A study on mechanical behavior of Kevlar fiber reinforced concrete under static and high-strain rate loading

Abstract

Reinforced concrete structures sometimes are deteriorated and damaged by seismic and blast wave loadings, and the resistance of fiber-reinforced concrete was tested at a loading of high-strain rate. Therefore, concrete structures were needed to improve the dynamic load resistance and energy absorption capabilities. In infrastructures, fiber is incorporated into concrete and is used to strengthen structures to increase its durability and resistance to high-strain rate loadings. In this study, the quasi-static and dynamic mechanical behaviors of Kevlar fiber-reinforced concrete were studied by the compressive strength test and Split Hopkinson Pressure Bar test, respectively. The 0.5% weight ratio Kevlar fiber content of KFRC specimens attained the highest strength in the quasi-static and dynamic test compared with benchmark and other 1.0%, 1.5% weight ratios. The KFRC specimens with the length of 12 mm and 24 mm exhibit similar effects in the quasi-static compressive strengths, but the KFRC specimens with the length of 24 mm fiber attained higher strain energies under dynamic loading.

Keywords

Kevlar fiber-reinforced concrete strain rate split Hopkinson pressure bar dynamic increase factor failure mechanism

Highlights

• Chopped Kevlar fiber with the lengths of 12 mm and 24 mm were integrated with Kevlar fiber-reinforced concrete (KFRC) specimens.

• Quasi-static and dynamic compressive strengths of the KFRC specimens were investigated.

• The dynamic increase factor (DIF) was calculated by dynamic compressive strength corresponds to quasi-static compressive strength.

• The dynamic failure photos, SHPB test evolution images, and optical microscopic images of KFRC specimens under high-strain rate loadings were discussed.

Introduction

Fiber-reinforced concrete (FRC) is mixed with chopped fibrous material, such as steel fiber, carbon fiber, glass fiber, basalt fiber, polypropylene fiber, and other fibers; those chopped fibers are distributed randomly in the concrete to reduce the micro-cracks and to improve the toughness of the concrete (Brandt, 2008; Gesoglu et al., 2016; Li and Obla, 1994). Fiber-reinforced concrete is widely applied in infrastructures, such as airport pavements, highway pavements, bridge expansion joints, tunnels, dams, etc. The mechanical behaviors of FRC vary depending on aggregate, fiber content, chopped fiber length, aspect ratio, fiber element, and fiber dispersion, and those effects were researched by many scholars in the last few decades (Felekoglu et al., 2014; Graham et al., 2013; Kang and Kim, 2011; Larson et al., 1990; Wu et al., 2016; Yoo et al., 2014; Zhou et al., 2012).

The materials of chopped fiber also influence the mechanical behaviors of FRC greatly owing to the different properties of the material, such as tensile strength, specific strength, elastic modulus, and elongation of break (Iyer, 2014; Pyo et al., 2016; Shi et al., 2020; Waghmare et al., 2022). If the fiber material has large elastic modulus and specific strength, the fiber material will have stronger stiffness and strength, thus, FRC containing fiber material has better mechanical strength and bending properties, such as carbon fiber, basalt fiber, and aramid fiber (Simões et al., 2017; Wu et al., 2020a; Yan et al., 2016). Aramid fiber is an organic fiber often used to make body armor. Aramid fiber has some advantages such as low density, chemical stability, great tensile strength, abrasion and impact resistibility, and high energy absorption. Adding aramid fiber into the concrete can increase the mechanical behaviors of FRC, especially in impact and high strain rate resistance (Li et al., 2021b). Therefore, adding different fibers such as aramid fiber, carbon fiber, steel fiber, glass fiber, and polyester fiber, might give the diverse mechanical properties of FRC.

Some studies point out that adding too much coarse aggregate might decrease the uniform dispersion of fibers in the concrete, and caused negative impacts on the compression and tensile behavior of FRC (Liu et al., 2016; Xu et al., 2019; Wu et al., 2020b). Besides, several studies investigated the fiber content of FRC in volume fraction or mass ratio; there is no correlation between the proportion of fiber content and the benefits from it. Adding too much fiber might easily form pores and generate fiber balls inside the concrete, which diminishes its strength and impact resistance, and workability tremendously (Ahmad and Umar, 2018; Kuder et al., 2007; Li et al., 2021a; Najim et al., 2018; Si et al., 2019). The study by Li et al. (2021a) showed that the static mechanical properties and high strain resistance of FRC were significantly improved when the carbon fiber content was 1% in weight ratio and the fibers were dispersed correctly. The opportune fiber content shows an important role in the mechanical behaviors of FRC.

Additionally, the mechanical properties of FRC are affected not only by the content of chopped fibers but also by the length of the chopped fibers. Fiber-reinforced concrete with shorter chopped fibers has better compressive strength than longer chopped fibers, whereas adding longer chopped fibers can improve the flexural strength of FRC more than shorter chopped fibers (Georgiou and Pantazopoulou, 2016; Jiang et al., 2014; Li et al., 2021). Moreover, Li et al. (2019) indicated that sizing on the fiber surface exerts a strong influence on the bonding force between fiber and cementitious composite due to its mechanical lubrication.

