# The Significance of Multi-Size Carbon Fibers on the Mechanical and Fracture Characteristics of Fiber Reinforced Cement Composites

^{1}

^{2}

^{*}

*Fibers*)

## Abstract

**:**

## 1. Introduction

## 2. Experimental Program

#### 2.1. Materials

_{f}= 7.2 μm diameter, 3 mm and 6 mm length, 416.7 and 833.3 aspect ratios, and Milled Carbon Microfibers (MCMF), with d

_{f}= 7.2 μm diameter, length of 150 μm and 200 μm, and 20.8 and 27.8 aspect ratios, as shown in Figure 1a. Both fibers have a tensile strength of ${\sigma}_{u}$ = 7137 MPa and elastic modulus is 242 GPa as reported by the manufacturer [2]. The critical fiber length can be estimated as ${l}_{c}=\frac{{\sigma}_{u}{d}_{f}}{2{\tau}_{av}}$, where ${\tau}_{av}$ is the average interface shear strength estimated as ${\tau}_{av}=0.2{\left({f}_{c}^{\prime}\right)}^{0.7}$ [3]. For a compressive strength ranging from 50–70 MPa, and the carbon microfibers used, ${l}_{c}$ was estimated to be in the range of 6.0 to 8.5 mm [3]. This means that some of the CCMF with 3.0- and 6.0-mm length might observe fiber rupture rather than fiber debonding.

#### 2.2. Mixing Protocol

#### 2.3. Flowability Test

_{1}, D

_{2}, D

_{3}, and D

_{4}), expressed as a percentage of the original base diameter (D

_{0}) as shown in Figure 3.

#### 2.4. Uniaxial Compression Test

#### 2.5. Modulus of Rupture Test

#### 2.6. Fracture Toughness Test

_{f}was evaluated by integrating the area under the Load-CMOD [62,63,64] calculated as:

#### 2.7. Scanning Electron Microscopy (SEM)

## 3. Results and Discussion

#### 3.1. Flowability

#### 3.2. Mechanical Properties

#### 3.3. Fracture Properties

_{IC}was observed at 28 days of age compared with G

_{IC}at seven days of age. Similar observations showing a decrease of ${G}_{IC}$ with time were reported for Ultra High Performance Concrete (UHPC) [64].

_{f}at both 7 and 28 days are shown in Figure 14c; it could be observed that G

_{f}is proportional to the total content of fiber, and fiber size distribution in the mix. The difference in fiber volume content is typically masking the effect of fiber size distribution on fracture energy. In the case of constant fiber volume, the maximum fracture energy would occur at the mix with fiber length equal to the critical fiber length [3,44]. The reduction with time in G

_{f}could also be observed for each respective mix. Similar to the modulus of rupture, the effect of fiber size distribution in this case could be represented as the average fiber length in the matrix, which relates to the fiber critical length.

## 4. Conclusions

_{f}were also proportional to both fiber volume content and fiber size distribution, with the first masking the latter. This could be explained as those fracture properties reflect a single crack Mode I failure.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Light microscopic images of CCMFs and MCMFs, and (

**b**) particle size distribution of the fine aggregate.

**Figure 6.**(

**a**) Flowability of different fiber/cement ratios and fiber mixing ratios, and (

**b**) linear regression for flowability at different mixing ratios with fiber content.

**Figure 7.**(

**a**) Compressive strength, (

**b**) modulus of rupture, and (

**c**) modulus of elasticity for the reference and carbon fiber reinforced cementitious composite mixes at 7 and 28 days of age.

