# Traditional Eddy Current–Pulsed Eddy Current Fusion Diagnostic Technique for Multiple Micro-Cracks in Metals

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Sample Preparation

_{r}is 1. The width of cracks is 0.3 mm, which is the minimal size processed by WEDM. The width of the cracks is much smaller than those in existing investigations of PEC crack characterization [3,4], so we called the cracks in the paper micro-cracks.

_{1}can be calculated according Equation (1) as 3.1 mm. According to [18], the maximum depth of a crack that can be detected by the PEC is 4δ

_{1}. The geometric parameters of the sample are shown in Figure 1.

_{1}is the standard skin depth, μ = μ

_{0}μ

_{r}and μ

_{0}= 4π × 10

^{−7}H/m, and ω

_{1}= 2πf

_{1}is the fundamental angular frequency of the excitation signal.

## 3. Traditional Eddy Current Technique to Locate Multiple Micro-Cracks

#### 3.1. Working Principle of Traditional Eddy Current Technique

_{1}in the driving coil creates an alternating magnetic field H

_{1}, which is the primary magnetic field and induces current I

_{2}in the sample. The eddy currents simultaneously generate a secondary magnetic field H

_{2}, which resists the variation of the primary magnetic field and changes the resultant magnetic field H. H is dependent on such factors as the lift-off l, the excitation frequency f, the sample’s electrical conductivity σ, the sample’s relative magnetic permeability μ

_{r}, and probe coil geometry parameters (the inner radius r

_{1}, the outer radius r

_{2}, height h, and the number of turns N). The Z-component of the magnetic flux density B

_{z}is commonly used as the detection signal because it is strong enough to be detected by a solid magnetic sensor (e.g., a Hall sensor, a GMR sensor, or a TMR sensor). Therefore, B

_{z}can be expressed as

#### 3.2. Experiments and Result Analysis

_{1}, P

_{2}, …, P

_{i}, …, and P

_{n}(Figure 2) are detected by the sigma 2008 digital conductivity meter (Figure 3), which is a conductivity meter designed according to the traditional eddy current working principle. Before the experiment, the sigma 2008 digital conductivity meter was calibrated by standard test blocks. In the experiment, the excitation frequency was 60 KHz, and the interval of the adjacent detection points was equal to 5 mm. The conductivities at the detection points are detected and plotted in Figure 4. From Figure 4, we can see that the micro-cracks have an obvious influence on the conductivity of the detection points. When the probe of the sigma 2008 digital conductivity meter approaches the micro-crack, the eddy current generated in the sample is seriously disturbed by the micro-crack because the conductivity of the micro-crack is much less than the conductivity of the sample. The closer the detection point is to the micro-crack, the stronger the influence of the micro-crack on the eddy current in the sample. Therefore, the peak value of the relationship between the conductivity along the sample can characterize the location of the micro-cracks.

_{r}is the calibration location of micro-cracks, L

_{m}represents the location characterized by the sigma 2008 digital conductivity meter, and E

_{a}and E

_{r}are the absolute error and relative error, respectively.

_{i}, while for case (b), the peak value appears at P

_{i}

_{+1}; therefore, the maximal systematic error is the interval of the adjacent detection points (5 mm in this paper). Therefore, the smaller the interval of the adjacent detection points, the more accurate the characterizations by the sigma 2008 digital conductivity meter. A smaller interval of the adjacent detection points means that more detection points and more conductivities should be measured, which will lower the localization efficiency.

## 4. Pulsed Eddy Current Technique to Quantitatively Characterize Micro-Cracks

#### 4.1. PEC Experimental Setup

_{0}is the amplitude and f is the excitation frequency of the square wave signal. Because the square wave signal contains rich information in the frequency domain, it is commonly used in crack characterization [1,2,6].

#### 4.2. Experimental Results

_{c}is the calibration depth of a micro-crack, V

_{peak}is the peak value of the voltage signal from the Hall sensor, D

_{m}is the characterization depth of a micro-crack, and E

_{a}and E

_{r}are the absolute error and the relative error, respectively.

