 Open Access
Mechanical Properties and Modeling of Amorphous Metallic FiberReinforced Concrete in Compression
 NgocHieu Dinh^{1},
 KyoungKyu Choi^{1}Email author and
 HeeSeung Kim^{1}
https://doi.org/10.1007/s4006901601449
© The Author(s) 2016
 Received: 30 December 2015
 Accepted: 26 April 2016
 Published: 2 June 2016
Abstract
The aim of this paper is to investigate the compressive behavior and characteristics of amorphous metallic fiberreinforced concrete (AMFRC). Compressive tests were carried out for two primary parameters: fiber volume fractions (V _{ f }) of 0, 0.3, 0.6 and 0.8 %; and design compressive strengths of 27, 35, and 50 MPa at the age of 28 days. Test results indicated that the addition of amorphous metallic fibers in concrete mixture enhances the toughness, strain corresponding to peak stress, and Poisson’s ratio at high stress level, while the compressive strength at the 28th day is less affected and the modulus of elasticity is reduced. Based on the experimental results, prediction equations were proposed for the modulus of elasticity and strain at peak stress as functions of fiber volume fraction and concrete compressive strength. In addition, an analytical model representing the entire stress–strain relationship of AMFRC in compression was proposed and validated with test results for each concrete mix. The comparison showed that the proposed modeling approach can properly simulate the entire stress–strain relationship of AMFRC as well as the primary mechanical properties in compression including the modulus of elasticity and strain at peak stress.
Keywords
 compressive strength
 amorphous metallic fibers
 fiberreinforced concrete
 Poisson’s ratio
 strain at peak stress
 modulus of elasticity
 stress–strain curve
1 Introduction
For several decades, significant research has been performed to improve binder materials (cement, fly ash, and slag) and adhesives (superplasticizer, etc.) suitable for high performance construction materials (Constantinides et al. 2003; Jeong et al. 2015; Le et al. 2014; Sriravindrarajah et al. 2012; Divsholi et al. 2014; Sorensen et al. 2014). Based on the progress in concrete technology, high strength concrete (HSC) with compressive strength of 100 MPa or above has been developed and applied in various construction fields. Nonetheless, such HSC generally shows severe brittle behavior in compression compared to normal strength concrete (NSC) (Gettu et al. 1990; Wittmann 2002); HSC suddenly loses its load carrying capacity after reaching peak compressive strength. Partly due to the brittleness of HSC, ACI 31814 (2014) limits the maximum value of \( \sqrt {f_{c}^{'} } \) to be 8.3 MPa in shear design of concrete structures. In addition, the ACI Manual of Concrete Practice (1998) limit the use of HSC in earthquake resisting structures.
For this reason, considerable research has been performed to improve the characteristics and the ductility of concrete (in particular HSC) in compression by the addition of fibers in concrete. In a study by Ezeldin and Balaguru (1992), the use of fibers in both NSC and HSC ranging from 35 to 85 MPa was found to increase toughness, compressive strength, strain corresponding to peak stress, and the secant modulus of elasticity. In addition, Ou et al. (2011) investigated the compressive stress–strain behavior of steel fiberreinforced concrete (SFRC) with a high reinforcing index, which was defined as the product of fiber volume fraction and fiber aspect ratio. Their study indicated that the addition of hookedend fibers to concrete matrix increases both material toughness and strain at the peak stress, while the modulus of elasticity and compressive strength of SFRC are less affected. Moreover, Chi et al. (2012) performed experiments to investigate the uniaxial compressive behavior of steelpolypropylene hybrid fiberreinforced concrete (HFRC). It was observed that the compressive behavior of concrete can be improved by the addition of hybrid fibers and showed a variation according to fiber volume fractions of steel and polypropylene fibers and aspect ratio of steel fibers. Based on the test results, the optimum proportion of hybrid fibers was also investigated to achieve enhanced compressive strength and ductile compressive behavior. Recently, Srikar et al. (2016) investigated the residual compressive properties of polypropylene fiber reinforced concrete exposed to high temperature by using digital image correlation method. It was reported that the polypropylene fibers improved the postpeak residual compressive strength and the toughness of concrete subjected to temperatures up to 300 °C. The stress–strain curves also show a significantly improvement in post peak behavior with increasing fiber volume fraction at all level of exposure temperatures.
Recently, newlydeveloped fibers, known as amorphous metallic fibers (AMF), have been investigated by numerous researchers. Choi and Ku (2014) performed flexural tests on amorphous metallic fiberreinforced concrete (AMFRC) and it was found that the addition of the fibers in concrete could significantly enhance flexural strength as well as toughness; a higher fiber volume fraction of up to 0.75 % could result in a more enhanced flexural behavior of concrete. Moreover, Hameed et al. (2010) and Won et al. (2012) demonstrated that the presence of amorphous metallic fibers increased the flexural toughness and strength and was more effective than the conventional steel fibers in terms of flexural toughness and strength. Additionally, Choi et al. (2014) investigated the shrinkage and corrosion resistance of amorphous metallic fiberreinforce cement composites and conclude that amorphous metallic fibers displayed higher corrosion resistance than did steel in every degradation environment, and plastic shrinkage crack control performance was excellent. More recently, experiments performed by Choi et al. (2015) showed that the addition of AMF into concrete could significantly reduce the free drying shrinkage by 24 %; and in the restraint shrinkage tests (ring tests and slab tests), AMF delay crack development time as well as reduced crack width to 36.5–74.6 % according to the fiber volume fraction. Notwithstanding this, the mechanical properties of AMFRC in compression were not adequately investigated in the above studies.
In this current study, a compressive test on AMFRC was performed with variations of fiber volume fraction and concrete compressive strength. Based on the test results, primary compressive characteristics were investigated in terms of the modulus of elasticity, Poisson’s ratio, strain corresponding to peak stress, and the toughness. In addition, an analytical model was proposed for simulating the entire compressive stress–strain curves of AMFRC as functions of the fiber volume fraction and concrete compressive strength.
2 Experimental Program
2.1 Materials
Concrete mix proportions.
Design strength (MPa)  Design air content (%)  Design slump flow (mm)  W/C^{a} (%)  S/a^{b} (%)  Unit content (kg/m^{3})  