Fiber-reinforced concrete not only increases the static mechanical performance and strength but also increases the resistance under high-strain rate loading. The stress–strain relationship of the material under different strain rate loadings was controlled by different mechanisms, and the selection of test methods with corresponding equipment highly depend on the strain rate conditions. Conventionally, a strain rate less than 10^-5 s^-1 is defined as creep. The strain rate between 10^-5 and 10^-1 s^-1 is quasi-static and greater than 10^-1 s^-1 is dynamic (Nemat-Nasser, 2000; Ngo et al., 2013). Generally, the extent of destruction increases with the increase in strain rate. The appearance of the specimen remained intact under the lower strain rates. Some micro-cracks propagate from the edge of the sample surface to the center. However, during the higher strain rate loading, the specimens were broken into different fragments (Chen et al., 2013; Yang et al., 2015; Li et al., 2016). Different strain rate regimes and their testing technique is shown in Table 1. The strain rate of the split Hopkinson pressure bar (SHPB) is between 50 and 10⁴ s^-1 (Chen et al., 2003; Zhao and Gary, 1996), which is widely used in the high strain rate loading experiment to investigate the dynamic increase factor (DIF) of concrete (Al-Mousawi et al., 1997; Chen et al., 2020). The compressive strength, post-peak load-carrying capacity, and energy absorption capability of FRC are increased with increasing the fiber content under quasi-static loading and high strain rate loading (Ganorkar et al., 2021; Hao and Hao, 2013; Xu et al., 2012a). The larger the aspect ratio of the steel fibers, the greater the improvement in static and dynamic compressive strength of ultra-high performance FRC (Su et al., 2016; Yoo and Banthia, 2017a). The static compressive strength of FRC that is contented with excess polypropylene fiber might be decreased due to the various dispersion, but the dynamic compressive strength, dynamic increase factor (DIF), and energy absorption capacity could be effectively increased (Chen et al., 2019). The material and content ratio of fiber have noteworthy effects on the dynamic properties of FRC (Zhang et al., 2022). Recently, the dynamic mechanical properties of FRC obtained great attention from engineers.

Table 1.

Strain rate regime, and its corresponding loading method and testing technique.

Strain rate range (s^-1)	Loading method	Testing technique
10^-5 <	Creep	Constant load or stress machine
10^-5 ∼ 10^-1	Quasi-static	Servo-hydraulic and screw machine
10^-1 ∼ 50	Dynamic (intermediate strain rates)	Free-fall impact
50 ∼ 10⁴	Dynamic (high strain rates)	Split Hopkinson pressure bar
> 10⁴	Dynamic (very high strain rates)	Taylor impact and plate impact

In this study, the Kevlar fiber-reinforced concrete (KFRC) specimens were prepared with different chopped fiber length and content weight ratios, and then experimented under quasi-static compressive strength and dynamic SHPB test; those data were used to calculate the DIF of FRC.

Materials

Kevlar fiber

Aramid fiber is an organic fiber and it can be divided into para-aramid and meta-aramid. Kevlar fiber is a kind of composite material manufactured and invented by DuPont in 1965, and it is a type of para-aramid fiber. Kevlar^® 29 fiber has excellent characteristics of non-conductivity, lightweight, high specific tensile strength, good chemical stability, and good weather resistance. Under the condition of the same weight, Kevlar fiber is 5 times as strong as steel wire, 2.5 times as strong as Grade E glass fiber and 10 times as strong as aluminum. Kevlar fiber also has better elongation than carbon fiber. The material properties of the Kevlar^® 29 fiber are shown in Table 2 (Fiber, 2011). The pneumatic airflow dispersion method is used to make the chopped Kevlar fiber evenly dispersed. The appearance of chopped Kevlar fibers before and after pneumatic dispersion are shown in Figure 1.

Table 2.

Material properties of Kevlar^® 29 fiber.

Material property	Value
Number of filaments per bundle	1000
Breaking tenacity (MPa)	2920
Tensile modulus (GPa)	70.5
Break elongation (%)	3.6
Density ( $g / c m^{3}$ )	1.44
Fiber diameter (μm)	12

Figure 1.

The appearance of chopped Kevlar fiber. (a) Before pneumatic dispersion and (b) After pneumatic dispersion.

Cement and aggregate

In this study, the Type I Portland cement was used, and it is produced by Taiwan Cement Corporation (Taipei, Taiwan). According to ASTM C33/C33M-18, the fineness modulus (F.M.) of fine aggregates is 3.15; and coarse aggregates is 6.35. The fineness modulus of aggregates is 5.16 and is shown in Table 3.

Table 3.

Fineness modulus of coarse aggregates.

Sieve	Sieve size (mm)	Weight retained (g)	Percent retained (%)	Cumulative percent retained (%)
3/2^″	37.5	0	0	0.0
3/4^″	19.0	0	0	0.0
3/8^″	9.5	604	22.1	22.1
No. 4	4.75	1112	40.6	62.7
No. 8	2.36	283	10.3	73.0
No. 16	1.18	216	7.9	80.9
No. 30	0.60	200	7.3	88.2
No. 50	0.30	128	4.7	92.9
No. 100	0.15	84	3.1	96.0
Pan		110	4	100.0
Total		2737	100

F.M. = 5.16.

Experimental plan and setup

In this study, Kevlar fiber was used and two kinds of specimens were made. The compression strength test and SHPB test were conducted to find the mechanical properties of the specimens. The specimen detailed naming of the specimens is shown in Table 4.

Table 4.

