# Influence of Matrix Strength on Bridging Performance of Fiber-Reinforced Cementitious Composite with Bundled Aramid Fiber

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Used Materials

^{3}and 27.8 kg/m

^{3}, respectively.

## 3. Uniaxial Tension Test of FRCC

#### 3.1. Specimens

^{2}. The slits were made by a concrete cutter after the hardening of FRCC to avoid the influence of the flow of the matrix at the casting. The notched rectangular prism specimens with slits have been generally utilized to investigate the tensile characteristics of cementitious materials, such as the FRCC, in the same way as concrete [26,27].

#### 3.2. Loading and Measurement

#### 3.3. Failure Patterns

#### 3.4. Tensile Load vs. Axial Deformation Relatioonship

## 4. Pullout Test of Individual Fiber

#### 4.1. Specimens

^{2}, and the thickness of the plate is one of the experimental parameters. The mold consists of two acrylic plates and three rubber plates. A total of five plates are fixed by bolts so as not to cause any visible deformation of the rubber plates. An individual fiber is positioned by the holes of the upper and lower rubber plates. A cementitious matrix is poured from the injection hole and the ventilator holes function so as not to make air voids. The thickness of the specimen is varied by changing the thickness of the middle rubber plate. The dimensions of the specimen and the mold are exactly the same as those used in the authors’ previous study [17].

#### 4.2. Loading and Measurement

#### 4.3. Failure Pattern and Pullout Load vs. Slip Relationship

#### 4.4. Evaluation of Maximum Pullout Load

_{max}) and compressive strength of the matrix (f

_{c}). The black plots show the average values of the maximum pullout loads in each series. It can be recognized that the maximum pullout loads increase as the matrix strength increases. Straight lines can be obtained by the least square method for each embedded length series of the specimens. The coefficients of the lines are different in each series. The maximum pullout load of longer embedded length specimens is highly influenced by the matrix strength. It is considered that the bond resistance of bundled fiber is due to a constant bond, along with the embedded fiber-like friction mechanism.

_{b}) and the coefficients of the lines (α) shown in Figure 13. The curve shown in the figure is obtained by the regression analysis as it is expressed by the powered function of the embedded length. Finally, the maximum pullout load can be evaluated by the following Equation (1).

_{max}= (0.388 l

_{b}

^{0.59}) f

_{c}

_{max}: maximum pullout load (N);

_{b}: embedded length of fiber (mm);

_{c}: compressive strength of matrix (MPa).

## 5. Calculation of Bridging Law and Comparison with Test Results

#### 5.1. Calculation Method of Bridging Law

#### 5.2. Comparison of Calculation Result with Uniaxial Tension Test Result

_{f}= V

_{f}A

_{m}/ A

_{f}η

_{f}

_{f}: number of effective fibers;

_{f}: fiber volume fraction;

_{m}: cross-sectional area of matrix;

_{f}: cross-sectional area of individual fiber;

_{f}: fiber effectiveness.

_{f}) of 1% and 2%. The calculation results show that the bridging strength shows a linear relationship up to a compressive strength of around 50 MPa. Beyond 50 MPa, the increment of bridging strength becomes small. This is due to the rupture of fiber in the calculation.

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Bundled aramid fiber used in this study: (

