# Thermoforming Process Effect on Performances of Thermoplastic/Recycled Carbon Fiber Composites
## 3 Results and Discussion
### Effect of Compatibility Between Polymer Matrix and rCF  
In composite materials, the compatibility between the matrix and the fiber plays a crucial role in determining the mechanical properties of the final material. The strong adhesion between these two components ensures effective stress transfer, enhancing the composite's strength, durability, and overall performance. Conversely, poor compatibility can lead to reduced mechanical resistance. Among the numerous models present in the literature, the Cox-Krenchel model is suitable for the evaluation of the elastic modulus for carbon fiber-reinforced composites (CFRC) and is found to yield good agreement with the experimental modulus for a range of carbon fiber lengths and volume fraction [41; 42; 43]. When stress is applied parallel to the fibers, the mechanical elastic modulus of the composite (\(E_{c}\)) is given by [44]:  
\[E_{c}=v_{f}E_{f}^{*}+v_{m}E_{m} \tag{5}\]  
where \(E_{f}^{*}\) is the effective elastic modulus of the recycled fibers (rCF), \(E_{m}\) is the elastic modulus of PA6 and MAPP matrices, \(v_{f}\) is the volume of the fibers expressed as a percentage  
Figure 12: Relationship between [PERSON]’s modulus and porosity for various MAPP/60 composite configurations. The graph shows a strong negative correlation (R\({}^{2}\) = 0.9929), with a linear regression equation of y = \(-\)173.01x + 23.659. Error bars represent the measurement uncertainties for each data point.  
and \(v_{m}\) is the volume of the matrix as a percentage. Making the necessary substitutions, the final equation becomes:  
\[E_{c}=v_{f}\eta E_{rCF}+(1-v_{f})E_{m} \tag{6}\]  
where \(\eta\) is the reinforcement efficiency factor, which depends on several factors, including the fiber aspect ratio (length to diameter ratio), the packing and orientation of the fibers, the compatibility between fibers and matrix, and the shear strength [45].  
For PA6/60 and MAPP/60, E\({}_{\text{c}}\) values of 19.3 GPa and 23.8 GPa were obtained, respectively. The significant difference recorded among the two materials is mainly related to the compatibility between the matrix and fibers. In particular, the effective elastic modulus (\(E_{f}^{*}\)) is 60 GPa for PA6/60 and 90 GPa for MAPP/60.  
The actual reinforcement of the rCF is mitigated by the parameter \(\eta\). By comparing the two systems, it is possible to note that the fibers are the same, with the same average aspect ratio and similar random distribution. The main difference is the interaction between fibers and the hosting matrix due to the surface roughness and chemical compatibility. Rough surfaces increase frictional force and interfacial adhesion between the reinforcement and the polymer, allowing us to obtain good interfacial shear strength values [45] for both the systems.  
Furthermore, in MAPP/60, the hydrophilic anhydride groups of the sizing reacted with the hydroxyl groups on the CF surface. This resulted in a stronger interfacial interaction and thus stronger adhesion with the matrix [46].  
Evidence of the strength at the interphase between fibers and reinforcement is the damping capacity (proportional to tan8): the rCF/PA6-60 has a tan8 of 0.3. At the same time, the rCF/MAPP60 shows a value of 0.2, which means a dissipation capacity of less than \(-30\%\) compared to similar conditions (polymer chain mobility). This means that the PA6-60-based composite dissipates more energy, which implies weak bonding with the reinforcement. Conversely, the MAPP/60 composite acts as a stiffer system with good adhesion between the matrix and reinforcement, thanks to the grafting of fibers promoted by maleic anhydride.