Effect of fiber geometric property on rate dependent flexural behavior of ultra-high-performance cementitious composite

Cement and Concrete Composites 86 (2018) 57e71

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Cement and Concrete Composites journal homepage: www.elsevier.com/locate/cemconcomp

Effect of fiber geometric property on rate dependent flexural behavior of ultra-high-performance cementitious composite Doo-Yeol Yoo a, Nemkumar Banthia b, Jin-Young Lee c, Young-Soo Yoon c, * a

Department of Architectural Engineering, Hanyang University, 222 Wangsimni-ro, Seongdong-gu, Seoul 04763, Republic of Korea Department of Civil Engineering, The University of British Columbia, 6250 Applied Science Lane, Vancouver, BC V6T 1Z4, Canada c School of Civil, Environmental and Architectural Engineering, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul 02841, Republic of Korea b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 23 February 2017 Received in revised form 24 July 2017 Accepted 1 November 2017 Available online 6 November 2017

In order to examine the rate dependent flexural performance of ultra-high-performance cementitious composite (UHPCC), a number of UHPCC beams containing three straight steel fibers with different aspect ratios of 65, 97.5, and 100 and one twisted steel fiber with an aspect ratio of 100 were fabricated and tested under quasi-static and impact loadings. Test results indicated that the use of long straight and twisted steel fibers resulted in improved quasi-static flexural performance, and their effectiveness was higher at large deflections. The twisted steel fiber was most effective at improving the deflection capacity and the number of micro-cracks under quasi-static flexural loading. In contrast, long straight steel fibers were more favorable than twisted steel fibers in terms of impact resistance and residual performance after impact damage. A lower sensitivity of the strain rate to the dynamic increase factor (DIF) was obtained for the post-cracking flexural strength than for the first-cracking strength, and the use of twisted steel fibers led to lower sensitivity to the strain rate on the DIF of post-cracking strength than that of straight ones. Finally, the higher strength concrete was less sensitive to the strain rate than the lower strength concrete. © 2017 Elsevier Ltd. All rights reserved.

Keywords: Ultra-high-performance concrete Flexural performance Image analysis Strain rate Dynamic increase factor

1. Introduction Interest in improving the resistance of civil infrastructures subjected to extreme loadings, such as earthquakes, impacts, and blasts, has increased because of an increase in terror threats worldwide. However, concerns have been raised about ordinary concrete over its ability to sufficiently resist such extreme loadings because of its inherent poor energy absorption capacity under high rate loading. Various methods have been developed to enhance its poor energy absorption capacity from the material perspective, i.e., the addition of discontinuous steel and polymeric fibers, strengthening using fiber-reinforced polymers, the inclusion of polymer coated textile reinforcements, etc. [1e3]. In particular, ultra-high-performance cementitious composite (UHPCC) with micro steel fibers, which was developed in the mid-1990s [4], exhibits extremely high mechanical strength (i.e., a compressive strength in excess of 150 MPa and a design tensile strength of

* Corresponding author. E-mail addresses: [email protected] (D.-Y. Yoo), [email protected] (N. Banthia), [email protected] (J.-Y. Lee), [email protected] (Y.-S. Yoon). https://doi.org/10.1016/j.cemconcomp.2017.11.002 0958-9465/© 2017 Elsevier Ltd. All rights reserved.

8 MPa) and energy absorption capacity (fracture energy observed up to 40 kJ/m2). Therefore, this material can be considered as a solution for ordinary concrete exhibiting poor energy absorption capacity under high rate loading, and thus, it has attracted much attention from researchers and engineers for enhancing the impact and blast resistances of concrete structures. Concrete shows different behaviors according to the strain rate; in general, a higher strength is obtained with an increase in the strain rate, which is considered in structural design in terms of the dynamic increase factor (DIF). The sensitivity to strain rate is also influenced by stress state; a minimum sensitivity to strain rate is obtained under compression, whereas a maximum sensitivity to strain rate is obtained under tension, and an intermediate value is obtained for flexure [5], which is attributed to the different failure mechanisms under compression, tension, and flexure. However, the studies on the response of concrete, especially UHPCC, at high rate loadings are in infancy in comparison with the studies on concrete under static loadings, despite the advantages, and thus, much work still remains. Most previous studies have focused on the compressive or tensile response of UHPCC at high loading rates using split-

