# Dynamic Crack Initiation Toughness of Shale under Impact Loading

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## Abstract

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## 1. Introduction

## 2. Methods and Materials

#### 2.1. Sample Preparation

#### 2.2. Test System and Principle

#### 2.3. Loading Method

## 3. Results and Analysis

#### 3.1. Effect of Bedding on Shale Crack Initiation Toughness

#### 3.2. Shale Fracture Mode

## 4. Discussion

## 5. Conclusions

- We studied the influence of bedding plane on dynamic crack initiation toughness of shale. Under the condition of parallel bedding plane loading, the bedding plane had a significant influence on the shale cracking. The shale had the lowest crack initiation toughness under Crack-splitter loading. Compared with the bedding plane and perpendicular loading directions, the shale cracking mainly depended on the strength of the rock mass, so the dynamic crack initiation toughness had a high value.
- We analyzed the effect of the loading rate on shale dynamic crack initiation toughness under three loading modes. The Crack-arrester loading mode had the strongest loading rate correlation and Crack-splitter had the weakest.
- We analyzed the fracture modes of shale under different loading conditions. When loading was carried out using Crack-arrester, the bedding planes can change the crack expansion direction and consume the most energy. The Crack-splitter loading only required a small amount of energy to achieve effective crack expansion.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**Three loading configurations tested. (

**a**) Crack-divider, (

**b**) Crack-splitter, (

**c**) Crack-arrester.

**Figure 5.**Relationships between dynamic crack initiation toughness of shale and loading rate under different loading configurations.

**Figure 6.**Fracture processes of shale samples for different loading configurations. (

**a**) Crack-divider; (

**b**) Crack-splitter; (

**c**) Crack-arrester.

Diameter D/mm | Thickness B/mm | Pre-Crack Length a/mm | Pre-Crack Width /mm | Pre-Crack Tip Width/mm |
---|---|---|---|---|

100 | 45 | 10 | 0.3 | 0.1 |

Bar Diameter/mm | Incident Bar Length/mm | Transmission Bar Length/mm | $\mathbf{Density}/(\mathbf{kg}/{\mathit{m}}^{3})$ | Elastic Modulus/GPa | Poisson’s Ratio | Longitudinal Wave Velocity /(m/s) |
---|---|---|---|---|---|---|

75 | 3500 | 3500 | 7800 | 210 | 0.3 | 5190 |

$\mathbf{Impact}\text{}\mathbf{Pressure}\text{}\left(\mathbf{M}\mathbf{P}\mathbf{a}\right)$ | Test Sample Number | $\mathbf{Loading}\text{}\mathbf{Rate}\text{}\left({10}^{4}\mathbf{M}\mathbf{P}\mathbf{a}\sqrt{\mathbf{m}}/\mathbf{s}\right)$ | $\mathbf{Dynamic}\text{}\mathbf{Crack}\text{}\mathbf{Initiation}\text{}\mathbf{Toughness}\text{}{\mathit{K}}_{\mathit{I}\mathit{d}}\left(\mathbf{M}\mathbf{P}\mathbf{a}\sqrt{\mathbf{m}}\right)$ | $\mathbf{Average}\text{}\mathbf{Dynamic}\text{}\mathbf{Crack}\text{}\mathbf{Initiation}\text{}\mathbf{Toughness}\left(\mathbf{M}\mathbf{P}\mathbf{a}\sqrt{\mathbf{m}}\right)$ |
---|---|---|---|---|