The naming and descriptions specimens.

	Naming	Description
Experimental methods	C	Compressive testing
Experimental methods	H	SHPB testing
Specimen type	C	Concrete
Fiber	B	Benchmark (without fiber)
	A	Aramid fiber
	0.5, 1.0, 1.5	Weight ratio (%)
	L6, L12, L24	Length (mm)
Gas pressure	P	Gas pressure (kgf/cm²)

For example, specimen H-C-A0.5L12-P1.4 represents the SHPB test of fiber-reinforced concrete with 12 mm chopped Kevlar fiber and a weight ratio of 0.5%, and the gas pressure is 1.4 kgf/cm². The planning of the Kevlar fiber-reinforced cementitious composite specimens was shown in Table 5.

Table 5.

Planning of Kevlar fiber-reinforced cementitious composite specimen quantity.

Experiment	Specimen type	Fiber weight proportion (%)	Specimen quantity of Kevlar fiber		Specimen quantity of benchmark
Experiment	Specimen type	Fiber weight proportion (%)	12 mm	24 mm	Specimen quantity of benchmark
Compressive testing	Concrete	0.5	5	5	5
		1	5	5
		1.5	5	5
SHPB testing	Concrete	0.5	20	20	20
		1	20	20
		1.5	20	20

Slump test

Generally, adding fiber will lead to a small slump of concrete; the Kevlar fiber-reinforced concrete (KFRC) after mixing uniformly was tamped into a 30 cm high slump cone in three layers and tamped 25 times at a time according to the ASTM C 143 concrete slump test method. Then, the top is scraped off with a scraper to make the upper edge flat. Pull up 30 cm high in 5 ± 2 seconds and wait for the concrete flow stops, the concrete slump is measured from the central collapse part, and the distance is the slump. The concrete flow is measured from the maximum diameter of the expanded circle and the diameter in the orthogonal direction of the maximum diameter, which is accurate to 1 mm and average.

Compressive test

The compressive strength testing was carried out in the material laboratory of the Department of Civil Engineering, National Taipei University of Technology. The experimental devices used include a universal testing machine (HT-9501 Series. Hong-Ta, Taipei, Taiwan) and data acquisition systems. A compressive strength test of concrete cylindrical specimens was done according to ASTM C39/C 39M-01 standards. The weight ratio of water to cement was fixed at 0.6; and the weight ratio of cement: fine aggregate: coarse aggregate was fixed at 1:1.05:2. The dimension of the cylindrical specimen is ϕ 10 cm × 20 cm.

Split Hopkinson pressure bar test

In SHPB testing, the force transmitted through the bar is usually modeled in the form of a stress wave, which is divided into the longitudinal wave and transverse wave according to the direction of action. A transverse wave is a wave in which the displacements of the medium are at right angles to the direction of propagation, while a longitudinal wave is a wave in which the displacement of the medium is in the same direction as, or the opposite direction to, the direction of propagation of the wave. However, in the case of the SHPB system, assuming that the stress wave is in the form of a longitudinal wave, the influence of the transverse wave is ignored. To satisfy the above conditions, the SHPB system must satisfy the following assumptions (Meyers, 1994):

(1) The density and thickness of the bar have homogeneous properties.

(2) The deformation of the bar obeys Hooke’s law.

(3) The deformation in the transverse direction of the rod is negligible, so each particle moves in the same direction.

The main components of the SHPB used in this test are the striker bar, incident bar, and transmitted bar, as shown in Figure 2(a). In the SHPB test, the incident wavelength is twice the length of the striker bar. Therefore, the length of the incident bar must be at least twice the length of the striker bar to ensure that there will be no reflected wave interference during the test. The striker bar is ejected by high-pressure gas with controlled pressure in the pressure storage chamber, and the velocity of the striker bar is obtained by measuring the shielding time between two points at a known distance. The data measured by the strain gauges on the incident bar and transmitted bar were recorded and transferred the recorded data to a personal computer for analysis. Then, the stress–time, strain–time, and strain rate–time relationships can be obtained (Nemat-Nasser et al., 1991, 1994).

Figure 2.

SHPB testing equipment. (a) Illustration figure of SHPB measurement system and (b) SHPB photo.

The compression waves measured at the incident bar and transmitted bar are expressed as incident wave and transmitted wave, respectively. The tensile waves measured at the incident bar is expressed as reflected wave (Sharma et al., 2011).

According to the principle of one-dimensional wave propagation theory, the SHPB test is used for dynamic mechanical test of materials; the stress, strain, and strain rate of materials can be obtained according to the following assumptions:

(1) The stress and velocity distributions are continuous not only at the interface between the incident bar and the sample but also at the interface between the sample and the transmitted bar.

(2) The radial inertia effects and barrelling effects were ignored.

(3) The stress and strain are uniformly distributed within the specimen along its long axis.

The average strain $ε_{a v g} (t)$ , average strain rate $\dot{ε} (t)$ , and average stress $σ_{a v g} (t)$ in the specimen can therefore be derived as (DoD, 2008; Chen et al., 2013)

ε_{a v g} (t) = - \frac{2 C_{0}}{L_{S}} \int_{0}^{t} (ε_{r}) d t

(1)

\dot{ε} (t) = - \frac{2 C_{0}}{L_{S}} (ε_{r})

(2)

σ_{a v g} (t) = \frac{A_{0} E}{A_{S}} (ε_{t})

(3)

where

C_{0}

is the propagation velocity of stress wave along the x-axis,

L_{S}

is the length of the specimen,

A_{0}

is the cross-sectional area of the incident and transmitted bars, and

A_{S}

is the cross-sectional area of the specimen.

