# Hybrid Finite Element–Smoothed Particle Hydrodynamics Modelling for Optimizing Cutting Parameters in CFRP Composites

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## Abstract

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## 1. Introduction

## 2. Modelling and Experimental

#### 2.1. Smoothed Particle Hydrodynamic Model

#### 2.2. Hybrid Model Development

#### 2.2.1. The FEM-SPH Hybrid Subroutine

#### 2.2.2. SPH Particle Dimensions

#### 2.3. Experimental

^{®}M21 carbon fibre/resin matrix composite material, consisting of pre-impregnated sheets with a thickness of 0.26 mm matching the fibre diameter of 7.5 microns and a fibre volume percentage of 60%, was prepared; several steps were implemented to enhance the process [55,56]. Initially, the pre-impregnated carbon fibre was meticulously cut into the desired dimensions using a sharp cutter, while ensuring a pristine and uncontaminated work surface through thorough cleaning. Subsequently, a plywood sheet was carefully positioned on the processing table and shielded with release film, followed by the layering of breather fabric and T800 pre-impregnated carbon fibre. To maintain uniformity in the fibre alignment, pen markings were used to indicate the orientation of the fibres, repeating this procedure until the desired number of layers was achieved. Finally, the fabrication of laminates was accomplished, with each layer set to specific fibre orientations of 0°, 45°, 90°, and 135°, respectively.

## 3. Results and Discussion

#### 3.1. Damage and Chip Formation

#### 3.1.1. FEM for 0° Finite Fibre Orientation

^{−4}s after the start of cutting. The tool’s advancement compresses fibres at the tip, causing the central fibre to buckle under axial force. Adjacent fibres bend and deflect on the rake face due to the opening force applied by the tool. Stress propagation extends beyond the tool, leading to brittle failure in the matrix around the tool and along the fibre direction due to significant fibre deformation. This effect is evident in the buckling of the central fibre.

^{−3}s, leading to fibre failure and the propagation of cracks perpendicular to the fibres’ axis, as depicted in Figure 8. The degree of bending deformation gradually reduces as the fibre located on the sample’s free surface is approached. When buckling occurs due to the compressive load, the central fibres break into pieces and get trapped between the tool and the workpiece. The development of axial forces often causes instability in front of the cutting tool, which may result in buckling failure. As the tool makes contact with the material, the fibres that deflect downwards experience compression, causing the upper section of the fibre in contact with the tool to fracture. This leads to the deformation of cohesive elements that bind the matrix and fibre together. The failure of the matrix then spreads radially outwards from the tool, primarily propagating in front of it in the direction of the fibres until reaching the model boundary.

^{−3}s is depicted in Figure 9. As the tool moves forward, the fibres above the cutting edge undergo a considerable bending deformation, resulting in the propagation of cracks towards the sample’s free surface through adjacent fibres. An axial load in front of the cutting tool results in an increase in deformation, which damages the fibres located under the cutting plane. This damage is visible in the form of cracks caused by compression. Furthermore, there is a significant rise in the matrix fracture, mainly near the tool, where most of the matrix elements are eliminated as they fail.

^{−3}s, the fibre’s buckling instability leads to the failure of fibres ahead of the tool and results in multiple fractures, as shown in Figure 10. The cutting area expands, causing the material to bend and slide along the tool’s rake face, while the compression zone below the tool also widens, and the matrix fracture may even extend to the EHM phase. To gain an understanding of the matrix failure within the material, a more comprehensive model is required. Based on the material deformation, the sample can be split into four horizontal strips. Strips one and four exhibit primarily fibre bending behaviour, while strips two and three experience mostly buckling. However, the fibre behaviour tends to shift towards bending as we move towards strips one and four.

#### 3.1.2. FEM-SPH Model for 0° Fibre Orientation

- a
- At damage variable (D) of =0.8.

