# Development of Detailed FE Numerical Models for Assessing the Replacement of Metal with Composite Materials Applied to an Executive Aircraft Wing

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## Abstract

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## 1. Introduction

## 2. Theoretical Background

- the Huth–Schwarmann method was used to calculate the shear and stiffness of the fasteners;
- a Nodal Constraint approach was used to link the degrees of freedom of the nodes of the different geometric model parts (separately meshed);
- failure criteria for metallic alloys and composite materials were adopted to assess the structural integrity of both composite and metal components;
- bearing factors were taken into account to investigate the stress distribution in the fastening zones for both metal and composite components;
- linearized buckling analyses were adopted to investigate the structural stability under service loads.

#### 2.1. Huth–Schwarmann Method

- Fastener: HL11/HL70-D4.8; HL11/HL70-D6.35; HL12/HL86-D4.0; HL12/HL86-D4.8; HL12/HL86-D6.35; HL12/HL86-D7.93; MBF2011-D4.2; MBF2011-D4.8; MBF2011-D6.35; MBF2012/13-D4.2; NAS1097-D3.2; NAS7902-D4.2; NAS8803/7603-D4.8; NAS9302B-D3.2.

- D is the fastener diameter
- t
_{1}and t_{2}represent the panels thickness - E
_{1}and E_{2}are the in plane Young Modulus of the material considered - E
_{f}is the Young Modulus of the fasteners.

- τ = shear stress;
- F = force;
- A = cross-sectional area of the bolt.

#### 2.2. Nodal Constraints

- “Single-Point Constraint”, which limits one or more DOFs of a single node;
- “Multi-Points Constraints” (MPC) that allow defining the movement of a group of “Slave” nodes, controlled by an equation or a “Master” node.

#### 2.3. Failure Criteria for Damage Assessment

- ${\epsilon}_{t}$ e ${\epsilon}_{t}^{UL}$ = Maximum Allowable Tensile Strain and Maximum Tensile Strain at Ultimate Load;
- ${\epsilon}_{c}$ e ${\epsilon}_{c}^{UL}$ = Maximum Allowable Compressive Strain and Maximum Compressive Strain at Ultimate Load;
- ${\gamma}_{t}$ e ${\gamma}_{t}^{UL}$ = Maximum Allowable Shear Strain and Maximum Shear Strain at Ultimate Load;

#### 2.4. Bearing

- tensile failure;
- shear failure;
- bearing failure.

_{bru}), the Maximum Bearing Stress (F

_{bru}), a Fitting Factor (FF), geometric forming factors (D

_{t}) and the Bearing Distribution Factor (θ).

- P
_{sh}= Shear load acting on the pin; - D = hole diameter;
- T = thickness;
- P
_{bru}(Allowable Bearing Load) = F_{bru}× D × t (is the theoretical maximum pressure which can be supported without Bearing failure; - F
_{bru}= Maximum Bearing Stress of the Material (is the theoretical maximum stress which can be supported without Bearing failure); - θ = Bearing Distribution Factor (θ takes into account the actual Bearing stress distribution around the hole and is a function of the t/D ratio);
- FF = Fitting Factor (a design analysis of structural joints and fittings shall consider a fitting factor of 1.15 to be applied to limit and ultimate the load conditions for all phases of service life.

#### 2.5. Linear Buckling

- ${K}_{aa}$ = Linear Stiffness;
- ${K}_{aa}^{d}$ = Differential Stiffness (load-dependent stiffness)
- ${\lambda}_{i}$ = eigenvalues (critical loads multipliers);
- ${\varphi}_{i}$ = eigenvectors (Buckling Modes).

## 3. FE Model

- Configuration 1: mesh size 10 mm
- Configuration 2: mesh size 5 mm
- Configuration 3: mesh size 2.5 mm

- Thickness extrapolation from the original metal component;
- Plies number assignment;
- Stacking sequence definition based on stiffness requirements and basic design rules with composites;
- FEM analysis verification of component strength and stiffness requirements.

- Quasi-Isotropic: uniform stiffness in all directions;
- Hard (more Plies at 0°)-Resistance for loads across the wingspan;
- Soft (more Plies 45°)-Improve Bearing issues for joints.

## 4. Numerical Results

- Maximum Allowable Strain for the composite components;
- Maximum Allowable Stress (Von Mises) for metallic components.

- ${\u03f5}_{T}=4500\mu \u03f5$;
- ${\u03f5}_{C}=-3500\mu \u03f5$;
- ${\mathsf{\sigma}}_{T}=$ 496 MPa (Al 7050-T7451);
- ${\mathsf{\sigma}}_{T}=$ 434 MPa (Al 2024-T3).

- Joint analysis;
- Bearing analysis of the metallic components;
- Bearing analysis of the composite components.