The SHPB is a pneumatic impact testing machine. The SHPB test in this study was carried out in the materials laboratory of the Environmental Information and Engineering Department of Chung Cheng Institute of Technology, National Defense University. The schematic illustration of the SHPB test setup with signal measurement instruments is shown in Figure 2(b). Its structure can be divided into six parts: high-pressure gas gun, air intake control unit, control unit, launch striker bar barrel, buffer bar and damper, and transparent cover.

Besides, two strain rates were used in this study including the “strain rate at failure” and “maximum strain rate.” The “strain rate at failure” was defined as the specimen reaches to the maximum stress (compressive strength) and defined as failure. The “maximum strain rate” was calculated from the SHPB testing data, and it is related to the gas pressure. This study used the “maximum strain rate” data to check whether the gas pressure is proper or not.

Results and discussions

Slump test result

This is the concrete mix proportion of this research: The weight ratio of water to cement was fixed at 0.6, and the weight ratio of cement to fine aggregate to coarse aggregate was fixed at 1:1.05:2. And add the weight ratio of 0.5%, 1.0%, and 1.5% Kevlar fiber, respectively. Table 6 shows the slump and flow test results of Kevlar fiber-reinforced concrete.

Table 6.

Kevlar fiber reinforced concrete Slump flow.

Fiber weight ratio (%)	Flow (cm)	Slump (cm)
0	41	24.2
0.5	15.5	10.2
1.0	13.3	3.9
1.5	11.8	1.8

Compressive test result

Table 7 shows the compressive strength of the benchmark and KFRC with the chopped Kevlar fiber of different lengths and different weight ratios. In terms of fiber length, the compressive strength of KFRC with 24 mm Kevlar fiber is slightly better than KFRC with 12 mm Kevlar fiber. In terms of fiber weight ratio, the compressive strength of KFRC with a fiber weight ratio of 0.5% is the best. However, the compressive strength of KFRC with a fiber weight ratio of 1.0% and 1.5% is similar. Figure 3 shows the bar chart of compressive strength for KFRC and benchmark specimens.

Table 7.

Compressive strengths of KFRC and benchmark.

Ratio/Fiber length	Benchmark	0.5%	1.0%	1.5%
12 mm (Increase%)	23.30	28.64 (22.94)	36.64 (14.34)	26.60 (14.16)
24 mm (Increase%)	23.30	28.85 (23.85)	26.89 (15.42)	26.67 (14.46)

(Unit: MPa).

Figure 3.

Bar chart of compressive strength for KFRC and benchmark.

Split Hopkinson pressure bar test result

The strain wave curves recorded by the strain gauges of the incident and transmitted bar are shown in Figure 4(a). After time translation, they are divided into the incident, reflected, and transmitted stress waves, as shown in Figure 4(b). Then the strain, stress, and strain rate of the specimen are calculated by Equations (1) to (3). The measured data are all input into the computer to calculate the corresponding stress–strain relationship. In addition, it can be judged whether the SHPB test conforms to the one-dimensional wave propagation theory, as shown in Figure 5.

Figure 4.

(a) The strain–time relationships of incident and transmitted bars and (b) The strain–time relationships of incident, reflected, and transmitted waves.

Figure 5.

The strain–time relationships of incident and transmitted-reflected waves.

Figure 6 shows the stress–strain curves of all specimens of H-C-A1.0L24 under the gas pressure 1.0 kgf/cm² and 1.4 kgf/cm², respectively. The SHPB test results are quite stable. Figure 7 shows the stress–strain curves of all types of specimens under quasi-static compression conditions and five gas pressures (dynamic compression conditions). The five gas pressures are 0.6, 0.8, 1.0, 1.2, and 1.4 kgf/cm². It can be found that stress increases with the increase of gas pressure. Table 8 shows the measured strain rate range of all types of specimens at designed gas pressures.

Figure 6.

(a) 1.0 kgf/cm² gas pressure and (b) 1.4 kgf/cm² gas pressure. The stress–strain curves of H-C-A1.5L12 specimens.

Figure 7.

(a) The stress–strain curves of benchmark under designed gas pressures, (b) The stress–strain curves of H-C-A0.5L12 specimens under designed gas pressures, (c) The stress–strain curves of H-C-A1.0L12 specimens under designed gas pressures, (d) The stress–strain curves of H-C-A1.5L12 specimens under designed gas pressures, (e) The stress–strain curves of H-C-A0.5L24 specimens under designed gas pressures, (f) The stress–strain curves of H-C-A1.0L24 specimens under designed gas pressures, and (g) The stress–strain curves of H-C-A1.5L24 specimens under designed gas pressures. The stress–strain curves of all specimens.

Table 8.

The strain rate range of the specimen at designed gas pressures.

