including the definition of the region of interest (ROI), width of asperities at the boundary, etc. Again, for the surface profile like Fig. 5(b), the surface parameter extraction is achieved by homogenizing the irregular asperities into identical rectangles with the same gap distance, like Fig. 5(c). It starts with doing interpolation but this is not mandatory, as this would benefit the accuracy more only when the asperities are extremely sharp. Second, the identical rectangle height $a_0$ represents the mean height of all asperities, and therefore can be approximated as $2\sigma$, with $\sigma$ the standard deviation of the surface profile. Third, the homogenization of irregular asperity width, should be done within a ROI, and it was defined as the whole region in between the highest and lowest profile point, across the whole length $l$. A series of horizontal reference lines (30 lines in this study) were assumed to be vertically distributed in the ROI with equal intervals. Thus, there were lots of intersections - the green dots in Fig. 5(b), which can be used to calculate each $b_i$ as a corresponding asperity width at a specific vertical position. And the identical rectangle width $b_0$ is the average of all $b_i$ values. Lastly, as the area of the ROI, as well as that of asperities and of gaps should be equivalent before and after homogenization, we have

$$ \frac{A_{gap}}{A_{asperity}} = \frac{k a_0 w_0}{k a_0 b_0} = \frac{w_0}{b_0} \qquad (2) $$

with $k$ the repeat numbers of identical rectangles. As the area of asperities and gaps can be calculated with numerical integration, the gap width $w_0$ can be obtained. For the GF/PP tape, three surface profiles were analyzed and the corresponding surface parameters showed small deviation, thus the average of them was finally used, given as $a_0 = 0.7693$, $b_0 = 9.5965$, and $w_0 = 10.2441$. These parameters also reflect the smooth nature of the GF/PP tape.
<figure><img src="image_414.png" /><figcaption>Fig. 5 Schematic of the surface parameter extraction</figcaption></figure>

Viscosity measurement. The viscosity of the identical rectangles, or that of asperities, might be the most significant input parameter. On the one hand, due to the thermoplastic matrix, the viscosity is temperature-dependent. On the other hand, researchers [4], [9] were always struggling with which viscosity value to use, between that of neat polymer and that of fiber/matrix mixture. Moreover, it is worth mentioning that the viscosity values between them can vary by order of magnitude[10]. However, we would like to argue that the determination of viscosity value can be even more complex. The purpose of characterizing a viscosity is to depict the squeeze flow behavior of the contacting tape surfaces. Therefore, the key to determining what viscosity to use is actually to determine what is going to be squeezed flow, contributing to the intimate contact evolution. Some researchers [9], [11] considered the fact of resin-rich surface layer and smooth surface, and then used the viscosity of neat polymer. While once not the case, researchers tend to use the viscosity of fiber/matrix mixture, which is normally obtained based on squeeze flow theory, through compressing a FRTPC laminate[12]. Those assumptions may be reasonable. However, it is also typical that there is a resin-rich surface layer but also surface defects like dry fibers, making things a bit complex and thus introducing the definition of “effective intimate contact[2]”. Moreover, it is often overlooked that what is squeezed flow (or melted), can vary a lot under different processing and parameters, even for the same tape. An example is given by the GF/PP tape, as shown in Fig. 1, which has thick resin-rich surface layers (more or less than 2 times the fiber diameter) and smooth surfaces. If it is used for compression molding and thus being thoroughly melted in the thickness direction, then for sure the viscosity of its fiber/matrix mixture should be used for intimate contact modeling. However, if it is used for laser assisted tape placement with the laser being confined to merely melt the resin-rich surface layer, then the viscosity of neat polymer should be used. Moreover, though we are pursuing to melt merely the resin-rich surface layer, this cannot always be ensured considering different parameters and different heat sources. Under such circumstances, the melting depth in the tape thickness direction varies, and the viscosity of the melting part varies accordingly, between the viscosity of neat polymer and that of fiber/matrix mixture of whole tape thickness. This is extremely tricky and to the authors’ knowledge, there is no good method to characterize the corresponding viscosity for such a problem. Therefore, at least it is necessary to check the melting depth under specific conditions before decision.

For the continuous welding setup, and the processing parameters used in the present study, we managed to limit the heat input to melt merely the resin-rich surface layer. Fig. 6(a) shows a cross-sectional micrograph and from which we can see that the resin-rich surface layers were well maintained and there were no fibers being squeezed into the resin-rich surface layers. And Fig. 6(b) shows exterior photo of the as-manufactured 2-ply laminates, where the exterior surfaces of the laminates were not melt and as smooth as raw tape. Finally, we can determine that the viscosity of neat PP can be used in this study. It was measured using an Anton Paar plate-plate rheometer, with a plate diameter of 25 mm. Considering the temperature dependency, the viscosity was
<figure><img src="image_425.png" /><figcaption>Fig. 5 Schematic of the surface parameter extraction</figcaption></figure>

Viscosity measurement. The viscosity of the identical rectangles, or that of asperities, might be the most significant input parameter. On the one hand, due to the thermoplastic matrix, the viscosity is temperature-dependent. On the other hand, researchers [4], [9] were always struggling with which viscosity value to use, between that of neat polymer and that of fiber/matrix mixture. Moreover, it is worth mentioning that the viscosity values between them can vary by order of magnitude[10]. However, we would like to argue that the determination of viscosity value can be even more complex. The purpose of characterizing a viscosity is to depict the squeeze flow behavior of the contacting tape surfaces. Therefore, the key to determining what viscosity to use is actually to determine what is going to be squeezed flow, contributing to the intimate contact evolution. Some researchers [9], [11] considered the fact of resin-rich surface layer and smooth surface, and then used the viscosity of neat polymer. While once not the case, researchers tend to use the viscosity of fiber/matrix mixture, which is normally obtained based on squeeze flow theory, through compressing a FRTPC laminate[12]. Those assumptions may be reasonable. However, it is also typical that there is a resin-rich surface layer but also surface defects like dry fibers, making things a bit complex and thus introducing the definition of “effective intimate contact[2]”. Moreover, it is often overlooked that what is squeezed flow (or melted), can vary a lot under different processing and parameters, even for the same tape. An example is given by the GF/PP tape, as shown in Fig. 1, which has thick resin-rich surface layers (more or less than 2 times the fiber diameter) and smooth surfaces. If it is used for compression molding and thus being thoroughly melted in the thickness direction, then for sure the viscosity of its fiber/matrix mixture should be used for intimate contact modeling. However, if it is used for laser assisted tape placement with the laser being confined to merely melt the resin-rich surface layer, then the viscosity of neat polymer should be used. Moreover, though we are pursuing to melt merely the resin-rich surface layer, this cannot always be ensured considering different parameters and different heat sources. Under such circumstances, the melting depth in the tape thickness direction varies, and the viscosity of the melting part varies accordingly, between the viscosity of neat polymer and that of fiber/matrix mixture of whole tape thickness. This is extremely tricky and to the authors’ knowledge, there is no good method to characterize the corresponding viscosity for such a problem. Therefore, at least it is necessary to check the melting depth under specific conditions before decision.

For the continuous welding setup, and the processing parameters used in the present study, we managed to limit the heat input to melt merely the resin-rich surface layer. Fig. 6(a) shows a cross-sectional micrograph and from which we can see that the resin-rich surface layers were well maintained and there were no fibers being squeezed into the resin-rich surface layers. And Fig. 6(b) shows exterior photo of the as-manufactured 2-ply laminates, where the exterior surfaces of the laminates were not melt and as smooth as raw tape. Finally, we can determine that the viscosity of neat PP can be used in this study. It was measured using an Anton Paar plate-plate rheometer, with a plate diameter of 25 mm. Considering the temperature dependency, the viscosity was
measured from 180 °C to 240 °C, with a decreasing angular frequency ω from 628 rad/s down to 0.1 rad/s. The as-measured data were fitted with the Carreau-Yasuda equation:

$$ \eta^*(\omega) = \eta_{\infty} + (\eta_0 - \eta_{\infty})(1 + (\lambda\omega)^a)^{(n-1)/a} \quad (3) $$

with the following parameters as given in Table. 2. The parameter η₀ is the viscosity at zero shear rate, and it is suitable to represent the viscosity of the squeezed polymer in this study. Based on those values, the temperature-dependent viscosity can be fitted in the form of Arrhenius equation:

$$ \mu(T) = (2.784E-5) * e^{\frac{6.287E+4}{8.31T}} \quad (4) $$

with E the activation energy, R the universal gas constant, and T in Kelvin.

<figure><img src="image_415.png" /><figcaption>Fig. 6. (a) the micrograph and (b) exterior photo of the as-manufactured 2-ply laminates</figcaption></figure>

<table><caption>Table 2. The fitted parameters for the complex viscosity of neat PP with the C-Y equation</caption><thead><tr><th>Temperature [°C]</th><th>η<sub>0</sub> [mPa.s]</th><th>η<sub>∞</sub> [mPa.s]</th><th>λ</th><th>a</th><th>n</th></tr></thead><tbody><tr><td>180</td><td>5.0451E+05</td><td>0.1000</td><td>0.0247</td><td>0.8032</td><td>0.4199</td></tr><tr><td>190</td><td>3.4846E+05</td><td>0.1000</td><td>0.0137</td><td>0.8034</td><td>0.3737</td></tr><tr><td>200</td><td>2.5713E+05</td><td>0.1000</td><td>0.0073</td><td>0.7481</td><td>0.2831</td></tr><tr><td>210</td><td>1.8655E+05</td><td>0.1000</td><td>0.0034</td><td>0.7607</td><td>0.0483</td></tr><tr><td>220</td><td>1.2484E+05</td><td>0.1000</td><td>0.0037</td><td>0.8684</td><td>0.1710</td></tr><tr><td>230</td><td>9.0521E+04</td><td>0.1000</td><td>0.0022</td><td>0.8516</td><td>0.0001</td></tr><tr><td>240</td><td>5.9637E+04</td><td>0.1000</td><td>0.0026</td><td>1.0445</td><td>0.0001</td></tr></tbody></table>

Compaction pressure measurement. Though the welding process is dynamic, we still measured the static pressure at room temperature instead. This is enough as the roller rotatory dynamic and the effect of molten matrix can be negligible for intimate contact development, and most researchers also made such an assumption for simplicity[2]. A piece of Fuji 4LW pressure measurement film was put on a tape, and between the compaction together. The measurement results, as shown in Fig. 7, reflect that the compaction area was small while asymmetric. The pressure distribution was more uniform than expected, indicating less edge effect. Thus, the compaction pressure was simplified into a uniform distribution of 0.107 MPa in a rectangle region of 3 mm width.

<figure><img src="image_416.png" /><figcaption>Fig. 7. The stained pattern on the pressure measurement film</figcaption></figure>

Modeling results. Now that we obtained all the desired data inputs, the Dᵢc can be plotted with related to time, as shown in Fig. 8. Of course, the higher the temperature, the shorter the time to
measured from 180 °C to 240 °C, with a decreasing angular frequency ω from 628 rad/s down to 0.1 rad/s. The as-measured data were fitted with the Carreau-Yasuda equation:

$$ \eta^*(\omega) = \eta_{\infty} + (\eta_0 - \eta_{\infty})(1 + (\lambda\omega)^a)^{(n-1)/a} \quad (3) $$

with the following parameters as given in Table. 2. The parameter η₀ is the viscosity at zero shear rate, and it is suitable to represent the viscosity of the squeezed polymer in this study. Based on those values, the temperature-dependent viscosity can be fitted in the form of Arrhenius equation:

$$ \mu(T) = (2.784E-5) * e^{\frac{6.287E+4}{8.31T}} \quad (4) $$

with E the activation energy, R the universal gas constant, and T in Kelvin.

<figure><img src="image_426.png" /><figcaption>Fig. 6. (a) the micrograph and (b) exterior photo of the as-manufactured 2-ply laminates</figcaption></figure>

<table><caption>Table 2. The fitted parameters for the complex viscosity of neat PP with the C-Y equation</caption><thead><tr><th>Temperature [°C]</th><th>η<sub>0</sub> [mPa.s]</th><th>η<sub>∞</sub> [mPa.s]</th><th>λ</th><th>a</th><th>n</th></tr></thead><tbody><tr><td>180</td><td>5.0451E+05</td><td>0.1000</td><td>0.0247</td><td>0.8032</td><td>0.4199</td></tr><tr><td>190</td><td>3.4846E+05</td><td>0.1000</td><td>0.0137</td><td>0.8034</td><td>0.3737</td></tr><tr><td>200</td><td>2.5713E+05</td><td>0.1000</td><td>0.0073</td><td>0.7481</td><td>0.2831</td></tr><tr><td>210</td><td>1.8655E+05</td><td>0.1000</td><td>0.0034</td><td>0.7607</td><td>0.0483</td></tr><tr><td>220</td><td>1.2484E+05</td><td>0.1000</td><td>0.0037</td><td>0.8684</td><td>0.1710</td></tr><tr><td>230</td><td>9.0521E+04</td><td>0.1000</td><td>0.0022</td><td>0.8516</td><td>0.0001</td></tr><tr><td>240</td><td>5.9637E+04</td><td>0.1000</td><td>0.0026</td><td>1.0445</td><td>0.0001</td></tr></tbody></table>

Compaction pressure measurement. Though the welding process is dynamic, we still measured the static pressure at room temperature instead. This is enough as the roller rotatory dynamic and the effect of molten matrix can be negligible for intimate contact development, and most researchers also made such an assumption for simplicity[2]. A piece of Fuji 4LW pressure measurement film was put on a tape, and between the compaction together. The measurement results, as shown in Fig. 7, reflect that the compaction area was small while asymmetric. The pressure distribution was more uniform than expected, indicating less edge effect. Thus, the compaction pressure was simplified into a uniform distribution of 0.107 MPa in a rectangle region of 3 mm width.

<figure><img src="image_427.png" /><figcaption>Fig. 7. The stained pattern on the pressure measurement film</figcaption></figure>

Modeling results. Now that we obtained all the desired data inputs, the Dᵢc can be plotted with related to time, as shown in Fig. 8. Of course, the higher the temperature, the shorter the time to
achieve full $D_{ic}$, due to the temperature-dependent viscosity. Even at 180 °C, just a bit higher than the melting point, a full intimate contact can be achieved within around 2.6 s. Furthermore, the compaction time of samples given in Table 1 can be estimated with the corresponding actual line speed and the width of compaction region, which is around 0.0571 s for samples S1, S2 and S3, while 0.0822 s for samples S4, S5 and S6. On this basis, the corresponding $D_{ic}$ can be calculated, as given in Table 3.

<figure><img src="image_417.png" /><figcaption>Fig. 8. The degree of intimate contact for the continuously welded GF/PP tape</figcaption></figure>

<table><caption>Table 3. The degree of intimate contact for all the samples in this study</caption><thead><tr><th>Sample index</th><th>S1</th><th>S2</th><th>S3</th><th>S4</th><th>S5</th><th>S6</th></tr></thead><tbody><tr><th>D<sub>ic</sub> [%]</th><td>56.49</td><td>61.44</td><td>53.65</td><td>66.47</td><td>73.63</td><td>61.73</td></tr></tbody></table>

## Experimental inspection of intimate contact

Accurate and efficient experimental inspection of intimate contact is sometimes challenging. Cross-sectional microscopy[13] may be a solution, but it mainly provides 1D info at the interface and normally it is labor-intensive. X-ray computed tomography[9] proved its capability, but unfortunately, the poor image contrast between entrapped air and PP (also some other light polymers) limits its application in some glass fiber reinforced composites[14]. The authors also used ultrasonic C-scan, for example, a C-scan image of sample S4 in Fig. 9(a) and its thresholding (with white denoting the non-contacting region) in Fig. 9(b), which resulted in an average $D_{ic}$ = 52.66%. According to the comparison with its cross-sectional microscopy, it turned out that, the thresholding and thus the $D_{ic}$ is not good due to fibers and matrix's anisotropy in such a thin laminate. Moreover, the distribution of non-contact regions is quite uneven, in a relatively large area. This indicates that the method of inspecting the intimate contact in a large area should be more representative, and necessary.

