#
Bond and Cracking Characteristics of PVA-Fiber-Reinforced Cementitious Composite Reinforced with Braided AFRP Bars^{ †}

^{1}

^{2}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Pullout Bond Test

#### 2.1. Outline of Pullout Bond Test [31]

^{2}, 120 × 120 mm

^{2}, and 140 × 140 mm

^{2}. To secure the specimens in the testing machine’s chuck, a steel coupler was affixed to the end of the FRP reinforcement using an expansion agent which is conventionally utilized for destroying rocks. There was no special attachment at the free end. The bond length was set to 54 mm, which was approximately four times the bar diameter. The experimental parameters included the cross-sections of the specimens and the fiber volume fractions of the FRCC (0%, 1%, 2%). Naming of the specimens followed a format based on fiber volume fractions (MT: 0%; PVA1%: 1.0%; and PVA2%: 2.0%) and cross-sections (A: 100 × 100 mm

^{2}, B: 120 × 120 mm

^{2}, and C: 140 × 140 mm

^{2}). Three specimens were manufactured for each parameter, resulting in a total of twenty-seven specimens.

#### 2.2. Modeling of Bond Constitutive Law

^{3}because there were no observable differences among the FRCC specimens. In the case of MT specimens, because test results for the softening branch could not be obtained, the ultimate slip ${s}_{\mathrm{u}}$ was empirically set to 1.5 mm. Table 5 shows the characteristic values derived from the trilinear model for each type of specimen. Figure 6 shows a comparison between the test results and trilinear model values. It can be seen that the trilinear model values are compatible with the test results, particularly with respect to behavior leading up to the maximum bond stress.

## 3. Pullout Bond Test with Long Bond Length

#### 3.1. Outline of Pullout Bond Test

#### 3.1.1. Specimens

^{2}(A series), 120 × 120 mm

^{2}(B series), and 140 × 140 mm

^{2}(C series). One braided AFRP bar was positioned at the center of each block. A steel coupler was affixed to the end of the reinforcement to fix the testing machine’s chuck. The bond length was 543 mm, approximately forty times the diameter of the FRP reinforcement. The experimental parameters included the cross-sections of the specimens and the fiber volume fractions of the FRCC (0%, 1%, or 2%). PVA fibers were used for the FRCC. Naming of the specimens followed a format based on fiber volume fractions (MT: 0%; PVA1%: 1.0%; and PVA2%: 2.0%) and cross-sections (A: 100 × 100 mm

^{2}; B: 120 × 120 mm

^{2}; and C: 140 × 140 mm

^{2}). One specimen was manufactured for each parameter, resulting in a total of nine specimens.

#### 3.1.2. Materials

#### 3.1.3. Loading Method

#### 3.2. Test Results

#### 3.2.1. Specimens after Loading

#### 3.2.2. Average Bond Stress–Loaded-end Slip Relationship

#### 3.3. Numerical Calculation of Bond Properties

#### 3.3.1. Method of Numerical Calculation

_{i}

_{−1}is the local bond stress, ${S}_{i-1}$ is the slip, and ${dS}_{i}$ is the increment of the slip.

#### 3.3.2. Comparison of Average Bond Stress–Loaded-end Slip Relationships

## 4. Bending Test of AFRP/PVA-FRCC Beams

#### 4.1. Outline of Bending Test

#### 4.1.1. Specimens

#### 4.1.2. Loading Method

#### 4.2. Test Results

#### 4.2.1. Specimens after Loading

#### 4.2.2. Load–Deflection Relationships

#### 4.2.3. Cracking Characteristics

^{2}cross-section specimen described in Section 2 (Figure 5) was utilized. Table 12 shows the values substituted into the formula. The tensile strength of FRCC was determined as the average cracking strength from the bending test of the 100 mm × 100 mm × 400 mm specimens, using the same mixing batch of PVA-FRCC. The cross-section of the FRCC corresponds to the equivalent cross-section of the FRCC supported by each tension bar, as shown in Figure 20.

