# Flexural Characteristics of Functionally Graded Fiber-Reinforced Cementitious Composite with Polyvinyl Alcohol Fiber

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

_{f}) varying in layers and the layered effect in bending specimens. The FG-FRCC specimens, in which V

_{f}increases from 0% in the compression zone to 2% in the tensile zone, are three-layered specimens using polyvinyl alcohol (PVA) FRCC that are fabricated and tested by a four-point bending test. The maximum load of the FG-FRCC specimens exhibits almost twice that of homogeneous specimens, even when the average of the fiber volume fraction in the whole specimen is 1%. The result of the section analysis, in which the stress–strain models based on the bridging law (tensile stress–crack width relationship owned by the fibers) consider the fiber orientation effect, shows a good adaptability with the experiment result.

## 1. Introduction

## 2. Experimental Program

#### 2.1. Tested FRCC

#### 2.2. Specimens

^{2}cross-section and 400 mm length, to be subjected to four-point bending test according to ISO 21914 [29]. The four-point bending test, in which the ratio of depth to span of the specimen is 1 by 3, is the most commonly-used method to determine flexural characteristics of cementitious composites including concrete [30]. The main test parameter is fiber volume fraction, V

_{f}, in three-layered specimens in which the height of each layer is equal to one-third the whole height of the cross-section. The list of the specimens is shown in Table 3 and illustrated in Figure 1. The specimens were grouped into two series by the casting days of FRCC, i.e., 1st day and 2nd day. The specimens in the 1st day were fabricated to compare the effect of fiber volume fraction in FG-FRCC, namely FG-FRCC specimens were layered with 0% (mortar), 1%, and 2% volume fraction from the compression zone to the tensile zone, respectively. The homogeneous specimens with 1% (Hmg-1%) and 2% (Hmg-2%) volume fraction were also fabricated. The specimens in the 2nd day were fabricated to compare the effect of the layer. Layer-1% and Layer-2% specimens were only layered with the same volume fraction of 1% and 2%, respectively. The homogeneous specimens were also fabricated. The FRCC with each fiber volume fraction in the same day casting was poured into the mold from the same mixing batch. The number of the specimens with each test parameter is three.

#### 2.3. Specimen Fabrication

#### 2.4. Loading and Measurement

## 3. Experimental Results

#### 3.1. Failure Pattern

#### 3.2. Load–Deflection Curve

#### 3.3. Maximum Load

## 4. Section Analysis and Comparison with Experimental Results

#### 4.1. Method of Section Analysis

_{max}, σ

_{2}, and δ

_{max}in tri-linear model are given by following equations as functions of orientation intensity, k. These equations have been proposed for same PVA fiber used in this study, and for fiber volume fraction of 2%.

_{max}= 2.0 k

^{0.30}(MPa)

_{2}= 0.60 k

^{0.73}(MPa)

_{max}= 0.20 k

^{0.18}(mm)

_{2}has been proposed as 0.45 mm, that corresponds to the crack width at which the individual fiber shows the maximum pullout load [31]. The reason that the maximum tensile stress in the bridging law reaches before δ

_{2}, is that individual fibers start rupturing before showing the maximum pullout load due to the reduction of the apparent rupture strength by orientation angle in the case of polymeric fibers [32]. The crack width δ

_{tu}, at which the tensile stress vanishes, is given as the half length of fiber. All fibers are completely pulled out when the crack width reaches the half of fiber length.

#### 4.2. Comparison of Maximum Bending Moment

_{e}M

_{max}= P

_{max}·l/6

_{e}M

_{max}: experimental maximum bending moment, P

_{max}: maximum load, l: span length.

