# An Experimental and Numerical Investigation to Characterize an Aerospace Composite Material with Open-Hole Using Non-Destructive Techniques

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Experimental Setup

#### 2.1. Infrared-Monitored Fatigue Tests

_{11}and α

_{22}are the surface coefficients of thermal expansion in 1 and 2 directions; Δσ

_{1}and Δσ

_{2}are the amplitudes of the principal stresses at the surface [64]. All these parameters can be found in the literature [65,66].

_{max}= 60 kN, a σ

_{min}= 0 kN and a frequency of 10 Hz to minimize non-adiabatic effect and reduce testing time [64]. The limit of cycles was established at 2 million. Figure 3 shows an example of the temperature variation measurement in a longitudinal specimen during fatigue testing with the geometry A.

#### 2.2. Digital Image Correlation Monitored Quasi-Static Tests

## 3. Numerical Model Implementation

#### Material Behavior

## 4. Results and Discussion

#### 4.1. Thermal Analysis Using Infrared Thermography

_{(x)}—T

_{0}where T

_{(x)}is the temperature of the material at x distance from the center of the hole in a vertical direction and T

_{0}is the initial temperature of the specimen. This expression defines the temperature origin at the hole and is used as an indicator of damage progression.

#### 4.2. Damage Analysis Using DIC Technique

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Geometries of the CFRP specimens. Samples of each geometry were cut considering both the longitudinal and transverse directions of the original laminate plate.

**Figure 6.**Representation of the finite element model generated considering the test conditions. A high level of discretization was defined at the stress concentration region.

**Figure 7.**Flowchart of the Progressive Damage Model implemented in the Abaqus user subroutine USDFLD.

**Figure 8.**Evolution of the surface temperature variation as a function of the number of load cycles in specimens cut at longitudinal direction for (

**a**) geometry A and (

**b**) geometry B.

**Figure 9.**(

**a**) Specimen temperature at breakage time for geometry A and (

**b**) failure mechanisms observed under optical microscope after breakage.

**Figure 10.**(

**a**) Specimen temperature at breakage time for geometry B and (

**b**) failure mechanisms observed under optical microscope after breakage.

**Figure 11.**Evolution of the surface temperature variation as function of the number of load cycles in specimens cut at transversal direction for (

**a**) geometry A and (

**b**) geometry B.

**Figure 13.**Comparison of displacement and strain fields between DIC estimation and numerical prediction for geometry A.

**Figure 14.**Comparison of displacement and strain field between DIC estimation and numerical prediction for geometry B.

**Table 1.**Surface temperature for control points of the specimen cut in transversal direction with geometry A.

Number of Cycles: | 230 | 560 | 921 |

Hot Point 1 (Waviness) | 29.2 °C | 36.9 °C | 41.2 °C |

Hot Point 2 (Hole) | 24.5 °C | 29.5 °C | 33.1 °C |

Cold Point | 20.0 °C | 23.5 °C | 25.4 °C |

**Table 2.**Surface temperature for control points of the specimen cut in transversal direction with geometry B.

Number of Cycles: | 806 | 1225 | 2165 | 3960 | 4911 |

Hot Point 1 (Waviness) | 29.4 °C | 40.0 °C | 47.4 °C | 54.2 °C | 57.4 °C |

Hot Point 2 (Hole) | 28.7 °C | 36.1 °C | 43.8 °C | 54.8 °C | 60.8 °C |

Cold Point | 21.8 °C | 24.5 °C | 26.2 °C | 27.7 °C | 28.8 °C |

**Table 3.**Surface temperature for control points of the specimen cut in transversal direction with geometry A.

Number of Cycles: | 1834 | 52,634 | 184,666 | 277,093 | 1,084,913 |

Hot Point 1 (Waviness) | 20.4 °C | 23.0 °C | 25.3 °C | 27.4 °C | 27.7 °C |

Hot Point 2 (Hole) | 21.5 °C | 24.2 °C | 25.6 °C | 27.0 °C | 27.1 °C |

Cold Point | 20.2 °C | 21.6 °C | 22.0 °C | 24.0 °C | 24.2 °C |

**Table 4.**Surface temperature for control points of the specimen cut in transversal direction with geometry B.

Number of Cycles: | 1817 | 35,616 | 169,575 | 916,870 | 1,932,253 |

Hot Point 1 (Waviness) | 21.5 °C | 23.0 °C | 26.5 °C | 28.4 °C | 30.3 °C |

Hot Point 2 (Hole) | 23.3 °C | 25.5 °C | 26.3 °C | 28.1 °C | 29.3 °C |

Cold Point | 21.1 °C | 22.0 °C | 22.2 °C | 24.2 °C | 26.0 °C |

Instant 1 | Instant 2 | Instant 3 | |||||
---|---|---|---|---|---|---|---|

Value | DIC | FEM | DIC | FEM | DIC | FEM | |

Xdirection | Max | 4.70 × 10^{−3} | 4.79 × 10^{−3} | 9.00 × 10^{−3} | 9.43 × 10^{−3} | 1.08 × 10^{−2} | 1.15 × 10^{−2} |