<figure><img src="image_418.png" /><figcaption>Fig. 9. (a) the C-scan image and (b) its thresholding result of a S4 sample</figcaption></figure>
achieve full $D_{ic}$, due to the temperature-dependent viscosity. Even at 180 °C, just a bit higher than the melting point, a full intimate contact can be achieved within around 2.6 s. Furthermore, the compaction time of samples given in Table 1 can be estimated with the corresponding actual line speed and the width of compaction region, which is around 0.0571 s for samples S1, S2 and S3, while 0.0822 s for samples S4, S5 and S6. On this basis, the corresponding $D_{ic}$ can be calculated, as given in Table 3.

<figure><img src="image_428.png" /><figcaption>Fig. 8. The degree of intimate contact for the continuously welded GF/PP tape</figcaption></figure>

<table><caption>Table 3. The degree of intimate contact for all the samples in this study</caption><thead><tr><th>Sample index</th><th>S1</th><th>S2</th><th>S3</th><th>S4</th><th>S5</th><th>S6</th></tr></thead><tbody><tr><th>D<sub>ic</sub> [%]</th><td>56.49</td><td>61.44</td><td>53.65</td><td>66.47</td><td>73.63</td><td>61.73</td></tr></tbody></table>

## Experimental inspection of intimate contact

Accurate and efficient experimental inspection of intimate contact is sometimes challenging. Cross-sectional microscopy[13] may be a solution, but it mainly provides 1D info at the interface and normally it is labor-intensive. X-ray computed tomography[9] proved its capability, but unfortunately, the poor image contrast between entrapped air and PP (also some other light polymers) limits its application in some glass fiber reinforced composites[14]. The authors also used ultrasonic C-scan, for example, a C-scan image of sample S4 in Fig. 9(a) and its thresholding (with white denoting the non-contacting region) in Fig. 9(b), which resulted in an average $D_{ic}$ = 52.66%. According to the comparison with its cross-sectional microscopy, it turned out that, the thresholding and thus the $D_{ic}$ is not good due to fibers and matrix's anisotropy in such a thin laminate. Moreover, the distribution of non-contact regions is quite uneven, in a relatively large area. This indicates that the method of inspecting the intimate contact in a large area should be more representative, and necessary.

<figure><img src="image_429.png" /><figcaption>Fig. 9. (a) the C-scan image and (b) its thresholding result of a S4 sample</figcaption></figure>
Afterward, the authors proposed to inspect the intimate contact by optical analysis on the delaminated surfaces. This was done by guiding the two tape feeding separately over a second roller right behind the compaction roller, this way the welded tapes can be immediately delaminated. Considering that the relaxation time of PP, which is the $\lambda$ in Table 2, is really small, we assume that all regions that achieve intimate contact should also start or even finish the autohealing, and thus there should be polymer chains across the interface in those regions. Therefore, once the tape is delaminated, those intimate contact regions should suffer from damage, normally plastic deformation and stress whitening. As can be seen from Fig. 10(a), there are milky opaque regions like the one denoted by a red dot, assumed to be intimate contact regions in this study. While the relatively translucent regions like the one denoted by a green dot are non-contacting. Following this idea, a better direct thresholding was obtained as shown in Fig. 10(b), and gave the $D_{ic}$ = 66.8%. This method inspects the intimate contact development of a large area in an efficient manner, giving a decent $D_{ic}$. However, it is worth mentioning that the delaminated surface image of weakly bonded samples may not have enough contrast, and therefore it is necessary to manually enhance the contrast at first.

<figure><img src="image_419.png" /><figcaption>Fig. 10. (a) an image of the delaminated surface and (b) its thresholding result of a S4 sample</figcaption></figure>

## Conclusion

In this study, we used the Lee and Springer model to estimate the $D_{ic}$ of continuously welded GF/PP, and proposed a method of optical analysis on the delaminated surfaces to investigate the $D_{ic}$, which gave a decent result and agreed well with the modeling result. More importantly, the authors contribute to the fulfillment of reliable data input extraction for mathematical modeling. Relatively robust criteria to process the scanned 3D surface topography were obtained through a small-scale parametric study, and the surface parameters can be automatically extracted from real 3D surfaces with the developed MATLAB script. This ensures the acquired surface parameters are solid and reliable. Moreover, the authors demonstrate the keys to determining the asperity viscosity to use, emphasizing that the melting depth of the tape in the thickness direction should also be taken into consideration, which highly depends on both the nature of the tape and the processing techniques as well as parameters.

## References

[1] I. Martin, D. Saenz Del Castillo, A. Fernandez, and A. Güemes, Advanced thermoplastic composite manufacturing by in-situ consolidation: A review, J. Compos. Sci., 4 (2020) 1–36. https://doi.org/10.3390/jcs4040149

[2] 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., 134 (2020) 105888. https://doi.org/10.1016/j.compositesa.2020.105888

[3] M. J. Donough, Shafaq, N. A. St John, A. W. Philips, and B. Gangadhara Prusty, Process Modelling of In-situ Consolidated Thermoplastic Composite by Automated Fibre Placement – A Review, Compos. Part A Appl. Sci. Manuf., (Dec. 2022) 107179. https://doi.org/10.1016/J.COMPOSITESA.2022.107179
Afterward, the authors proposed to inspect the intimate contact by optical analysis on the delaminated surfaces. This was done by guiding the two tape feeding separately over a second roller right behind the compaction roller, this way the welded tapes can be immediately delaminated. Considering that the relaxation time of PP, which is the $\lambda$ in Table 2, is really small, we assume that all regions that achieve intimate contact should also start or even finish the autohealing, and thus there should be polymer chains across the interface in those regions. Therefore, once the tape is delaminated, those intimate contact regions should suffer from damage, normally plastic deformation and stress whitening. As can be seen from Fig. 10(a), there are milky opaque regions like the one denoted by a red dot, assumed to be intimate contact regions in this study. While the relatively translucent regions like the one denoted by a green dot are non-contacting. Following this idea, a better direct thresholding was obtained as shown in Fig. 10(b), and gave the $D_{ic}$ = 66.8%. This method inspects the intimate contact development of a large area in an efficient manner, giving a decent $D_{ic}$. However, it is worth mentioning that the delaminated surface image of weakly bonded samples may not have enough contrast, and therefore it is necessary to manually enhance the contrast at first.

<figure><img src="image_430.png" /><figcaption>Fig. 10. (a) an image of the delaminated surface and (b) its thresholding result of a S4 sample</figcaption></figure>

## Conclusion

In this study, we used the Lee and Springer model to estimate the $D_{ic}$ of continuously welded GF/PP, and proposed a method of optical analysis on the delaminated surfaces to investigate the $D_{ic}$, which gave a decent result and agreed well with the modeling result. More importantly, the authors contribute to the fulfillment of reliable data input extraction for mathematical modeling. Relatively robust criteria to process the scanned 3D surface topography were obtained through a small-scale parametric study, and the surface parameters can be automatically extracted from real 3D surfaces with the developed MATLAB script. This ensures the acquired surface parameters are solid and reliable. Moreover, the authors demonstrate the keys to determining the asperity viscosity to use, emphasizing that the melting depth of the tape in the thickness direction should also be taken into consideration, which highly depends on both the nature of the tape and the processing techniques as well as parameters.

## References

[1] I. Martin, D. Saenz Del Castillo, A. Fernandez, and A. Güemes, Advanced thermoplastic composite manufacturing by in-situ consolidation: A review, J. Compos. Sci., 4 (2020) 1–36. https://doi.org/10.3390/jcs4040149

[2] 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., 134 (2020) 105888. https://doi.org/10.1016/j.compositesa.2020.105888

[3] M. J. Donough, Shafaq, N. A. St John, A. W. Philips, and B. Gangadhara Prusty, Process Modelling of In-situ Consolidated Thermoplastic Composite by Automated Fibre Placement – A Review, Compos. Part A Appl. Sci. Manuf., (Dec. 2022) 107179. https://doi.org/10.1016/J.COMPOSITESA.2022.107179
[4] W. Il Lee and G. S. Springer, A Model of the Manufacturing Process of Thermoplastic Matrix Composites, J. Compos. Mater., 21 (1987) 1017-1055.
https://doi.org/10.1177/002199838702101103

[5] F. Yang and R. Pitchumani, A fractal Cantor set based description of interlaminar contact evolution during thermoplastic composites processing, J. Mater. Sci., 36 (2001) 4661-4671.
https://doi.org/10.1023/A:1017950215945

[6] F. Yang and R. Pitchumani, Fractal description of interlaminar contact development during thermoplastic composites processing, J. Reinf. Plast. Compos., 20 (2001) 536-546.

[7] A. Levy, D. Heider, J. Tierney, and J. W. Gillespie, Inter-layer thermal contact resistance evolution with the degree of intimate contact in the processing of thermoplastic composite laminates, J. Compos. Mater., 48 (2014) 491-503.

[8] M. A. Khan, P. Mitschang, and R. Schledjewski, Identification of some optimal parameters to achieve higher laminate quality through tape placement process, Adv. Polym. Technol., 29 (Jun. 2010) 98-111.
https://doi.org/10.1002/adv.20177

[9] P. M. Schaefer, T. Guglhoer, M. G. R. Sause, and K. Drechsler, Development of intimate contact during processing of carbon fiber reinforced Polyamide-6 tapes, J. Reinf. Plast. Compos., 36 (2017) 593-607.
https://doi.org/10.1177/0731684416687041

[10] P. M. Schäfer, Consolidation of carbon fiber reinforced polyamide 6 tapes using laser-assisted tape placement. Technische Universität München, 2017.

[11] W. J. B. Grouve, L. L. Warnet, B. Rietman, H. A. Visser, and R. Akkerman, Optimization of the tape placement process parameters for carbon-PPS composites, Compos. Part A Appl. Sci. Manuf., 50 (2013) 44-53.
https://doi.org/10.1016/j.compositesa.2013.03.003

[12] J. Engmann, C. Servais, and A. S. Burbidge, Squeeze flow theory and applications to rheometry: A review, J. Nonnewton. Fluid Mech., 132 (2005) 1-27.

[13] O. Çelik et al., The influence of inter-laminar thermal contact resistance on the cooling of material during laser assisted fiber placement, Compos. Part A Appl. Sci. Manuf., 145 (2021) 106367.

[14] J. Zhou, F. Desplentere, and J. Ivens, µCT-based internal microstructure analysis in continuous fiber reinforced thermoplastics, in *ITHEC 2022 Conference Proceedings*, CONGRESS BREMEN & MESSE BREMEN, 2022.
[4] W. Il Lee and G. S. Springer, A Model of the Manufacturing Process of Thermoplastic Matrix Composites, J. Compos. Mater., 21 (1987) 1017-1055.
https://doi.org/10.1177/002199838702101103

[5] F. Yang and R. Pitchumani, A fractal Cantor set based description of interlaminar contact evolution during thermoplastic composites processing, J. Mater. Sci., 36 (2001) 4661-4671.
https://doi.org/10.1023/A:1017950215945

[6] F. Yang and R. Pitchumani, Fractal description of interlaminar contact development during thermoplastic composites processing, J. Reinf. Plast. Compos., 20 (2001) 536-546.

[7] A. Levy, D. Heider, J. Tierney, and J. W. Gillespie, Inter-layer thermal contact resistance evolution with the degree of intimate contact in the processing of thermoplastic composite laminates, J. Compos. Mater., 48 (2014) 491-503.

[8] M. A. Khan, P. Mitschang, and R. Schledjewski, Identification of some optimal parameters to achieve higher laminate quality through tape placement process, Adv. Polym. Technol., 29 (Jun. 2010) 98-111.
https://doi.org/10.1002/adv.20177

[9] P. M. Schaefer, T. Guglhoer, M. G. R. Sause, and K. Drechsler, Development of intimate contact during processing of carbon fiber reinforced Polyamide-6 tapes, J. Reinf. Plast. Compos., 36 (2017) 593-607.
https://doi.org/10.1177/0731684416687041

[10] P. M. Schäfer, Consolidation of carbon fiber reinforced polyamide 6 tapes using laser-assisted tape placement. Technische Universität München, 2017.

[11] W. J. B. Grouve, L. L. Warnet, B. Rietman, H. A. Visser, and R. Akkerman, Optimization of the tape placement process parameters for carbon-PPS composites, Compos. Part A Appl. Sci. Manuf., 50 (2013) 44-53.
https://doi.org/10.1016/j.compositesa.2013.03.003

[12] J. Engmann, C. Servais, and A. S. Burbidge, Squeeze flow theory and applications to rheometry: A review, J. Nonnewton. Fluid Mech., 132 (2005) 1-27.

[13] O. Çelik et al., The influence of inter-laminar thermal contact resistance on the cooling of material during laser assisted fiber placement, Compos. Part A Appl. Sci. Manuf., 145 (2021) 106367.

[14] J. Zhou, F. Desplentere, and J. Ivens, µCT-based internal microstructure analysis in continuous fiber reinforced thermoplastics, in *ITHEC 2022 Conference Proceedings*, CONGRESS BREMEN & MESSE BREMEN, 2022.
# Composite forming post-manufacture: reducing complexity and de-risking manufacture

PALUBISKI Dominic R.¹,ª*, LONGANA Marco L.², DULIEU-BARTON Janice M.¹, HAMERTON Ian¹, and IVANOV Dmitry S.¹,ᵇ

¹Bristol Composites Institute, School of Civil, Aerospace, and Design Engineering, Faculty of Science and Engineering, University of Bristol, Queen's Building, University Walk, Bristol, BS8 1TR, U.K

²Department of Chemistry, Material, and Chemical Engineering, Politecnico di Milano, Milan, Italy

ªdominic.palubiski@bristol.ac.uk, ᵇdmitry.ivanov@bristol.ac.uk

**Keywords:** Composites, Modular Forming, Multi-Matrix Systems, Post-Manufacture Forming

**Abstract.** Forming is a high-risk operation as the deformation of precursors, such as preforms or prepregs, is difficult to control. Aiming at de-risking manufacturing and improving processing logistics, a new forming concept is presented involving pre-structuring, i.e. producing fully cured flat structure with integrated formable hinge regions, and assembly, where the part is given the targeted shape using localised forming in the hinge regions. Such a technique becomes feasible if (a) the hinges are produced with the aid of covalent adaptive networks (CANs, cross-linked polymers that can flow when heated above a certain temperature), (b) the excess fibre length (that can occur in the process of forming) is incorporated at the pre-structuring stage. Hence, we pursue an idea of multi-matrix continuously-reinforced composites (MMCRC) with embedded fibre path features, where the main body of composites structure is produced with a conventional epoxy matrix and the hinged areas are produced with reformable CANs. The current paper explores the potential and limitations of this technology in manufacturing trials. It is demonstrated that the presented concept can yield high quality solutions. It is highlighted that an improved manufacturing procedure using specially designed and portable machinery would enable application of the MIMCRC technology in the field, facilitating repair and efficient transportation.