## 5. Conclusions

- In the pullout bond test, a trilinear model for the bond constitutive law (bond stress–loaded-end slip relationship) was proposed.
- According to the pullout bond test with specimens of long bond length, the bond strength increased with increases in both the fiber volume fraction and the cross-section of the specimens. These characteristics can be attributed to the fiber bridging effect, which results in control of crack width opening.
- Bond behavior with a long bond length was analyzed numerically using the proposed bond constitutive law. The calculated average bond stress–loaded-end slip relationships favorably fitted the test results.
- The bending test results for AFRP/PVA-FRCC beam specimens showed that the number of cracks increased with the increases in fiber volume fraction. The maximum loads recorded for each type of specimen were as follows: MT: 154 kN; PVA1%: 217 kN; PVA2%: 198 kN; and PVA2%C: 229 kN. In the case of specimens with a fiber volume fraction of 2%, the load reached its maximum value due to the compression fracture of the FRCC, and cyclic loading had no discernible effect.
- The adaptability of the crack width prediction formula, considering the bond constitutive law and the fiber bridging law with respect to PVA-FRCC, was discussed. The reinforcement strain–crack width relationship obtained from the bending test exhibited good compatibility with the crack width prediction formula.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 11.**The infinitesimal element of FRCC reinforced with AFRP bar under tensile conditions in the i-th section. (i = 1, 2, 3,...).

Type | Common Factor | Cross-Section | Fiber Volume Fraction | Number of Specimens |
---|---|---|---|---|

MT-A | Height: 100 mm Bond length: 54 mm (=4d) Reinforcement: Braided AFRP bar (Diameter 13.58 mm) Fiber type of FRCC: PVA | 100 mm × 100 mm (A series) | - | 3 |

PVA1%-A | 1.0% | 3 | ||

PVA2%-A | 2.0% | 3 | ||

MT-B | 120 mm × 120 mm (B series) | - | 3 | |

PVA1%-B | 1.0% | 3 | ||

PVA2%-B | 2.0% | 3 | ||

MT-C | 140 mm × 140 mm (C series) | - | 3 | |

PVA1%-C | 1.0% | 3 | ||

PVA2%-C | 2.0% | 3 |

Reinforcement | Diameter (mm) | Tensile Strength (MPa) | Elastic Modulus (GPa) |
---|---|---|---|

Braided AFRP bar | 13.58 | 1261 | 66.0 |

Fiber | Length (mm) | Diameter (mm) | Tensile Strength (MPa) | Elastic Modulus (GPa) |
---|---|---|---|---|

PVA | 12 | 0.10 | 1200 | 28 |

Type | Unit Weight (kg/m^{3}) | PVA Fiber (kg) | Compressive Strength (MPa) | Elastic Modulus (GPa) | |||
---|---|---|---|---|---|---|---|

W | C | S | F | ||||

MT | 380 | 678 | 484 | 291 | 0 | 48.8 | 17.5 |

PVA 1% | 13 | 46.2 | 17.0 | ||||

PVA 2% | 26 | 47.1 | 16.4 |

Specimens | ${\mathit{\tau}}_{1}$ (MPa) | ${\mathit{s}}_{1}$ (mm) | ${\mathit{k}}_{1}$ (N/mm ^{3}) | ${\mathit{\tau}}_{\mathbf{m}\mathbf{a}\mathbf{x}}$ (MPa) | ${\mathit{s}}_{\mathbf{m}\mathbf{a}\mathbf{x}}$ (mm) | ${\mathit{k}}_{\mathit{u}}$ (N/mm ^{3}) | ${\mathit{s}}_{\mathit{u}}$ (mm) |
---|---|---|---|---|---|---|---|

MT-A | 4.37 | 0.21 | 20.9 | 5.46 | 0.45 | −5.18 | 1.50 |

MT-B | 4.92 | 0.39 | 12.7 | 6.15 | 0.80 | −8.83 | 1.50 |

MT-C | 4.21 | 0.26 | 16.5 | 5.26 | 0.44 | −4.97 | 1.50 |

PVA1%-A | 5.42 | 0.38 | 14.2 | 6.77 | 1.16 | −0.30 | 23.7 |

PVA1%-B | 5.03 | 0.31 | 16.2 | 6.29 | 1.30 | 22.3 | |

PVA1%-C | 5.29 | 0.55 | 9.55 | 6.61 | 4.05 | 26.1 | |

PVA2%-A | 5.59 | 0.29 | 19.6 | 6.99 | 1.03 | 24.3 | |

PVA2%-B | 6.52 | 0.61 | 10.7 | 8.15 | 3.39 | 30.5 | |

PVA2%-C | 5.89 | 0.42 | 14.0 | 7.36 | 3.80 | 28.3 |

Type | Common Factors | Cross-Section | Volume Fraction | Number of Specimens |
---|---|---|---|---|

MT-A | Height: 600 mm Bond length: 543 mm (=40d) Reinforcement: Braided AFRP bar (Diameter 13.52 mm) Fiber type of FRCC: PVA | 100 mm × 100 mm (A series) | - | 1 |