Min | −4.65 × 10^{−3} | −4.79 × 10^{−3} | −8.70 × 10^{−3} | −9.43 × 10^{−3} | −1.06 × 10^{−2} | −1.15 × 10^{−2} | |

Y direction | Max | 1.21 × 10^{−2} | 1.21 × 10^{−2} | 2.50 × 10^{−2} | 2.38 × 10^{−2} | 3.10 × 10^{−2} | 2.90 × 10^{−2} |

Min | −1.22 × 10^{−2} | −1.21 × 10^{−2} | −2.55 × 10^{−2} | −2.38 × 10^{−2} | −3.10 × 10^{−2} | −2.90 × 10^{−2} |

Instant 1 | Instant 2 | Instant 3 | |||||
---|---|---|---|---|---|---|---|

Value | DIC | FEM | DIC | FEM | DIC | FEM | |

Xdirection | Max | 8.40 × 10^{−3} | 8.42 × 10^{−3} | 1.44 × 10^{−2} | 1.49 × 10^{−2} | 2.12 × 10^{−2} | 2.12 × 10^{−2} |

Min | −8.30 × 10^{−3} | −8.46 × 10^{−3} | −1.42 × 10^{−2} | −1.49 × 10^{−2} | −2.08 × 10^{−2} | −2.13 × 10^{−2} | |

Ydirection | Max | 1.80 × 10^{−2} | 1.76 × 10^{−2} | 3.15 × 10^{−2} | 3.09 × 10^{−2} | 4.55 × 10^{−2} | 4.41 × 10^{−2} |

Min | −1.82 × 10^{−2} | −1.76 × 10^{−2} | −3.20 × 10^{−2} | −3.10 × 10^{−2} | −4.65 × 10^{−2} | −4.42 × 10^{−2} |

Instant 1 | Instant 2 | Instant 3 | |||||
---|---|---|---|---|---|---|---|

Value | DIC | FEM | DIC | FEM | DIC | FEM | |

Maximum Principal Strain | Max | 2.68 × 10^{−3} | 2.96 × 10^{−3} | 5.55 × 10^{−3} | 6.06 × 10^{−3} | 7.60 × 10^{−3} | 8.49 × 10^{−3} |

Min | 1.20 × 10^{−4} | 1.26 × 10^{−4} | 2.00 × 10^{−4} | 2.22 × 10^{−4} | 3.00 × 10^{−4} | 3.11 × 10^{−4} | |

Minimum Principal Strain | Max | −1.10 × 10^{−4} | −8.81 × 10^{−5} | −1.00 × 10^{−4} | −1.44 × 10^{−4} | −2.00 × 10^{−4} | −2.04 × 10^{−4} |

Min | −1.15 × 10^{−3} | −1.92 × 10^{−3} | −2.15 × 10^{−3} | −3.62 × 10^{−3} | −3.24 × 10^{−3} | −5.44 × 10^{−3} |

Instant 1 | Instant 2 | Instant 3 | |||||
---|---|---|---|---|---|---|---|

Value | DIC | FEM | DIC | FEM | DIC | FEM | |

Maximum Principal Strain | Max | 2.76 × 10^{−3} | 2.73 × 10^{−3} | 4.28 × 10^{−3} | 5.38 × 10^{−3} | 5.10 × 10^{−3} | 7.58 × 10^{−3} |

Min | 2.80 × 10^{−4} | 2.96 × 10^{−4} | 5.60 × 10^{−4} | 5.83 × 10^{−4} | 6.80 × 10^{−4} | 7.39 × 10^{−4} | |

Minimum Principal Strain | Max | −8.00 × 10^{−5} | −9.76 × 10^{−5} | −1.50 × 10^{−4} | −1.90 × 10^{−4} | −2.00 × 10^{−4} | −2.46 × 10^{−4} |

Min | −1.36 × 10^{−3} | −1.65 × 10^{−3} | −2.58 × 10^{−3} | −3.24 × 10^{−3} | −3.22 × 10^{−3} | −4.77 × 10^{−3} |

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**MDPI and ACS Style**

Feito, N.; Calvo, J.V.; Belda, R.; Giner, E.
An Experimental and Numerical Investigation to Characterize an Aerospace Composite Material with Open-Hole Using Non-Destructive Techniques. *Sensors* **2020**, *20*, 4148.
https://doi.org/10.3390/s20154148

**AMA Style**

Feito N, Calvo JV, Belda R, Giner E.
An Experimental and Numerical Investigation to Characterize an Aerospace Composite Material with Open-Hole Using Non-Destructive Techniques. *Sensors*. 2020; 20(15):4148.
https://doi.org/10.3390/s20154148

**Chicago/Turabian Style**

Feito, Norberto, José Vicente Calvo, Ricardo Belda, and Eugenio Giner.
2020. "An Experimental and Numerical Investigation to Characterize an Aerospace Composite Material with Open-Hole Using Non-Destructive Techniques" *Sensors* 20, no. 15: 4148.
https://doi.org/10.3390/s20154148