# The Size Effect on Flexural Fracture of Polyolefin Fibre-Reinforced Concrete

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Programme

#### 2.1. Materials and Specimen Fabrication

^{3}and a Blaine surface of 400–450 m

^{2}/kg. The silica aggregate contained two coarse size ranges: 4–8 mm grit and 8–12 mm gravel with a maximum size of 12.7 mm. The sand size range was 0–2 mm. Polycarboxilate-based superplasticizer, named Sika-Viscocrete 5720 (ManuSIKA, Madrid, Spain), with a density of 1090 kg/m³ and a solid content of 36% was also included in the mix. The mix formulation is shown in Table 1 and was that used in previous experimental campaigns [25]. The 48 mm long macro fibres type SikaFiber, with an embossed surface, were added to the mix in a volume fraction of 1.1%, equivalent to 10 kg/m³. Table 1 also shows the main fibre properties. The visual aspect of the fibres can be seen in Figure 2.

_{500}= 6 s and the diameter of the patty d

_{m}= 570 mm. Concrete was poured into the moulds from one end, leaving the concrete flows towards the opposite end with the only compaction action being its own weight as it is recommended by the standards and bibliography [24,27]. The fresh specimens were covered with plastic film to keep the upper surface from drying. The beams were unmoulded 24 h later and placed in a humid chamber at 20 °C and 90% of relative humidity for a minimum of 28 days (the point when they were ready for testing).

#### 2.2. Testing Development

## 3. Results

_{sp}the length of the ligament resisting section.

_{R,j}= 3F

_{j}L/2bh

_{sp}

^{2}

#### 3.1. Fracture Behaviour Results

_{LOP}, then after the first crack is generated there is a sharply descendent branch down to a minimum post-cracking load value, L

_{MIN,}followed by a reloading branch when the fibres start assuming the internal tension stresses up to a relative maximum post-cracking load (L

_{REM}) and lastly descending branch where the fibres are either breaking or sliding inside the concrete matrix. This reloading branch remained active up to a deflection value of about 5 mm. It is worth noting that all specimens maintained some residual load for deflections as high as 15 mm.

#### 3.2. Fracture Surface Analysis

## 4. Discussion

#### 4.1. Size Effect and Strength-CMOD Curves

_{R1}and f

_{R3}which are the main values of strength used in structural design.

_{LOP}), the curve of the small specimens presents a higher peak-stress level compared with the other sizes, as can be understood by observing Figure 9. The strength values at the limit of proportionality were 5.86 MPa, 5.07 MPa and 3.85 MPa for, respectively, the small, medium and large specimens. Therefore, the small specimens experienced stresses 52.2% higher than the large size specimens (the scale effect). In such a sense, the expected following size effect classical law for concrete occurs: the larger the size, the lower are the strengths obtained. Since the limit of proportionality (f

_{LOP}) is controlled by the concrete matrix, not by the fibres, the size effect observed is in accordance with the results of previous published works for plain concrete, such as [32].

_{LOP}) trend to decrease as a consequence of the specimen size increase and behave inversely to size. Contrarily, the rest of residual strengths behaved in the same direct sense as the fracture surface size, the number of fibres and the specimen size. In Figure 10 these tendencies can be observed for the three sizes with respect to the proportionality limit (f

_{LOP}), minimum strength value at the end of the discharge branch (f

_{MIN}) and the strengths for the CMOD values of 0.5 mm and 2.5 mm (f

_{R1}and f

_{R3}) in relation to specimen depth D. It was then necessary to analyse the effect of the fibre counting and orientation on the residual strength in order to decouple these effects from the size effect.

_{MIN}) the curve shows increasing strength values which mean an increase in the fracture energy up to a second relative maximum (f

_{REM}) and a smoothly decreasing residual strength. This behaviour shows the superior ductility and toughness of PFRC compared with unreinforced concrete.

_{R1}, f

_{R3}, f

_{min}and f

_{REM}as a function of the number of fibres in the fracture surface. As can be seen, keeping constant the volume fraction, the number of fibres in the fracture surface in the smallest specimens is about 50, in the medium-sized specimens around 100 and close to 200 for the largest specimens. To assess the size effect in f

_{min}, Figure 12 was performed. In this figure, the results of Figure 11a were extended by a linear fitting for the comparison with the same number of fibres. It has been shown [33] that residual strength in fibre-reinforced concrete is directly related with the number of fibres in the fracture surface. Figure 12 shows that with the same number of fibres there is a clear size effect. Considering, for example, 50 fibres the strength of the large specimens (point A) corresponds to a minimum value of 0.48 MPa, whereas this value increases to 0.78 MPa (point B) for medium-size specimens and reaches 1.11 MPa (point C) in case of small specimens. This data means a 231% strength increment in the small specimens in relation to the big specimens. Again, this behaviour confirmed that the size effect occurred for PFRC elements, according to the classical theory of size effect for quasi-brittle materials [32].