**Introduction**

Manufacturing composite components typically includes high-risk forming actions that result in morphological defects that typically occur when reinforcement materials are conformed to produce geometric features. The evolution of such defects is difficult to avoid and may lead to a high rate of part scrappage. It is imperative to reduce material usage and time lost at the manufacturing stage to enable the adoption of composite materials in broader market segments and to provide lower cost solutions. The defects are formed either during layup/deposition or occur as part of consolidation/forming processes and can take on a range of forms, from the presence of resin-rich regions, to misaligned fibres, and delaminations [1,2]. If the defects remain in the cured component they may result in reduced in-service performance and can lead to an early failure.

There are various mechanisms for the formation of fibre-path defects, mostly associated with compressive forces acting on compliant precursor, constrained ply-to-ply and/or ply-to-tool interaction, excessive shearing, stack bending, or a combination of these. The resultant precursor deformations are typically manifested through ply buckling, fibre crimp, in-plane waviness, ply separation, and thickness variations, etc. The probability of defects evolving are particularly high with large movement/rotations of preforms, conforming materials to complex shapes, particularly

<figure><img src="image_420.png" /></figure>
# Composite forming post-manufacture: reducing complexity and de-risking manufacture

PALUBISKI Dominic R.¹,ª*, LONGANA Marco L.², DULIEU-BARTON Janice M.¹, HAMERTON Ian¹, and IVANOV Dmitry S.¹,ᵇ

¹Bristol Composites Institute, School of Civil, Aerospace, and Design Engineering, Faculty of Science and Engineering, University of Bristol, Queen's Building, University Walk, Bristol, BS8 1TR, U.K

²Department of Chemistry, Material, and Chemical Engineering, Politecnico di Milano, Milan, Italy

ªdominic.palubiski@bristol.ac.uk, ᵇdmitry.ivanov@bristol.ac.uk

**Keywords:** Composites, Modular Forming, Multi-Matrix Systems, Post-Manufacture Forming

**Abstract.** Forming is a high-risk operation as the deformation of precursors, such as preforms or prepregs, is difficult to control. Aiming at de-risking manufacturing and improving processing logistics, a new forming concept is presented involving pre-structuring, i.e. producing fully cured flat structure with integrated formable hinge regions, and assembly, where the part is given the targeted shape using localised forming in the hinge regions. Such a technique becomes feasible if (a) the hinges are produced with the aid of covalent adaptive networks (CANs, cross-linked polymers that can flow when heated above a certain temperature), (b) the excess fibre length (that can occur in the process of forming) is incorporated at the pre-structuring stage. Hence, we pursue an idea of multi-matrix continuously-reinforced composites (MMCRC) with embedded fibre path features, where the main body of composites structure is produced with a conventional epoxy matrix and the hinged areas are produced with reformable CANs. The current paper explores the potential and limitations of this technology in manufacturing trials. It is demonstrated that the presented concept can yield high quality solutions. It is highlighted that an improved manufacturing procedure using specially designed and portable machinery would enable application of the MIMCRC technology in the field, facilitating repair and efficient transportation.

**Introduction**

Manufacturing composite components typically includes high-risk forming actions that result in morphological defects that typically occur when reinforcement materials are conformed to produce geometric features. The evolution of such defects is difficult to avoid and may lead to a high rate of part scrappage. It is imperative to reduce material usage and time lost at the manufacturing stage to enable the adoption of composite materials in broader market segments and to provide lower cost solutions. The defects are formed either during layup/deposition or occur as part of consolidation/forming processes and can take on a range of forms, from the presence of resin-rich regions, to misaligned fibres, and delaminations [1,2]. If the defects remain in the cured component they may result in reduced in-service performance and can lead to an early failure.

There are various mechanisms for the formation of fibre-path defects, mostly associated with compressive forces acting on compliant precursor, constrained ply-to-ply and/or ply-to-tool interaction, excessive shearing, stack bending, or a combination of these. The resultant precursor deformations are typically manifested through ply buckling, fibre crimp, in-plane waviness, ply separation, and thickness variations, etc. The probability of defects evolving are particularly high with large movement/rotations of preforms, conforming materials to complex shapes, particularly

<figure><img src="image_431.png" /></figure>

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those involving double-curvature, and for forming operations that occur across a majority of the laminate. The concept presented here addresses the challenge of defect mitigation in cases involving prominent bending and deep drawing deformations over corner geometries.

The proposed concept, named Multi-Matrix Continuously-Reinforced Composites (MMCRC), is illustrated in Fig. 1. Separate composite precursors comprising formable and non-formable material are connected by continuous reinforcement. Such composites have been proven to yield benefits through added functionality [3], improved mechanical performance [4], and potential for composite repair [5]. In a forming context, the allocation of different domains to different matrices permits the production of a ‘flat’ pre-structure first, followed by folding the formable regions to the desired geometry using localised heat and pressure. As the formable material takes shape, the unconfigurable material outside the forming zone restricts any undesirable deformations. By enabling local forming operations by introducing pre-structures, it is expected that better control of the material state is achieved at relatively low heat and pressure demands. Limiting the allowable deformations in manufacturing is known to result in defect mitigation, as observed by Turk et al. [6], where matrix patches were integrated into dry preform at critical locations. Alongside defect mitigation, additional benefits include a reduction in lay-up time; improved manufacturing logistics (where the flat pre-structure parts could be easily transported to assembly locations); locality of forming regions (allows the use of reformable matrices with challenging processing characteristics that would be prohibitive for the overall construction); reinforcement continuity (ensuring efficient load transfer); and the allocation of formable matrix strictly where it is needed (minimizing the impact of new materials on overall cost and permits greater design flexibility).

<figure><img src="image_421.png" /><figcaption>Figure 1. The post-manufacture forming concept, utilizing the MIMCRC design concept.</figcaption></figure>

Among the candidates for formable regions, covalent adaptive networks (CANs), also known as vitrimers [7], present a particular interest. These are a modern class of plastics that are similar to thermosets mechanically and in their structural chemistry, while (through the addition of reversible chemical side chains) are able to be reformed at temperatures in a similar manner to thermoplastics. What is particularly attractive about vitrimers is that (a) processing temperatures to form and reverse the cross-linking are relatively low (50-200 °C), (b) their viscosity is much lower compared to thermoplastics, (c) they are compatible with host thermosetting resins in non-reformable domains. Vitrimer resins can use typical thermoset chemistry for cure, such as epoxy ring-opening, allowing for improved chemical integration into the bulk thermoset structure. This
those involving double-curvature, and for forming operations that occur across a majority of the laminate. The concept presented here addresses the challenge of defect mitigation in cases involving prominent bending and deep drawing deformations over corner geometries.

The proposed concept, named Multi-Matrix Continuously-Reinforced Composites (MMCRC), is illustrated in Fig. 1. Separate composite precursors comprising formable and non-formable material are connected by continuous reinforcement. Such composites have been proven to yield benefits through added functionality [3], improved mechanical performance [4], and potential for composite repair [5]. In a forming context, the allocation of different domains to different matrices permits the production of a ‘flat’ pre-structure first, followed by folding the formable regions to the desired geometry using localised heat and pressure. As the formable material takes shape, the unconfigurable material outside the forming zone restricts any undesirable deformations. By enabling local forming operations by introducing pre-structures, it is expected that better control of the material state is achieved at relatively low heat and pressure demands. Limiting the allowable deformations in manufacturing is known to result in defect mitigation, as observed by Turk et al. [6], where matrix patches were integrated into dry preform at critical locations. Alongside defect mitigation, additional benefits include a reduction in lay-up time; improved manufacturing logistics (where the flat pre-structure parts could be easily transported to assembly locations); locality of forming regions (allows the use of reformable matrices with challenging processing characteristics that would be prohibitive for the overall construction); reinforcement continuity (ensuring efficient load transfer); and the allocation of formable matrix strictly where it is needed (minimizing the impact of new materials on overall cost and permits greater design flexibility).

<figure><img src="image_432.png" /><figcaption>Figure 1. The post-manufacture forming concept, utilizing the MIMCRC design concept.</figcaption></figure>

Among the candidates for formable regions, covalent adaptive networks (CANs), also known as vitrimers [7], present a particular interest. These are a modern class of plastics that are similar to thermosets mechanically and in their structural chemistry, while (through the addition of reversible chemical side chains) are able to be reformed at temperatures in a similar manner to thermoplastics. What is particularly attractive about vitrimers is that (a) processing temperatures to form and reverse the cross-linking are relatively low (50-200 °C), (b) their viscosity is much lower compared to thermoplastics, (c) they are compatible with host thermosetting resins in non-reformable domains. Vitrimer resins can use typical thermoset chemistry for cure, such as epoxy ring-opening, allowing for improved chemical integration into the bulk thermoset structure. This
is an important feature for MMCRCs, although the major contribution to the strength of the vitrimer-thermoset interface is mechanical bridging of continuous reinforcement.

The main challenge of the presented concept is that the fibres are constrained within non-formable regions and cannot slide with respect to each other during forming. This creates a danger of trapping excess length and generating defects at the stage of folding pre-structures, as the fibre paths in upper and lower plies must be different when formed. Some of the forming challenges for MMCRCs were previously reported by Palubiski et al. [5]. Even though the laminate was not produced by bending the pre-structure, the high viscosity and long working times of the vitrimer led to fibre winkling and poor geometrical compliance. The study also revealed a high sensitivity of the forming operation to defect morphology and consistency of sample quality. In the context of pre-structuring, there is a particular need to incorporate the excess length at the stage of making the flat pre-structure. The current paper examines the feasibility of incorporating such features and examines the forming operations required to handling such pre-structures.

## Concept Implementation: Materials, Feature Design and Manufacture

A L-shaped corner geometry was chosen for the demonstrator due to its frequent use within composite parts. In addition, this simple shape does not involve shear deformations, which needs to be addressed separately, and allows only pure bending to be examined. The shape of the excess feature must be designed in a way that respects the different fibre lengths after forming on the inner side of the corner, on the mid-plane, and at the outer surface. For simplicity, the inner side of the corner in the pre-structure was chosen to be flat, then each subsequent ply increases in length, thus creating an embossed region resembling a non-buckled wrinkle. The embossed region can be mathematically represented by hyperbolic secant, (Equation 1) [8],

$$w = A \sech(Bx) \qquad (1)$$

where A is the highest point of the feature, and B is the shape parameter and can be roughly estimated as 1/8th of the embossed region span. The excess length, Δ, can then be calculated using Equation 2.

$$\Delta = A^2B/3 \qquad (2)$$

To capture the correct excess length, the final target geometry was determined, with a calculated 3.5 mm final sample thickness, with a 6.4 mm inner corner radius. These values were chosen to align with standards on testing through-thickness strength of composites, ASTM D6145 [9].

Manufacturing samples for post-manufacture forming began with Vitrimax™ T100, a proprietary imine-linked vitrimer (ex Mallinda, Inc.) [10], which was mixed in accordance with the manufacturer's standard directions, 1:2.5 (epoxy:imine hardener), at 80 °C and left to cool and cure for 24 hours at room temperature. The cured vitrimer was broken into small pieces no larger than 5 mm³ and evenly spread into a flat thin film mould, which was heated to 140 °C and then pressed at 6 bar for 2 hours to produce a 0.3 mm thick vitrimer film of width 20 mm and length 150 mm.

Dry carbon fibre (3K, 2x2 twill with a cloth weight of 210 g.m⁻², Pyrofil HT TR 30S 3L ex Easy Composites Ltd) [11] was used as the reinforcement. To produce the vitrimer region with the feature in the form of an 'embossed region', a bespoke tool was designed as shown in Fig. 2. The geometry of the recess was determined using the procedure described above so that the embossed region shape accommodated the excess length required for the outer ply of the final L-shaped panel. A [0/90]₁₅ laminate was laid up, with a single film of vitrimer between each ply and one on the top of the stack, placed so the 20 mm width straddled the recess. The fibres in the plies were orientated so that they were either aligned with the recess, or transverse to the recess in the bespoke
is an important feature for MMCRCs, although the major contribution to the strength of the vitrimer-thermoset interface is mechanical bridging of continuous reinforcement.

The main challenge of the presented concept is that the fibres are constrained within non-formable regions and cannot slide with respect to each other during forming. This creates a danger of trapping excess length and generating defects at the stage of folding pre-structures, as the fibre paths in upper and lower plies must be different when formed. Some of the forming challenges for MMCRCs were previously reported by Palubiski et al. [5]. Even though the laminate was not produced by bending the pre-structure, the high viscosity and long working times of the vitrimer led to fibre winkling and poor geometrical compliance. The study also revealed a high sensitivity of the forming operation to defect morphology and consistency of sample quality. In the context of pre-structuring, there is a particular need to incorporate the excess length at the stage of making the flat pre-structure. The current paper examines the feasibility of incorporating such features and examines the forming operations required to handling such pre-structures.

## Concept Implementation: Materials, Feature Design and Manufacture

A L-shaped corner geometry was chosen for the demonstrator due to its frequent use within composite parts. In addition, this simple shape does not involve shear deformations, which needs to be addressed separately, and allows only pure bending to be examined. The shape of the excess feature must be designed in a way that respects the different fibre lengths after forming on the inner side of the corner, on the mid-plane, and at the outer surface. For simplicity, the inner side of the corner in the pre-structure was chosen to be flat, then each subsequent ply increases in length, thus creating an embossed region resembling a non-buckled wrinkle. The embossed region can be mathematically represented by hyperbolic secant, (Equation 1) [8],

$$w = A \sech(Bx) \qquad (1)$$

where A is the highest point of the feature, and B is the shape parameter and can be roughly estimated as 1/8th of the embossed region span. The excess length, Δ, can then be calculated using Equation 2.

$$\Delta = A^2B/3 \qquad (2)$$

To capture the correct excess length, the final target geometry was determined, with a calculated 3.5 mm final sample thickness, with a 6.4 mm inner corner radius. These values were chosen to align with standards on testing through-thickness strength of composites, ASTM D6145 [9].

Manufacturing samples for post-manufacture forming began with Vitrimax™ T100, a proprietary imine-linked vitrimer (ex Mallinda, Inc.) [10], which was mixed in accordance with the manufacturer's standard directions, 1:2.5 (epoxy:imine hardener), at 80 °C and left to cool and cure for 24 hours at room temperature. The cured vitrimer was broken into small pieces no larger than 5 mm³ and evenly spread into a flat thin film mould, which was heated to 140 °C and then pressed at 6 bar for 2 hours to produce a 0.3 mm thick vitrimer film of width 20 mm and length 150 mm.

Dry carbon fibre (3K, 2x2 twill with a cloth weight of 210 g.m⁻², Pyrofil HT TR 30S 3L ex Easy Composites Ltd) [11] was used as the reinforcement. To produce the vitrimer region with the feature in the form of an 'embossed region', a bespoke tool was designed as shown in Fig. 2. The geometry of the recess was determined using the procedure described above so that the embossed region shape accommodated the excess length required for the outer ply of the final L-shaped panel. A [0/90]₁₅ laminate was laid up, with a single film of vitrimer between each ply and one on the top of the stack, placed so the 20 mm width straddled the recess. The fibres in the plies were orientated so that they were either aligned with the recess, or transverse to the recess in the bespoke
tool. A laminate size of over 150 mm width and 100 mm length was used to ensure the final composite was large enough for forming. This lay-up was then sealed into a vacuum bag and the tooling placed externally on top of the bag.