Water  Cement  Fine aggregate  Coarse aggregate  Admixture^{c}  AMF^{d} content  
27  4.0 ± 1.0  150 ± 50  55  51.8  202  367  884  811  0.2  – 
0.4  21.6  
0.6  43.2  
0.8  57.6  
35  45  43.8  216  480  695  880  0.2  –  
0.4  21.6  
0.6  43.2  
0.8  57.6  
50  35  44.3  236  675  592  733  0.2  –  
0.4  21.6  
0.6  43.2  
0.8  57.6 
2.2 Mixing, Casting, and Curing Procedure
The concrete was mixed using a compulsive concrete mixer with a capacity of 0.6 m^{3}. First, the dry aggregate and cement were mixed for 1 min. Then, 80 % of water was added and mixing was continued for a further 1 min. The mixing was then continued with the fibers for 2 min. Finally, the remaining water along with the superplasticizer was poured gradually and mixing was continued for an additional 3 min.
2.3 Test Setup
The compressive test for cylindrical specimens was carried out according to ASTM C39 (2015). Before testing, the cylinders were flattened at both ends to ensure smooth surfaces to transfer the uniform load. The test was conducted using a hydraulicallypowered machine with a capacity of 1000 kN. A data acquisition system was connected to the computer to record the load and strain data.
3 Experimental Results and Discussions
3.1 Properties of Fresh Concrete
The characteristics of fresh concrete using amorphous metal fibers were investigated based on an air content test and slumpflow test for each concrete mixture according to standards of ASTM C231 (2014) and ASTM C143 (2015).
3.2 Characteristics of Hardened Concrete
Summary of test results.
Type  Normalized compressive strength^{a}  Normalized strain at peak stress^{b}  Normalized elastic modulus^{c}  Normalized Toughness index^{d}  Normalized ultimate strain^{e} 

