# Damage Detection Using d15 Piezoelectric Sensors in a Laminate Beam Undergoing Three-Point Bending

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## Abstract

**:**

## 1. Introduction

## 2. Theoretical Background

#### 2.1. Shear-Mode (d15) PZTs

#### 2.2. Damage Index

## 3. Experiment

#### 3.1. Specimen Design and Fabrication

#### 3.2. Quasi-Static Three-Point Bending

_{fn}is the combined flexural rigidity of the laminate specimen at nth loading cycle, L is the length between loading supports, F is the mid-span load at nth loading cycle, and δ is the mid-span deflection at nth loading cycle. The stress induced in the laminate specimen can be calculated as [34]:

#### 3.3. Experimental Method

- Apply an increasing quasi-static load on the specimen until mid-span deflection reaches δ
_{n}, then remove the applied mid-span load. - At no-load condition state, actuate d15 PZTs with a voltage frequency sweep (V
_{i}) from 200 kHz to 1600 kHz by measuring the voltage (V_{o}) across a sensing resistor (R_{s}= 100 Ω) and the PZT element, then calculate the impedance, $Z={R}_{s}\left({V}_{i}/{V}_{o}\right)$. - Apply fast Fourier transform method and band-pass filter to the harmonic signals and identify the first resonance frequency, ${f}_{1}^{EM}$, for each d15 PZT.
- Continue the test if the difference between the baseline resonant peak and the measured resonant is less than α, which is set as 1% of the baseline resonant peak.
- Perform ultrasonic inspection by actuating bondline-embedded d15 PZTs. The excitation signal shown in Figure 6 is a five-peak sine signal centered at 30 kHz and modulated by a Hann window, $w(n)=0.5\left[1-\mathrm{cos}(2\pi n/N)\right],0\le \mathrm{n}\le \mathrm{N}$, where $N+1$ is the length of the window.
- Denoise senor signals using discrete wavelet transform with Coiflet wavelet performed at level six wavelet decomposition and applying the universal threshold $\sqrt{2\mathrm{ln}(.)}$, to the wavelet coefficients.
- Determine the maximum voltage, V
_{max}of the first arrival in sensor signals and the phase shift, ϕ_{max}with respect to baseline signals. - Calculate damage index values based on PCC and NSE methods using Equations (6) and (7), respectively.
- Repeat loading the specimen at a higher mid-span deflection by β increment, 0.1 mm herein.
- Stop the test when mid-span deflection reaches δ
_{m}that is calculated based on flexural rigidity of the laminate specimen.

## 4. Results and Discussion

#### 4.1. Wave Propagation Analysis

#### 4.2. Joint Degradation

^{2}at which a mixed-mode (flexural) crack developed and was located 21 mm from the applied load. The mixed-mode crack was formed at about 45 degrees plane as result of the adhesive layer between loading supports being subjected to both normal and transverse shear stresses. Residual stresses that accompany plastic deformation in localized areas such as at the applied load or at the loading supports can modulate the propagating waves in the laminate, therefore distortions in received signals prior to the flexural cracking are expected to reflect the effects of plastic deformation and joint defects.

^{6}N/mm

^{2}for the deflection range between 0–0.9 mm using Equation (8). This was followed by a significant drop in the flexural strength by more than 65%. By increasing mid-span deflection from 1 mm to 3.3 mm, its flexural rigidity significantly reduced and continuously decreased beyond 1 mm mid-deflection. Furthermore, flexural rigidity provides an indication of damage severity, particularly disbonding among the laminate layers. The three-point bending test was stopped when flexural rigidity reached almost zero.

#### 4.3. Electromechanical Impedance

#### 4.4. Ultrasonic Inspection

#### 4.5. Influence of Preload Condition

^{2}. The applied load at mid-span produces normal stresses across the thickness between loading supports, thus the propagating waves are anticipated to be modulated and be reflected on the received signals. However, this resulting distortion from a small applied load is expected to have negligible effect as compared to the effect of damage on the propagating waves. The results strongly suggest that the applied load on the specimen caused a geometric change to the bondline damage resulting in significant distortion to the propagating waves. As previously discussed in Section 4.4, the mixed-mode crack was observed and fully developed in the bondline at 0.9 mm mid-span deflection, and that was followed by plastic deformation causing the crack to remain open resulting in low distortion in received signals over the range 1–2.3 mm mid-span deflection as shown in Figure 11. Therefore, in the preload condition at 1.3 mm mid-span deflection, the applied load is anticipated to open the mixed-mode crack and disbonds while the antisymmetric waves transmitted through the bondline cause higher scattering of the propagating waves.

## 5. Conclusions

## 6. Future Work

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Schematic of a d15 piezoelectric transducer with fundamental wave modes depicted in the direction of wave propagation.

**Figure 2.**Schematic diagram of laminate specimen with two d15 lead zirconate titanate (PZT) transducers (15 mm × 15 mm × 1 mm) embedded in the bondline and d31 PZT sensor (6 mm × 0.25 mm) mounted on the surface of the bottom aluminum sheet.

**Figure 3.**Experimental setup of health monitoring experiment and magnified view of laminate specimen under three-point bending test.

**Figure 4.**Laminate specimen under a quasi-static three-point bending force applied cyclically at mid-span.

**Figure 5.**Flowchart of ultrasonic health monitoring experiment for a laminate specimen with surface-mounted and bondline-embedded PZT transducers.