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D.-Y. Yoo et al. / Cement and Concrete Composites 86 (2018) 57e71

Hopkinson pressure bar (SHPB) and strain energy frame impact machine (SEFIM) [6e9]. Rong et al. [6] estimated the dynamic compressive behavior of UHPCC with various steel fiber contents and noted that the impact resistance was enhanced by using more fibers and that the compressive strength, strain capacity, and ultimate strain increased with increasing strain rate. Pyo and El-Tawil [7] captured the strain-hardening behavior of UHPCC with steel fibers at high strain rates ranging from 90 to 145/s using a 1.55-mlong brass transmitter bar, and they indicated that the highly enhanced tensile strength and strain capacity of the UHPCC was obtained under increasing strain rates. Wille et al. [8] indicated that twisted steel fibers provided a lower tensile strength at high rate loadings than straight steel fibers, owing to their limiting strain rate sensitivity. The strain rates applied in their study [8] were ranged from 0.0001 to 0.1/s. Since the highest rate, i.e., 0.1/s, generally represents a seismic loading [10,11], the strain rate used was proper for seismic performance but insufficient to evaluate the impact resistance. Tran et al. [9] also performed tensile impact tests of UHPCC containing various steel fibers using the SEFIM. In their study [9], the higher strain rates from 5 to 24/s were applied and reported that twisted steel fibers exhibited the best tensile performance under quasi-static rates, but poorer impact resistance was obtained with twisted steel fibers than straight steel fibers because of their breakage at high rates unlike straight fibers. However, to the best of authors' knowledge, there is no published study yet on examining the effect of steel fiber type on the impact resistance of UHPCC under flexure at a strain rate higher than 100/s. The relationship between DIF and strain rate, which is the most important information for impact resistance, varies according to the stress state (i.e., compression, tension, and flexure) [5], so that the implication of steel fiber type on impact resistance of UHPCC under flexure needs to be examined. In the same vein, the flexural test has been adopted by numerous researchers to indirectly evaluate the tensile behavior of concrete and to investigate the effect of fibers on the post-cracking behavior and energy absorption capacity, owing to its several advantages (i.e., easy to carry out and useful to obviously compare the post-cracking behavior according to fiber type and dosage). However, only very limited studies [12] have been performed to examine the flexural response of UHPCC including only a single type of straight steel fibers at high rate loadings compared with its dynamic compressive or tensile behavior. The dynamic response is influenced by the stress state [5], and as a result, there remains a pressing need to examine the flexural response of UHPCC at high rate loadings. Accordingly, the aim of this study is to investigate the rate dependent flexural response of UHPCCs with various steel fibers. In order to evaluate the implication of the steel fiber type on the postcracking response, three types of straight steel fibers with different aspect ratios of 65, 97.5, and 100 and one type of twisted steel fiber with an aspect ratio of 100 were considered. The specific objectives are: (1) to evaluate the effects of fiber type and aspect ratio on the flexural performance at both quasi-static and impact loadings considering the fiber distribution characteristics, (2) to discover the deflection-hardening response at high rate loadings, (3) to evaluate the effect of potential energy on the flexural performance, and (4) to evaluate the strain rate sensitivity of flexural strength. Additionally, a simple method to predict the residual capacity after impact damage was introduced. 2. Experimental program 2.1. Materials, mixture proportions, and specimen preparation