0.54 | ${P}_{1}$-1 | 21.65 | 11.53 | 12.17 |

${P}_{1}$-2 | 22.36 | 12.38 | ||

${P}_{1}$-3 | 23.72 | 12.61 | ||

0.56 | ${P}_{1}$-4 | 25.33 | 13.65 | 13.66 |

${P}_{1}$-5 | 25.26 | 13.60 | ||

${P}_{1}$-6 | 25.64 | 13.72 | ||

0.58 | ${P}_{1}$-7 | 28.15 | 14.38 | 14.90 |

${P}_{1}$-8 | 28.72 | 14.87 | ||

${P}_{1}$-9 | 29.39 | 15.44 | ||

0.60 | ${P}_{1}$-10 | 33.75 | 16.67 | 16.28 |

${P}_{1}$-11 | 32.51 | 16.14 | ||

${P}_{1}$-12 | 32.48 | 16.03 |

$\mathbf{Impact}\text{}\mathbf{Pressure}\text{}\left(\mathbf{M}\mathbf{P}\mathbf{a}\right)$ | Test Sample Number | $\mathbf{Loading}\text{}\mathbf{Rate}\text{}\left({10}^{4}\mathbf{M}\mathbf{P}\mathbf{a}\sqrt{\mathbf{m}}/\mathbf{s}\right)$ | $\mathbf{Dynamic}\text{}\mathbf{Crack}\text{}\mathbf{Initiation}\text{}\mathbf{Toughness}\text{}{\mathit{K}}_{\mathit{I}\mathit{d}}$$\left(\mathbf{M}\mathbf{P}\mathbf{a}\sqrt{\mathbf{m}}\right)$ | $\mathbf{Average}\text{}\mathbf{Dynamic}\text{}\mathbf{Crack}\text{}\mathbf{Initiation}\text{}\mathbf{Toughness}\text{}\left(\mathbf{M}\mathbf{P}\mathbf{a}\sqrt{\mathbf{m}}\right)$ |
---|---|---|---|---|

0.54 | ${P}_{2}$-1 | 20.50 | 10.13 | 9.87 |

${P}_{2}$-2 | 20.11 | 9.87 | ||

${P}_{2}$-3 | 19.51 | 9.60 | ||

0.56 | ${P}_{2}$-4 | 23.41 | 11.23 | 11.31 |

${P}_{2}$-5 | 23.06 | 11.14 | ||

${P}_{2}$-6 | 24.56 | 11.56 | ||

0.58 | ${P}_{2}$-7 | 27.20 | 12.00 | 11.99 |

${P}_{2}$-8 | 27.40 | 12.08 | ||

${P}_{2}$-9 | 26.71 | 11.89 | ||

0.60 | ${P}_{2}$-10 | 30.60 | 12.57 | 12.80 |

${P}_{2}$-11 | 30.12 | 12.24 | ||

${P}_{2}$-12 | 31.07 | 13.58 |

$\mathbf{Impact}\text{}\mathbf{Pressure}\text{}\left(\mathbf{M}\mathbf{P}\mathbf{a}\right)$ | Test Sample Number | $\mathbf{Loading}\text{}\mathbf{Rate}\text{}\left({10}^{4}\mathbf{M}\mathbf{P}\mathbf{a}\sqrt{\mathbf{m}}/\mathbf{s}\right)$ | $\mathbf{Dynamic}\text{}\mathbf{Crack}\text{}\mathbf{Initiation}\text{}\mathbf{Toughness}\text{}{\mathit{K}}_{\mathit{I}\mathit{d}}$$\left(\mathbf{M}\mathbf{P}\mathbf{a}\sqrt{\mathbf{m}}\right)$ | $\mathbf{Average}\text{}\mathbf{Dynamic}\text{}\mathbf{Crack}\text{}\mathbf{Initiation}\text{}\mathbf{Toughness}\text{}\left(\mathbf{M}\mathbf{P}\mathbf{a}\sqrt{\mathbf{m}}\right)$ |
---|---|---|---|---|

0.54 | ${P}_{3}$-1 | 21.64 | 12.67 | 13.32 |

${P}_{3}$-2 | 22.41 | 13.43 | ||

${P}_{3}$-3 | 23.24 | 13.87 | ||

0.56 | ${P}_{3}$-4 | 25.82 | 15.61 | 15.75 |

${P}_{3}$-5 | 26.63 | 16.40 | ||

${P}_{3}$-6 | 25.57 | 15.24 | ||

0.58 | ${P}_{3}$-7 | 33.37 | 19.71 | 18.97 |

${P}_{3}$-8 | 32.62 | 18.78 | ||

${P}_{3}$-9 | 32.17 | 18.42 | ||

0.60 | ${P}_{3}$-10 | 38.06 | 23.77 | 22.51 |

${P}_{3}$-11 | 36.55 | 21.59 | ||

${P}_{3}$-12 | 37.23 | 22.18 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Yang, G.; Li, X.; Bi, J.; Cheng, S.
Dynamic Crack Initiation Toughness of Shale under Impact Loading. *Energies* **2019**, *12*, 1636.
https://doi.org/10.3390/en12091636

**AMA Style**

Yang G, Li X, Bi J, Cheng S.
Dynamic Crack Initiation Toughness of Shale under Impact Loading. *Energies*. 2019; 12(9):1636.
https://doi.org/10.3390/en12091636

**Chicago/Turabian Style**

Yang, Guoliang, Xuguang Li, Jingjiu Bi, and Shuaijie Cheng.
2019. "Dynamic Crack Initiation Toughness of Shale under Impact Loading" *Energies* 12, no. 9: 1636.
https://doi.org/10.3390/en12091636