Gas pressure (kgf/cm²)	Maximum strain rate range (s^-1)
0.6	221.86 ∼ 267.88
0.8	247.79 ∼ 357.62
1.0	276.51 ∼ 434.44
1.2	361.55 ∼ 439.83
1.4	375.25 ∼ 542.10

Tables 9 and 10 show the compressive stresses of the benchmark specimen and KFRC specimens with 12 mm and 24 mm lengths Kevlar fiber and different weight ratios under the designed gas pressure loadings. The results show that the KFRC specimens with a 0.5% fiber weight ratio have the highest compressive stresses. Figure 8 explained the compressive strength of KFRC is highly dependent on the Kevlar fiber content, and the higher Kevlar fiber weight ratios of KFRC might have more pores than less Kevlar fiber weight ratios of KFRC. Figure 8(a) exhibits optimal fiber content without pores in KFRC, and Figure 8(b) exhibits the high fiber content with some pores in KFRC. In this study, KFRC with a 0.5% weight ratio is the optimal fiber content and it has the highest compressive strength compared with other fiber weight ratios.

Table 9.

The compressive stresses of the benchmark specimen and KFRC specimens with the 12 mm Kevlar fiber under designed gas pressure loadings.

Gas pressure (kgf/cm²)	Specimens	Fiber weight ratio (%)	Strain rate at failure (s^-1)	Maximum strain rate (s^-1)	Stress (MPa) (Increase%)
0.6	H-C-B	0	212.32	233.15	102.43
	H-C-A0.5L12	0.5	197.18	231.45	122.76 (19.84)
	H-C-A1.0L12	1.0	185.66	222.70	110.14 (7.52)
	H-C-A1.5L12	1.5	226.05	240.85	86.46 (-15.60)
0.8	H-C-B	0	231.57	278.12	111.14
	H-C-A0.5L12	0.5	185.91	356.37	132.61 (19.32)
	H-C-A1.0L12	1.0	308.87	357.62	111.48 (0.30)
	H-C-A1.5L12	1.5	232.81	301.83	102.72 (-7.58)
1.0	H-C-B	0	245.90	276.51	109.95
	H-C-A0.5L12	0.5	207.88	434.44	164.04 (49.20)
	H-C-A1.0L12	1.0	186.51	317.28	135.20 (22.96)
	H-C-A1.5L12	1.5	162.31	344.61	100.36 (-8.72)
1.2	H-C-B	0	311.85	420.05	118.53
	H-C-A0.5L12	0.5	234.99	439.83	153.63 (29.61)
	H-C-A1.0L12	1.0	193.53	382.43	128.50 (8.42)
	H-C-A1.5L12	1.5	249.03	423.78	93.52 (-21.10)
1.4	H-C-B	0	320.83	424.24	124.15
	H-C-A0.5L12	0.5	206.76	472.62	155.38 (25.16)
	H-C-A1.0L12	1.0	251.93	407.10	147.29 (18.64)
	H-C-A1.5L12	1.5	285.88	542.10	108.85 (-12.32)

Table 10.

The compressive stresses of the benchmark specimen and KFRC specimens with the 24 mm Kevlar fiber under designed gas pressure loadings.

Gas pressure (kgf/cm²)	Name	Fiber weight ratio (%)	Strain rate at failure (s^-1)	Maximum strain rate (s^-1)	Stress (MPa) (Increase %)
0.6	H-C-B	0	212.32	233.15	102.43
	H-C-A0.5L24	0.5	143.06	221.86	114.31 (11.60)
	H-C-A1.0L24	1.0	173.78	223.83	107.40 (4.85)
	H-C-A1.5L24	1.5	160.10	267.88	91.57 (-10.60)
0.8	H-C-B	0	231.57	278.12	111.14
	H-C-A0.5L24	0.5	160.19	278.11	121.66 (9.46)
	H-C-A1.0L24	1.0	179.16	247.79	117.34 (5.57)
	H-C-A1.5L24	1.5	208.63	335.54	96.44 (-13.22)
1.0	H-C-B	0	245.90	276.51	109.95
	H-C-A0.5L24	0.5	170.28	335.54	130.79 (18.96)
	H-C-A1.0L24	1.0	232.66	310.77	118.55 (7.82)
	H-C-A1.5L24	1.5	232.37	368.45	119.16 (8.38)
1.2	H-C-B	0	311.85	420.05	118.53
	H-C-A0.5L24	0.5	131.02	361.55	154.91 (30.69)
	H-C-A1.0L24	1.0	272.91	382.25	126.47 (6.70)
	H-C-A1.5L24	1.5	258.26	433.68	130.07 (9.74)
1.4	H-C-B	0	320.83	424.24	124.15
	H-C-A0.5L24	0.5	279.10	420.48	162.81 (31.14)
	H-C-A1.0L24	1.0	244.82	460.60	162.75 (31.09)
	H-C-A1.5L24	1.5	276.13	375.25	140.17 (12.90)

Figure 8.

(a) Optimal fiber content and (b) High fiber content. Illustration figures of the optimal and high fiber contents in KFRC.

The energy accumulated in a specimen owing to deformation is defined as strain energy which can be obtained by integrating the area of the stress–strain curve and multiplying the volume of the specimen. Table 11 shows the strain energy of the benchmark specimen and KFRC specimens under quasi-static and dynamic loadings. Figure 9 shows the bar chart of the strain energy; the strain energies of KFRC specimens with the 24 mm Kevlar fiber are higher than the energies of the KFRC specimens with the 12 mm Kevlar fiber.

Table 11.

The strain energy of the benchmark specimen and KFRC specimens.

