# Ultrasonic Phased Array Imaging Approach Using Omni-Directional Velocity Correction for Quantitative Evaluation of Delamination in Composite Structure

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theory and Method

#### 2.1. BRM (Low-Angle Velocity Measurement)

#### 2.2. High-Angle Velocity Measurement

_{1}described in Equation (13) and ${v}_{2}$ is wave velocity of 90° plies as a function of elastic stiffness matrix. Note that ${v}_{2}$ is independent of C under the assumption of homogeneity. Therefore, Equations (16) and (17) can be simplified to $M={C}_{11}+{C}_{44}$ and $N={C}_{11}{C}_{44}$, respectively. Accordingly, the velocity ${v}_{qP}$ = ($\sqrt{\frac{{C}_{11}}{\rho}}$) is obtained from Equation (9), implying that wave velocity on the CFRP isotropic plane indicated by Equation (6) is identical to that on the anisotropic plane in the direction θ of 0°.

_{0}is employed to represent the angle between the line from the incidence to the back wall reflection and the normal to the back wall. Specifically, θ

_{0}may be defined by:

_{1}and θ

_{2}are the refraction angles of 0° and 90° plies, respectively. In addition, h

_{1}and h

_{2}are the thickness of 0° and 90° plies, respectively.

_{0}can be calculated by the arc tangent of the ratio between the element spacing and the thickness of the test block h

_{0}, the refraction angles θ

_{1}and θ

_{2}in the plies of different directions can be obtained from Equations (18) and (19) if the C, h

_{1}and h

_{2}are known. Subsequently, the change in wave velocity with increasing angle in the 0° plies may be estimated, whereas it is impractical to express θ

_{1}and θ

_{2}in terms of a formula containing the elastic constant C through Equations (18) and (19). Consequently, θ

_{2}can be written as a function of θ

_{1}:

_{exp}at N different angles has been experimentally measured, it is compared with the theoretical one t

_{theo}defined in Equation (17) to determine the optimal refraction angle θ

_{1}, which is thought to be the actual refraction angle. Under the assumption that the 90° ply is isotropic, the relation curve between velocity and angle for the 0° ply can be computed by Equations (18) and (20).

## 3. Experimental Setup

^{3}was designed and fabricated to contain the artificial defects with specified size. More specifically, the specimen contains 23 unidirectional plies of the same thickness stacked in a repeating sequence of two orientation angles (e.g., 0°and 90°). As shown in Figure 5, the release films were embedded during manufacturing to simulate the delamination defects, which were located at depths of 3 mm and 5 mm and had a diameter of 8 mm. Figure 6 displays the experimental setup of the phased array detection and cross-section of the bespoke CFRP test block.

## 4. Results and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**The diagram of (

**a**) the three-dimensional matrix of ${M}_{T}\times {M}_{R}\times n$ and (

**b**) the transformed two-dimensional matrix of ${M}_{\Delta}\times n$.

**Figure 2.**Normalized time domain waveform with different transmit-receiving intervals ∆, ∆ = 0 (

**a**) and ∆ = 29 (

**b**).

**Figure 6.**Experimental setup of the phased array detection (

**a**) and a cross-section of the test block (

**b**).

**Figure 8.**The diagrams of (

**a**) measured discrete velocities at the angles from 0° to 45.8° and (

**b**) the theoretical fitting curve from 0° to 90°.

**Figure 10.**TFM imaging results for the 3 mm deep delamination defect using delay law of (

**a**) constant velocity, (

**b**) piecewise constant velocity, (

**c**) linear velocity and (

**d**) theoretical velocity as well as the 5 mm deep delamination defect using delay law of (

**e**) constant velocity, (

**f**) piecewise constant velocity, (

**g**) linear velocity, and (

**h**) theoretical velocity.

**Figure 11.**TFM imaging intensities for 3 mm deep defects along lines at (

**a**) x = 1.1 mm and (

**b**) z = 3 mm, as well as the 5 mm deep defects along lines at (

**c**) x = 1.1 mm and (

**d**) z = 5 mm.

Constant Velocity (C) | Piecewise Constant Velocity (P) | Linear Velocity (L) | Linear Velocity (L) | |
---|---|---|---|---|

Average intensity | −14.4254 | −8.0159 | −6.0752 | −5.0412 |

Std of intensity | 3.8881 | 1.5922 | 0.94358 | 0.86467 |

Average intensity | −20.4436 | −22.1136 | −20.7535 | −21.0696 |

Std of intensity | 5.5022 | 5.9473 | 5.6156 | 6.2298 |

Constant Velocity (C) | Piecewise Constant Velocity (P) | Linear Velocity (L) | Linear Velocity (L) | |
---|---|---|---|---|

Average intensity | −12.0681 | −3.7233 | −2.6446 | −1.5202 |

Std of intensity | 1.5661 | 0.8938 | 0.8842 | 0.9431 |

Average intensity | −23.4903 | −25.8872 | −24.3567 | −23.473 |

Std of intensity | 5.6004 | 7.1157 | 7.7815 | 7.4145 |

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**MDPI and ACS Style**

Xu, X.; Fan, Z.; Chen, X.; Cheng, J.; Bu, Y.
Ultrasonic Phased Array Imaging Approach Using Omni-Directional Velocity Correction for Quantitative Evaluation of Delamination in Composite Structure. *Sensors* **2023**, *23*, 1777.
https://doi.org/10.3390/s23041777

**AMA Style**

Xu X, Fan Z, Chen X, Cheng J, Bu Y.
Ultrasonic Phased Array Imaging Approach Using Omni-Directional Velocity Correction for Quantitative Evaluation of Delamination in Composite Structure. *Sensors*. 2023; 23(4):1777.
https://doi.org/10.3390/s23041777

**Chicago/Turabian Style**

Xu, Xiangting, Zhichao Fan, Xuedong Chen, Jingwei Cheng, and Yangguang Bu.
2023. "Ultrasonic Phased Array Imaging Approach Using Omni-Directional Velocity Correction for Quantitative Evaluation of Delamination in Composite Structure" *Sensors* 23, no. 4: 1777.
https://doi.org/10.3390/s23041777