# Experimental and Numerical Studies on Fiber Deformation and Formability in Thermoforming Process Using a Fast-Cure Carbon Prepreg: Effect of Stacking Sequence and Mold Geometry

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Experimental

#### 2.1. Materials and Sample Preparation

#### 2.2. Measurement of the Non-Linear Mechanical Behaviors of the Prepreg at Elevated Temperatures

_{S}(γ) is the torque per original unit area that is needed to deform the fabric in shear, F

_{sh}is the normalized shear force and F is the power made through the clamping force.

#### 2.3. Mold Geometry

#### 2.4. Thermoforming Apparatus and Procedure

#### 2.5. Forming Simulation

_{L}) and transverse (η

_{T}) terms of viscosity in either isothermal or temperature-dependent forming conditions.

## 3. Results and Discussion

#### 3.1. Material Properties of the Resin

#### 3.2. Mechanical Properties of Prepreg at the Process Temperature

^{−4}(GPa). The rotation between the warp and weft due to the shear force is limited when shear strain is 0.403 rad, which is also known as the shear locking angle [30]. The shear modulus in the shear locking angle region decreased to 2.01 × 10

^{−5}GPa. Deformation beyond the locking angle leads to wrinkles in the specimen, which is caused by out-of-plane deformation or buckling. After passing second inflection points, a fractional increase in the shear modulus of 4.78 × 10

^{−5}GPa was then observed upon aligning the reoriented yarns in the loading direction. The shear angle range below 0.8 rad was considered in this study, because the scattering range of the obtained shear modulus values above 0.8 rad was significantly wide to use as input data in thermoforming simulation. On the other hand, a coarse and irregular plain woven pattern of glass (PW glass) causes more indefinite inflection points and shear locking areas in the shear stress-shear strain curve in comparison with PW carbon. In the case of the UD carbon, the plateau region of the graph after a sharp increase in the stiffness indicates that the fabric straightens without interference between the bundles [10].