_{LOP}) but also in the post-cracking strength values.

#### 4.2. Fracture Energy

_{F}) of all the mixes was analysed by means of the load-deflection curves and processed by using Equation (4).

_{f}was the fracture work borne by the sample, b the width of the sample (50 mm) and h

_{sp}the length of the ligament (0.5D for each size).

#### 4.3. Video-Extensometry

## 5. Concluding Remarks

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Size effect on member strength (adapted from Reference [18]).

**Figure 7.**Average fracture curves for the three specimen sizes: (

**a**) load-crack mouth opening displacement (CMOD) plots; (

**b**) load-mid-span deflection (LVDT).

**Figure 9.**Residual strength-CMOD curves: (

**a**) complete test; (

**b**) for a notch tip opening up to 0.5 mm.

**Figure 10.**Plots of average values of proportionality limit strength (f

_{LOP}), minimum strength at the end of discharging branch (f

_{MIN}), CMOD opening of 0.5 mm (f

_{R1}) and CMOD of 2.5 mm (f

_{R3}) versus the total specimen depth D.

**Figure 11.**Tendency lines of the distinct residual strength values in relation to the number of fibres for the three specimen sizes: (

**a**) for the minimum strength (f

_{MIN}), (

**b**) for CMOD of 0.5 mm (f

_{R1}), (

**c**) for CMOD of 2.5 mm (f

_{R3}) and (

**d**) for the maximum residual post-cracking strength (f

_{REM}).

**Figure 12.**Fitting lines of the relationship average minimum residual strength versus number of fibres.

Material | SCC10 | PF48 Fibre Properties | |
---|---|---|---|

Cement (kg/m^{3}) | 375 | Length (mm) | 48 |

Limestone (kg/m^{3}) | 200 | Equivalent diameter (mm) | 0.903 |

Water (kg/m^{3}) | 188 | Aspect ratio | 53 |

Water/cement | 0.5 | Tensile strength (MPa) | >400 |

Gravel (kg/m^{3}) | 245 | Density (g/cm^{3}) | 0.91 |

Grit (kg/m^{3}) | 367 | Modulus of elasticity (GPa) | >6 |

Sand (kg/m^{3}) | 918 | Fibre shape | Straight |

Superplasticizer (% cement) | 1.25 | Surface structure | Rough |

PF48 (kg/m^{3}) | 10 | Fibres per kg | 32,895 |

Fibre volume fraction (%) | 1.10 |

Specimen | Units | Length (mm) | Width (mm) | High (mm) |
---|---|---|---|---|

Large | 3 | 1350 | 50 | 300 |

Medium | 2 | 675 | 50 | 150 |

Small | 3 | 340 | 50 | 75 |

**Table 3.**Average number of fibres in the fracture surface with their coefficient of variation (c.v.) and the overall orientation factor (θ) for each specimen size.

Specimen | Fibres (c.v.) | Orientation Factor (θ) |
---|---|---|

Large | 178 (0.10) | 0.63 |

Medium | 106 (0.03) | 0.62 |

Small | 57 (0.08) | 0.72 |

**Table 4.**Fracture energy values (N/m) for different deflection values and the coefficient of variation.

Specimen | G_{F} (1 mm) | G_{F} (5 mm) | G_{F} (10 mm) | G_{F} (15 mm) |
---|---|---|---|---|

Large | 249 (0.06) | 1436 (0.21) | 2979 (0.21) | 3939 (0.15) |

Medium | 242 (0.01) | 1374 (0.01) | 2495 (0.01) | 2722 (0.05) |

Small | 163 (0.25) | 1296 (0.18) | 2947 (0.18) | 3330 (0.17) |

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**MDPI and ACS Style**

Picazo, Á.; Alberti, M.G.; Gálvez, J.C.; Enfedaque, A.; Vega, A.C. The Size Effect on Flexural Fracture of Polyolefin Fibre-Reinforced Concrete. *Appl. Sci.* **2019**, *9*, 1762.
https://doi.org/10.3390/app9091762

**AMA Style**

Picazo Á, Alberti MG, Gálvez JC, Enfedaque A, Vega AC. The Size Effect on Flexural Fracture of Polyolefin Fibre-Reinforced Concrete. *Applied Sciences*. 2019; 9(9):1762.
https://doi.org/10.3390/app9091762

**Chicago/Turabian Style**

Picazo, Álvaro, Marcos G. Alberti, Jaime C. Gálvez, Alejandro Enfedaque, and Abner C. Vega. 2019. "The Size Effect on Flexural Fracture of Polyolefin Fibre-Reinforced Concrete" *Applied Sciences* 9, no. 9: 1762.
https://doi.org/10.3390/app9091762