<figure><img src="image_422.png" /><figcaption>Figure 2. Mould for manufacturing pre-structures with the excess length feature. The width of the feature is 13.91 mm, with an embossment height of 5.95 mm. The mould surface is the outer surface of the corner in final shape.</figcaption></figure>

The bagged lay-up and excess length tooling were hot pressed, following the cycle in Table 1, using a Hare 50TUP4C hydraulic press. After cooling to room temperature, the pressure was removed and the partially infused preform is then bagged flat for resin infusion of the dry preform arms. Gurit PRIME™ 37 and Ampreg™ 3X extra-slow hardener [12] (100:29 weight ratio respectively) was mixed and then degassed for 30 minutes before infusion. Once infused, the part was cured at 25 °C for 13 hours, followed by a post cure at 50 °C for 16 hours. Then 100 mm lengths were cut for the final manufacturing procedure of forming into the L-shape for the demonstrator.

<table><caption>Table 1. Manufacturing parameters for vitrimer hot press infusion.</caption><thead><tr><td>Step</td><td>Pressure [bar]</td><td>Temperature [°C]</td><td>Time [minutes]</td></tr></thead><tbody><tr><td>1</td><td>0</td><td>140</td><td>120</td></tr><tr><td>2</td><td>0.1</td><td>140</td><td>10</td></tr><tr><td>3</td><td>0.2</td><td>140</td><td>10</td></tr><tr><td>4</td><td>0.4</td><td>140</td><td>10</td></tr><tr><td>5</td><td>8</td><td>140</td><td>120</td></tr></tbody></table>

A polished edge of the produced panel was optically imaged prior to forming into the L-shape using a Zeiss Axio Imager.M2 microscope and the proprietary software. The epoxy thermoset arms showed good infusion with minimal voids or defects. The ‘flat’ formed panel embossed region shows a very resin rich structure with evenly spaced plies (Fig. 3). The fibres conform well to the excess length shape change with minimal observed defects. Due to the reduced
tool. A laminate size of over 150 mm width and 100 mm length was used to ensure the final composite was large enough for forming. This lay-up was then sealed into a vacuum bag and the tooling placed externally on top of the bag.

<figure><img src="image_433.png" /><figcaption>Figure 2. Mould for manufacturing pre-structures with the excess length feature. The width of the feature is 13.91 mm, with an embossment height of 5.95 mm. The mould surface is the outer surface of the corner in final shape.</figcaption></figure>

The bagged lay-up and excess length tooling were hot pressed, following the cycle in Table 1, using a Hare 50TUP4C hydraulic press. After cooling to room temperature, the pressure was removed and the partially infused preform is then bagged flat for resin infusion of the dry preform arms. Gurit PRIME™ 37 and Ampreg™ 3X extra-slow hardener [12] (100:29 weight ratio respectively) was mixed and then degassed for 30 minutes before infusion. Once infused, the part was cured at 25 °C for 13 hours, followed by a post cure at 50 °C for 16 hours. Then 100 mm lengths were cut for the final manufacturing procedure of forming into the L-shape for the demonstrator.

<table><caption>Table 1. Manufacturing parameters for vitrimer hot press infusion.</caption><thead><tr><td>Step</td><td>Pressure [bar]</td><td>Temperature [°C]</td><td>Time [minutes]</td></tr></thead><tbody><tr><td>1</td><td>0</td><td>140</td><td>120</td></tr><tr><td>2</td><td>0.1</td><td>140</td><td>10</td></tr><tr><td>3</td><td>0.2</td><td>140</td><td>10</td></tr><tr><td>4</td><td>0.4</td><td>140</td><td>10</td></tr><tr><td>5</td><td>8</td><td>140</td><td>120</td></tr></tbody></table>

A polished edge of the produced panel was optically imaged prior to forming into the L-shape using a Zeiss Axio Imager.M2 microscope and the proprietary software. The epoxy thermoset arms showed good infusion with minimal voids or defects. The ‘flat’ formed panel embossed region shows a very resin rich structure with evenly spaced plies (Fig. 3). The fibres conform well to the excess length shape change with minimal observed defects. Due to the reduced
consolidation pressure within the embossed region, along with the viscous nature of the vitrimer, there is consistent sporadic dry fibre sections within the core of the tows. These were expected due to the forming conditions to create the embossed region. During final forming to the L-shape and consolidation, it was expected that the embossed vitrimer region would experience higher impregnation forces and so the vitrimer would infiltrating the inner fibres of the final formed component.

<figure><img src="image_423.png" /><figcaption>Figure 3. Pre-formed vitrimer embossed region.</figcaption></figure>

## Final Forming

To form the final L-shaped panel a ‘flat’ panel, as produced above, was heated locally in the embossed vitrimer region to above the vitrimer disassociation temperature and mechanically formed when the vitrimer is in this softened state. The initial forming was undertaken using a Shimadzu Autograph AGS-X electromechanical test machine with the panel and tooling placed within a heated chamber held at 140 °C, as shown in Fig. 4a. The support for the tooling consisted of a fixed bottom mount, an extender support, and a flat plate for the lower female tool. For the upper male tool, a fixed top mount, two extender supports, and a fixture attachment mount were used. Both sets of extenders were necessary to allow the placement of the tooling within the oven. For forming, a crosshead speed of 0.5 mm.min⁻¹ was used, which took roughly 2 hours. An average 50 N force was required throughout the forming process.

Final consolidation was undertaken using a hot press, as the extended tool supports required to produce the L-shape in a controlled manner in the oven mounted on the test machine, risked buckling. Instead, the male and female tools, with the panel between, were heated to 140 °C and then pressed at 6 bar for 60 minutes. The panel was allowed to cool to room temperature before pressure was removed.
consolidation pressure within the embossed region, along with the viscous nature of the vitrimer, there is consistent sporadic dry fibre sections within the core of the tows. These were expected due to the forming conditions to create the embossed region. During final forming to the L-shape and consolidation, it was expected that the embossed vitrimer region would experience higher impregnation forces and so the vitrimer would infiltrating the inner fibres of the final formed component.

<figure><img src="image_434.png" /><figcaption>Figure 3. Pre-formed vitrimer embossed region.</figcaption></figure>

## Final Forming

To form the final L-shaped panel a ‘flat’ panel, as produced above, was heated locally in the embossed vitrimer region to above the vitrimer disassociation temperature and mechanically formed when the vitrimer is in this softened state. The initial forming was undertaken using a Shimadzu Autograph AGS-X electromechanical test machine with the panel and tooling placed within a heated chamber held at 140 °C, as shown in Fig. 4a. The support for the tooling consisted of a fixed bottom mount, an extender support, and a flat plate for the lower female tool. For the upper male tool, a fixed top mount, two extender supports, and a fixture attachment mount were used. Both sets of extenders were necessary to allow the placement of the tooling within the oven. For forming, a crosshead speed of 0.5 mm.min⁻¹ was used, which took roughly 2 hours. An average 50 N force was required throughout the forming process.

Final consolidation was undertaken using a hot press, as the extended tool supports required to produce the L-shape in a controlled manner in the oven mounted on the test machine, risked buckling. Instead, the male and female tools, with the panel between, were heated to 140 °C and then pressed at 6 bar for 60 minutes. The panel was allowed to cool to room temperature before pressure was removed.
Panel Manufacture and Forming Results

Despite successful realisation of the concept the suggested technique was sensitive to variation in manufacturing procedures. These included asymmetries resulting from uneven heating making the panels susceptible to unintended forming scenarios. As can be seen in the Fig. 4b some forming operations produced samples with significant wrinkling and defects. The multiple support linkages required resulted in multiple points with small degrees of movement as indicated in Fig. 4a. When the panel was being formed, an inaccuracy in positioning of material with respect to the forming rig or asymmetry in heating could result in asymmetrical forming that accumulates the excess length as it progresses. Additionally, the vitrimer extended beyond the embossed region by roughly 5-15 mm either side on all samples, and in this case the entire hinge region became soft and started to sag under its own weight. As the panel sagged, the resultant movement could unpredictably shift the centre of the embossment to misalign with the tooling.

<figure><img src="image_424.png" /><figcaption>Figure 4. ‘a’ shows the forming set up with the tooling (grey), connected to the supports (black) within the oven (yellow). The points of linkage movement are highlighted with red circles. The second image, b, showcasing wrinkles produced during initial forming trials due to poor tooling alignment.</figcaption></figure>

A primary conclusion is that a more highly controlled forming procedure is required for producing the pre-structure that utilises specifically designed machinery, rather than the set-up in the test machine. Such machinery would not only allow for more secure positioning of the panel, but also implement targeting heating of only the formable region. In addition, the current forming tooling applies forming forces (via the female tool) to the epoxy arms. Applying the force directly to the vitrimer region would allow for the final shape to be ‘pinched’ into form, and aid in reducing defect formation.
Panel Manufacture and Forming Results

Despite successful realisation of the concept the suggested technique was sensitive to variation in manufacturing procedures. These included asymmetries resulting from uneven heating making the panels susceptible to unintended forming scenarios. As can be seen in the Fig. 4b some forming operations produced samples with significant wrinkling and defects. The multiple support linkages required resulted in multiple points with small degrees of movement as indicated in Fig. 4a. When the panel was being formed, an inaccuracy in positioning of material with respect to the forming rig or asymmetry in heating could result in asymmetrical forming that accumulates the excess length as it progresses. Additionally, the vitrimer extended beyond the embossed region by roughly 5-15 mm either side on all samples, and in this case the entire hinge region became soft and started to sag under its own weight. As the panel sagged, the resultant movement could unpredictably shift the centre of the embossment to misalign with the tooling.

<figure><img src="image_435.png" /><figcaption>Figure 4. ‘a’ shows the forming set up with the tooling (grey), connected to the supports (black) within the oven (yellow). The points of linkage movement are highlighted with red circles. The second image, b, showcasing wrinkles produced during initial forming trials due to poor tooling alignment.</figcaption></figure>

A primary conclusion is that a more highly controlled forming procedure is required for producing the pre-structure that utilises specifically designed machinery, rather than the set-up in the test machine. Such machinery would not only allow for more secure positioning of the panel, but also implement targeting heating of only the formable region. In addition, the current forming tooling applies forming forces (via the female tool) to the epoxy arms. Applying the force directly to the vitrimer region would allow for the final shape to be ‘pinched’ into form, and aid in reducing defect formation.
Even with the limitations of the apparatus used in the initial trials, successful forming operations were achieved, with Fig. 5 showing the three stages in the procedure to produce the final panel. At each stage a strip of material was cut from the panel to provide a coupon for further investigation. The top image in Fig. 5 shows a coupon from the ‘flat’ panel with the embossed MMCRC region before forming. The middle image in Fig. 5 shows a coupon after the first forming to the L-shape. There are observable delaminations occurring in this stage of the forming process, as the vitrimer cannot flow through the thermoset epoxy matrix and is also unable to flow fast enough through individual plies. This results in the vitrimer at the centre of the panel pushing the laminates apart, resulting in the delaminations. The slow forming time (2 hours with a 0.5 mm.min⁻¹ head speed) was decided upon to best minimize any delamination damage in the unrepairable epoxy regions. In the next consolidation step (not shown in Fig. 5), the delaminations were removed, with excess vitrimer resin squeezed out the ends of the corner region of the panel. The bottom image shows a coupon from the final formed panel after consolidation. The process was successfully able to form the composite panel with minimal defects observed. It is worth emphasizing that the manufacturing sequence de-risks not only forming but also infusions. Manufacturing the ‘flat’ panel is less susceptible to uncontrolled race-tracking typical for complex features [5] and minimises the risks of dry regions or excessive porosity.

<figure><img src="image_425.png" /><figcaption>Figure 5. The three stages of manufacture outlined in this paper. Top is the initial MMCRC 'flat' panel, with a vitrimer excess length region and typical epoxy arms. The middle is the panel after forming, with ply separation present due to vitrimer flow. The bottom section is the final panel after consolidation.</figcaption></figure>

A micrograph of the coupon after the final consolidation is shown in Fig. 6. It can be seen that the delaminations have been consolidated and repaired with no obvious fibre damage or wrinkling is present in the entire corner region. The confidence in the delamination repair has been shown in previous work [5] with multiple reprocessing stages not significantly effecting the properties of the system [13,14]. However, the process has not been perfected yet, with some vitrimer rich regions still extant and some dry spots still present. It considered that an improved forming regime using bespoke machinery, as mentioned above, would reduce the defects.
Even with the limitations of the apparatus used in the initial trials, successful forming operations were achieved, with Fig. 5 showing the three stages in the procedure to produce the final panel. At each stage a strip of material was cut from the panel to provide a coupon for further investigation. The top image in Fig. 5 shows a coupon from the ‘flat’ panel with the embossed MMCRC region before forming. The middle image in Fig. 5 shows a coupon after the first forming to the L-shape. There are observable delaminations occurring in this stage of the forming process, as the vitrimer cannot flow through the thermoset epoxy matrix and is also unable to flow fast enough through individual plies. This results in the vitrimer at the centre of the panel pushing the laminates apart, resulting in the delaminations. The slow forming time (2 hours with a 0.5 mm.min⁻¹ head speed) was decided upon to best minimize any delamination damage in the unrepairable epoxy regions. In the next consolidation step (not shown in Fig. 5), the delaminations were removed, with excess vitrimer resin squeezed out the ends of the corner region of the panel. The bottom image shows a coupon from the final formed panel after consolidation. The process was successfully able to form the composite panel with minimal defects observed. It is worth emphasizing that the manufacturing sequence de-risks not only forming but also infusions. Manufacturing the ‘flat’ panel is less susceptible to uncontrolled race-tracking typical for complex features [5] and minimises the risks of dry regions or excessive porosity.

<figure><img src="image_436.png" /><figcaption>Figure 5. The three stages of manufacture outlined in this paper. Top is the initial MMCRC 'flat' panel, with a vitrimer excess length region and typical epoxy arms. The middle is the panel after forming, with ply separation present due to vitrimer flow. The bottom section is the final panel after consolidation.</figcaption></figure>

A micrograph of the coupon after the final consolidation is shown in Fig. 6. It can be seen that the delaminations have been consolidated and repaired with no obvious fibre damage or wrinkling is present in the entire corner region. The confidence in the delamination repair has been shown in previous work [5] with multiple reprocessing stages not significantly effecting the properties of the system [13,14]. However, the process has not been perfected yet, with some vitrimer rich regions still extant and some dry spots still present. It considered that an improved forming regime using bespoke machinery, as mentioned above, would reduce the defects.
<figure><img src="image_426.png" /><figcaption>Figure 6. The vitrimer corner region after forming. While some dry zones and resin rich zones still exist, the fibres have been formed to the correct geometry with minimal wrinkling observed.</figcaption></figure>

## Conclusions

The concept of utilizing vitrimers in the form of additional features to ease the forming of composites parts to reduce fibre wrinkling and damage has been successfully achieved. The rudimentary manufacturing procedure used to form the part, based on utilising a standard test machine and testing oven resulted in variation that led to defects forming due to uneven heating and small variations in the rig/tool/material positioning. To eliminate the anomalies caused in the forming process specially designed machinery is being developed that provides a more uniform introduction of bending accuracy and localised heating targeted at the vitrimer embossed corner region. The machinery gradually encourages the vitrimer to form in the corner region and reduce the build-up of excess resin. The outcome of the work will be included in a future publication. Importantly, the work in the present paper has demonstrated the concept and manufacturing feasibility of a procedure for producing pre-structured Multi-Matrix Continuously-Reinforced Composite flat panels. The concept is a promising route for future composite design where handling and forming on site both improves transportability and reduces geometry defects.