#### 4.1. Failure Criteria Applied to the Composite Components

#### 4.2. Failure Criteria Applied to Metallic Components

#### 4.3. Buckling Analysis

#### 4.4. Final Considerations

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 5.**MPCs used for load applications (transfer of loads from one master node to a set of predefined nodes).

**Figure 10.**Geometrical information. (

**a**) Half-wing dimensions and stacking sequence view of the upper skin highlighted by different colours; (

**b**) stacking sequence details of the composite upper half wing; (

**c**) thickness trend of the aluminium upper half wing.

**Figure 11.**Geometrical information. (

**a**) Stacking sequence view of the lower skin highlighted by different colours; (

**b**) stacking sequence details of the composite lower half wing; (

**c**) thickness trend of the aluminium lower half wing.

**Figure 14.**Maximum tensile strain. (

**a**) Laminae direction 0°; (

**b**) laminae direction 90°; (

**c**) laminae direction ±45°.

**Figure 15.**Maximum compressive strain. (

**a**) Laminae direction 0°; (

**b**) laminae direction 90°; (

**c**) laminae direction ±45°.

**Figure 17.**Buckling analysis output. (

**a**) Bending up; (

**b**) bending down; (

**c**) flap only; (

**d**) take off; (

**e**) landing.

Part | Material |
---|---|

Rib BL0 | Al 7050-T7451 |

Fuselage Fitting | Al 7050-T7451 |

Rib ST 225 Fitting | Al 7050-T7451 |

Flap Fitting | Al 7050-T7451 |

Splice | Al 7050-T7451 |

Rib TE | Al 2024-T3 |

Upper Panel | CFRP-IM7/977-2 |

Lower Panel | CFRP-IM7/977-2 |

Rear spar | CFRP-IM7/977-2 |

Front spar | CFRP-IM7/977-2 |

Upper Stringer | CFRP-IM7/977-2 |

Lower Stringer | CFRP-IM7/977-2 |

Rib ST 225 | CFRP-IM7/977-2 |

Closing Rib | CFRP-IM7/977-2 |

Al 7050-T7451 Properties | |
---|---|

Density [t/mm^{3}] | 2.83 × 10^{−9} |

F_{tu} [GPa] | 0.468 |

F_{ty} [GPa] | 0.406 |

F_{cy} [GPa] | 0.420 |

F_{su} [GPa] | 0.296 |

F_{bru} (e/D = 2.0) [GPa] | 0.972 |

E [GPa] | 71.016 |

E_{c} [GPa] | 73.084 |

Al 2024-T3 Properties | |
---|---|

Density [t/mm^{3}] | 2.78 × 10^{−9} |

F_{tu} [GPa] | 0.434 |

F_{ty} [GPa] | 0.289 |

F_{cy} [GPa] | 0.268 |

F_{su} [GPa] | 0.268 |

F_{bru} (e/D = 2.0) [GPa] | 0.889 |

E [GPa] | 72.394 |

E_{c} [GPa] | 73.773 |

Μ | 0.33 |

IM7/977-2 Composite Properties | |
---|---|

Density [t/mm^{3}] | 1.58 × 10^{−9} |

E_{1} [GPa] | 153.0 |

E_{2} = E_{3} [GPa] | 10.30 |

G_{12} = G_{13} [GPa] | 6.0 |

G_{23} [GPa] | 3.7 |

ν_{12} = ν_{13} | 0.30 |

ν_{23} | 0.40 |

Loading Condition | Description |
---|---|

Bending Up | Aerodynamic Loads + Flap Loads |

Bending Down | Aerodynamic Loads + Flap Loads |

Flap Only | Flap Loading Introduction |

Take-off | Aerodynamic Loads + Flap Loads |

Landing | Aerodynamic Loads + Flap Loads |

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**MDPI and ACS Style**

Acanfora, V.; Petillo, R.; Incognito, S.; Mirra, G.M.; Riccio, A.
Development of Detailed FE Numerical Models for Assessing the Replacement of Metal with Composite Materials Applied to an Executive Aircraft Wing. *Aerospace* **2021**, *8*, 178.
https://doi.org/10.3390/aerospace8070178

**AMA Style**

Acanfora V, Petillo R, Incognito S, Mirra GM, Riccio A.
Development of Detailed FE Numerical Models for Assessing the Replacement of Metal with Composite Materials Applied to an Executive Aircraft Wing. *Aerospace*. 2021; 8(7):178.
https://doi.org/10.3390/aerospace8070178

**Chicago/Turabian Style**

Acanfora, Valerio, Roberto Petillo, Salvatore Incognito, Gerardo Mario Mirra, and Aniello Riccio.
2021. "Development of Detailed FE Numerical Models for Assessing the Replacement of Metal with Composite Materials Applied to an Executive Aircraft Wing" *Aerospace* 8, no. 7: 178.
https://doi.org/10.3390/aerospace8070178