## 5. Conclusions

- Clear separation between layers in the FG-FRCC was not observed in the four-point bending test. It is considered that the bond between layers is enough to transmit shear stress under pure bending by the pouring fabrication method for PVA-FRCC having self-consolidating properties.
- The maximum load of the FG-FRCC specimens exhibited almost twice that of the homogeneous specimens, even when the average of fiber volume fraction in whole specimen is 1%.
- The ratio of the maximum load of the three-layered specimens with the same fiber volume fraction to that of the homogeneous specimens is 1.02 and 1.08 for the 1% and 2% volume fractions, respectively. The thinner thickness may be required to show the more effective contribution of the layer causing the two-dimensional fiber orientation.
- Section analysis, in which the stress–strain models based on the bridging law considering the fiber orientation effect was conducted. The ratio of the experimental maximum moment to the analysis result ranges from 0.89 to 1.18. It is considered that the section analysis result considering the fiber orientation shows a good adaptability with the experiment result.
- The analysis result shows that the maximum moment of the FG-FRCC specimen is 1.63 times that of the homogeneous specimen with the same whole fiber volume fraction of 1%. It is considered that the bending moment reaches the maximum when the tensile force in the tension side layer becomes maximum in the case of the FG-FRCC.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Balaguru, P.N.; Shah, S.P. Introduction, Fiber-Reinforced Cement Composites; McGraw-Hill: New York, NY, USA, 1992; pp. 1–15. [Google Scholar]
- Zollo, R.F. Collated Fibrillated Polypropylene Fibers in FRC. In Proceedings of the Fiber Reinforced Concrete International Symposium (ACI SP-81), Detroit, MI, USA, 1 November 1984; pp. 397–409. [Google Scholar]
- Naaman, A.E.; Reinhardt, H.W. High Performance Fiber Reinforced Cement Composites: HPFRCC 2; E. & FN Spon: London, UK, 1996. [Google Scholar]
- Li, V.C. From Micromechanics to Structural Engineering—The Design of Cementitious Composites for Civil Engineering Applications. JSCE J. Struct. Mech. Earthq. Eng.
**1993**, 10, 37–48. [Google Scholar] [CrossRef][Green Version] - Rokugo, K.; Kanda, T. Strain Hardening Cement Composites: Structural Design and Performance; RILEM State-of-the-Art Reports 6; E. & FN Spon: London, UK, 2013. [Google Scholar]
- Li, V.C. Engineered Cementitious Composites (ECC)—Bendable Concrete for Sustainable and Resilient Infrastructure; Springer: Berlin/Heidelberg, Germany, 2019. [Google Scholar]
- Arulanandam, P.M.; Singh, S.B.; Kanakubo, T.; Sivasubramanian, M.V.R. Behavior of Engineered Cementitious Composite Structural Elements—A Review. Indian Concr. J.
**2020**, 94, 5–28. [Google Scholar] - Li, V.C. Large volume, high-performance applications of fibers in civil engineering. J. Appl. Polym. Sci.
**2002**, 83, 660–686. [Google Scholar] [CrossRef][Green Version] - Bohidar, S.K.; Sharma, R.; Mishra, P.R. Functionally Graded Materials: A Critical Review. Int. J. Res.
**2014**, 1, 289–301. [Google Scholar] - El-Galy, I.M.; Saleh, B.I.; Ahmed, M.H. Functionally graded materials classifications and development trends from industrial point of view. SN Appl. Sci.
**2019**, 1, 1378. [Google Scholar] [CrossRef][Green Version] - Zhou, W.; Zhang, R.; Ai, S.; He, R.; Pei, Y.; Fang, D. Load distribution in threads of porous metal–ceramic functionally graded composite joints subjected to thermomechanical loading. Compos. Struct.
**2015**, 134, 680–688. [Google Scholar] [CrossRef][Green Version] - Zhou, W.; Ai, S.; Chen, M.; Zhang, R.; He, R.; Pei, Y.; Fang, D. Preparation and thermodynamic analysis of the porous ZrO
_{2}/(ZrO_{2}+ Ni) functionally graded bolted joint. Compos. Part B Eng.**2015**, 82, 13–22. [Google Scholar] [CrossRef] - Mahamood, R.M.; Akinlabi, E.T. Introduction to Functionally Graded Materials. In Functionally Graded Materials, Topics in Mining, Metallurgy and Materials Engineering; Springer: Cham, Switzerland, 2017. [Google Scholar] [CrossRef]