**Figure 6.**Waveform signals obtained from laminate specimen with d31 PZT and d15 PZT transducers for wave propagation paths: (

**a**) PZT-1 → PZT-2 and (

**b**) PZT-1 → PZT-3.

**Figure 7.**(

**a**) Load–deflection response of laminate specimen under three-point bending test at: (

**b**) pristine state; (

**c**) flexural cracking at 0.9 mm mid-span deflection; and (

**d**) disbonding at 3.3 mm mid-span deflection.

**Figure 8.**Electromechanical impedance (EMI) response of bondline-embedded d15 PZTs at the pristine state with a frequency range containing the first EM resonance for: (

**a**) d15 PZT-1 and (

**b**) d15 PZT-2.

**Figure 9.**Comparison of waveform signals collected from bondline-embedded d15 PZT and surface mounted d31 PZT sensors at 1 mm deflection (left column) and 3.3 mm deflection (right column) for wave propagation paths: (

**a**,

**b**) PZT-1 → PZT-2 and (

**c**,

**d**) PZT-1 → PZT-3.

**Figure 10.**Maximum voltage amplitude (left column) and phase shift (right column) from waveform signals collected from bondline-embedded d15 PZT and surface mounted d31 PZT sensors for wave propagation paths: (

**a**,

**b**) PZT-1 → PZT-2; (

**c**,

**d**) PZT-1 → PZT-3; and (

**e**,

**f**) PZT-2 → PZT-1.

**Figure 11.**Damage index values based on Pearson correlation coefficient (PCC) and normalized signal energy (NSE) methods calculated for the first arrival of sensor signals received by: (

**a**) d15 PZT-2; (

**b**) d31 PZT-3; and (

**c**) d15 PZT-1.

**Figure 13.**Comparison of voltage signals from laminate specimen at no-preload condition (left column) and 50 N mid-span preload (right column) at 1.3 mm three-point loading cycle: (

**a**,

**b**) d15 PZT-2 sensor and (

**c**,

**d**) d31 PZT-3 sensor.

**Figure 14.**Scattered signals from laminate specimen at no-preload condition (left column) and 50 N mid-span preload (right column) at 1.3 mm three-point loading cycle: (

**a**,

**b**) d15 PZT-2 sensor and (

**c**,

**d**) d31 PZT-3 sensor.

**Table 1.**Material properties of the shear-mode piezoelectric transducer, Hysol EA9394, and Aluminum 6061 [16].

Property | Unit | Symbol | PZT-5A | Adhesive | Aluminum |
---|---|---|---|---|---|

Young’s Modulus | 10^{9} N/m^{2} | Y_{11} | 61.0 | 4.24 | 68.9 |

10^{9} N/m^{2} | Y_{33} | 53.2 | 4.24 | 68.9 | |

Shear’s Modulus | 10^{9} N/m^{2} | G_{12} | 22.6 | 1.46 | 25.9 |

10^{9} N/m^{2} | G_{13} | 10.5 | 1.46 | 25.9 | |

Poisson’s ratio | 1 | v_{12} | 0.35 | 0.45 | 0.33 |

1 | v_{13} | 0.44 | 0.45 | 0.33 | |

Density | kg/m^{3} | ρ | 7600 | 1360 | 2700 |

Dielectric permittivity | 8.854 µF/m | ε_{11} | 1851 | ------ | ------ |

8.854 µF/m | ε_{13} | 1581 | ------ | ------ | |

Piezoelectric coefficient | 10^{−12} m/V | d_{15} | 584 | ------ | ------ |

10^{−12} m/V | d_{31} | −171 | ------ | ------ | |

10^{−12} m/V | d_{33} | 374 | ------ | ------ |

**Table 2.**Summary of wave propagation results including time of flight (ToF) and group velocity for waveform signals from bondline-embedded d15 and surface-mounted d31 PZT sensors at no-load condition.

Wave Propagation Path | Time of Flight (μs) | Group Velocity (m/s) |
---|---|---|

PZT-1 → PZT-2 | 116.6 | 1157.8 |

PZT-1 → PZT-3 | 118.1 | 1143.1 |

PZT-2 → PZT-1 | 116.4 | 1159.8 |

**Table 3.**Damage indices of PCC and NSE for signals obtained from d15 PZT-2 and d31 PZT-3 at 0 N (no-preload condition) and at 50 N preload applied on the specimen at 1.3 mm three-point loading cycle.

Wave Propagation Path | 0 N | 50 N | ||
---|---|---|---|---|

PCC | NSE | PCC | NSE | |

PZT-1 → PZT-2 | 0.5644 | 0.1790 | 1.2886 | 0.6947 |

PZT-1 → PZT-3 | 0.5398 | 0.1657 | 1.1829 | 0.6724 |

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**MDPI and ACS Style**

Altammar, H.; Dhingra, A.; Salowitz, N.
Damage Detection Using d15 Piezoelectric Sensors in a Laminate Beam Undergoing Three-Point Bending. *Actuators* **2019**, *8*, 70.
https://doi.org/10.3390/act8040070

**AMA Style**

Altammar H, Dhingra A, Salowitz N.
Damage Detection Using d15 Piezoelectric Sensors in a Laminate Beam Undergoing Three-Point Bending. *Actuators*. 2019; 8(4):70.
https://doi.org/10.3390/act8040070

**Chicago/Turabian Style**

Altammar, Hussain, Anoop Dhingra, and Nathan Salowitz.
2019. "Damage Detection Using d15 Piezoelectric Sensors in a Laminate Beam Undergoing Three-Point Bending" *Actuators* 8, no. 4: 70.
https://doi.org/10.3390/act8040070