PVA1%-A | 1.0% | 1 | ||

PVA2%-A | 2.0% | 1 | ||

MT-B | 120 mm × 120 mm (B series) | - | 1 | |

PVA1%-B | 1.0% | 1 | ||

PVA2%-B | 2.0% | 1 | ||

MT-C | 140 mm × 140 mm (C series) | - | 1 | |

PVA1%-C | 1.0% | 1 | ||

PVA2%-C | 2.0% | 1 |

Reinforcement | Diameter (mm) | Tensile Strength (MPa) | Elastic Modulus (GPa) |
---|---|---|---|

Braided AFRP bar | 13.52 | 1315 | 66.6 |

Type | Compressive Strength (MPa) | Elastic Modulus (GPa) |
---|---|---|

MT | 61.5 | 20.2 |

PVA1% | 58.7 | 19.0 |

PVA2% | 60.1 | 19.1 |

Specimens | ${\mathit{\tau}}_{1}$ (MPa) | ${\mathit{s}}_{1}$ (mm) | ${\mathit{k}}_{1}$ (N/mm ^{3}) | ${\mathit{\tau}}_{\mathbf{m}\mathbf{a}\mathbf{x}}$ (MPa) | ${\mathit{s}}_{\mathbf{m}\mathbf{a}\mathbf{x}}$ (mm) | ${\mathit{s}}_{\mathit{u}}$ (mm) |
---|---|---|---|---|---|---|

PVA1%-A | 2.93 | 0.38 | 7.68 | 3.66 | 1.16 | 23.7 |

PVA1%-B | 2.72 | 0.31 | 8.75 | 3.40 | 1.30 | 22.3 |

PVA1%-C | 2.85 | 0.55 | 5.16 | 3.57 | 4.05 | 26.1 |

PVA2%-A | 3.02 | 0.29 | 10.6 | 3.78 | 1.03 | 24.3 |

PVA2%-B | 3.52 | 0.61 | 5.76 | 4.40 | 3.39 | 30.5 |

PVA2%-C | 3.18 | 0.42 | 7.58 | 3.97 | 3.80 | 28.3 |

Type | Common Factor | Loading Method | Fiber Volume Fraction |
---|---|---|---|

MT | Reinforcement: Braided AFRP bar (Diameter 13.52 mm) p _{t} = 1.04(%)Fiber type of FRCC: PVA | Monotonic loading | - |

PVA1% | 1% | ||

PVA2% | 2% | ||

PVA2%-C | One-sided cyclic loading |

Type | Compressive Strength (MPa) | Elastic Modulus (GPa) |
---|---|---|

MT | 42.4 | 17.4 |

PVA1% | 47.5 | 16.6 |

PVA2% | 41.2 | 15.9 |

PVA2%-C | 47.0 | 16.4 |

Parameters | MT | PVA1% | PVA2% | PVA2%C | |
---|---|---|---|---|---|

Braided AFRP bar | ${A}_{s}$(mm^{2}) | 143.6 | |||

${\phi}_{s}$(mm) | 43 | ||||

${E}_{s}$(GPa) | 66 | ||||

FRCC | ${A}_{c}$(mm^{2}) | 6000 | |||

${E}_{c}$(GPa) | 17.4 | 16.6 | 15.9 | 16.4 | |

${\sigma}_{cr}$(MPa) | 2.82 |

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## Share and Cite

**MDPI and ACS Style**

Takasago, S.; Kanakubo, T.; Kobayashi, H.; Sasaki, H.
Bond and Cracking Characteristics of PVA-Fiber-Reinforced Cementitious Composite Reinforced with Braided AFRP Bars. *Fibers* **2023**, *11*, 107.
https://doi.org/10.3390/fib11120107

**AMA Style**

Takasago S, Kanakubo T, Kobayashi H, Sasaki H.
Bond and Cracking Characteristics of PVA-Fiber-Reinforced Cementitious Composite Reinforced with Braided AFRP Bars. *Fibers*. 2023; 11(12):107.
https://doi.org/10.3390/fib11120107

**Chicago/Turabian Style**

Takasago, Shugo, Toshiyuki Kanakubo, Hiroya Kobayashi, and Hideto Sasaki.
2023. "Bond and Cracking Characteristics of PVA-Fiber-Reinforced Cementitious Composite Reinforced with Braided AFRP Bars" *Fibers* 11, no. 12: 107.
https://doi.org/10.3390/fib11120107