^{−4}s was illustrated in Figure 13. It was observed that the finite elements in the FEM-SPH model exhibited a behaviour similar to the classic FEM results. The central fibre was found to buckle, and the surrounding fibres were subjected to bending because of the cutting opening action. The key difference between the two models, however, was the fact that the finite elements that were removed from the hybrid model were transformed into particles.

^{−3}s (as depicted in Figure 14), there is an increase in the bending of the fibres located above the cutting edge, ultimately leading to failure. Meanwhile, the fibres located below the machining plane bend downwards, causing cracks to appear in the material. This is the point at which the differences between the FEM and hybrid models become apparent. When observing the hybrid model, two notable features can be identified. Firstly, there is a noticeable build-up of particles around the tool edge. Secondly, due to the damaged material, a larger amount of the material is influenced during cutting. Consequently, stress propagation is significantly more extensive in the hybrid model when compared with the FEM. This is noticeable in the workpiece upper corner, where the hybrid model shows upward bending deformation, whereas the FEM depicts the fibre remaining in its original configuration (as shown in Figure 14a–c). Furthermore, the finite elements representing the matrix material in the corner fail in the hybrid model, which is different from the FEM. Hence, the impact of the tool’s opening action is not limited to the damaged material but also extends to the material located at a significant distance from it. The FEM model indicates that the compression of fibres causes the stretching of cohesive elements, leading to debonding in the area ahead of the cutting tool, as shown in Figure 14d. Despite this, a significant number of cohesive elements were eliminated from the model due to the matrix failure, highlighting the material’s brittle behaviour.

^{−3}s, as shown in Figure 15. During the cutting process, a crack is observed to travel perpendicularly from the tool’s cutting edge towards the workpiece surface. This behaviour is caused by several failure mechanisms. The crack initiation occurs in front of the tool due to buckling, and then it expands away from the edge because of bending failure. The model also demonstrates that the material under the cutting tool undergoes compression, leading to visible deformations of the particles at the sample’s vertical free edge, which protrude outward.

^{−3}s, as shown in Figure 16, the hybrid model demonstrates a similar agglomeration of fractured fibres and the matrix as the FEM. However, in contrast to the FEM model, the failed matrix elements in the agglomeration were clearly shown in the hybrid model. The area located in front of the tool can be categorized into four separate strips, with strips one and four exhibiting bending of fibres and strips two and three showing primarily buckling. Additionally, the tool’s movement causes the SPH particles to accumulate around the cutting edge.

^{−2}s. Even though both models generate continuous chips, the hybrid model produces a larger chip than the FEM because there is more material near the cutting edge that prevents the tool from losing contact with the workpiece and avoids separation. The thrust force that occurs is caused by the pressure from the material acting on the clearance face. Additionally, the SPH model has the capability to predict and simulate the bounce-back phenomenon. When the material particles fail, they interact with the remaining SPH particles based on the assigned constitutive model, creating a cracked material that can undergo elastic recovery.

- b
- At damage variable (D) of 0.1.

^{−4}. Figure 19 shows a slight deviation from the previous models, where the fibres at the centre fail near the advancing tool, leading to their compression and bending. The presence of stiffer, broken material in front of the cutting tool triggers local failure due to compression instability before buckling, which was observed in the earlier models. This phenomenon results in a deviation from the previous models and highlights the importance of the material’s stiffness and the impact of its failure on the cutting process.

^{−3}s (as depicted in Figure 20), the previously mentioned phenomenon becomes more apparent. Specifically, during the cutting process, the finite elements of the matrix that are located near the fibres begin to fail. When a stiffer and broken material is introduced into the matrix, it can decrease the deformation of the fibres caused by axial loads, leading to their failure due to compression stress. This occurrence enables us to observe how the tool motion affects the sample, causing the fibres to bend upwards above the cutting edge and downwards below it. Consequently, as a result of the downward force exerted by the tool, fractures and cracks emerge in the fibres located below it.