#### 3.3. Square-Cup Drawing Test

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- International Council on Clean Transportation. Global Passenger Vehicle Standards. 2014. Available online: http://theicct.org/info-tools/global-passenger-vehicle-standards (accessed on 15 December 2016).
- Sherwood, J.A.; Fetfatsidis, K.A.; Gorczyca, J.L.; Berger, L. Fabric thermostamping in polymer matrix composite. In Manufacturing Techniques for Polymer Matrix Composites (PMCs); Advani, S.G., Hsiao, K.-T., Eds.; Elsevier: New York, NY, USA, 2012; pp. 139–179. [Google Scholar]
- Knibbs, R.H.; Morris, J.B. The effects of fibre orientation on the physical properties of composites. Composites
**1974**, 5, 209–218. [Google Scholar] [CrossRef] - Fuller, J.D.; Wisnom, M.R. Exploration of the potential for pseudo-ductility in thin ply CFRP angle-ply laminates via an analytical method. Compos. Sci. Technol.
**2015**, 112, 8–15. [Google Scholar] [CrossRef] - Wang, P.; Hamila, N.; Boisse, P. Thermoforming simulation of multilayer composites with continuous fibres and thermoplastic matrix. Compos. Part B
**2013**, 52, 127–136. [Google Scholar] [CrossRef] - Sorrentino, L.; Bellini, C. Potentiality of Hot Drape Forming to produce complex shape parts in composite material. Int. J. Adv. Manuf. Technol.
**2016**, 85, 945–954. [Google Scholar] [CrossRef] - Wang, P.; Hamila, N.; Pineau, P.; Boisse, P. Thermomechanical analysis of thermoplastic composite prepregs using bias-extension test. J. Thermoplast. Compos. Mater.
**2014**, 27, 679–698. [Google Scholar] [CrossRef] - Lee, W.; Padvoiskis, J.; Cao, J.; de Luycker, E.; Boisse, P.; Morestin, F.; Chen, J.; Sherwood, J. Bias-extension of woven composite fabrics. Int J Mater Form.
**2008**, 1, 895–898. [Google Scholar] [CrossRef] - Guzman, E.; Hamila, N.; Boisse, P. Thermomechanical analysis, modelling and simulation of the forming of pre-impregnated thermoplastics composites. Compos. Part A
**2014**, 78, 211–222. [Google Scholar] [CrossRef] - Gorczyca, J. A Study of the Frictional Behavior of a Plain-Weave Fabric during the Thermostamping Process. Ph.D. Thesis, Department of Mechanical Engineering, University of Massachusetts Lowell, Lowell, MA, USA, January 2004. [Google Scholar]
- Ersoy, N.; Potter, K.; Wisnom, M.R.; Clegg, M.J. An experimental method to study the frictional processes during composites manufacturing. Compos. Part A
**2005**, 36, 1536–1544. [Google Scholar] [CrossRef] - Thije, R.H.W.; Akkerman, R.; Ubbink, M.; van der Meer, L. A lubrication approach to friction in thermoplastic composites forming processes. Compos. Part A
**2011**, 42, 950–960. [Google Scholar] [CrossRef] - Zhang, W.; Ren, H.; Lu, J.; Zhang, Z.; Su, L.; Wang, J.; Zeng, D.; Su, X.; Cao, J. Experimental Methods to Characterize the Woven Composite Prepreg Behavior during the Preforming Process. In Proceedings of the Thirty-First Technical Conference of the American Society for Composites 2016, Williamsburg, VA, USA, 19–21 September 2016. [Google Scholar]
- Cao, J.; Akkerman, R.; Boisse, P.; Chen, J.; Cheng, H.S.; de Graaf, E.F.; Gorczyca, J.L.; Harrison, P.; Hivet, G.; Launay, J.; et al. Characterization of mechanical behavior of woven fabrics: Experimental methods and benchmark results. Compos. Part A
**2008**, 39, 1037–1053. [Google Scholar] [CrossRef] - Groh, F.; Kappel, F.; Hühne, C.; Brymerski, W. Experimental Investigation of Process Induced Deformations of Automotive Composites with Focus on Fast Curing Epoxy Resins. In Proceedings of the 20th International Conference on Comosite Materials (ICCM-20), Copenhagen, Denmark, 19–24 July 2015. [Google Scholar]
- Geissberger, R.; Maldonado, J.; Bahamonde, N.; Keller, A.; Dransfeld, C.; Masania, K. Rheological modelling of thermoset composite processing. Compos. Part B
**2017**, 124, 182–189. [Google Scholar] [CrossRef] - Seong, D.G.; Kim, S.; Um, M.K.; Song, S.S. Flow-induced deformation of unidirectional carbon fiber preform during the mold filling stage in liquid composite molding process. J. Compos. Mater.
**2017**, 52, 1265–1277. [Google Scholar] [CrossRef] - Boisse, P. Simulations of Composite Reinforcement Forming, Woven Fabric Engineering; Dubrovski, P.D., Ed.; InTech: Rijeka, Croatia, 2010; ISBN 978-9-53-307194-7. Available online: https://hal.archives-ouvertes.fr/hal-01635297/document (accessed on 26 October 2016).
- Xue, P.; Peng, X.; Cao, J. A non-orthogonal constitutive model for characterizing woven composites. Compos. Part A
**2003**, 34, 183–193. [Google Scholar] [CrossRef] - Liang, B.; Hamila, N.; Peillon, M.; Boisse, P. Analysis of thermoplastic prepreg bending stiffness during manufacturing and of its influence on wrinkling simulations. Compos. Part A
**2014**, 67, 111–122. [Google Scholar] [CrossRef] - Alshahrani, H.; Hojjati, M. A new test method for the characterization of the bending behavior of textile prepregs. Compos. Part A
**2017**, 97, 128–140. [Google Scholar] [CrossRef] - Creech, G. Mesoscopic Finite Element Modelling of Non-Crimp Fabrics for Drape and Failure Analyses. Ph.D. Thesis, Cranfield University, Cranfield, UK, 2006. [Google Scholar]
- Lee, W.; Um, M.K.; Byun, J.H. Numerical study on thermo-stamping of woven fabric composites based on double-dome stretch forming. Int. J. Mater. Form.
**2010**, 3, 1217–1227. [Google Scholar] [CrossRef] - Lee, W.; Cao, J. Numerical simulations on double-dome forming of woven composites using the coupled non-orthogonal constitutive model. Int. J. Mater. Form.
**2009**, 2, 145–148. [Google Scholar] - Cartwright, B.K.; de Luca, P.; Wang, J.; Stellbrink, K.; Paton, R. Some proposed experimental tests for use in finite element simulation of composite forming. In Proceedings of the 12th International Conference on Composite Materials (ICCM-12), Paris, France, 5–9 July 1999. [Google Scholar]
- Dusi, M.R.; Lee, W.I.; Ciriscioli, P.R.; Springer, G.S. Cure Kinetics and Viscosity of Fiberite 976 Resin. J. Compos. Mater.
**1987**, 21, 243–261. [Google Scholar] [CrossRef] - Ersoy, N.; Garstka, T.; Potter, K.; Wisnom, M.; Porter, D.; Stringer, G. Modelling of the spring-in phenomenon in curved parts made of a thermosetting composite. Compos. Part A
**2010**, 41, 410–418. [Google Scholar] [CrossRef] - Lightfoot, J.; Wisnom, M.; Potter, K. Defects in woven preforms: Formation mechanisms and the effects of laminate design and layup protocol. Compos. Part A
**2013**, 51, 99–107. [Google Scholar] [CrossRef] - Launay, J.; Hivet, G.; Duong, A.; Boisse, P. Experimental analysis of the influence of tensions on in plane shear behaviour of woven composite reinforcements. Compos. Sci. Technol.
**2008**, 68, 506–515. [Google Scholar] [CrossRef] - Prodromou, A.; Chen, J. On the relationship between shear angle and wrinkling of textile composite preforms. Compos. Part A
**1997**, 28, 491–503. [Google Scholar] [CrossRef] - Wang, P.; Legrand, X.; Boisse, P.; Hamila, N.; Soulat, D. Experimental and numerical analyses of manufacturing process of a composite square box part: Comparison between textile reinforcement forming and surface 3D weaving. Compos. Part B
**2015**, 78, 26–34. [Google Scholar] [CrossRef]