- Saleh, B.; Jiang, J.; Fathi, R.; Al-hababi, T.; Xu, Q.; Wang, L.; Song, D.; Ma, A. 30 Years of functionally graded materials: An overview of manufacturing methods, Applications and Future Challenges. Compos. Part B
**2020**, 201, 108376. [Google Scholar] [CrossRef] - Koizumi, M.; Niino, M. Overview of FGM Research in Japan. MRS Bull.
**1995**, 20, 19–21. [Google Scholar] [CrossRef] - Roesler, J.; Bordelon, A.; Gaedicke, C.; Park, K.; Paulino, G.H. Fracture behavior and properties of functionally graded fiber-reinforced concrete. AIP Conf. Proc.
**2008**, 973, 513–518. [Google Scholar] [CrossRef][Green Version] - Naghibdehi, M.G.; Mastali, M.; Sharbatdar, K.K.; Naghibdehi, M.G. Flexural performance of functionally graded RC cross-section with steel and PP fibres. Mag. Concr. Res.
**2014**, 66, 219–233. [Google Scholar] [CrossRef] - Naghibdehi, M.G.; Naghipour, M.; Rabiee, M. Behaviour of functionally graded reinforced-concrete beams under cyclic loading. Građevinar
**2015**, 67, 427–439. [Google Scholar] [CrossRef] - Shen, B.; Hubler, M.; Paulino, H.G.; Struble, J.L. Functionally-graded fiber-reinforced cement composite: Processing, microstructure, and properties. J. Cem. Concr. Compos.
**2008**, 30, 663–673. [Google Scholar] [CrossRef] - Ferrara, L.; Park, Y.D.; Shah, S.P. A method for mix-design of fiber-reinforced self-compacting concrete. Cem. Concr. Res.
**2007**, 37, 957–971. [Google Scholar] [CrossRef] - Ferrara, L.; Park, Y.D.; Shah, S.P. Correlation among Fresh State Behavior, Fiber Dispersion and Toughness Properties of SFRCs. J. Mater. Civ. Eng.
**2008**, 20, 493–501. [Google Scholar] [CrossRef] - Laranjeira, F.; Aguado, A.; Molins, C.; Grünewald, S.; Walraven, J.; Cavalaro, S. Framework to Predict the Orientation of Fibers in FRC: A Novel Philosophy. Cem. Concr. Res.
**2012**, 42, 752–768. [Google Scholar] [CrossRef] - Dupont, D.; Vandewalle, L. Distribution of Steel Fibres in Rectangular Sections. Cem. Concr. Compos.
**2005**, 27, 391–398. [Google Scholar] [CrossRef] - Kanakubo, T. Tensile Characteristics Evaluation Method for Ductile Fiber-Reinforced Cementitious Composites. J. Adv. Concr. Technol.
**2006**, 4, 3–17. [Google Scholar] [CrossRef][Green Version] - Xia, J.; Mackie, K. Axisymmetric Fiber Orientation Distribution of Short Straight Fiber in Fiber-Reinforced Concrete. ACI Mater. J.
**2014**, 111, 133–141. [Google Scholar] [CrossRef] - Li, V.C.; Wang, S. On High Performance Fiber Reinforced Cementitious Composites. In Proceedings of the JCI Symposium on Ductile Fiber-Reinforced Cementitious Composites, Tokyo, Japan, 4–5 December 2003; pp. 13–23. [Google Scholar]
- Kanakubo, T.; Miyaguchi, M.; Asano, K. Influence of Fiber Orientation on Bridging Performance of Polyvinyl Alcohol Fiber-Reinforced Cementitious Composite. ACI Mater. J.
**2016**, 113, 131–141. [Google Scholar] [CrossRef] - Japanese Industrial Standards. Fly Ash for Use in Concrete, JIS A 6201:2015. Available online: https://www.jisc.go.jp/app/jis/general/GnrJISSearch.html (accessed on 20 March 2021).
- International Standard. Test Methods for Fibre-Reinforced Cementitious Composites—Bending Moment—Curvature Curve by Four-Point Bending Test. ISO 21914:2019. Available online: https://www.iso.org/standard/72163.html (accessed on 20 March 2021).
- International Standard. Testing of Concrete—Part 4: Strength of Hardened Concrete. ISO 1920-4:2020. Available online: https://www.iso.org/standard/72260.html (accessed on 20 March 2021).
- Ozu, Y.; Miyaguchi, M.; Kanakubo, T. Modeling of Bridging Law for PVA Fiber-Reinforced Cementitious Composite Considering Fiber Orientation. J. Civ. Eng. Archit.
**2018**, 12, 651–661. [Google Scholar] [CrossRef] - Kanda, T.; Li, V.C. Interface Property and Apparent Strength of High-Strength Hydrophilic Fiber in Cement Matrix. ASCE J. Mater. Civ. Eng.
**1998**, 10, 5–13. [Google Scholar] [CrossRef][Green Version]