#### 3.1.3. FEM for 90º Fibre Orientation

#### 3.1.4. FEM-SPH for 90º Finite Orientation

^{3}MPa compared with 1.17 × 10

^{3}MPa), resulting in a large area of failed matrix and cohesive elements. The discrepancy in behaviour between the two models was due to the existence of fractured material, which was indicated by the presence of SPH particles. The element deletion typically reduces stress levels by reducing the amount of material. However, the transformation from FEM to SPHs resulted in the fractured elements transferring the cutting tool action to the undamaged workpiece. In the FEM, the cohesive elements experience significant deformation as they try to keep the matrix and fibre phases together.

#### 3.2. Experimental Validation

#### 3.2.1. The Cutting Forces

#### 3.2.2. Chip Formation and Type

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**The subroutine incorporates a matrix material model for both (

**a**) finite element modelling and (

**b**) SPH particles.

**Figure 4.**Fibre material model implemented in the subroutine for finite elements (

**a**) tension, (

**b**) compression.

**Figure 5.**The position and deformation of particles under compression loading in (

**a**) dormant, (

**b**) activated SPHs, and (

**c**) SPH deformation.

**Figure 7.**FEM configuration at 5.77 × 10

^{−4}s for the 0° fibre orientation (

**a**) fibre section, (

**b**) matrix section.

**Figure 8.**FEM configuration at 1.79 × 10

^{−3}s for the 0° fibre orientation, (

**a**) fibre section, (

**b**) matrix section).

**Figure 9.**FEM configuration at time 2.84 × 10

^{−3}s for the 0° fibre orientation, (

**a**) fibre section, (

**b**) matrix section.

**Figure 10.**FEM configuration at 4.5 × 10

^{−3}s for the 0° fibre orientation, (

**a**) fibre section, (

**b**) matrix section.

**Figure 11.**FEM configuration at 1.09 × 10

^{−2}s for the 0° fibre orientation, (

**a**) fibre section, (

**b**) matrix section.

**Figure 13.**FEM-SPH hybrid model configuration at 5.77 × 10

^{−4}s for the 0° fibre orientation and D = 0.8, (

**a**) fibre section, (

**b**) matrix section.

**Figure 14.**FEM-SPH model at 1.79 × 10

^{−3}s for the 0° fibre orientation and D = 0.8, (

**a**) fibre section, (

**b**) magnified matrix section, (

**c**) matrix section, (

**d**) cohesive elements behaviour.

**Figure 15.**Hybrid model configuration at 2.85 × 10

^{−3}s for the 0° fibre orientation and a matrix damage variable of 0.8.

**Figure 16.**FEM-SPH model configuration at 2.85 × 10

^{−3}s for the 0° fibre orientation and a matrix damage of 0.8, (

**a**) fibre section, (

**b**) matrix section.

**Figure 17.**FEM-SPH model at 2.85 × 10

^{−3}s for the 0° fibre orientation and a matrix damage of 0.8, (

**a**) fibre side, (

**b**) matrix side.

**Figure 18.**The condition of the cohesive elements after the simulation is completed in the FEM-SPH model for the 0° fibre orientation using a matrix damage of 0.8.

**Figure 19.**Hybrid model at 5.77 × 10

^{−4}s for the 0° fibre orientation using a matrix damage of 0.1.

**Figure 20.**FEM-SPH model configuration at 1.79 × 10

^{−3}s for the 0° fibre orientation and D = 0.1, (

**a**) fibre section, (

**b**) matrix section.

**Figure 21.**Hybrid model configuration at 2.85 × 10

^{−3}s for the 0° fibre orientation using a matrix damage variable of 0.1.