**Figure 2.**Thermoforming experimental apparatus for (

**a**) open, (

**b**) closed square-cup mold, (

**c**) Type 1 with a 20 mm mold thickness and 110° draft angle (

**top**) Type 2 with a 40 mm mold thickness and 90° draft angle (

**bottom**).

**Figure 3.**(

**a**) Viscosity dynamic scan; (

**b**) Degree of cure versus time at different temperatures for the fast-cure epoxy resin.

**Figure 4.**(

**a**) Non-linear stress-strain curves for each prepreg at 100 °C; (

**b**) Enlargement of UD 0° prepreg images after a high temperature tensile test.

**Figure 5.**Comparison between the theoretical shear strain (angle) of for (

**a**) Plain–woven (PW) carbon; (

**b**) PW glass and (

**c**) UD carbon prepreg and real shear angle measurements; (

**d**) PW carbon; (

**e**) PW glass and (

**f**) UD carbon prepreg at a high temperature.

**Figure 6.**(

**a**) Inner layer and (

**b**) outer layer of the thermoformed square-cup for the Type 1 mold design with the pattern 1 prepreg laminate.

**Figure 7.**(

**a**) Inner layer and (

**b**) outer layer of the thermoformed square-cup for the Type 2 mold design with the pattern 1 prepreg laminate.

**Figure 8.**(

**a**) Inner layer and (

**b**) outer layer of the thermoformed square-cup for the Type 1 mold design with the pattern 2 prepreg laminate.

**Figure 9.**Shear-dominated regions of the PW carbon prepreg at ①, ② and ③, (

**a**) Shear angle measurement at the inner corner of ③, (

**b**) Averaging the shear angle by connecting imaginary lines between two rhombic shapes.

**Figure 10.**Predicted shear angles in the Type 1 mold design with the pattern 1 prepreg laminate at corner 1, corner 2, corner 3, corner 4 using the PAM-FORM simulation (From top view).