## References

[1] Hassan MH, Othman AR, Kamaruddin S. A review on the manufacturing defects of complex-shaped laminate in aircraft composite structures. The International Journal of Advanced Manufacturing Technology 2017;91:4081–94. https://doi.org/10.1007/s00170-017-0096-5

[2] Lukaszewicz DH-JA, Ward C, Potter KD. The engineering aspects of automated prepreg layup: History, present and future. Compos B Eng 2012;43:997–1009. https://doi.org/10.1016/j.compositesb.2011.12.003

[3] Radhakrishnan A, Georgillas I, Hamerton I, Shaffer MSP, Ivanov DS. Manufacturing Multi-Matrix Composites: Out-of-Vacuum Bag Consolidation. J Manuf Sci Eng 2023;145. https://doi.org/10.1115/1.4063091

[4] Stanier D, Gent I, Roy SS, Hamerton I, Potluri P, Ivanov DS. Mechanical Behaviour of Patterned Multi-Matrix Composites with Gradient Properties. 2016.

[5] Palubiski DR, Longana ML, Dulieu-Barton JM, Hamerton I, Ivanov DS. Multi-matrix continuously-reinforced composites: A novel route to sustainable repair of composite structures. Mater Des 2023;235:112446. https://doi.org/10.1016/J.MATDES.2023.112446
<figure><img src="image_437.png" /><figcaption>Figure 6. The vitrimer corner region after forming. While some dry zones and resin rich zones still exist, the fibres have been formed to the correct geometry with minimal wrinkling observed.</figcaption></figure>

## Conclusions

The concept of utilizing vitrimers in the form of additional features to ease the forming of composites parts to reduce fibre wrinkling and damage has been successfully achieved. The rudimentary manufacturing procedure used to form the part, based on utilising a standard test machine and testing oven resulted in variation that led to defects forming due to uneven heating and small variations in the rig/tool/material positioning. To eliminate the anomalies caused in the forming process specially designed machinery is being developed that provides a more uniform introduction of bending accuracy and localised heating targeted at the vitrimer embossed corner region. The machinery gradually encourages the vitrimer to form in the corner region and reduce the build-up of excess resin. The outcome of the work will be included in a future publication. Importantly, the work in the present paper has demonstrated the concept and manufacturing feasibility of a procedure for producing pre-structured Multi-Matrix Continuously-Reinforced Composite flat panels. The concept is a promising route for future composite design where handling and forming on site both improves transportability and reduces geometry defects.

## References

[1] Hassan MH, Othman AR, Kamaruddin S. A review on the manufacturing defects of complex-shaped laminate in aircraft composite structures. The International Journal of Advanced Manufacturing Technology 2017;91:4081–94. https://doi.org/10.1007/s00170-017-0096-5

[2] Lukaszewicz DH-JA, Ward C, Potter KD. The engineering aspects of automated prepreg layup: History, present and future. Compos B Eng 2012;43:997–1009. https://doi.org/10.1016/j.compositesb.2011.12.003

[3] Radhakrishnan A, Georgillas I, Hamerton I, Shaffer MSP, Ivanov DS. Manufacturing Multi-Matrix Composites: Out-of-Vacuum Bag Consolidation. J Manuf Sci Eng 2023;145. https://doi.org/10.1115/1.4063091

[4] Stanier D, Gent I, Roy SS, Hamerton I, Potluri P, Ivanov DS. Mechanical Behaviour of Patterned Multi-Matrix Composites with Gradient Properties. 2016.

[5] Palubiski DR, Longana ML, Dulieu-Barton JM, Hamerton I, Ivanov DS. Multi-matrix continuously-reinforced composites: A novel route to sustainable repair of composite structures. Mater Des 2023;235:112446. https://doi.org/10.1016/J.MATDES.2023.112446
[6] Turk MA, Vermes B, Thompson AJ, Belnoue JP-H, Hallett SR, Ivanov DS. Mitigating forming defects by local modification of dry preforms. Compos Part A Appl Sci Manuf 2020;128:105643. https://doi.org/10.1016/j.compositesa.2019.105643

[7] Leibler L, Tournilhac F, Capelot M, Montarnal D. Silica-Like Malleable Materials from Permanent Organic Networks. Science (1979) 2011;334:965-8. https://doi.org/10.1126/science.1211649

[8] Ivanov DS, Volatier J, Rosli A, Nixon-Pearson O, Belnoue JP-H, Potter K, et al. Novel Methods of Assessing Inter-Ply Properties of Toughened Prepregs in Application to the Analysis of Fibre Path Defects. 20th International Conference on Composite Materials, Copenhagen: 2015.

[9] ASTM. D6415/D6415M 2013. https://doi.org/10.1520/D6415_D6415M-06AR13

[10] Mallinda n.d. https://mallinda.com/product/ (accessed August 16, 2022).

[11] Easy Composites n.d. https://www.easycomposites.co.uk/ (accessed August 16, 2022).

[12] Gurit Prime Resin Systems n.d. https://www.gurit.com/en/our-business/composite-materials/liquids/infusion (accessed August 16, 2022).

[13] Taynton P, Yu K, Shoemaker RK, Jin Y, Qi HJ, Zhang W. Heat- or water-driven malleability in a highly recyclable covalent network polymer. Advanced Materials 2014;26:3938-42. https://doi.org/10.1002/ADMA.201400317

[14] Kissounko DA, Taynton P, Kaffer C. New material: vitrimers promise to impact composites. Reinforced Plastics 2018;62:162-6. https://doi.org/10.1016/j.repl.2017.06.084
[6] Turk MA, Vermes B, Thompson AJ, Belnoue JP-H, Hallett SR, Ivanov DS. Mitigating forming defects by local modification of dry preforms. Compos Part A Appl Sci Manuf 2020;128:105643. https://doi.org/10.1016/j.compositesa.2019.105643

[7] Leibler L, Tournilhac F, Capelot M, Montarnal D. Silica-Like Malleable Materials from Permanent Organic Networks. Science (1979) 2011;334:965-8. https://doi.org/10.1126/science.1211649

[8] Ivanov DS, Volatier J, Rosli A, Nixon-Pearson O, Belnoue JP-H, Potter K, et al. Novel Methods of Assessing Inter-Ply Properties of Toughened Prepregs in Application to the Analysis of Fibre Path Defects. 20th International Conference on Composite Materials, Copenhagen: 2015.

[9] ASTM. D6415/D6415M 2013. https://doi.org/10.1520/D6415_D6415M-06AR13

[10] Mallinda n.d. https://mallinda.com/product/ (accessed August 16, 2022).

[11] Easy Composites n.d. https://www.easycomposites.co.uk/ (accessed August 16, 2022).

[12] Gurit Prime Resin Systems n.d. https://www.gurit.com/en/our-business/composite-materials/liquids/infusion (accessed August 16, 2022).

[13] Taynton P, Yu K, Shoemaker RK, Jin Y, Qi HJ, Zhang W. Heat- or water-driven malleability in a highly recyclable covalent network polymer. Advanced Materials 2014;26:3938-42. https://doi.org/10.1002/ADMA.201400317

[14] Kissounko DA, Taynton P, Kaffer C. New material: vitrimers promise to impact composites. Reinforced Plastics 2018;62:162-6. https://doi.org/10.1016/j.repl.2017.06.084
# A solid-beam approach for mesoscopic analysis of textile reinforcements forming simulation

LACROIX Baptiste¹,ᵃ*, COLMARS Julien¹,ᵇ, PLATZER Auriane¹,ᶜ, NAOUAR Naim¹,ᵈ, VIDAL-SALLÉ Emmanuelle¹,ᵉ, BOISSE Philippe¹

¹Université de Lyon, INSA-Lyon, LaMCoS UMR5259, F-69621, France

ᵃbaptiste.lacroix@insa-lyon.fr, ᵇjulien.colmars@insa-lyon.fr, ᶜauriane.platzer@insa-lyon.fr

ᵈnaim.naouar@insa-lyon.fr, ᶜemmanuelle.vidal-salle@insa-lyon.fr

**Keywords:** Meso-Scale Model, Solid-Beam, Fibrous Element, Hyperelastic

**Abstract.** Draping and forming of textile reinforcements are usually performed thanks to finite element models with continuous media assumption. The specific purpose of mesoscale model is to faithfully reproduces defects like yarn buckling or gapping during the process. Such defects are crucial outputs because they have huge impacts on mechanical and permeability properties of the whole textile. However, mesoscopic analysis usually leads to expensive computation cost and needs to be optimized to propose a cost-effective response to this problem. Thus, this document aims to develop a solid-beam approach for mesoscale model, with coarse geometric assumption but with finite element and constitutive law formulation taking into account the fibrous aspect of the fabric.

**Introduction**

The principle of mesoscopic analysis is to consider each yarn of a reinforcement as a continuous medium which mimics the geometric description of the fabric, as for example, its weaving pattern. Thanks to periodicity, textile studies can be reduced to a representative volume element (RVE), or unit-cell. The RVE can be either modelled from CAD software or deduced from micro-computed tomography (µCT) which enables to access to characteristics within the textile [1, 2]. It can be especially useful when yarn cross section shape and contact areas are critical inputs of the simulation. Such models are commonly meshed with isoparametric hexahedral elements associated with transverse isotropic 3D constitutive laws, either hypoelastic [2, 3] or hyperelastic [4]. Typically, mesoscopic RVE analysis can be relevant to simulate characterization test of woven fabrics [5].

When the purpose consists in modelling the entire textile, macroscopic scale is often chosen because of its efficiency. It can predict defects such as wrinkling [6, 7] but mesoscale models are necessary to highlight yarn buckling or gaping. However, very detailed and rich modelling might not be the most accurate because of their high computational costs (about one week of computation in case of forming simulation). To tackle this problem, some mixed meso-macro models have been proposed to give local mesoscopic analysis on macroscopic model. These works were mostly focused on 2D and 3D woven fabrics forming processes [8, 9].

Some assumptions can be made to simplify models and get more efficient computation with full mesoscopic analysis [10], but these models must be optimized to improve kinematic fidelity regarding experimental results.

To properly model the behaviour of textiles, classical Cauchy mechanics is not relevant, as has been experimentally highlighted [11]. Indeed, since fibrous media kinematics is guided by quasi-inextensibility of fibres and their relative sliding, tension and bending stiffness must be independent [12, 13]. These considerations motivated the development of a new finite element formulation which include the fibrous aspect [14, 15], which has mainly been used for macroscopic analysis so far.

<figure><img src="image_427.png" /></figure>
# A solid-beam approach for mesoscopic analysis of textile reinforcements forming simulation

LACROIX Baptiste¹,ᵃ*, COLMARS Julien¹,ᵇ, PLATZER Auriane¹,ᶜ, NAOUAR Naim¹,ᵈ, VIDAL-SALLÉ Emmanuelle¹,ᵉ, BOISSE Philippe¹

¹Université de Lyon, INSA-Lyon, LaMCoS UMR5259, F-69621, France

ᵃbaptiste.lacroix@insa-lyon.fr, ᵇjulien.colmars@insa-lyon.fr, ᶜauriane.platzer@insa-lyon.fr

ᵈnaim.naouar@insa-lyon.fr, ᶜemmanuelle.vidal-salle@insa-lyon.fr

**Keywords:** Meso-Scale Model, Solid-Beam, Fibrous Element, Hyperelastic

**Abstract.** Draping and forming of textile reinforcements are usually performed thanks to finite element models with continuous media assumption. The specific purpose of mesoscale model is to faithfully reproduces defects like yarn buckling or gapping during the process. Such defects are crucial outputs because they have huge impacts on mechanical and permeability properties of the whole textile. However, mesoscopic analysis usually leads to expensive computation cost and needs to be optimized to propose a cost-effective response to this problem. Thus, this document aims to develop a solid-beam approach for mesoscale model, with coarse geometric assumption but with finite element and constitutive law formulation taking into account the fibrous aspect of the fabric.

**Introduction**

The principle of mesoscopic analysis is to consider each yarn of a reinforcement as a continuous medium which mimics the geometric description of the fabric, as for example, its weaving pattern. Thanks to periodicity, textile studies can be reduced to a representative volume element (RVE), or unit-cell. The RVE can be either modelled from CAD software or deduced from micro-computed tomography (µCT) which enables to access to characteristics within the textile [1, 2]. It can be especially useful when yarn cross section shape and contact areas are critical inputs of the simulation. Such models are commonly meshed with isoparametric hexahedral elements associated with transverse isotropic 3D constitutive laws, either hypoelastic [2, 3] or hyperelastic [4]. Typically, mesoscopic RVE analysis can be relevant to simulate characterization test of woven fabrics [5].

When the purpose consists in modelling the entire textile, macroscopic scale is often chosen because of its efficiency. It can predict defects such as wrinkling [6, 7] but mesoscale models are necessary to highlight yarn buckling or gaping. However, very detailed and rich modelling might not be the most accurate because of their high computational costs (about one week of computation in case of forming simulation). To tackle this problem, some mixed meso-macro models have been proposed to give local mesoscopic analysis on macroscopic model. These works were mostly focused on 2D and 3D woven fabrics forming processes [8, 9].

Some assumptions can be made to simplify models and get more efficient computation with full mesoscopic analysis [10], but these models must be optimized to improve kinematic fidelity regarding experimental results.

To properly model the behaviour of textiles, classical Cauchy mechanics is not relevant, as has been experimentally highlighted [11]. Indeed, since fibrous media kinematics is guided by quasi-inextensibility of fibres and their relative sliding, tension and bending stiffness must be independent [12, 13]. These considerations motivated the development of a new finite element formulation which include the fibrous aspect [14, 15], which has mainly been used for macroscopic analysis so far.

<figure><img src="image_438.png" /></figure>
In the present work, the formulation is extended to mesoscopic scale by modelling yarns as fibrous beams with deformable cross section. A new fibrous solid-beam element is developed for this purpose.

## Bending behaviour

In order to ensure independence between tension and bending behaviour, a specific kinematic-based method called neighbour element method (NEM) is used. It has been initially developed for stamping simulation of metal sheets [16], to calculate curvature of shell element, for out-of-plane bending, without using rotational degrees of freedom (DOF). The principle holds in the fact that rotations can be directly expressed through out-of-plane displacement of neighbouring elements nodes. In addition, specific boundary conditions must be defined when an has no neighbour, as proposed in [17, 18].

To calculate their curvature, fibres are considered as Bernoulli beams (see Fig.1), which means that their curvature is linear along their neutral axis and can be entirely determined by the cross-section rotation of each side (see $\theta_i$ in Fig.1). In the case of a 2D problem, the NEM is represented in Fig. 2 and can be summarized as follows.

<figure><img src="image_428.png" /><figcaption>Fig.1°: Scheme of the parametric curve of the neutral axis of a Bernoulli beam.</figcaption></figure>

For each beam of the model, its relative rotation with respect to its neighbour, (see $\alpha_i$ in Fig.2) is known from the initial undeformed configuration. The rotation angle can be calculated thanks to the projection of the nodal displacement in the normal direction. Moreover, the two circular arcs interpolating either the three nodes on the left ($k, l, m$) (red curve on Fig.2) or the three nodes on the right ($l, m, p$) (green curve on Fig.2) enable to calculate the cross-section orientation with relative rotation angles.

