#
Comparison of Fracture Resistance of the Normal and High Strength Concrete Evaluated by Brazilian Disc Test^{ †}

^{1}

^{2}

^{3}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Theoretical Background

_{ij}represents the stress tensor components, K

_{I}, K

_{II}are the stress intensity factors (SIF) for mode I and mode II, respectively, ${f}_{i,j}^{I}\left(\theta \right)$, ${f}_{i,j}^{II}\left(\theta \right)$, are known shape functions for mode I and mode II usually written as Y

_{I}and Y

_{II}, T (or T-stress) represents the second term independent on r, O

_{ij}represents higher order terms, and r, θ are the polar coordinates (with origin at the crack tip; crack faces lie along the x-axis).

#### 2.1. Brazilian Disc Test

_{I}(a/R, α), Y

_{II}(a/R, α) are dimensionless shape functions for mode I and mode II, respectively. Geometry functions Y

_{I}and Y

_{II}used in Equations (2) and (3) can be found in [8,9].

_{xx}and σ

_{yy}are the stress components in front of the crack tip in direction for θ = 0°.

#### 2.2. GMTS Criterion

_{0}and can be determined from:

_{0}is then used for evaluation of beginning of mixed mode I/II on BDC specimen.

#### Application of the GMTS on Brazilian Disc Specimen

_{I}= K

_{IC}, K

_{II}= 0 and θ

_{0}= 0°, this assumption leads into Equation (7):

_{IC}is materials’ fracture toughness. Fracture resistance for both modes is expressed by ratio K

_{I}/K

_{IC}and K

_{II}/K

_{IC}. This ratio is obtained from Equation (7) by dividing the whole expression by K

_{I}, K

_{II}, respectively.

_{0}for any combination of modes I and II depends on K

_{I}, K

_{II}, T, and r

_{C}. Critical distance r

_{C}can be evaluated from Equations (8) and (9) for plane stress and plane strain respectively [11].

## 3. Materials

#### 3.1. Normal Strength Concrete

^{3}and poured immediately into molds. A polycarboxylates-based superplasticizer was used to reach good workability [10].

#### 3.2. High Strength Concrete

^{3}and poured into molds.

## 4. Experimental Measurement

## 5. Results and Discussion

_{C}. From Figure 3 it can be noted, that the MTS criterion is very conservative for both materials. The GMTS criterion predict fracture resistance with great agreement especially for plane strain boundary conditions.

## 6. Conclusions

- The fracture toughness measured on the HSC material is higher in all investigated cases than for the traditional C 50/60 material.
- The experimental results done on the HSC material showed higher fracture resistance in mixed mode I/II than the traditional C 50/60 material.
- The fracture resistance of the C 50/60 material is characterized best by r
_{C}for plain strain, yet for HSC, it is better to use value of r_{C}for fine aggregate.

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Mixed mode fracture toughness diagram for C 50/60 (

**a**) and HSC (

**b**) materials, using various critical distances r

_{C}.

Specimen nmr. | Inclination Angle α [°] | Diameter D [mm] | Thickness B [mm] | Notch Length 2a [mm] | a/R [-] |
---|---|---|---|---|---|

6_03 | 0 | 149.200 | 31.380 | 60.210 | 0.404 |

6_09 | 0 | 149.182 | 29.927 | 60.170 | 0.403 |

6_01 | 0 | 149.155 | 31.440 | 60.920 | 0.408 |

6_01 | 5 | 149.162 | 31.440 | 60.920 | 0.408 |

6_05 | 10 | 149.143 | 30.580 | 60.140 | 0.403 |

6_04 | 10 | 149.162 | 30.973 | 60.040 | 0.403 |

6_04 | 15 | 149.208 | 30.970 | 60.040 | 0.402 |

6_06 | 15 | 149.214 | 32.390 | 60.150 | 0.403 |

6_02 | 25.2 | 149.180 | 30.770 | 60.110 | 0.403 |

6_07 | 25.2 | 149.205 | 31.173 | 59.940 | 0.402 |

Specimen nmr. | Inclination Angle α [°] | Diameter D [mm] | Thickness B [mm] | Notch Length 2a [mm] | a/R [-] |
---|---|---|---|---|---|

6_2_02 | 0 | 149.09 | 29.43 | 59.70 | 0.400 |

6_2_01 | 0 | 149.15 | 29.99 | 59.44 | 0.399 |

6_2_05 | 5 | 149.23 | 28.35 | 59.91 | 0.401 |

6_2_10 | 10 | 149.32 | 28.48 | 59.27 | 0.396 |

6_2_11 | 10 | 149.01 | 27.57 | 60.13 | 0.403 |

6_2_08 | 15 | 149.18 | 28.09 | 60.06 | 0.403 |

6_2_09 | 15 | 149.28 | 28.70 | 59.96 | 0.402 |

6_2_06 | 20 | 149.21 | 28.33 | 60.01 | 0.402 |

6_2_07 | 20 | 149.12 | 28.45 | 60.03 | 0.403 |

6_2_03 | 25.2 | 149.18 | 28.45 | 59.81 | 0.400 |

6_2_04 | 25.2 | 149.23 | 28.96 | 59.93 | 0.402 |

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**MDPI and ACS Style**

Miarka, P.; Seitl, S.; Bílek, V. Comparison of Fracture Resistance of the Normal and High Strength Concrete Evaluated by Brazilian Disc Test. *Proceedings* **2018**, *2*, 399.
https://doi.org/10.3390/ICEM18-05236

**AMA Style**

Miarka P, Seitl S, Bílek V. Comparison of Fracture Resistance of the Normal and High Strength Concrete Evaluated by Brazilian Disc Test. *Proceedings*. 2018; 2(8):399.
https://doi.org/10.3390/ICEM18-05236

**Chicago/Turabian Style**

Miarka, Petr, Stanislav Seitl, and Vlastimil Bílek. 2018. "Comparison of Fracture Resistance of the Normal and High Strength Concrete Evaluated by Brazilian Disc Test" *Proceedings* 2, no. 8: 399.
https://doi.org/10.3390/ICEM18-05236