# A Novel Finite Element Method Approach in the Modelling of Edge Trimming of CFRP Laminates
## 3 FE Model Characteristics  
This work focused on analysing the tool wear influence on machining forces in composite edge trimming. It was achieved by developing 2D FE plane strain simulations in Abaqus/Explicit. In the FE model, just the cutting tool teeth of the three flute, zero helix, and milling tool were  
Figure 4: Three flute Polycrystalline Diamond (PCD) cutting tool with optical edge radius measurements.  
Figure 3: Edge trimming set-up: (**a**) separate pieces and (**b**) assembled set.  
simulated to reduce the computational cost. The initial laminate geometry was modelled to mimic the tool path when one cutting edge starts the material removal, as shown in Figure 5. CFRP mechanical and strength properties are shown in Tables 1 and 2, respectively.  
In the above tables, \(E_{11}\) and \(E_{22}\) represent the composite Young modulus in directions parallel and perpendicular to the fibre, respectively. The terms \(G_{12}\) and \(\
u_{12}\) are the composite shear modulus and the Poisson's ratio, respectively. \(X_{T}\) and \(X_{C}\) denote the longitudinal traction and longitudinal compression laminate strengths, respectively, whereas variables \(Y_{T}\) and \(Y_{C}\) indicate the transversal traction and transversal compression laminate strengths, respectively. Finally, the term \(S_{12}\) is the shear composite strength.  
The boundary conditions were selected to reproduce the cutting condition observed in real trials reliably. The displacement at the bottom of the laminate was fixed to simulate the fixtures' clamping conditions. The horizontal displacement was restricted to zero on the lateral sides to avoid the simulated laminate bending while the cutter is in contact with the workpiece. A total of 82,376 quadrilateral CPSR4 elements were employed in this research. The mesh employed was designed to guarantee the right balance between the accuracy and the model's computational cost. The element size of 10 \(\upmu\)m in the cutting area was selected because machining forces converge around this element size; the element sizes gradually increased until achieving a maximum size of 200 \(\upmu\)m at the laminate borders. The FE model partitions and meshed distribution used in this research are illustrated in Figures 5 and 6.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Material** & \(\mathbf{E_{1}(GPa)}\) & \(\mathbf{E_{2}(GPa)}\) & \(\mathbf{G_{12}(GPa)}\) & \(\mathbf{v_{12}}\) \\ \hline CFRP [44] & 148 & 7.7 & 4.7 & 0.3 \\ \hline \hline \end{tabular}
\end{table}
Table 1: CFRP mechanical properties.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Material** & \(\mathbf{X_{T}(MPa)}\) & \(\mathbf{X_{C}(MPa)}\) & \(\mathbf{Y_{T}(MPa)}\) & \(\mathbf{Y_{C}(MPa)}\) & \(\mathbf{S_{12}(MPa)}\) \\ \hline CFRP [44] & 2375 & 1465 & 51 & 119 & 112 \\ \hline \hline \end{tabular}
\end{table}
Table 2: CFRP strength properties.  
Figure 5: Mesh zoom of the closed area next to the cutter tool edge.  
The cutting tool was treated as a solid rigid body to reduce the FE model's computational cost. This approach is plausible because of the high rigidity and hardness of the Polycrystalline Diamond (PCD) milling tool and the low deformations levels suffered at the cutting tool tip compared to the machined composite laminate. A constant Coulomb friction coefficient of 0.1 was used to model the friction between the PCD cutter and CFRP laminates accurately [45].