**Figure 8.**Comparison of unnotched beam bending mean and variance response for the (

**a**) reference and carbon fiber reinforced cementitious composite mixes ((

**b**) CH2, (

**c**) ML2, (

**d**) ML8, (

**e**) H2, and (

**f**) H5) at seven days of age. Each graph represents the mean of five tested samples.

**Figure 9.**Comparison of unnotched beam bending mean and variance response for the (

**a**) reference and carbon fiber reinforced cementitious composite mixes ((

**b**) CH2, (

**c**) ML2, (

**d**) ML8, (

**e**) H2, and (

**f**) H5) at 28 days of age. Each graph represents the mean of five tested samples.

**Figure 10.**Comparison of notched bending response for the mean and variance (

**a**) reference and carbon fiber reinforced cementitious composite mixes ((

**b**) CH2, (

**c**) ML2, (

**d**) ML8, (

**e**) H2, and (

**f**) H5) at seven days of age. Each graph represents the mean of five tested samples.

**Figure 11.**Comparison of notched bending mean and variance response for the (

**a**) reference and carbon fiber reinforced cementitious composite mixes ((

**b**) CH2, (

**c**) ML2, (

**d**) ML8, (

**e**) H2, and (

**f**) H5) at 28 days of age. Each graph represents the mean of five tested samples.

**Figure 12.**Comparison of CMOD mean and variance response for the (

**a**) reference and carbon fiber reinforced cementitious composite mixes ((

**b**) CH2, (

**c**) ML2, (

**d**) ML8, (

**e**) H2, and (

**f**) H5) at seven days of age. Each graph represents the mean of five tested samples.

**Figure 13.**Comparison of CMOD mean and variance response for the (

**a**) reference and carbon fiber reinforced cementitious composite mixes ((

**b**) CH2, (

**c**) ML2, (

**d**) ML8, (

**e**) H2, and (

**f**) H5) at 28 days of age. Each graph represents the mean of five tested samples.

**Figure 14.**Comparison of fracture toughness represented by (

**a**) critical energy release rate G

_{IC}, (

**b**) plastic energy release rate J

_{IC}, and (

**c**) fracture toughness G

_{f}for the reference and carbon fiber reinforced cementitious composite mixes at 7 and 28 days of age.

**Figure 15.**SEM images of sample (

**a**) chopped (CH2), (

**b**) milled (M2), and (

**c**) hybrid mix (H2). Circular marks indicate signs of fiber rupture. Rectangular marks indicate signs of fiber pull-out.

Component | Reference (R) | Chopped 2% (CH2) | Milled 2% (ML2) | Milled 8% (ML8) | Hybrid 2% (H2) | Hybrid 5% (H5) | |
---|---|---|---|---|---|---|---|

Cement | 934.2 | ||||||

Silica Fume | 93.4 | ||||||

Sand | 934.2 | ||||||

Water | 256.9 | ||||||

Superplasticizer | 16.3 | ||||||

CCMF (% wt. cement) | L = 3 mm | - | 1.0 | - | - | 0.2 | 0.5 |

L = 6 mm | - | 1.0 | - | - | 0.2 | 0.5 | |

MCMF (% wt. cement) | L = 150 μm | - | - | 1.0 | 4.0 | 0.8 | 2.0 |

L = 200 μm | - | - | 1.0 | 4.0 | 0.8 | 2.0 |

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**MDPI and ACS Style**

Abdellatef, M.; Heras Murcia, D.; Hogancamp, J.; Matteo, E.; Stormont, J.; Taha, M.M.R.
The Significance of Multi-Size Carbon Fibers on the Mechanical and Fracture Characteristics of Fiber Reinforced Cement Composites. *Fibers* **2022**, *10*, 65.
https://doi.org/10.3390/fib10080065

**AMA Style**

Abdellatef M, Heras Murcia D, Hogancamp J, Matteo E, Stormont J, Taha MMR.
The Significance of Multi-Size Carbon Fibers on the Mechanical and Fracture Characteristics of Fiber Reinforced Cement Composites. *Fibers*. 2022; 10(8):65.
https://doi.org/10.3390/fib10080065

**Chicago/Turabian Style**

Abdellatef, Mohammed, Daniel Heras Murcia, Joshua Hogancamp, Edward Matteo, John Stormont, and Mahmoud M. Reda Taha.
2022. "The Significance of Multi-Size Carbon Fibers on the Mechanical and Fracture Characteristics of Fiber Reinforced Cement Composites" *Fibers* 10, no. 8: 65.
https://doi.org/10.3390/fib10080065