Loading method/Specimen	Quasi-static loading	Dynamic loading
Loading method/Specimen	Quasi-static loading	P0.6	P0.8	P1.0	P1.2	P1.4
C-B	14.43	76.83	104.45	132.10	168.00	184.01
C-A0.5L12	13.89	83.58	122.29	121.61	148.18	151.57
C-A1.0L12	12.70	68.45	165.65	130.52	101.34	167.51
C-A1.5L12	11.18	93.18	106.33	95.77	130.15	183.23
C-A0.5L24	13.55	88.72	78.20	91.15	71.47	226.29
C-A1.0L24	11.39	70.64	122.34	157.20	173.55	219.68
C-A1.5L24	9.64	69.30	122.61	120.66	177.04	199.59

(Unit: N·m).

Figure 9.

Bar chart of the strain energy for KFRC and benchmark.

With the increase of gas pressure, the strain rate increases, and the destruction degree of failure increases. The failure photos of each specimen were shown in Figures 10, 11, 12, and 13. It can be found that the appearance of KFRC specimens is relatively intact at lower gas pressure. At higher gas pressure, the appearance of benchmark specimens and KFRC specimens is almost broken. The dynamic failure photos of KFRC with 24 mm Kevlar fiber are similar to KFRC with 12 mm Kevlar fiber under the same dynamic compression condition, as shown in Figure 14.

Figure 10.

(a) 0.6 kgf/cm² gas pressure, (b) 0.8 kgf/cm² gas pressure, (c) 1.0 kgf/cm² gas pressure, (d) 1.2 kgf/cm² gas pressure, and (e) 1.4 kgf/cm² gas pressure. The dynamic failure photos of benchmark under different gas pressure loadings.

Figure 11.

Figure 12.

Figure 13.

Figure 14.

(a) H-C-A1.0L24-P0.6, (b) H-C-A1.0L24-P1.4, (c) H-C-A1.0L12-P0.6, and (d) H-C-A1.0L12-P1.4. Comparing the dynamic failure photos of H-C-A1.0L24 and H-C-A1.0L12.

The failure process of H-C-B-P0.6 and H-C-A1.0L24-P0.6 was shown in Figures 15 and 16. It can be seen that the cracks of KFRC were less than the benchmark specimen under the dynamic compression conditions of 0.6 kgf/cm² gas pressure. The failure evolutions of H-C-B-P1.4 and H-C-A1.0L24-P1.4 were shown in Figures 17 and 18.

Figure 15.

(a) 228 µs and (b) 1021 µs. The failure evolutions of specimen H-C-B-P0.6 at 20,000 FPS.

Figure 16.

(a) 246 µs and (b) 1034 µs. The failure evolutions of specimen H-C-A1.0L24-P0.6 at 20,000 FPS.

Figure 17.

(a) 328 µs and (b) 824 µs. The failure evolutions of specimen H-C-B-P 1.4 at 20,000 FPS.

Figure 18.

(a) 274 µs and (b) 872 µs. The failure evolutions of specimen H-C-A1.0L24-P1.4 at 20,000 FPS.

Figure 19 is the optical microscopic photo of H-C-A1.5L24-P0.6 specimens after SHPB testing. It can be seen that there are micro-cracks on the specimen. It means chopped Kevlar fiber can generate a bridging effect to reduce cracks growth. However, Figure 20 is the optical microscopic photo of H-C-A1.5L24-P1.4 specimens after SHPB testing, and the specimen was broken. It can be seen that chopped Kevlar fiber mostly occurs to slippage failure, and can no longer resist more loading.

Figure 19.

Optical Microscope photo of H-C-A1.5L24-P0.6 after SHPB testing.

Figure 20.

Optical Microscope photo of H-C-A1.5L24-P0.6 after SHPB testing.

In the SHPB test, the peak value of compressive stress is dynamic compressive strength, and the ratio of dynamic compressive strength to quasi-static compressive strength is defined as the dynamic increase factor ( $D I F_{f^{'} c}$ ), and shown in Equation (4)

D I F_{f^{'} c} = f_{i m p a c t}^{'} / f_{c}^{'}

(4)

where

f_{i m p a c t}^{'}

is dynamic compressive strength and

f_{c}^{'}

quasi-static compressive strength.

In this study, $D I F_{f^{'} c}$ is divided into two types according to the quasi-static compressive strength. $D I F_{1}$ was calculated from quasi-static and dynamic compressive strength of the specimens, both the concrete proportions are the same; and $D I F_{2}$ was calculated from the quasi-static benchmark specimen and the dynamic compressive strength of the KFRC specimen, the equations are shown in equations (5) and (6)

D I F_{1} = f_{i m p a c t}^{'} / f_{c}^{'}

(5)

D I F_{2} = f_{i m p a c t}^{'} / f_{c B}^{'}

(6)

where

f_{c B}^{'}

is the quasi-static compressive strength of the benchmark specimen.

The dynamic increase factor for benchmark concrete specimens and KFRC specimens are shown in Tables 12 –18. Figure 21 shows the comparison of

D I F_{1}

and

D I F_{2}

with the test data obtained from UFC (UFC 3-340-02, 2008). Figure 22 shows the comparison of

D I F_{1}

and

D I F_{2}

with the test data obtained from CEB (Committee Euro-International Du Beton, 2013).

Table 12.

The dynamic increase factor for benchmark concrete specimen.

