# Characterization of Fatigue Crack Growth Based on Acoustic Emission Multi-Parameter Analysis

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. Material and Methods

#### 2.1. Fatigue Crack Growth Test

#### 2.2. AE Monitoring Instrument

#### 2.3. Extraction of Multiple AE Parameters

## 3. Results and Discussion

#### 3.1. Fatigue Crack Growth Behavior

^{2}can be found in Figure 3b. The computed crack growth rate behavior will be further correlated with the AE multi-parameter analysis for characterizing different stages of FCG, which will be presented in the next section.

#### 3.2. Characterization of FCG via AE Multi-Parameter Analysis

#### 3.2.1. AE Time Domain Parameters

#### 3.2.2. AE Frequency Domain Parameter

#### 3.2.3. Coefficient of Variance of AE Data

#### 3.3. Quantitative Correlations between Crack Growth Rate and AE Parameters

#### 3.4. Fatigue Fracture Mechanism

## 4. Conclusions

- (1)
- Based on the combined analyses of AE time domain parameters and crack growth rate, four stages of FCG (i.e., stage A, B, C and D) of 2.25Cr1Mo0.25V steel can be distinguished. The four stages correspond to crack initiation, stable crack growth with low crack growth rate, stable crack growth with high crack growth rate, and unstable crack growth, respectively. The continuous emergence of a large number of AE signals with high count (>100) and high energy (>40 mV·ms) in stages C and D can help to provide early and effective warning signs for accelerated crack growth.
- (2)
- The centroid frequency of AE signals caused by FCG of 2.25Cr1Mo0.25V steel is distributed in a narrow range of 170–220 kHz. The centroid frequency may not be appropriate for assessing the crack growth condition due to low variability, however, the occurrence of such a frequency band can help to identify possible crack growth signals.
- (3)
- Linear correlations are found between crack growth rate and different AE parameters for quantifying crack growth. However, it should be noted that these quantitative correlations are only valid in current laboratory conditions. This is because AE signals are highly influenced by the sensor/source distance, specimen’s geometry and coupling quality [2], and consequently the quantitative relationships between AE and crack growth rate may not be obtained in the industrial environment. Before the practical application of this approach, the above-mentioned factors should be taken into account to reach a reliable quantification of fatigue crack of engineering structures.
- (4)
- The AE multi-parameter analysis is recommended for damage characterization due to its advantage of reducing errors in using individual AE parameters. In this study, based on the multi-parameter analysis, one can conclude the count, energy and kurtosis are superior parameters for both qualitatively and quantitatively characterizing the FCG of 2.25Cr1Mo0.25V steel.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Time domain waveforms (

**a**,

**c**) and their corresponding FFT spectrums (

**b**,

**d**) of AE signals detected at the fatigue loading cycle of (

**a**,

**b**) 49,251 and (

**c**,

**d**) 178,705 of specimen No. 1. The threshold is also included in the time domain waveform for comparing the peak amplitude of two signals.

**Figure 3.**(

**a**) Fatigue crack length and crack growth rate versus fatigue cycles of 2.25Cr1Mo0.25V steel. (

**b**) Fatigue crack growth rate versus stress intensity factor range (ΔK) in the double logarithm coordinate.

**Figure 4.**The variations of (

**a**) amplitude, (

**b**) count, (

**c**) energy and (

**d**) entropy versus fatigue cycles of specimen No. 1. The change in crack growth rate is also included for understanding the AE behaviors in different stages.

**Figure 5.**The variations of (

**a**) RA value, (

**b**) RMS, (

**c**) kurtosis and (

**d**) crest factor versus fatigue cycles of specimen No. 1. The change in crack growth rate is also included for understanding the AE behaviors in different stages.