## 5. Fusion NDT Technique Based on TEC and PEC

#### 5.1. Fusion Strategy

#### 5.2. Experimental Results and Analysis

_{f}= −4.36V

_{peak}

^{2}+ 75.73 V

_{peak}− 34.71

_{peak}is the peak value of the voltage signal from the Hall sensor and D

_{f}is the crack depth by the fused NDT technique. According to (4), we can obtain the different crack depths, which are listed in Table 3. In Table 3, the errors of the TEC–PEC fused testing platform from the experiments are also listed.

_{ad}and E

_{rd}are the absolute and relative error, respectively. As can be seen from Table 2, the maximal absolute error of the fusion NDT system is 0.13 mm when the crack depth is 6 mm, and the maximal relative error is 2.5% when the crack depth is 4 mm. The location error by TEC is the main reason for error in the fused NDT technique.

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 5.**Two extreme cases of detection point P

_{i}and P

_{i}

_{+1}: (

**a**) P

_{i}located at the left wall of the micro-crack; (

**b**) P

_{i}

_{+1}located at the right wall of the micro-crack.

**Figure 6.**The module diagram of the pulsed eddy current (PEC) testing platform. PC, personal computer.

**Figure 7.**Time domain signal of PEC experiments: (

**a**) whole period; (

**b**) the differential signal from 0 ms to 0.45 ms.

**Figure 11.**The original signal (

**a**) and differential signal (

**b**) of the fused nondestructive testing (NDT) technique by experiment.

Microcrack # | Depth (mm) | L_{r} (mm) | L_{m} (mm) | E_{a} (mm) | E_{r} (%) |
---|---|---|---|---|---|

1 | 8 | 36.15 | 35 | 1.15 | 3.18 |

2 | 7 | 72.3 | 70 | 2.3 | 3.18 |

3 | 6 | 108.4 | 105 | 3.45 | 3.18 |

4 | 5 | 144.6 | 140 | 4.6 | 3.18 |

5 | 4 | 180.7 | 175 | 5.75 | 3.18 |

6 | 3 | 216.9 | 215 | 1.9 | 0.88 |

7 | 2 | 253.0 | 250 | 3.05 | 1.20 |

8 | 1 | 289.2 | 285 | 4.2 | 1.45 |

D_{c} (mm) | 3 | 4 | 5 | 6 | 7 |

V_{peak} (mV) | 165.1 | 233.7 | 263.5 | 281.9 | 295.2 |

D_{m} (mm) | 3.01 | 3.90 | 5.09 | 6.07 | 6.90 |

E_{a} | 0.01 | 0.10 | 0.09 | 0.07 | 0.09 |

E_{r} (%) | 0.33 | 2.50 | 1.80 | 1.17 | 1.29 |

D_{c} (mm) | 3 | 4 | 5 | 6 | 7 |

L_{m} (mm) | 105 | 140 | 175 | 215 | 250 |

D_{f} (mm) | 3.04 | 3.90 | 5.02 | 6.13 | 6.88 |

E_{ad} (mm) | 0.04 | 0.10 | 0.02 | 0.13 | 0.12 |

E_{rd} (%) | 1.33 | 2.5 | 0.4 | 2.16 | 1.71 |

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**MDPI and ACS Style**

Wang, Z.; Yu, Y.
Traditional Eddy Current–Pulsed Eddy Current Fusion Diagnostic Technique for Multiple Micro-Cracks in Metals. *Sensors* **2018**, *18*, 2909.
https://doi.org/10.3390/s18092909

**AMA Style**

Wang Z, Yu Y.
Traditional Eddy Current–Pulsed Eddy Current Fusion Diagnostic Technique for Multiple Micro-Cracks in Metals. *Sensors*. 2018; 18(9):2909.
https://doi.org/10.3390/s18092909

**Chicago/Turabian Style**

Wang, Zhenwei, and Yating Yu.
2018. "Traditional Eddy Current–Pulsed Eddy Current Fusion Diagnostic Technique for Multiple Micro-Cracks in Metals" *Sensors* 18, no. 9: 2909.
https://doi.org/10.3390/s18092909