Specimen	Type of compressive strength	Strain rate at failure (s^-1)	Compressive strength (MPa)	$D I F_{1}$
C-C-B	$f_{c}^{'}$	0.0001	23.30	1
H-C-B-P0.6	$f_{i m p a c t}^{'}$	212.32	102.43	4.40
H-C-B-P0.8	$f_{i m p a c t}^{'}$	231.57	111.14	4.77
H-C-B-P1.0	$f_{i m p a c t}^{'}$	245.90	109.95	4.72
H-C-B-P1.2	$f_{i m p a c t}^{'}$	311.85	118.53	5.09
H-C-B-P1.4	$f_{i m p a c t}^{'}$	320.83	124.15	5.33

Table 13.

The dynamic increase factor for fiber-reinforced concrete with 12 mm Kevlar fiber and a weight ratio of 0.5%.

Specimen	Type of compressive strength	Strain rate at failure (s^-1)	Compressive strength (MPa)	$D I F_{1}$	$D I F_{2}$
C-C-B	$f_{c B}^{'}$	0.0001	23.30		1
C-C-A0.5L12	$f_{c}^{'}$	0.0001	28.64	1
H-C-A0.5L12 -P0.6	$f_{i m p a c t}^{'}$	197.18	122.76	4.29	5.27
H-C-A0.5L12 -P0.8	$f_{i m p a c t}^{'}$	185.91	132.61	4.63	5.69
H-C-A0.5L12 -P1.0	$f_{i m p a c t}^{'}$	207.88	138.55	4.84	5.95
H-C-A0.5L12 -P1.2	$f_{i m p a c t}^{'}$	234.99	153.63	5.36	6.59
H-C-A0.5L12 -P1.4	$f_{i m p a c t}^{'}$	206.76	155.38	5.42	6.67

Table 14.

The dynamic increase factor for fiber-reinforced concrete with 12 mm Kevlar fiber and a weight ratio of 1.0%.

Specimen	Type of compressive strength	Strain rate at failure (s^-1)	Compressive strength (MPa)	$D I F_{1}$	$D I F_{2}$
C-C-B	$f_{c B}^{'}$	0.0001	23.30		1
C-C-A1.0L12	$f_{c}^{'}$	0.0001	26.64	1
H-C-A1.0L12 -P0.6	$f_{i m p a c t}^{'}$	185.66	110.14	4.13	4.73
H-C-A1.0L12 -P0.8	$f_{i m p a c t}^{'}$	308.87	111.48	4.18	4.78
H-C-A1.0L12 -P1.0	$f_{i m p a c t}^{'}$	186.51	135.20	5.07	5.80
H-C-A1.0L12 -P1.2	$f_{i m p a c t}^{'}$	193.53	128.50	4.82	5.52
H-C-A1.0L12 -P1.4	$f_{i m p a c t}^{'}$	251.93	147.29	5.53	6.32

Table 15.

The dynamic increase factor for fiber-reinforced concrete with 12 mm Kevlar fiber and a weight ratio of 1.5%.

Specimen	Type of compressive strength	Strain rate at failure (s^-1)	Compressive strength (MPa)	$D I F_{1}$	$D I F_{2}$
C-C-B	$f_{c B}^{'}$	0.0001	23.30		1
C-C-A1.5L12B	$f_{c}^{'}$	0.0001	26.60	1
H-C-A1.5L12 -P0.6	$f_{i m p a c t}^{'}$	226.05	86.46	3.25	3.71
H-C-A1.5L12 -P0.8	$f_{i m p a c t}^{'}$	232.81	102.72	3.86	4.41
H-C-A1.5L12 -P1.0	$f_{i m p a c t}^{'}$	162.31	100.36	3.77	4.31
H-C-A1.5L12 -P1.2	$f_{i m p a c t}^{'}$	249.03	93.52	3.52	4.01
H-C-A1.5L12 -P1.4	$f_{i m p a c t}^{'}$	285.88	108.85	4.09	4.67

Table 16.

The dynamic increase factor for fiber-reinforced concrete with 24 mm Kevlar fiber and a weight ratio of 0.5%.

Specimen	Type of compressive strength	Strain rate at failure (s^-1)	Compressive strength (MPa)	$D I F_{1}$	$D I F_{2}$
C-C-B	$f_{c B}^{'}$	0.0001	23.30		1
C-C-A0.5L24	$f_{c}^{'}$	0.0001	28.85	1
H-C-A0.5L24 -P0.6	$f_{i m p a c t}^{'}$	143.06	114.31	3.96	4.91
H-C-A0.5L24 -P0.8	$f_{i m p a c t}^{'}$	160.19	121.66	4.22	5.22
H-C-A0.5L24 -P1.0	$f_{i m p a c t}^{'}$	170.28	130.79	4.53	5.61
H-C-A0.5L24 -P1.2	$f_{i m p a c t}^{'}$	131.02	154.91	5.37	6.65
H-C-A0.5L24 -P1.4	$f_{i m p a c t}^{'}$	279.10	162.81	5.64	6.99

Table 17.

The dynamic increase factor for fiber-reinforced concrete with 24 mm Kevlar fiber and a weight ratio of 1.0%.