**Figure 6.**The variations of (

**a**) AE energy and (

**b**) crest factor versus fatigue cycles of specimen No. 2.

**Figure 7.**The variations of normalized cumulative AE parameters versus fatigue cycles of (

**a**) specimen No. 1 and (

**b**) specimen No. 2.

**Figure 8.**The distributions of (

**a**,

**c**) AE count and (

**b**,

**d**) energy in four stages of FCG of specimen (

**a**,

**b**) No. 1 and (

**c**,

**d**) No. 2. The colored regions represent the middle 50% of values, that is, the range between the 25% and 75% percentile. The range between the top and bottom lines is 1.5 times the interquartile range (IQR).

**Figure 9.**The variation of centroid frequency versus fatigue cycles of specimen (

**a**) No. 1 and (

**b**) No. 2.

**Figure 10.**The logarithm of crack growth rate versus the logarithm of (

**a**) AE count rate, (

**b**) energy rate, (

**c**) entropy rate, and (

**d**) kurtosis rate of two specimens. The linear regression results including the median and the 95% prediction interval are also included.

**Figure 11.**Linear regression results between crack growth rate and different AE parameters including the results of (

**a**) R-square and (

**b**) the sum of squares due to error (SSE).

**Figure 12.**Typical fatigue-fracture surface morphology observed at the crack length of (

**a**) 5.1 mm (ΔK = 22.94 MPa·m

^{1/2}, $da/dN$ = 6.96·10

^{−5}mm/cycle) and (

**b**) 16.6 mm (ΔK = 40.25 MPa·m

^{1/2}, $da/dN$ = 2.78·10

^{−4}mm/cycle). The direction of fatigue crack propagation is from bottom to top.

AE Parameter | Definition |
---|---|

Amplitude/peak amplitude | Largest voltage peak of the signal waveform. It is expressed in a decibel scale where 1 μV at the sensor is defined as 0 dB. |

Count/ring-down count | Number of times where AE signal exceeds the employed threshold |

Energy | Measured area under the rectified signal envelope above the threshold |

Information entropy | Information or Shannon’s entropy of AE waveform. It denotes the disorder or uncertainty of the probability amplitude distribution. |

Rise time | Time interval between the point where the AE signal exceeds the threshold and the point where the peak amplitude occurs |

Duration | Time interval from the point where the AE signal exceeds the threshold to the last point where it crosses the threshold |

Rise angle (RA) | Ratio of rise time to amplitude |

Root mean square (RMS) | Square root of average of squared value of the signal |

Kurtosis | Measure of the “tailedness” of the AE signal |

Crest factor | Ratio of the peak value to the RMS value |

Centroid frequency | Weighted average of the frequency content calculated by performing fast Fourier transform |

AE Parameter | Amplitude | Count | Energy | Entropy | RA | RMS | Kurtosis | Crest Factor |
---|---|---|---|---|---|---|---|---|

Specimen 1 | 0.045 | 2.406 | 1.402 | 0.235 | 1.693 | 0.115 | 1.003 | 0.244 |

Specimen 2 | 0.829 | 1.683 | 1.735 | 1.189 | 2.082 | 1.369 | 1.291 | 1.342 |

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**MDPI and ACS Style**

Chai, M.; Lai, C.; Xu, W.; Duan, Q.; Zhang, Z.; Song, Y. Characterization of Fatigue Crack Growth Based on Acoustic Emission Multi-Parameter Analysis. *Materials* **2022**, *15*, 6665.
https://doi.org/10.3390/ma15196665

**AMA Style**

Chai M, Lai C, Xu W, Duan Q, Zhang Z, Song Y. Characterization of Fatigue Crack Growth Based on Acoustic Emission Multi-Parameter Analysis. *Materials*. 2022; 15(19):6665.
https://doi.org/10.3390/ma15196665

**Chicago/Turabian Style**

Chai, Mengyu, Chuanjing Lai, Wei Xu, Quan Duan, Zaoxiao Zhang, and Yan Song. 2022. "Characterization of Fatigue Crack Growth Based on Acoustic Emission Multi-Parameter Analysis" *Materials* 15, no. 19: 6665.
https://doi.org/10.3390/ma15196665