<figure><img src="image_429.png" /><figcaption>Fig.2°: Illustration of the NEM for one beam element in 2D</figcaption></figure>

Each increment of relative rotation $\alpha_i$ can be calculated with the incremental nodal displacement. As an example, this would be the formula for the $kl$ two node Bernoulli beam represented in Fig.2:

$$ \delta\alpha_1 = \frac{1}{L}(n_1 \cdot \delta u_l - n_1 \cdot \delta u_m) \quad (1) $$
In the present work, the formulation is extended to mesoscopic scale by modelling yarns as fibrous beams with deformable cross section. A new fibrous solid-beam element is developed for this purpose.

## Bending behaviour

In order to ensure independence between tension and bending behaviour, a specific kinematic-based method called neighbour element method (NEM) is used. It has been initially developed for stamping simulation of metal sheets [16], to calculate curvature of shell element, for out-of-plane bending, without using rotational degrees of freedom (DOF). The principle holds in the fact that rotations can be directly expressed through out-of-plane displacement of neighbouring elements nodes. In addition, specific boundary conditions must be defined when an has no neighbour, as proposed in [17, 18].

To calculate their curvature, fibres are considered as Bernoulli beams (see Fig.1), which means that their curvature is linear along their neutral axis and can be entirely determined by the cross-section rotation of each side (see $\theta_i$ in Fig.1). In the case of a 2D problem, the NEM is represented in Fig. 2 and can be summarized as follows.

<figure><img src="image_439.png" /><figcaption>Fig.1°: Scheme of the parametric curve of the neutral axis of a Bernoulli beam.</figcaption></figure>

For each beam of the model, its relative rotation with respect to its neighbour, (see $\alpha_i$ in Fig.2) is known from the initial undeformed configuration. The rotation angle can be calculated thanks to the projection of the nodal displacement in the normal direction. Moreover, the two circular arcs interpolating either the three nodes on the left ($k, l, m$) (red curve on Fig.2) or the three nodes on the right ($l, m, p$) (green curve on Fig.2) enable to calculate the cross-section orientation with relative rotation angles.

<figure><img src="image_440.png" /><figcaption>Fig.2°: Illustration of the NEM for one beam element in 2D</figcaption></figure>

Each increment of relative rotation $\alpha_i$ can be calculated with the incremental nodal displacement. As an example, this would be the formula for the $kl$ two node Bernoulli beam represented in Fig.2:

$$ \delta\alpha_1 = \frac{1}{L}(n_1 \cdot \delta u_l - n_1 \cdot \delta u_m) \qquad (1) $$
with $n_1$ the unitary vector normal to the neutral axis elements, $\delta u_l$ and $\delta u_m$ the nodal incremental displacement of nodes $k$ and $l$ respectively.

The proposed NEM is implemented in an explicit dynamic framework [19]. Summing over the increments for large displacement simulation, the integrated curvature $\chi$ of the element $lm$ then writes:

$$ \chi(s) = \frac{\partial^2 N_l}{\partial x^2} \theta_l + \frac{\partial^2 N_m}{\partial x^2} \theta_m \qquad (2) $$

where $s \in [0; 1]$ is the local coordinate of the beam element in its reference configuration (see Fig.1), $N_l$ and $N_m$ are the shape function associated to the bending mode, defined by:

$$ N_l(s) = L_2(s^3 - s^2); \quad N_m(s) = L_2(s^3 - 2s^2 + s) \qquad (3) $$

with $L_2$ the length of the element of interest $lm$ (see Fig.2). Then, the cross-section rotations at the nodes $k$ and $l$ are obtained by:

$$ \theta_l = \frac{-L_2}{L_2+L_1}(\alpha_1 + \alpha_2); \quad \theta_m = \frac{L_2}{L_2+L_3}(\alpha_3 - \alpha_2) \qquad (4) $$

For a 3D formulation of the NEM, we assume that the curvature can be represented by a first order tensor whose components are deduced from the 2D formulation in two orthogonal planes containing the fibre direction.

As for the material response, even if irreversible phenomena occur when a yarn is bent cyclically [20], elastic behaviour is sufficient to simulate textile forming process [21]. The present work thus assumes isotropic linear elastic bending behaviour, which has shown quite convincing results in previous fibrous element studies [14,15].

## Behaviour of the yarn

A yarn can be composed of thousands of more or less aligned fibres which are mostly free to rearrange and slide between each other. Consequently, the fibre direction is a preferential one and can be used to describe the material behaviour. It implies that a transverse isotropic law should be applied. Moreover, it has been stated that the fibre density does not evolve in the section orthogonal to the fibre direction [22]. As a consequence, the spheric and deviatoric parts of the stress tensor, reduced to the cross section, are decoupled. To achieving this decoupling, Charmetant et al. [23] proposed a transverse isotropic hyperelastic fibrous model, which relies on four deformation modes represented in Figure 3:

(a) Elongation of the fibres

(b) Compaction, representative of fibre density in the cross section

(c) Distortion, representative of fibre rearrangement in the cross section

(d) Longitudinal shearing, representative of fibre sliding

<figure><img src="image_430.png" /><figcaption>Fig.3°: Charmetant law modes, a) elongation, b) compaction, c) distortion, d) shearing.</figcaption></figure>

Charmetant work was based on a special mode decomposition proposed by Criscione et al. [24] who defined, based on the assumption of transverse isotropy, an orthogonal frame in which the deformation gradient tensor F is written:
with $n_1$ the unitary vector normal to the neutral axis elements, $\delta u_l$ and $\delta u_m$ the nodal incremental displacement of nodes $k$ and $l$ respectively.

The proposed NEM is implemented in an explicit dynamic framework [19]. Summing over the increments for large displacement simulation, the integrated curvature $\chi$ of the element $lm$ then writes:

$$ \chi(s) = \frac{\partial^2 N_l}{\partial x^2} \theta_l + \frac{\partial^2 N_m}{\partial x^2} \theta_m \quad (2) $$

where $s \in [0; 1]$ is the local coordinate of the beam element in its reference configuration (see Fig.1), $N_l$ and $N_m$ are the shape function associated to the bending mode, defined by:

$$ N_l(s) = L_2(s^3 - s^2); \quad N_m(s) = L_2(s^3 - 2s^2 + s) \quad (3) $$

with $L_2$ the length of the element of interest $lm$ (see Fig.2). Then, the cross-section rotations at the nodes $k$ and $l$ are obtained by:

$$ \theta_l = \frac{-L_2}{L_2+L_1}(\alpha_1 + \alpha_2); \quad \theta_m = \frac{L_2}{L_2+L_3}(\alpha_3 - \alpha_2) \quad (4) $$

For a 3D formulation of the NEM, we assume that the curvature can be represented by a first order tensor whose components are deduced from the 2D formulation in two orthogonal planes containing the fibre direction.

As for the material response, even if irreversible phenomena occur when a yarn is bent cyclically [20], elastic behaviour is sufficient to simulate textile forming process [21]. The present work thus assumes isotropic linear elastic bending behaviour, which has shown quite convincing results in previous fibrous element studies [14,15].

## Behaviour of the yarn

A yarn can be composed of thousands of more or less aligned fibres which are mostly free to rearrange and slide between each other. Consequently, the fibre direction is a preferential one and can be used to describe the material behaviour. It implies that a transverse isotropic law should be applied. Moreover, it has been stated that the fibre density does not evolve in the section orthogonal to the fibre direction [22]. As a consequence, the spheric and deviatoric parts of the stress tensor, reduced to the cross section, are decoupled. To achieving this decoupling, Charmetant et al. [23] proposed a transverse isotropic hyperelastic fibrous model, which relies on four deformation modes represented in Figure 3:

(a) Elongation of the fibres

(b) Compaction, representative of fibre density in the cross section

(c) Distortion, representative of fibre rearrangement in the cross section

(d) Longitudinal shearing, representative of fibre sliding

<figure><img src="image_441.png" /><figcaption>Fig.3°: Charmetant law modes, a) elongation, b) compaction, c) distortion, d) shearing.</figcaption></figure>

Charmetant work was based on a special mode decomposition proposed by Criscione et al. [24] who defined, based on the assumption of transverse isotropy, an orthogonal frame in which the deformation gradient tensor $F$ is written:
$$[\underline{F}] = \begin{bmatrix} f_m & f_{m1} & f_{m1} \\ 0 & f_{11} & 0 \\ 0 & 0 & f_{22} \end{bmatrix}_{(\underline{M}, \underline{N}_1, \underline{N}_2)} \qquad (5)$$

where $\underline{M}$ is the unitary vector that represents the preferred direction of the fibres, and $(\underline{N}_1, \underline{N}_2)$ are two orthogonal unitary vectors, in the cross section, that stays orthogonal throughout the transformation. One of the Charmetant law innovation was to build a physically based set of invariants easily measurable experimentally. All of them are expressed from the deformation gradient tensor components (5):

$$I_{elong} = \ln(f_m); \quad I_{comp} = \frac{1}{2}\ln(f_{11}f_{22}); \quad I_{dist} = \frac{1}{2}\ln\left(\frac{f_{11}}{f_{22}}\right); \quad I_{shear} = \sqrt{\frac{f_{11}^2+f_{22}^2}{f_m^2}} \qquad (6)$$

Given the independency of each deformation mode, the energy potential is written as the sum of every single mode potential written as:

$$W_{elong} = \frac{1}{2} K_{elong} I_{elong}^2; \quad W_{comp} = K_{comp} I_{comp}^p \quad \text{if } I_{comp} \le 0 \text{ or } W_{comp} = 0; \\ W_{dist} = \frac{1}{2} K_{dist} I_{dist}^2; \quad W_{shear} = \frac{1}{2} K_{cis} I_{dist}^2 \qquad (7)$$

## Fibrous Finite Element Formulation

The present formulation is based on various assumptions [14, 15]:

* Fictive fibres are considered all along the thickness of the element and they can be seen as unitary cross section Bernoulli beams sharing the same nodes as the element.

* Deformation modes are fully independent so they might not obey to the same material law and do not need to be integrated in the same way into the element.

* NEM are used [16, 17, 18].

In the case of the solid-beam element, fictive fibres are located at the edge of the hexahedral element and are aligned with the $\xi$ direction corresponding to the anisotropic one, i.e. the fibre's direction, as represented in Figure 4. Therefore, the deformation modes occurring in the fibre direction (resp. cross section) are referred to as "longitudinal modes" (res. "transverse modes").
$$[\underline{F}] = \begin{bmatrix} f_m & f_{m1} & f_{m1} \\ 0 & f_{11} & 0 \\ 0 & 0 & f_{22} \end{bmatrix}_{(\underline{M}, \underline{N}_1, \underline{N}_2)} \qquad (5)$$

where $\underline{M}$ is the unitary vector that represents the preferred direction of the fibres, and $(\underline{N}_1, \underline{N}_2)$ are two orthogonal unitary vectors, in the cross section, that stays orthogonal throughout the transformation. One of the Charmetant law innovation was to build a physically based set of invariants easily measurable experimentally. All of them are expressed from the deformation gradient tensor components (5):

$$I_{elong} = \ln(f_m); \quad I_{comp} = \frac{1}{2}\ln(f_{11}f_{22}); \quad I_{dist} = \frac{1}{2}\ln\left(\frac{f_{11}}{f_{22}}\right); \quad I_{shear} = \sqrt{\frac{f_{11}^2+f_{22}^2}{f_m^2}} \qquad (6)$$

Given the independency of each deformation mode, the energy potential is written as the sum of every single mode potential written as:

$$W_{elong} = \frac{1}{2} K_{elong} I_{elong}^2; \quad W_{comp} = K_{comp} I_{comp}^p \quad \text{if } I_{comp} \le 0 \text{ or } W_{comp} = 0; \\ W_{dist} = \frac{1}{2} K_{dist} I_{dist}^2; \quad W_{shear} = \frac{1}{2} K_{cis} I_{dist}^2 \qquad (7)$$

## Fibrous Finite Element Formulation

The present formulation is based on various assumptions [14, 15]:

* Fictive fibres are considered all along the thickness of the element and they can be seen as unitary cross section Bernoulli beams sharing the same nodes as the element.

* Deformation modes are fully independent so they might not obey to the same material law and do not need to be integrated in the same way into the element.

* NEM are used [16, 17, 18].

In the case of the solid-beam element, fictive fibres are located at the edge of the hexahedral element and are aligned with the $\xi$ direction corresponding to the anisotropic one, i.e. the fibre's direction, as represented in Figure 4. Therefore, the deformation modes occurring in the fibre direction (resp. cross section) are referred to as "longitudinal modes" (res. "transverse modes").
<figure><img src="image_431.png" /><figcaption>Fig. 4: Fibrous solid-beam element scheme in its reference configuration.</figcaption></figure>

The tension behaviour is assumed to be linear elastic and will be integrated in a single Gauss point into the beam element. The same assumption is done for the bending behaviour, whose curvature will be calculated thanks to NEM at two Gauss points. The hexahedral element is a classical reduced integrated one with the transverse isotropic hyperelastic Charmetant law [23]. It handles the thickness behaviour of the yarn, which means compaction, transverse shear and longitudinal shear, illustrated in Figure 5.

<figure><img src="image_432.png" /><figcaption>Fig. 5: Thickness behaviour deformation modes a) transverse compression, b) transverse shear, c) longitudinal shear.</figcaption></figure>

Contrary to Charmetant law, tension deformation potential is considered null because superimposed beam elements already ensure this mode and the quasi-inextensibility of fibres. Consequently, since beams and hexahedral elements share the same nodes, longitudinal length will not extend when the element is compressed.
<figure><img src="image_442.png" /><figcaption>Fig. 4: Fibrous solid-beam element scheme in its reference configuration.</figcaption></figure>

The tension behaviour is assumed to be linear elastic and will be integrated in a single Gauss point into the beam element. The same assumption is done for the bending behaviour, whose curvature will be calculated thanks to NEM at two Gauss points. The hexahedral element is a classical reduced integrated one with the transverse isotropic hyperelastic Charmetant law [23]. It handles the thickness behaviour of the yarn, which means compaction, transverse shear and longitudinal shear, illustrated in Figure 5.

<figure><img src="image_443.png" /><figcaption>Fig. 5: Thickness behaviour deformation modes a) transverse compression, b) transverse shear, c) longitudinal shear.</figcaption></figure>

Contrary to Charmetant law, tension deformation potential is considered null because superimposed beam elements already ensure this mode and the quasi-inextensibility of fibres. Consequently, since beams and hexahedral elements share the same nodes, longitudinal length will not extend when the element is compressed.
## Numerical Analysis

The efficiency and accuracy of this fibrous solid-beam element has been tested throughout the simulation of a cantilever test and compared with an experiment performed with a set of several layers of Hexcel G986 reinforcement held together by soft threads [14]. The right tip of the sample is clamped and the rest is free and subjected to its own weight. This test is relevant for observing material normal orientation, drawn in white on Fig. 6 (a), as it has been done by Boisse et al. [11] to show that neither Kirchhoff nor Reissner assumptions hold.

A qualitative comparison between experimental and numerical results has been performed based on kinematic considerations such as the orientations of material normal, the shape of the free tip and the thickness evolution along the longitudinal axis.