**Figure 22.**(

**a**,

**b**) Hybrid model configuration at 1.09 × 10

^{−2}s for the 0° fibre orientation when implementing a matrix damage of 0.1, (

**c**) cohesive elements’ configuration.

**Figure 23.**FEM configuration at 4.2 × 10

^{−4}s for the 90° fibre orientation, (

**a**) fibre section, (

**b**) matrix section, (

**c**) Cohesive elements behaviour—Matrix side.

**Figure 24.**FEM configuration at 1.46 ×10

^{−3}s for the 90° fibre orientation (

**a**) fibre section, (

**b**) matrix section.

**Figure 25.**(

**a**,

**b**) FEM configuration at 2.26 × 10

^{−3}s for the 90° fibre orientation, (

**c**) cohesive elements’ configuration.

**Figure 27.**(

**a**,

**b**) FEM-SPH model at 1.46 × 10

^{−3}s, (

**c**) cohesive elements at 1.46 × 10

^{−3}s, and (

**d**) FEM-SPH model at time 2.72 × 10

^{−3}.

**Figure 29.**The chip developed during cutting for the fibre orientation at 0° in the (

**a**) FEM, (

**b**) FEM-SPH model, and (

**c**) experimental results.

**Figure 30.**The formed chips for the fibre orientation at 90° in (

**a**) FEM, (

**b**) FEM-SPH model, and (

**c**) experimental results.

Material | Property | Value |
---|---|---|

Carbon fibre | Elastic constants Longitudinal strength | E_{1} = 294 GPa, E_{2} = E_{3} = 14 GPaGPa, G _{23} = 5.5 GPaν_{12} = ν_{13} = 0.2, ν_{23} = 0.25G_{12} = G_{13} = 28 GPa X _{t}= 5.88 GPa, X_{c}= 3.288 GPa |

Compressive strain failure | 0.155 | |

Compressive yield | 594.5 MPa | |

Epoxy matrix | Elastic constants | E = 2.96 GPa, ν = 0.4 |

Interface | Failure strength fracture Normal strength shear energy | σ_{u} = 74.7 MPa τ_{max} = 25 MPa G^{c}= 0.05σ _{max} = 167.5 MPaN/mm ^{2} |

**Table 2.**The thrust force (measured in N/mm) obtained from the FEM-SPH model, FEM, and experimental measurements.

Trust Force at Samples with Fibre Orientation of 0° | Trust Force at Samples with Fibre Orientation of 90° | |
---|---|---|

Measured experimentally | 35.68 N/mm | 59.29 N/mm |

Calculated using the FEM model | −3.03 N/mm | −4.28 N/mm |

Calculated using the hybrid model with D = 0.8 | 14.2 N/mm | N/A |

Calculated using the hybrid model with D = 0.1 | 16.1 N/mm | 24.9 N/mm |

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Abena, A.; Ataya, S.; Hassanin, H.; El-Sayed, M.A.; Ahmadein, M.; Alsaleh, N.A.; Ahmed, M.M.Z.; Essa, K.
Hybrid Finite Element–Smoothed Particle Hydrodynamics Modelling for Optimizing Cutting Parameters in CFRP Composites. *Polymers* **2023**, *15*, 2789.
https://doi.org/10.3390/polym15132789

**AMA Style**

Abena A, Ataya S, Hassanin H, El-Sayed MA, Ahmadein M, Alsaleh NA, Ahmed MMZ, Essa K.
Hybrid Finite Element–Smoothed Particle Hydrodynamics Modelling for Optimizing Cutting Parameters in CFRP Composites. *Polymers*. 2023; 15(13):2789.
https://doi.org/10.3390/polym15132789

**Chicago/Turabian Style**

Abena, Alessandro, Sabbah Ataya, Hany Hassanin, Mahmoud Ahmed El-Sayed, Mahmoud Ahmadein, Naser A. Alsaleh, Mohamed M. Z. Ahmed, and Khamis Essa.
2023. "Hybrid Finite Element–Smoothed Particle Hydrodynamics Modelling for Optimizing Cutting Parameters in CFRP Composites" *Polymers* 15, no. 13: 2789.
https://doi.org/10.3390/polym15132789