Plain 27  1.01  1.05  1.01  0.96  1.06 
0.99  0.92  1.01  1.14  0.79  
1.05  1.01  1.07  0.97  0.93  
0.97  1.02  0.97  0.95  1.23  
0.98  1.01  0.95  0.98  0.99  
f _{ c } = 28.69 MPa  ε _{ o } = 2.40 × 10^{−3}  E _{ c } = 24.93 GPa  I = 2.21  ε _{ ou } = 4.97 × 10^{−3}  
AMF 2703  0.95  0.99  0.94  1.01  0.89 
1.02  0.99  1.01  1.13  1.12  
1.08  1.04  1.10  1.23  1.15  
0.95  0.95  0.96  0.84  0.88  
1.00  1.03  1.00  0.79  0.97  
f _{ c } = 27.85 MPa  ε _{ o } = 2.54 × 10^{−3}  E _{ c } = 23.33 GPa  I = 3.61  ε _{ ou } = 7.82 × 10^{−3}  
AMF 2706  0.93  0.87  0.91  0.87  0.84 
1.01  1.02  1.03  1.11  1.13  
1.00  1.10  1.08  0.97  1.03  
1.00  0.98  0.98  1.01  0.98  
1.07  1.03  1.00  1.05  1.02  
f _{ c } = 28.17 MPa  ε _{ o } = 2.80 × 10^{−3}  E _{ c } = 21.79 GPa  I = 4.30  ε _{ ou } = 8.30 × 10^{−3}  
AMF 2708  0.97  1.00  0.98  0.99  1.12 
1.00  1.00  1.01  0.93  0.96  
0.98  0.96  0.97  1.03  1.03  
1.04  1.06  1.05  1.10  0.95  
1.01  0.98  1.00  0.96  0.94  
f _{ c } = 28.64 MPa  ε _{ o } = 3.02 × 10^{−3}  E _{ c } = 18.94 GPa  I = 4.52  ε _{ ou } = 9.58 × 10^{−3}  
Plain 35  1.03  0.98  1.02  0.94  0.98 
1.01  1.03  1.01  1.05  1.02  
0.97  0.97  0.97  0.97  1.02  
1.05  1.08  1.03  0.98  1.08  
0.95  0.93  0.97  1.06  0.90  
f _{ c } = 39.27 MPa  ε _{ o } = 2.49 × 10^{−3}  E _{ c } = 28.44 GPa  I = 2.43  ε _{ ou } = 4.50 × 10^{−3}  
AMF 3503  0.99  0.99  0.96  1.07  0.94 
0.99  1.00  0.99  0.99  1.03  
0.96  0.97  1.05  0.96  1.04  
1.03  1.01  1.02  1.05  1.03  
1.02  1.02  0.98  0.93  0.96  
f _{ c } = 39.92 MPa  ε _{ o } = 2.62 × 10^{−3}  E _{ c } = 27.20 GPa  I = 3.97  ε _{ ou } = 6.65 × 10^{−3}  
AMF 3506  0.96  0.95  1.02  1.02  0.94 
0.99  0.99  1.05  1.03  1.01  
1.02  1.02  0.99  0.98  1.01  
1.03  1.05  1.00  1.01  1.03  
1.00  0.99  0.95  0.95  1.01  
f _{ c } = 41.46 MPa  ε _{ o } = 2.85 × 10^{−3}  E _{ c } = 25.31 GPa  I = 4.25  ε _{ ou } = 7.86 × 10^{−3}  
AMF 3508  1.03  1.01  1.02  0.93  1.00 
0.92  0.94  0.92  1.01  0.98  
1.03  1.04  1.03  1.01  1.06  
1.00  1.03  0.99  1.01  1.00  
1.03  0.98  1.03  1.04  0.96  
f _{ c } = 39.88 MPa  ε _{ o } = 3.22 × 10^{−3}  E _{ c } = 23.58 GPa  I = 4.49  ε _{ ou } = 9.91 × 10^{−3}  
Plain 50  1.00^{f}  0.98^{f}  1.00^{f}  0.82^{f}  0.64^{f} 
1.13  1.10  1.10  0.96  1.09  
1.08  1.04  1.02  1.06  1.07  
0.95  0.95  0.95  0.97  0.96  
0.84  0.91  0.93  1.01  0.88  
f _{ c } = 52.31 MPa  ε _{ o } = 2.59 × 10^{−3}  E _{ c } = 31.11 GPa  I = 2.20  ε _{ ou } = 4.33 × 10^{−3}  
AMF 5003  1.03  0.99  1.02  1.05  1.01 
1.14  1.15  1.06  0.79  0.95  
1.00  0.98  1.01  0.97  0.93  
0.86  0.93  0.92  1.08  1.02  
0.97  0.96  0.99  1.11  1.08  
f _{ c } = 51.02 MPa  ε _{ o } = 2.65 × 10^{−3}  E _{ c } = 29.21 GPa  I = 4.18  ε _{ ou } = 6.56 × 10^{−3}  
AMF 5006  0.94  0.92  0.94  0.99  0.92 
1.03  1.09  1.07  1.03  1.15  
1.02  1.00  0.99  0.98  0.94  
1.03  1.04  1.00  1.01  1.05  
0.99  0.95  1.00  1.00  0.95  
f _{ c } = 51.56 MPa  ε _{ o } = 2.87 × 10^{−3}  E _{ c } = 26.89 GPa  I = 4.31  ε _{ ou } = 7.86 × 10^{−3}  
AMF 5008  1.07  0.99  1.14  1.03  0.90 
1.02  0.92  1.03  0.94  0.92  
0.99  1.02  0.94  1.00  1.05  
0.93  1.08  0.89  1.00  1.14  
1.00  0.99  1.00  1.04  1.00  
f _{ c } = 49.86 MPa  ε _{ o } = 3.34 × 10^{−3}  E _{ c } = 25.07 GPa  I = 4.52  ε _{ ou } = 10.00 × 10^{−3} 
3.2.1 Compressive Strength and Strain at Peak Stress
The strength test results are summarized in Table 2. In this table, the compressive strength of each test specimen normalized by the average value for each concrete mix are reported. The measured average compressive strengths of plain concrete at the 28th day were 28.69, 39.27, and 52.30 MPa, while the design strengths were 27, 35, and 50 MPa.
3.2.2 Failure Modes
3.2.3 Modulus of Elasticity
3.2.4 Toughness Index
3.2.5 Poisson’s Ratio
4 Modeling and its Validation of Compressive Characteristics of AMFRC
4.1 Modulus of Elasticity
Figure 14 compares the prediction obtained from Eq. (3) and the test results. The figure shows a relatively good correlation between the experimental data and the predicted results. However, since the value of the elastic modulus of concrete strongly depends on the nature of coarse aggregate (Baalbaki et al. 1991; Aïtcin and Mehta 1990; Gutierrez and Canovas 1995), for different aggregate types, the above equation needs to be adjusted.
4.2 Strain at Peak Stress
In Eq. (6), \( E_{c} \) is the modulus of elasticity of plain concrete Eq. (4).
4.3 Stress–Strain Relationship
To date, many analytical models have been developed to represent the stress–strain curve for plain concrete under uniaxial compression. Among the models, the expression proposed by Carreira and Chu (1985) was used as a basis in this study to obtain the stress–strain relationship for both plain concrete and AMFRC. The model was also used in Ezeldin and Balaguru (1992), Mansur et al. (1999), Nataraja et al. (1999), and Araújo (2002).
5 Conclusions