Specimen	Type of compressive strength	Strain rate at failure (s^-1)	Compressive strength (MPa)	$D I F_{1}$	$D I F_{2}$
C-C-B	$f_{c B}^{'}$	0.0001	23.30		1
C-C-A1.0L24	$f_{c}^{'}$	0.0001	26.89	1
H-C-A1.0L24 -P0.6	$f_{i m p a c t}^{'}$	173.78	107.40	3.99	4.61
H-C-A1.0L24 -P0.8	$f_{i m p a c t}^{'}$	179.16	117.34	4.36	5.04
H-C-A1.0L24 -P1.0	$f_{i m p a c t}^{'}$	232.66	118.55	4.41	5.09
H-C-A1.0L24 -P1.2	$f_{i m p a c t}^{'}$	272.91	126.47	4.70	5.43
H-C-A1.0L24 -P1.4	$f_{i m p a c t}^{'}$	244.82	162.75	6.05	6.99

Table 18.

Dynamic increase factor for fiber-reinforced concrete with 24 mm chopped Kevlar fiber and a weight ratio of 1.5%.

Specimen	Type of compressive strength	Strain rate at failure (s^-1)	Compressive strength (MPa)	$D I F_{1}$	$D I F_{2}$
C-C-B	$f_{c B}^{'}$	0.0001	23.30		1
C-C-A1.5L24	$f_{c}^{'}$	0.0001	26.67	1
H-C-A1.5L24 -P0.6	$f_{i m p a c t}^{'}$	160.10	91.57	3.43	3.93
H-C-A1.5L24 -P0.8	$f_{i m p a c t}^{'}$	208.63	96.44	3.62	4.14
H-C-A1.5L24 -P1.0	$f_{i m p a c t}^{'}$	232.37	119.16	4.47	5.11
H-C-A1.5L24 -P1.2	$f_{i m p a c t}^{'}$	258.26	130.07	4.88	5.58
H-C-A1.5L24 -P1.4	$f_{i m p a c t}^{'}$	276.13	140.17	5.26	6.02

Figure 21.

(a) Comparison of $D I F_{1}$ and (b) Comparison of $D I F_{2}$ . Comparison of $D I F_{1}$ and $D I F_{2}$ in this study and UFC (Concrete f ^′c = 6000 psi).

Figure 22.

(a) Comparison of $D I F_{1}$ and (b) Comparison of $D I F_{2}$ . Comparison of $D I F_{1}$ and $D I F_{2}$ in this study and CEB.

Concrete is a brittle material. However, by adding fiber to the concrete, the mechanical properties of fiber-reinforced concrete are improved, especially under a high strain rate. As seen from the SHPB test results of the C-A05L12 KFRC specimen shown in Table 9, Table 10, and Figure 7, the higher the strain-rate loading (high gas pressure), the higher the compressive strength and DIF value. Besides, the strain energy of the KFRC specimen was also increased since the compressive strength and strain were increased under the higher strain-rate loading based on Table 11. According to past research, the improvement rate of impact resistance of fiber reinforced concrete is much higher than the improvement rate of compressive and flexural strength (Wang et al., 2012; Xu et al., 2012b; Yoo and Banthia, 2017b). Along with the above reasons, the DIF of KFRC is higher than that of normal concrete.

Conclusion

According to the experimental results of this study, the following conclusions can be drawn as follows:

1. After adding Kevlar fiber into concrete, the slump and flow decrease with the increase of fiber weight ratio.

2. The KFRC specimens increase compressive strength by 14–24% more than the benchmark specimen (C-C-B). The compressive strength of C-C-A0.5L24 specimens is the highest. In terms of fiber length, the compressive strength of KFRC with 24 mm Kevlar fiber is better than 12 mm Kevlar fiber.

3. Under dynamic loading, the dynamic strength decreases with the increase of chopped Kevlar fiber weight ratio for most of the cases.

4. In the quasi-static and dynamic compressive strengths of the specimen, there is no significant difference between KFRC specimens with the 12 mm Kevlar fiber and KFRC specimens with the 24 mm Kevlar fiber. However, it can be seen that the strain energies of the KFRC specimen with 24 mm Kevlar fiber are higher than the energies of the KFRC specimens with the 12 mm Kevlar fiber.

5. The comparative analysis results of the experimental data of this research and the $D I F_{f^{'} c}$ curves of UFC and CEB show that the $D I F_{f^{'} c}$ of KFRC are all on the curve, which shows that the KFRC strain rate sensitivity of $D I F_{f^{'} c}$ is higher than that of the materials used in UFC and CEB.

6. The results show that the appearance of KFRC specimens is more complete than that of benchmark specimens under 0.6 kgf/cm² and 0.8 kgf/cm² gas pressure loading. It means that the Kevlar fiber filaments are evenly distributed in the specimen and can take tensile force to reduce the failure of the specimen at the dynamic loading which the strain rate at failure is 143 s^-1 to 320 s^-1.

7. It is recommended to install strain gauges on the specimen so that mechanical analysis can be carried out from more directions.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was funded by the Ministry of Science and Technology of Taiwan government, under contract No. MOST 110-2221-E-027-031, and the “Research Center of Energy Conservation for New Generation of Residential, Commercial, and Industrial Sectors” from The Featured Areas Research Center Program within the framework of the Higher Education Sprout Project by the Ministry of Education (MOE) in Taiwan under contract No. L7101101-19.

ORCID iDs

Yeou-Fong Li

Ying-Kuan Tsai

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