**Figure 11.**Comparison between the experimental and simulation results for the shear angle at (

**a**) corner 1; (

**b**) corner 2; (

**c**) corner 3; (

**d**) corner 4 as illustrated in Figure 10.

Model Name | Type | Thickness (Standard Deviation) (mm) | Resin Content (vol %) | Weight (g/m^{2}) |
---|---|---|---|---|

7628 | Plain woven (PW) glass | 0.305 (±3.1 × 10^{−6}) | 42 | 209 |

CF-3327 | Plain woven (PW) carbon | 0.269 (±5.7 × 10^{−6}) | 42 | 200 |

CU-190 | Unidirectional (UD) carbon | 0.202 (±3.8 × 10^{−6}) | 38 | 190 |

Ply | Pattern 1 | Pattern 2 |
---|---|---|

1 | Carbon PW | UD 0° |

2 | UD 0° | UD +45° |

3 | UD +45° | UD −45° |

4 | UD −45° | Glass PW |

5 | Glass PW | Glass PW |

6 | Glass PW | Glass PW |

7 | UD −45° | Glass PW |

8 | UD +45° | UD −45° |

9 | UD 0° | UD +45° |

10 | Carbon PW | UD 0° |

**Table 3.**Average and standard deviation of strength and Young’s modulus from three repeated measurements for unidirectional (UD) 0° (red), PW carbon (green), PW glass (blue) and UD carbon 90° at 100 °C.

Prepreg | UD Carbon 0° | PW Carbon | PW Glass | UD Carbon 90° |
---|---|---|---|---|

Strength (MPa) | 280.1 (±18.3) | 72.2 (±5.3) | 30.0 (±1.1) | 1.4 × 10^{−3} (±1.6 × 10^{−4}) |

Modulus (GPa) | 60.4 (±3.7) | 11.2 (±1.1) | 0.57 (±0.04) | 2.9 × 10^{−2} (±2.6 × 10^{−3}) |

**Table 4.**Coefficient of friction between tool and prepreg with three repeated friction force measurements at the thermoforming conditions.

Prepreg | UD Carbon 0° | UD Carbon 90° | PW Carbon |
---|---|---|---|

Coefficient of friction | 0.050 | 0.063 | 0.202 |

Standard deviation | 0.007 | 0.010 | 0.011 |

**Table 5.**Coefficient of friction of five different prepreg-prepreg patterns against our process parameters.

No. | Interface | Coefficient of Friction (COF) | Standard Deviation |
---|---|---|---|

1 | PW carbon/UD 0° | 0.180 | 0.002 |

2 | UD 0°/UD +45° | 0.078 | 0.002 |

3 | UD +45°/UD −45° | 0.074 | 0.005 |

4 | PW glass/UD −45° | 0.162 | 0.004 |

5 | PW glass/PW glass | 0.157 | 0.004 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Bae, D.; Kim, S.; Lee, W.; Yi, J.W.; Um, M.K.; Seong, D.G.
Experimental and Numerical Studies on Fiber Deformation and Formability in Thermoforming Process Using a Fast-Cure Carbon Prepreg: Effect of Stacking Sequence and Mold Geometry. *Materials* **2018**, *11*, 857.
https://doi.org/10.3390/ma11050857

**AMA Style**

Bae D, Kim S, Lee W, Yi JW, Um MK, Seong DG.
Experimental and Numerical Studies on Fiber Deformation and Formability in Thermoforming Process Using a Fast-Cure Carbon Prepreg: Effect of Stacking Sequence and Mold Geometry. *Materials*. 2018; 11(5):857.
https://doi.org/10.3390/ma11050857

**Chicago/Turabian Style**

Bae, Daeryeong, Shino Kim, Wonoh Lee, Jin Woo Yi, Moon Kwang Um, and Dong Gi Seong.
2018. "Experimental and Numerical Studies on Fiber Deformation and Formability in Thermoforming Process Using a Fast-Cure Carbon Prepreg: Effect of Stacking Sequence and Mold Geometry" *Materials* 11, no. 5: 857.
https://doi.org/10.3390/ma11050857