**a**) chopped fiber with 30 mm length; (

**b**) close-up of the cross-section; (

**c**) condition of bundling of yarns.

**Figure 4.**Failure modes of specimen in uniaxial tension test: (

**a**) tensile failure; (

**b**) bending failure.

**Figure 5.**Examples of crack pattern (tensile failure): (

**a**) Fc24-N; (

**b**) Fc24-1%; (

**c**) Fc24-2%; (

**d**) Fc36-N; (

**e**) Fc36-1%; (

**f**) Fc36-2%; (

**g**) Fc48-N; (

**h**) Fc48-1%; (

**i**) Fc48-2%.

**Figure 7.**Tensile load-axial deformation relationship in uniaxial tension test: (

**a**) Fc24-1%; (

**b**) Fc24-2%; (

**c**) Fc36-1%; (

**d**) Fc36-2%; (

**e**) Fc48-1%; (

**f**) Fc48-2%.

**Figure 8.**Relationship between maximum load and experimental parameters: (

**a**) compressive strength; (

**b**) fiber volume fraction.

**Figure 9.**Pullout specimen: (

**a**) dimensions of pullout specimen; (

**b**) constitution of mold; (

**c**) setup of mold.

**Figure 11.**Example of pullout specimen: (

**a**) before loading; (

**b**) after loading; (

**c**) pulled out fiber.

**Figure 12.**Pullout load-slip relationship in pullout test: (

**a**) Fc24-4 mm; (

**b**) Fc24-8 mm; (

**c**) Fc24-12 mm; (

**d**) Fc36-4 mm; (

**e**) Fc36-8 mm; (

**f**) Fc36-12 mm; (

**g**) Fc48-4 mm; (

**h**) Fc48-8 mm; (

**i**) Fc48-12 mm.

**Figure 13.**Relationship between maximum pullout load and compressive strength: (

**a**) specimens with 4 mm embedded length; (

**b**) specimens with 8 mm embedded length; (

**c**) specimens with 12 mm embedded length.

**Figure 15.**Comparison of tensile load-rack width curve between uniaxial tension test results and bridging law calculation: (

**a**) Fc24-1%; (

**b**) Fc24-2%; (

**c**) Fc36-1%; (

**d**) Fc36-2%; (

**e**) Fc48-1%; (

**f**) Fc48-2%.

Fiber Type | Diameter | Length | Tensile Strength | Elastic Modulus |
---|---|---|---|---|

Aramid | 0.5 mm | 30 mm | 3432 MPa ^{1} | 73 GPa ^{1} |

^{1}Obtained from original yarns.

Series | W/C | FA/B | Unit Weight (kg/m^{3}) | |||
---|---|---|---|---|---|---|

W | C | FA | S | |||

Fc24 | 0.785 | 0.500 | 380 | 484 | 484 | 484 |

Fc36 | 0.560 | 0.300 | 380 | 678 | 291 | 484 |

Fc48 | 0.436 | 0.100 | 380 | 872 | 97 | 484 |

Series | Fiber Volume Fraction (%) | Curing Time (d) | Compressive Strength (MPa) | Elastic Modulus (GPa) |
---|---|---|---|---|

Fc24 | 0 (None) 1 2 | 25 | 38.3 35.6 33.3 | 14.2 13.6 13.0 |

Fc36 | 0 (None) 1 2 | 32 | 54.6 48.2 46.1 | 18.2 17.8 17.6 |

Fc48 | 0 (None) 1 2 | 45 | 71.4 66.9 63.7 | 20.0 19.7 19.3 |

Series | Specimen No. | Load at First Crack (kN) | Maximum Load (kN) | Average Max. Load (STDV) (kN) |
---|---|---|---|---|

Fc24-N | 1 2 | 4.99 4.24 | 4.99 4.24 | 4.61 (0.53) |

Fc24-1% | 1 2 3 4 5 | 6.57 5.23 6.58 6.37 5.38 | 8.88 8.54 9.76 8.49 9.28 | 8.99 (0.53) |

Fc24-2% | 2 3 4 | 8.66 7.54 7.40 | 13.33 12.05 12.41 | 12.60 (0.66) |

Fc36-N | 1 2 3 | 5.35 5.40 5.30 | 5.35 5.40 5.30 | 5.35 (0.05) |

Fc36-1% | 1 2 3 4 5 | 7.51 9.53 8.10 7.69 8.94 | 9.75 9.53 11.95 11.21 10.65 | 10.62 (1.01) |

Fc36-2% | 4 | 10.34 | 15.10 | 15.10 |

Fc48-N | 2 3 4 | 6.30 8.51 5.87 | 6.30 8.51 5.87 | 6.89 (1.42) |

Fc48-1% | 1 2 3 4 5 | 11.03 9.20 11.54 11.97 7.71 | 13.25 12.82 11.80 11.97 13.33 | 12.63 (0.71) |

Fc48-2% | 2 3 4 | 10.71 12.54 10.55 | 18.28 17.27 15.53 | 17.03 (1.39) |

Parameter | Input | |
---|---|---|

Cross-sectional area of individual fiber, A_{f} (mm^{2}) | 0.196 | |

Length of fiber, l_{f} (mm) | 30 | |

Apparent rupture strength of fiber [17], σ_{fu} (MPa) | σ_{fu} = 1080 × e^{−0.667ψ} | |

Bilinear model [17] | Maximum pullout load, P_{max} (N)Crack width at P _{max}, w_{max} (mm) | P_{max} = (0.388 l_{b} ^{0.59}) f_{c}w _{max} = 0.13 l_{b} ^{0.64} |

Elliptic distribution [17] | Orientation intensity for x-y plane, k_{xy}Orientation intensity for z-x plane, k _{zx}Principle orientation angle, θ _{r} | 1.5 6 0 |

_{b}: Embedded length of fiber (mm), f

_{c}: Compressive strength (MPa).

