# Comparison of Experimentally Determined Two-Dimensional Strain Fields and Mapped Ultrasonic Data Processed by Coda Wave Interferometry

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## Abstract

**:**

## 1. Introduction

## 2. Principles of Measuring Methods

#### 2.1. Strain Measurements

#### 2.1.1. Fiber Optic Sensors

#### 2.1.2. Digital Image Correlation

#### 2.2. Ultrasound

## 3. Experiments

#### 3.1. Method of Investigation

#### 3.2. Test Set-Up

#### 3.3. Results

#### 3.3.1. Strain

#### 3.3.2. Ultrasound

## 4. Comparison of US Results and Strain Fields

#### 4.1. Non-Cracked to Slightly Cracked State

#### 4.2. Completed Crack Pattern and Increasing Crack Widening

## 5. Discussion and Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

US | Ultrasonic |

CWI | Code Wave Interferometry |

DIC | Digital Image Correlation |

FOS | Fiber Optic Sensor |

RC | Reinforced Concrete |

NDT | Non-Destructive Testing |

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**Figure 3.**In classical ultrasonic (US) measurements, travel times are recorded and calculated via the ballistic waves. (

**a**) Ballistic wave between source and receiver. Using coda waves, changes of travel time within a larger segment, described by (

**b**) the sensitivity kernel (red), can be resolved.

**Figure 4.**A comparison of measurements with embedded transducers in a concrete beam shows the small influence of subtle changes. While in the first arrivals (bottom left) no change is visible, small differences in the later coda part indicate a change in the specimen (bottom right).

**Figure 7.**(

**a**,

**b**) Strain from Fiber Optic Sensors (FOS) for an applied load of $F=10\phantom{\rule{0.166667em}{0ex}}\mathrm{kN}$ and (

**c**) strain from Digital Image Correlation (DIC) for an applied load of $F=160\phantom{\rule{0.166667em}{0ex}}\mathrm{kN}$ and marked US transducer positions.

**Figure 8.**Stepwise Correlation Coefficient $CC$ and cumulative Relative Velocity Change $dv/v$ for selected transducer pairs in the (

**a**) compressive and (

**b**) tensile zone.

**Figure 9.**(

**a**,

**c**) Strain fields derived by FOS measurements assigned to their respective heights, (

**b**,

**d**) Relative Velocity Change presented as Attribute Maps. The two upper figures show the respective results for a load of $F=10$ kN, while the two lower Figures do so for $F=25$ kN.

**Figure 10.**(

**a**,

**c**) Strain fields from DIC, (

**b**,

**d**) Relative Velocity Changes $dv/v$ presented as Attribute Maps. Figures above show results for a load of $F=75$ kN, Figures below for $F=120$ kN, respectively.

${\mathbf{f}}_{\mathbf{ck},\mathbf{cube}}$ | ${\mathbf{f}}_{\mathbf{ctm}}$ | ${\mathbf{E}}_{\mathbf{cm}}$ |
---|---|---|

$[\mathbf{N}/{\mathbf{mm}}^{\mathbf{2}}]$ | $[\mathbf{N}/{\mathbf{mm}}^{\mathbf{2}}]$ | $[\mathbf{N}/{\mathbf{mm}}^{\mathbf{2}}]$ |

35.0 | 2.5 | 28,618 |

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**MDPI and ACS Style**

Clauß, F.; Epple, N.; Ahrens, M.A.; Niederleithinger, E.; Mark, P. Comparison of Experimentally Determined Two-Dimensional Strain Fields and Mapped Ultrasonic Data Processed by Coda Wave Interferometry. *Sensors* **2020**, *20*, 4023.
https://doi.org/10.3390/s20144023

**AMA Style**

Clauß F, Epple N, Ahrens MA, Niederleithinger E, Mark P. Comparison of Experimentally Determined Two-Dimensional Strain Fields and Mapped Ultrasonic Data Processed by Coda Wave Interferometry. *Sensors*. 2020; 20(14):4023.
https://doi.org/10.3390/s20144023

**Chicago/Turabian Style**

Clauß, Felix, Niklas Epple, Mark Alexander Ahrens, Ernst Niederleithinger, and Peter Mark. 2020. "Comparison of Experimentally Determined Two-Dimensional Strain Fields and Mapped Ultrasonic Data Processed by Coda Wave Interferometry" *Sensors* 20, no. 14: 4023.
https://doi.org/10.3390/s20144023