Boundary conditions of the numerical model are:

* Right tip nodes clamped.

* Left tip nodes vertical displacement imposed.

<figure><img src="image_433.png" /><figcaption>Fig. 6°: Cantilever test on a multilayer reinforcement comparison between experiment and simulation</figcaption></figure>

Since each layer is free to slide on its neighbours, the free tip of the sample has a bevel shape and the material normal stays vertical. Furthermore, the thickness of the sample doesn't change because the plies are held together and thus no delamination can appear. Thanks to this results, fibrous solid-beam element model will be able to properly simulate kinematic response of yarns.

## Summary

A new solid-beam finite element formulation based on phenomenological observations on textile reinforcements is developed. It is a generalization of the fibrous element formulation for a mesoscopic modelling purpose. The neighbour element method is used to calculate curvature, which ensures that bending behaviour is fully independent of the other deformation modes. These modes are taken into account using Charmetant transverse isotropic hyperelastic law.

This element will be tested on mesoscopic models soon. A characterization campaign is also yet to be done to identify Charmetant law parameters.
## Numerical Analysis

The efficiency and accuracy of this fibrous solid-beam element has been tested throughout the simulation of a cantilever test and compared with an experiment performed with a set of several layers of Hexcel G986 reinforcement held together by soft threads [14]. The right tip of the sample is clamped and the rest is free and subjected to its own weight. This test is relevant for observing material normal orientation, drawn in white on Fig. 6 (a), as it has been done by Boisse et al. [11] to show that neither Kirchhoff nor Reissner assumptions hold.

A qualitative comparison between experimental and numerical results has been performed based on kinematic considerations such as the orientations of material normal, the shape of the free tip and the thickness evolution along the longitudinal axis.

Boundary conditions of the numerical model are:

* Right tip nodes clamped.

* Left tip nodes vertical displacement imposed.

<figure><img src="image_444.png" /><figcaption>Fig. 6°: Cantilever test on a multilayer reinforcement comparison between experiment and simulation</figcaption></figure>

Since each layer is free to slide on its neighbours, the free tip of the sample has a bevel shape and the material normal stays vertical. Furthermore, the thickness of the sample doesn't change because the plies are held together and thus no delamination can appear. Thanks to this results, fibrous solid-beam element model will be able to properly simulate kinematic response of yarns.

## Summary

A new solid-beam finite element formulation based on phenomenological observations on textile reinforcements is developed. It is a generalization of the fibrous element formulation for a mesoscopic modelling purpose. The neighbour element method is used to calculate curvature, which ensures that bending behaviour is fully independent of the other deformation modes. These modes are taken into account using Charmetant transverse isotropic hyperelastic law.

This element will be tested on mesoscopic models soon. A characterization campaign is also yet to be done to identify Charmetant law parameters.
## References

[1] N. Naouar, E. Vidal-Sallé, J. Schneider, E. Maire, et P. Boisse, « Meso-scale FE analyses of textile composite reinforcement deformation based on X-ray computed tomography », *Composite Structures*, vol. 116, p. 165-176, sept. 2014. https://doi.org/10.1016/j.compstruct.2014.04.026

[2] G. Hivet et P. Boisse, « Consistent 3D geometrical model of fabric elementary cell. Application to a meshing preprocessor for 3D finite element analysis », *Finite Elements in Analysis and Design*, vol. 42, n° 1, p. 25-49, oct. 2005. https://doi.org/10.1016/j.finel.2005.05.001

[3] P. Badel, E. Vidal-Sallé, et P. Boisse, « Large deformation analysis of fibrous materials using rate constitutive equations », *Computers & Structures*, vol. 86, n° 11-12, p. 1164-1175, juin 2008. https://doi.org/10.1016/j.compstruc.2008.01.009

[4] R. Zheng, « A unit-cell mesoscale modelling of biaxial non-crimp-fabric based on a hyperelastic approach », Materials Research Proceedings 28, mai 2023, p. 285-292. doi: 10.21741/9781644902479-31

[5] Q. T. Nguyen et al., « Mesoscopic scale analyses of textile composite reinforcement compaction », *Composites Part B: Engineering*, vol. 44, n° 1, p. 231-241, janv. 2013. https://doi.org/10.1016/j.compositesb.2012.05.028

[6] P. Boisse, N. Hamila, E. Vidal-Sallé, et F. Dumont, « Simulation of wrinkling during textile composite reinforcement forming. Influence of tensile, in-plane shear and bending stiffnesses », *Composites Science and Technology*, vol. 71, n° 5, p. 683-692, mars 2011. https://doi.org/10.1016/j.compscitech.2011.01.011

[7] B. Chen, J. Colmars, N. Naouar, et P. Boisse, « A hypoelastic stress resultant shell approach for simulations of textile composite reinforcement forming », *Composites Part A: Applied Science and Manufacturing*, vol. 149, p. 106558, oct. 2021. https://doi.org/10.1016/j.compositesa.2021.106558

[8] A. Iwata, T. Inoue, N. Naouar, P. Boisse, et S. V. Lomov, « Coupled meso-macro simulation of woven fabric local deformation during draping », *Composites Part A: Applied Science and Manufacturing*, vol. 118, p. 267-280, mars 2019. https://doi.org/10.1016/j.compositesa.2019.01.004

[9] J. Wang, P. Wang, N. Hamila, et P. Boisse, « Meso-Macro Simulations of the Forming of 3D Non-Crimp Woven Fabrics », *Textiles*, vol. 2, n° 1, p. 112-123, févr. 2022. https://doi.org/10.3390/textiles2010006

[10] S. Gatouillat, A. Bareggi, E. Vidal-Sallé, et P. Boisse, « Meso modelling for composite preform shaping – Simulation of the loss of cohesion of the woven fibre network », *Composites Part A: Applied Science and Manufacturing*, vol. 54, p. 135-144, nov. 2013. https://doi.org/10.1016/j.compositesa.2013.07.010

[11] P. Boisse, N. Hamila, et A. Madeo, « The difficulties in modeling the mechanical behaviour of textile composite reinforcements with standard continuum mechanics of Cauchy. Some possible remedies », *International Journal of Solids and Structures*, vol. 154, p. 55-65, déc. 2018. https://doi.org/10.1016/j.ijsolstr.2016.12.019

[12] P. Boisse, J. Colmars, N. Hamila, N. Naouar, et Q. Steer, « Bending and wrinkling of composite fibre preforms and prepregs. A review and new developments in the draping simulations », *Composites Part B: Engineering*, vol. 141, p. 234-249, mai 2018. https://doi.org/10.1016/j.compositesb.2017.12.061

[13] D. Dörr, F. J. Schirmaier, F. Henning, et L. Kärger, « A viscoelastic approach for modeling bending behaviour in finite element forming simulation of continuously fibre reinforced
## References

[1] N. Naouar, E. Vidal-Sallé, J. Schneider, E. Maire, et P. Boisse, « Meso-scale FE analyses of textile composite reinforcement deformation based on X-ray computed tomography », *Composite Structures*, vol. 116, p. 165-176, sept. 2014. https://doi.org/10.1016/j.compstruct.2014.04.026

[2] G. Hivet et P. Boisse, « Consistent 3D geometrical model of fabric elementary cell. Application to a meshing preprocessor for 3D finite element analysis », *Finite Elements in Analysis and Design*, vol. 42, n° 1, p. 25-49, oct. 2005. https://doi.org/10.1016/j.finel.2005.05.001

[3] P. Badel, E. Vidal-Sallé, et P. Boisse, « Large deformation analysis of fibrous materials using rate constitutive equations », *Computers & Structures*, vol. 86, n° 11-12, p. 1164-1175, juin 2008. https://doi.org/10.1016/j.compstruc.2008.01.009

[4] R. Zheng, « A unit-cell mesoscale modelling of biaxial non-crimp-fabric based on a hyperelastic approach », Materials Research Proceedings 28, mai 2023, p. 285-292. doi: 10.21741/9781644902479-31

[5] Q. T. Nguyen et al., « Mesoscopic scale analyses of textile composite reinforcement compaction », *Composites Part B: Engineering*, vol. 44, n° 1, p. 231-241, janv. 2013. https://doi.org/10.1016/j.compositesb.2012.05.028

[6] P. Boisse, N. Hamila, E. Vidal-Sallé, et F. Dumont, « Simulation of wrinkling during textile composite reinforcement forming. Influence of tensile, in-plane shear and bending stiffnesses », *Composites Science and Technology*, vol. 71, n° 5, p. 683-692, mars 2011. https://doi.org/10.1016/j.compscitech.2011.01.011

[7] B. Chen, J. Colmars, N. Naouar, et P. Boisse, « A hypoelastic stress resultant shell approach for simulations of textile composite reinforcement forming », *Composites Part A: Applied Science and Manufacturing*, vol. 149, p. 106558, oct. 2021. https://doi.org/10.1016/j.compositesa.2021.106558

[8] A. Iwata, T. Inoue, N. Naouar, P. Boisse, et S. V. Lomov, « Coupled meso-macro simulation of woven fabric local deformation during draping », *Composites Part A: Applied Science and Manufacturing*, vol. 118, p. 267-280, mars 2019. https://doi.org/10.1016/j.compositesa.2019.01.004

[9] J. Wang, P. Wang, N. Hamila, et P. Boisse, « Meso-Macro Simulations of the Forming of 3D Non-Crimp Woven Fabrics », *Textiles*, vol. 2, n° 1, p. 112-123, févr. 2022. https://doi.org/10.3390/textiles2010006

[10] S. Gatouillat, A. Bareggi, E. Vidal-Sallé, et P. Boisse, « Meso modelling for composite preform shaping – Simulation of the loss of cohesion of the woven fibre network », *Composites Part A: Applied Science and Manufacturing*, vol. 54, p. 135-144, nov. 2013. https://doi.org/10.1016/j.compositesa.2013.07.010

[11] P. Boisse, N. Hamila, et A. Madeo, « The difficulties in modeling the mechanical behaviour of textile composite reinforcements with standard continuum mechanics of Cauchy. Some possible remedies », *International Journal of Solids and Structures*, vol. 154, p. 55-65, déc. 2018. https://doi.org/10.1016/j.ijsolstr.2016.12.019

[12] P. Boisse, J. Colmars, N. Hamila, N. Naouar, et Q. Steer, « Bending and wrinkling of composite fibre preforms and prepregs. A review and new developments in the draping simulations », *Composites Part B: Engineering*, vol. 141, p. 234-249, mai 2018. https://doi.org/10.1016/j.compositesb.2017.12.061

[13] D. Dörr, F. J. Schirmaier, F. Henning, et L. Kärger, « A viscoelastic approach for modeling bending behaviour in finite element forming simulation of continuously fibre reinforced
composites », *Composites Part A: Applied Science and Manufacturing*, vol. 94, p. 113-123, mars 2017. https://doi.org/10.1016/j.compositesa.2016.11.027

[14] B. Liang, J. Colmars, et P. Boisse, « A shell formulation for fibrous reinforcement forming simulations », *Composites Part A: Applied Science and Manufacturing*, vol. 100, p. 81-96, sept. 2017. https://doi.org/10.1016/j.compositesa.2017.04.024

[15] R. Bai, J. Colmars, N. Naouar, et P. Boisse, « A specific 3D shell approach for textile composite reinforcements under large deformation », *Composites Part A: Applied Science and Manufacturing*, vol. 139, p. 106135, déc. 2020. https://doi.org/10.1016/j.compositesa.2020.106135

[16] M. Brunet et F. Sabourin, « A simplified triangular shell element with a necking criterion for 3-D sheet-forming analysis », *Journal of Materials Processing Technology*, vol. 50, n° 1-4, p. 238-251, mars 1995. https://doi.org/10.1016/0924-0136(94)01384-D

[17] F. Sabourin et M. Vives, « Eléments finis triangulaires pour la simulation de l'emboutissage: Aspects de base », *Revue Européenne des Éléments Finis*, vol. 10, n° 1, p. 7-53, janv. 2001. https://doi.org/10.1080/12506559.2001.11869238

[18] F. Sabourin et M.1 Brunet, "Detailed formulation of the rotation-free triangular element "S3" for general purpose shell analysis", *Engineering Computations*, Vol. 23 Iss 5 pp. 469 – 502, juil 2006. https://doi.org/10.1108/02644400610671090

[19] T. Belytschko et al., « Non linear finite elements for continua and structures », first ed, John Wiley & Sons, 1998.

[20] E. De Bilbao, D. Soulat, G. Hivet, et A. Gasser, « Experimental Study of Bending Behaviour of Reinforcements », *Exp Mech*, vol. 50, n° 3, p. 333-351, mars 2010. https://doi.org/10.1007/s11340-009-9234-9

[21] T. Abdul Ghafour, J. Colmars, et P. Boisse, « The importance of taking into account behaviour irreversibilities when simulating the forming of textile composite reinforcements », *Composites Part A: Applied Science and Manufacturing*, vol. 127, p. 105641, déc. 2019. https://doi.org/10.1016/j.compositesa.2019.105641

[22] P. Badel, E. Vidal-Sallé, E. Maire, et P. Boisse, « Simulation and tomography analysis of textile composite reinforcement deformation at the mesoscopic scale », *Composites Science and Technology*, vol. 68, n° 12, p. 2433-2440, sept. 2008. https://doi.org/10.1016/j.compscitech.2008.04.038

[23] A. Charmetant, E. Vidal-Sallé, et P. Boisse, « Hyperelastic modelling for mesoscopic analyses of composite reinforcements », *Composites Science and Technology*, vol. 71, n° 14, p. 1623-1631, sept. 2011. https://doi.org/10.1016/j.compscitech.2011.07.004

[24] J. Huang, P. Boisse, N. Hamila, et Y. Zhu, « Simulation of Wrinkling during Bending of Composite Reinforcement Laminates », *Materials*, vol. 13, n° 10, p. 2374, mai 2020. https://doi.org/10.3390/ma13102374
composites », *Composites Part A: Applied Science and Manufacturing*, vol. 94, p. 113-123, mars 2017. https://doi.org/10.1016/j.compositesa.2016.11.027

[14] B. Liang, J. Colmars, et P. Boisse, « A shell formulation for fibrous reinforcement forming simulations », *Composites Part A: Applied Science and Manufacturing*, vol. 100, p. 81-96, sept. 2017. https://doi.org/10.1016/j.compositesa.2017.04.024

[15] R. Bai, J. Colmars, N. Naouar, et P. Boisse, « A specific 3D shell approach for textile composite reinforcements under large deformation », *Composites Part A: Applied Science and Manufacturing*, vol. 139, p. 106135, déc. 2020. https://doi.org/10.1016/j.compositesa.2020.106135

[16] M. Brunet et F. Sabourin, « A simplified triangular shell element with a necking criterion for 3-D sheet-forming analysis », *Journal of Materials Processing Technology*, vol. 50, n° 1-4, p. 238-251, mars 1995. https://doi.org/10.1016/0924-0136(94)01384-D

[17] F. Sabourin et M. Vives, « Eléments finis triangulaires pour la simulation de l'emboutissage: Aspects de base », *Revue Européenne des Éléments Finis*, vol. 10, n° 1, p. 7-53, janv. 2001. https://doi.org/10.1080/12506559.2001.11869238

[18] F. Sabourin et M.1 Brunet, "Detailed formulation of the rotation-free triangular element "S3" for general purpose shell analysis", *Engineering Computations*, Vol. 23 Iss 5 pp. 469 – 502, juil 2006. https://doi.org/10.1108/02644400610671090

[19] T. Belytschko et al., « Non linear finite elements for continua and structures », first ed, John Wiley & Sons, 1998.