**Table 6.**Comparison between uniaxial tension test results and bridging law calculation (Fc24 Series).

Series | Specimen No. | Maximum Load (kN) | Number of Fibers on Fracture Surface | Max. Load per Fiber (N) | ||
---|---|---|---|---|---|---|

Top | Bottom | Total | ||||

Fc24-1% (f _{c} = 35.6 MPa) | 1 2 3 4 5 | 8.88 8.54 9.76 8.49 9.28 | 99 90 109 95 103 | 106 108 112 97 109 | 205 198 221 192 212 | 43.33 43.13 44.15 44.23 43.76 |

Calculation | 4.73 | V_{f} A_{m} / A_{f} η_{f}= 0.01 × (60 × 70)/0.196 × 0.544 | 117 | 40.54 | ||

Fc24-2% (f _{c} = 33.3 MPa) | 2 3 4 | 13.33 12.05 12.41 | 182 159 174 | 151 145 129 | 333 304 303 | 40.04 39.63 40.96 |

Calculation | 8.84 | V_{f} A_{m} / A_{f} η_{f}= 0.02 × (60 × 70)/0.196 × 0.544 | 233 | 37.91 |

**Table 7.**Comparison between uniaxial tension test results and bridging law calculation (Fc36 Series).

Series | Specimen No. | Maximum Load (kN) | Number of Fibers on Fracture Surface | Max. Loadper Fiber (N) | ||
---|---|---|---|---|---|---|

Top | Bottom | Total | ||||

Fc36-1% (f _{c} = 48.2 MPa) | 1 2 3 4 5 | 9.75 9.53 11.95 11.21 10.65 | 96 89 118 107 101 | 82 79 109 93 95 | 178 168 227 200 196 | 54.76 56.73 52.63 56.07 54.33 |

Calculation | 6.31 | V_{f} A_{m} / A_{f} η_{f}= 0.01 × (60 × 70)/0.196 × 0.544 | 117 | 54.12 | ||

Fc36-2% (f _{c} = 46.1 MPa) | 4 | 15.10 | 163 | 152 | 315 | 47.92 |

Calculation | 12.16 | V_{f} A_{m} / A_{f} η_{f}= 0.02 × (60 × 70)/0.196 × 0.544 | 233 | 52.16 |

**Table 8.**Comparison between uniaxial tension test results and bridging law calculation (Fc48 Series).

Series | Specimen No. | Maximum Load (kN) | Number of Fibers on Fracture Surface | Max. Loadper Fiber (N) | ||
---|---|---|---|---|---|---|

Top | Bottom | Total | ||||

Fc48-1% (f _{c} = 66.9 MPa) | 1 2 3 4 5 | 13.25 12.82 11.80 11.97 13.33 | 101 105 92 97 107 | 97 86 94 101 99 | 198 191 186 198 206 | 66.91 67.13 63.44 60.46 64.72 |

Calculation | 7.76 | V_{f} A_{m} / A_{f} η_{f}= 0.01 × (60 × 70)/0.196 × 0.544 | 117 | 66.59 | ||

Fc48-2% (f _{c} = 63.7 MPa) | 2 3 4 | 18.28 17.27 15.53 | 156 163 131 | 148 144 149 | 304 307 280 | 60.14 56.25 55.46 |

Calculation | 15.16 | V_{f} A_{m} / A_{f} η_{f}= 0.02 × (60 × 70)/0.196 × 0.544 | 233 | 65.03 |

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**MDPI and ACS Style**

Kanakubo, T.; Shi, H.; Wang, J.
Influence of Matrix Strength on Bridging Performance of Fiber-Reinforced Cementitious Composite with Bundled Aramid Fiber. *J. Compos. Sci.* **2022**, *6*, 131.
https://doi.org/10.3390/jcs6050131

**AMA Style**

Kanakubo T, Shi H, Wang J.
Influence of Matrix Strength on Bridging Performance of Fiber-Reinforced Cementitious Composite with Bundled Aramid Fiber. *Journal of Composites Science*. 2022; 6(5):131.
https://doi.org/10.3390/jcs6050131

**Chicago/Turabian Style**

Kanakubo, Toshiyuki, Haohui Shi, and Jin Wang.
2022. "Influence of Matrix Strength on Bridging Performance of Fiber-Reinforced Cementitious Composite with Bundled Aramid Fiber" *Journal of Composites Science* 6, no. 5: 131.
https://doi.org/10.3390/jcs6050131