The addition of amorphous metallic fibers to concrete reduces the workability according to fiber volume fraction and increases the air contents of fresh concrete mixture in a range of 0.4–0.6 %.

Generally, amorphous metallic fibers don’t affect the compressive strength of concrete, the difference in compressive strength between the amorphous metal fiberreinforced concrete and plain concrete is only 0.17–2.93 %. However, strain corresponding to peak stress, ultimate strain and toughness in compression were found to be increased proportionally to the fiber dosage in the concrete mix.

The elastic modulus shows a decreasing tendency with increasing fiber volume fraction.

The existing of amorphous metallic fibers in concrete matrix reduces the expansion of concrete in the horizontal direction, which contributes to the stabilization of Poisson’s ratio in high stress level.

Equations to predict the modulus of elasticity and the strain at peak stress of amorphous metal fiberreinforced concrete were proposed as functions of fiber volume fraction and the concrete compressive strength, and were validated by the test results. The prediction by the equations showed a good correlation with the test data.

A stress–strain curve is also proposed to represent the complete stress–strain relationship based on multilinear regression analysis method. The proposed modeling approach was found to present a good correlation with the experimental results.
However, the application of the proposed model is limited to the test condition of this study: the maximum aggregate size of 13 mm and fiber length of 30 mm. Thus, further investigation and validation are necessary for different test conditions.
Declarations
Acknowledgments
This research was supported by the National Research Foundation of Korea Grant funded by the Korean Government (NRF2014R1A1A2053499).
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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