**Figure 1.**Specimens: (

**a**) fiber-reinforced cementitious composite (FG-FRCC); (

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

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

**d**) Hmg-1%; (

**e**) Hmg-2%.

**Figure 2.**Fabrication of specimen: (

**a**) mold before casting; (

**b**) after pouring the first layer; (

**c**) pouring the second layer 60 min after the first layer pouring; (

**d**) after pouring the third layer.

**Figure 3.**Four-point bending test setup and positions of linear variable displacement transducers (LVDTs).

**Figure 8.**Tri-linear model for bridging law of PVA-FRCC [31].

**Figure 10.**Stress distribution in cross-section at the maximum moment: (

**a**) 1st day FG-FRCC; (

**b**) 1st day Hmg-1%; (

**c**) 1st day Hmg-2%.

Water by Binder Ratio | Sand by Binder Ratio | Unit Weight (kg/m^{3}) | |||
---|---|---|---|---|---|

Water | Cement | Fly Ash | Sand | ||

0.39 | 0.50 | 380 | 678 | 291 | 484 |

Cement: High early strength Portland cement | |||||

Fly ash: Type II of Japanese Industrial Standard (JIS A 6201) [28] | |||||

Sand: Size under 0.2 mm | |||||

High-range water-reducing admixture: Binder × 0.6% |

Type | Density (g/cm ^{3}) | Diameter (mm) | Length (mm) | Tensile Strength (MPa) | Elastic Modulus (GPa) |
---|---|---|---|---|---|

PVA | 1.30 | 0.10 | 12 | 1200 | 28 |

Test Series (Casting Day) | Specimen ID | Remarks | Fiber Volume Fraction, V _{f} | Number of Specimens |
---|---|---|---|---|

1st day | FG-FRCC | Functionally graded | 0, 1, 2% | 3 for each parameter |

Hmg-1% | Homogeneous | 1% | ||

Hmg-2% | Homogeneous | 2% | ||

2nd day | Layer-1% | Three-layer | 1% | 3 for each parameter |

Layer-2% | Three-layer | 2% | ||

Hmg-1% | Homogeneous | 1% | ||

Hmg-2% | Homogeneous | 2% |

Test Series (Casting Day) | Specimen ID | Comp. Strength (MPa) | Experiment | Section Analysis | Ratio of Experiment to Analysis_{e}M_{max}/_{a}M_{max} | |||
---|---|---|---|---|---|---|---|---|

Max. Bending Moment_{e}M_{max}(kN·m) | Curvature at_{e}M_{max}(μ/mm) | Max. Bending Moment_{a}M_{max}(kN·m) | Neutral Axis from Comp. Edge (mm) | |||||

Avg. | STDV | |||||||

1stday | FG-FRCC | ^{1} | 1.079 | 0.047 | 209 | 0.950 | 19.5 | 1.14 |

Hmg-1% | 46.4 | 0.570 | 0.079 | 129 | 0.583 | 14.7 | 0.98 | |

Hmg-2% | 41.1 | 1.281 | 0.090 | 178 | 1.087 | 20.6 | 1.18 | |

2ndday | Layer-1% | 44.3 | 0.528 | 0.006 | 99 | 0.581 | 15.0 | 0.91 |

Layer-2% | 42.4 | 1.126 | 0.041 | 157 | 1.090 | 20.3 | 1.03 | |

Hmg-1% | 44.3 | 0.519 | 0.024 | 107 | 0.581 | 15.0 | 0.89 | |

Hmg-2% | 42.4 | 1.047 | 0.189 | 205 | 1.090 | 20.3 | 0.96 |

^{1}Compressive strengths for V

_{f}= 0%, 1%, and 2% are 40.9, 46.4, and 41.1 MPa, respectively.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 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 (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Kanakubo, T.; Koba, T.; Yamada, K. Flexural Characteristics of Functionally Graded Fiber-Reinforced Cementitious Composite with Polyvinyl Alcohol Fiber. *J. Compos. Sci.* **2021**, *5*, 94.
https://doi.org/10.3390/jcs5040094

**AMA Style**

Kanakubo T, Koba T, Yamada K. Flexural Characteristics of Functionally Graded Fiber-Reinforced Cementitious Composite with Polyvinyl Alcohol Fiber. *Journal of Composites Science*. 2021; 5(4):94.
https://doi.org/10.3390/jcs5040094

**Chicago/Turabian Style**

Kanakubo, Toshiyuki, Takumi Koba, and Kohei Yamada. 2021. "Flexural Characteristics of Functionally Graded Fiber-Reinforced Cementitious Composite with Polyvinyl Alcohol Fiber" *Journal of Composites Science* 5, no. 4: 94.
https://doi.org/10.3390/jcs5040094