[20] E. De Bilbao, D. Soulat, G. Hivet, et A. Gasser, « Experimental Study of Bending Behaviour of Reinforcements », *Exp Mech*, vol. 50, n° 3, p. 333-351, mars 2010. https://doi.org/10.1007/s11340-009-9234-9

[21] T. Abdul Ghafour, J. Colmars, et P. Boisse, « The importance of taking into account behaviour irreversibilities when simulating the forming of textile composite reinforcements », *Composites Part A: Applied Science and Manufacturing*, vol. 127, p. 105641, déc. 2019. https://doi.org/10.1016/j.compositesa.2019.105641

[22] P. Badel, E. Vidal-Sallé, E. Maire, et P. Boisse, « Simulation and tomography analysis of textile composite reinforcement deformation at the mesoscopic scale », *Composites Science and Technology*, vol. 68, n° 12, p. 2433-2440, sept. 2008. https://doi.org/10.1016/j.compscitech.2008.04.038

[23] A. Charmetant, E. Vidal-Sallé, et P. Boisse, « Hyperelastic modelling for mesoscopic analyses of composite reinforcements », *Composites Science and Technology*, vol. 71, n° 14, p. 1623-1631, sept. 2011. https://doi.org/10.1016/j.compscitech.2011.07.004

[24] J. Huang, P. Boisse, N. Hamila, et Y. Zhu, « Simulation of Wrinkling during Bending of Composite Reinforcement Laminates », *Materials*, vol. 13, n° 10, p. 2374, mai 2020. https://doi.org/10.3390/ma13102374
# Considering the viscoelastic material behavior in a solid-shell element for thermoforming simulation

MITSCH Johannes¹,ª*, SCHÄFER Bastian¹,ᵇ, WANK Jan Paul¹,ᶜ and KÄRGER Luise¹,ᵈ

¹Karlsruhe Institute of Technology (KIT), Institute of Vehicle System Technology (FAST) – Lightweight Engineering, 76131 Karlsruhe Germany

ªJohannes.Mitsch@kit.edu

**Keywords:** Solid-Shell, Thermoforming, Process Simulation, Finite Element-Analysis

**Abstract.** To predict manufacturing effects in the thermoforming process for fiber reinforced plastics the Finite Element Method is widely used. Most macroscopic simulation methods are based on conventional two-dimensional shell elements which are not capable of modeling the material behavior in thickness direction using constitutive equations. At the same time, standard three-dimensional element formulations are not suitable for the forming simulation of thin textiles due to numerical locking phenomena and the lack of a possible membrane-bending-decoupling. Previous studies focused on a specialized solid-shell element formulation which provides anisotropic but purely elastic material modeling. Since purely elastic approaches cannot accurately describe the deformation behavior in the thermoforming process, the provided element formulation is enhanced to rate-dependent viscoelastic material modeling. Numerical studies are carried out that reveal that the membrane-bending-decoupling is preserved for the viscoelastic material model. Virtual coupon tests demonstrate the rate-dependent material behavior in the solid-shell element. The obtained results show that the general approach of the viscoelastic material behavior within the solid-shell element is suitable to address out-of-plane phenomena in thermoforming simulations.

**Introduction**

Fiber reinforced plastics (FRPs) like thermoplastic tapes provide great lightweight potential due to their high mass specific stiffness and strength while also having the possibility to be tailored for specific applications [1]. Precise computer-aided component design is the key to component concepts with reliable high load-bearing capacity combined with low masses.

Most macroscopic simulations of the forming process of thermoplastic tapes are based on conventional shell elements [2]. Since FRP components are usually thin, conventional shells provide efficient simulation of the in-plane membrane and out-of-plane bending behavior. However, the material modeling in thickness direction is not possible since conventional shells are only two-dimensional. To enable material modeling in thickness direction three-dimensional element types must be used. Standard three-dimensional element formulations are not suitable for the forming simulation of thin textiles due to numerical locking phenomena and the lack of a possible membrane-bending-decoupling [3]. Therefore, specialized element formulations, like solid-shell elements are required.

The focus of this work is the simulation of the thermoforming process of preimpregnated textile composites, e.g., thermoplastic tapes. Due to the influence of the matrix, the material behavior, and the bending behavior of preimpregnated FRPs is rate- and temperature-dependent. Hence, (thermo-)viscoelastic material modeling is crucial for the proper simulation of the thermoforming process of preimpregnated textile composites. Thus, purely elastic approaches are unsuitable for modeling the material behavior in forming simulation of thermoplastic composites [4–6]. Dörr et al. [7,8] use a Voigt-Kelvin and a generalized Maxwell approach to model the isothermal

<figure><img src="image_434.png" /></figure>
# Considering the viscoelastic material behavior in a solid-shell element for thermoforming simulation

MITSCH Johannes¹,ª*, SCHÄFER Bastian¹,ᵇ, WANK Jan Paul¹,ᶜ and KÄRGER Luise¹,ᵈ

¹Karlsruhe Institute of Technology (KIT), Institute of Vehicle System Technology (FAST) – Lightweight Engineering, 76131 Karlsruhe Germany

ªJohannes.Mitsch@kit.edu

**Keywords:** Solid-Shell, Thermoforming, Process Simulation, Finite Element-Analysis

**Abstract.** To predict manufacturing effects in the thermoforming process for fiber reinforced plastics the Finite Element Method is widely used. Most macroscopic simulation methods are based on conventional two-dimensional shell elements which are not capable of modeling the material behavior in thickness direction using constitutive equations. At the same time, standard three-dimensional element formulations are not suitable for the forming simulation of thin textiles due to numerical locking phenomena and the lack of a possible membrane-bending-decoupling. Previous studies focused on a specialized solid-shell element formulation which provides anisotropic but purely elastic material modeling. Since purely elastic approaches cannot accurately describe the deformation behavior in the thermoforming process, the provided element formulation is enhanced to rate-dependent viscoelastic material modeling. Numerical studies are carried out that reveal that the membrane-bending-decoupling is preserved for the viscoelastic material model. Virtual coupon tests demonstrate the rate-dependent material behavior in the solid-shell element. The obtained results show that the general approach of the viscoelastic material behavior within the solid-shell element is suitable to address out-of-plane phenomena in thermoforming simulations.

**Introduction**

Fiber reinforced plastics (FRPs) like thermoplastic tapes provide great lightweight potential due to their high mass specific stiffness and strength while also having the possibility to be tailored for specific applications [1]. Precise computer-aided component design is the key to component concepts with reliable high load-bearing capacity combined with low masses.

Most macroscopic simulations of the forming process of thermoplastic tapes are based on conventional shell elements [2]. Since FRP components are usually thin, conventional shells provide efficient simulation of the in-plane membrane and out-of-plane bending behavior. However, the material modeling in thickness direction is not possible since conventional shells are only two-dimensional. To enable material modeling in thickness direction three-dimensional element types must be used. Standard three-dimensional element formulations are not suitable for the forming simulation of thin textiles due to numerical locking phenomena and the lack of a possible membrane-bending-decoupling [3]. Therefore, specialized element formulations, like solid-shell elements are required.

The focus of this work is the simulation of the thermoforming process of preimpregnated textile composites, e.g., thermoplastic tapes. Due to the influence of the matrix, the material behavior, and the bending behavior of preimpregnated FRPs is rate- and temperature-dependent. Hence, (thermo-)viscoelastic material modeling is crucial for the proper simulation of the thermoforming process of preimpregnated textile composites. Thus, purely elastic approaches are unsuitable for modeling the material behavior in forming simulation of thermoplastic composites [4–6]. Dörr et al. [7,8] use a Voigt-Kelvin and a generalized Maxwell approach to model the isothermal

<figure><img src="image_445.png" /></figure>
viscoelastic material behavior. Subsequently, this approach was further developed to a thermoviscoelastic material law [9].

In context of the forming simulation for thermoplastic composite prepregs, Xiong [10] and Xiong et al. [11] present a prismatic solid-shell element to display consolidation and compaction. The approach is based on a DKT plate element with an additional degree of freedom in the middle of the element. A viscoelastic material law based on a generalized Maxwell model is utilized to model both the in-plane shear behavior and the compaction behavior. Another approach to display non-elastic material properties in thickness direction of preimpregnated textile composites is presented by Mulye et al. [12]. A so-called pinching shell element is introduced which is based on a shell element. In their work an elasto-plastic material model is chosen

The 3D hexahedral solid-shell element considered in the present study continues the investigations by Schäfer et al. [3,13]. Initially based on the work of Schwarz and Reese [14,15] who proposed a solid-shell element with only translational degrees of freedom for isotropic material laws, Pagani et al. [16] extended the formulation to the explicit case. Schäfer et al. [3,13] enhanced the element formulation for anisotropic elastic material laws. An approach for a membrane-bending-decoupling, which is based on a Taylor series approximation of the strain, is also presented. The considered solid-shell element is implemented by means of a user-element (VUEL) for the FEM solver ABAQUS/EXPLICIT. The implementation of the user-element is done using the MATHEMATICA-based programming environment ACEGEN [17] which allows symbolic implementation and differentiation in combination with runtime optimization.

In this work the solid-shell element is extended to viscoelastic material behavior. For this, the Voigt-Kelvin model is implemented and evaluated separately for the membrane and the bending part. To evaluate the viscoelastic material law, the deformation gradient **F** is needed to derive the deformation rate tensor **D** from the rate of the Green-Lagrange strain tensor **E**. Since the Green-Lagrange strain tensor **E** is modified using the enhanced assumed strain- (EAS) and the assumed natural strain- (ANS) method, the corresponding deformation gradient **F** cannot solely be described by the node displacements within the element. Hence, an alternative method to calculate an effective deformation gradient **F**<sub>tec</sub> is presented. An alternative approach to ensure numerical stability is considered. It is shown that the decomposition of the membrane- and bending-behavior still holds. Numerical studies are carried out to demonstrate the rate-dependency of the implemented viscoelastic material behavior for both the membrane and the bending behavior.

## Solid-Shell Element

*Solid-shell formulation.* The 3D hexahedral solid-shell element considered in the present study is based on the work of Schäfer et al. [3,13]. Its eight nodes have only translational degrees of freedom. It is implemented as a user-element (VUEL) in ABAQUS/EXPLICIT. A reduced integration scheme is used for the in-plane deformations. Thus, there is only one single integration point in the center of the shell plane. Along the thickness direction of the element, multiple integration points are located to account for the material behavior in the out-of-plane direction. Analogously to Schäfer et al. [3,13], the total Green-Lagrange strain tensor **E** is modified using the EAS- and the ANS-concept. The EAS-concept introduced by Simo et al. [18–20] helps to prevent volumetric and Poisson thickness locking by introducing an enhanced strain **E**<sub>e</sub>. It is added to the compatible strain **E**<sub>c</sub> for the total strain **E** = **E**<sub>c</sub> + **E**<sub>e</sub>. The compatible part **E**<sub>c</sub> is solely dependent on the displacements **u**<sub>i</sub> of the eight nodes within the element. The ANS-method introduced by Hughes and Tezduya [21] helps to prevent transverse shear and curvature thickness locking. More comprehensive explanations on the ANS- and EAS-concepts are given by [14,15,22]. In the following, **E**<sub>mod</sub> denotes the modified strain using the EAS- and ANS-method.

Using a Taylor expansion for the compatible strain **E**<sub>c</sub> with respect to the element-center enables the decomposition of the total strain **E**<sub>mod</sub> into (cf. [13–15])
viscoelastic material behavior. Subsequently, this approach was further developed to a thermoviscoelastic material law [9].

In context of the forming simulation for thermoplastic composite prepregs, Xiong [10] and Xiong et al. [11] present a prismatic solid-shell element to display consolidation and compaction. The approach is based on a DKT plate element with an additional degree of freedom in the middle of the element. A viscoelastic material law based on a generalized Maxwell model is utilized to model both the in-plane shear behavior and the compaction behavior. Another approach to display non-elastic material properties in thickness direction of preimpregnated textile composites is presented by Mulye et al. [12]. A so-called pinching shell element is introduced which is based on a shell element. In their work an elasto-plastic material model is chosen

The 3D hexahedral solid-shell element considered in the present study continues the investigations by Schäfer et al. [3,13]. Initially based on the work of Schwarz and Reese [14,15] who proposed a solid-shell element with only translational degrees of freedom for isotropic material laws, Pagani et al. [16] extended the formulation to the explicit case. Schäfer et al. [3,13] enhanced the element formulation for anisotropic elastic material laws. An approach for a membrane-bending-decoupling, which is based on a Taylor series approximation of the strain, is also presented. The considered solid-shell element is implemented by means of a user-element (VUEL) for the FEM solver ABAQUS/EXPLICIT. The implementation of the user-element is done using the MATHEMATICA-based programming environment ACEGEN [17] which allows symbolic implementation and differentiation in combination with runtime optimization.

In this work the solid-shell element is extended to viscoelastic material behavior. For this, the Voigt-Kelvin model is implemented and evaluated separately for the membrane and the bending part. To evaluate the viscoelastic material law, the deformation gradient **F** is needed to derive the deformation rate tensor **D** from the rate of the Green-Lagrange strain tensor **E**. Since the Green-Lagrange strain tensor **E** is modified using the enhanced assumed strain- (EAS) and the assumed natural strain- (ANS) method, the corresponding deformation gradient **F** cannot solely be described by the node displacements within the element. Hence, an alternative method to calculate an effective deformation gradient **F**<sub>tec</sub> is presented. An alternative approach to ensure numerical stability is considered. It is shown that the decomposition of the membrane- and bending-behavior still holds. Numerical studies are carried out to demonstrate the rate-dependency of the implemented viscoelastic material behavior for both the membrane and the bending behavior.

## Solid-Shell Element

*Solid-shell formulation.* The 3D hexahedral solid-shell element considered in the present study is based on the work of Schäfer et al. [3,13]. Its eight nodes have only translational degrees of freedom. It is implemented as a user-element (VUEL) in ABAQUS/EXPLICIT. A reduced integration scheme is used for the in-plane deformations. Thus, there is only one single integration point in the center of the shell plane. Along the thickness direction of the element, multiple integration points are located to account for the material behavior in the out-of-plane direction. Analogously to Schäfer et al. [3,13], the total Green-Lagrange strain tensor **E** is modified using the EAS- and the ANS-concept. The EAS-concept introduced by Simo et al. [18–20] helps to prevent volumetric and Poisson thickness locking by introducing an enhanced strain **E**<sub>e</sub>. It is added to the compatible strain **E**<sub>c</sub> for the total strain **E** = **E**<sub>c</sub> + **E**<sub>e</sub>. The compatible part **E**<sub>c</sub> is solely dependent on the displacements **u**<sub>i</sub> of the eight nodes within the element. The ANS-method introduced by Hughes and Tezduya [21] helps to prevent transverse shear and curvature thickness locking. More comprehensive explanations on the ANS- and EAS-concepts are given by [14,15,22]. In the following, **E**<sub>mod</sub> denotes the modified strain using the EAS- and ANS-method.
Using a Taylor expansion for the compatible strain **E**<sub>c</sub> with respect to the element-center enables the decomposition of the total strain **E**<sub>mod</sub> into (cf. [13–15])