# Thermoforming Simulation of Woven Carbon Fiber Fabric/Polyurethane Composite Materials
## 3 Finite Element Simulation  
The simulation of the thermoforming process by a finite element method was executed using the commercial software LS-DYNA R10.0. To consider the fiber angle change during  
Figure 4: Forming conditions for the U-shaped structure. Figure 5: Punch and die for the small luggage structure. the thermoforming process, the above-mentioned discrete method was adopted under the explicit mode. A computational micro-mechanical material model was implemented in a material card, MAT 234 in LS-DYNA, for the woven fiber fabric, and it was originally from [PERSON] et al. [18]. In this approach, the representative volume technique extracted from the deformed pattern of the loosely woven fabric material model consisted of an undulated fill yarn crossed over an undulated warp yarn. Then, they were simplified and represented as a pin-joint mechanism of viscoelastic bars connected by a rigid link. This mechanism described the in-plane rotation of the yarns as a trellis mechanism and described the straightening of the undulated yarns. The orthogonal yarns in loose fabric were allowed to rotate until the lateral contact between the neighbor yarns caused the locking phenomenon. The behavior of the yarns was considered viscoelasticity, in which a Kelvin-Voight model was combined with a Maxwell model without the dashpot. Finally, to transform the stress of the yarns to the stress of the element, the representative volume cell was considered to be parallelepiped. There are a lot of carbon fiber parameters that need to be input in this discrete approach. To be concise, only some main material parameters are shown in Table 1. To describe the behavior of the thermoplastic resin in LS-DYNA, the material card MAT 004 was selected, because this card is suitable for elasticity, plasticity, and thermal analysis. In this work, the resin was simplified to be under elasticity, but its Young's modulus could be varied with temperature, as illustrated in Figure 2. The density and Poisson's ratio of the resin were 1.2 g/cm\({}^{3}\) and 0.45, respectively. The thermoplastic composite blank, which had four layers of fiber fabrics, was treated as one object, which was meshed by shell elements. Only one shell element was used along the thickness direction. In the discrete approach, each shell element included five resin layers and four fiber fabric layers that were alternatively interlaced, as illustrated in Figure 6a. The thickness of the resin layer and the fabric layer in the element was calculated from the 1 mm total thickness of the blank and the fiber volume fraction of 0.4. Hence, they were 0.12 mm and 0.1 mm, respectively. To have a suitable layer number combination for the blank, other combinations were also discussed, and the above nine-layer combination had the best simulation results [11]. Figure 6b shows the mesh of the blank with the U-shaped punch and the blank holder, in which 1 \(\times\) 1 mm shell elements were used. For the small luggage, because of the symmetry, only half of the system was meshed as shown in Figure 6c, and all shell elements were also 1 \(\times\) 1 mm. To reduce the calculation in these two cases, the punch, the blank holder, and the die were considered rigid bodies, even though a Young's modulus of 210 GPa, Poisson's ratio of 0.3, and density of 7.83 g/cm\({}^{3}\) were assigned. The conditions of the thermoforming process are described in Figure 4. As is shown, the temperatures of different parts were different, and there was heat conduction. Therefore, this structural forming simulation was coupled with the transient thermal analysis, and the final temperature of all parts was reduced to 25 \({}^{\circ}\)C after the simulation. In addition, due to the contact of different parts, the friction coefficient was 0.2 for the static case and 0.1 for the dynamic case.