summarized in Table 1. Type 1 Portland cement and ultra-fine silica fume were included as cementitious materials. The detailed chemical compositions and physical properties of the cementitious materials are given in Table 2. As fine aggregate, silica sand with a maximum grain size smaller than 0.5 mm was used, while a filler with a diameter of 2 mm, including 98% SiO2, was included in the mixture. The silica sand and filler were not reacted with water but filling the pores. In accordance with previous studies [13,14], the compressive strength of UHPCC was insignificantly affected by the use of coarse aggregate, whereas the tensile and flexural performance of UHPCC deteriorated noticeably. This is because, according to Collepardi et al. [13], the existence of coarse aggregate led to restraint of a great portion of cement matrix shrinkage and it caused reduced the bond strength of fibers and homogeneity. Consequently, the tensile and flexural strengths was much smaller for the case of including coarse aggregate than that without coarse aggregate. Therefore, even though using coarse aggregate has some beneficial effects on UHPCC, such as reducing the production cost and autogenous shrinkage, coarse aggregate was excluded from the mixture in this study to provide better flexural performance under both quasi-static and impact loadings, similar to a conventional UHPCC [4]. In order to obtain adequate fluidity and viscosity, a high-range water-reducing admixture, polycarboxylate superplasticizer (SP) with a density of 1.01 g/cm3 and 30% solid content, was added as 2% of the cement mass. A water-to-bidder (W/B) ratio of 0.2 was used in this study, and it was calculated by dividing a total water content by a total amount of cementitious materials, as summarized in Table 1. To investigate the effects of the fiber geometrical properties, i.e., aspect ratio and shape, on the flexural performance under quasistatic and impact loadings, three types of straight steel fibers with different aspect ratios of 65, 97.5, and 100 and one type of twisted steel fiber with an aspect ratio of 100 were considered. The twisted fibers had a triangular section and three ribs within the fiber length. Since several design recommendations [15,16] suggested tension-softening models based on UHPCC mixtures with 2% by volume (2 vol%) of straight steel fibers, most previous studies [17,18] have conducted the structural tests using UHPCC containing 2 vol% of steel fibers. Accordingly, the four types of steel fibers were all included at 2 vol% for consistency. In addition, based on preliminary mixing results [19], a UHPCC mixture containing 2 vol% of steel fibers with an aspect ratio higher than 100 showed some formation of fiber balls, which caused poor fiber dispersion. Therefore, a maximum aspect ratio of 100 was adopted in this study for both straight and twisted steel fibers. The detailed geometric and physical properties of the steel fibers used are given in Table 3. The specimens are divided into three series; (1) the specimens without fiber (NF), (2) specimens with straight steel fibers (SX), and (3) specimens with twisted steel fibers (TX). The letters NF, S, T, and X indicate no fiber, straight steel fiber, twisted steel fiber, and fiber aspect ratio, respectively. For example, S65 denotes UHPCC containing straight steel fibers with an aspect ratio of 65. The detailed mixing sequence of UHPCC is given in a previous paper [19]. In accordance with the flow table tests in ASTM C 1437 [20], average flow values from 240 to 250 mm were obtained for all

Table 1 Mix proportion. W/B

0.2 a

The mixture proportions used in the present study are

Unit weight (kg/m3) Water

Cement

Silica fume

Silica sand

Filler

Superplasticizera

160.3

788.5

197.1

867.4

236.6

52.6

Superplasticizer includes 30% solid (¼ 15.8 kg/m3) and 70% water (¼ 36.8 kg/ m3).

D.-Y. Yoo et al. / Cement and Concrete Composites 86 (2018) 57e71 Table 2 Chemical compositions and physical properties of cementitious materials. Composition % (mass)

Cement

Silica fume

CaO Al2O3 SiO2 Fe2O3 MgO SO3 Specific surface area (cm2/g) Density (g/cm3)

61.33 6.40 21.01 3.12 3.02 2.30 3,413 3.15

0.38 0.25 96.00 0.12 0.10 e 200,000 2.10

test specimens, and no segregation of steel fibers from the matrix was observed. In accordance with the findings from a previous study [21], the flexural behavior of UHPCC is significantly affected by the casing method because the fiber orientation, which varies by the casting method, strongly influences the fiber bridging curve, a dominant factor that affects the post-cracking flexural behavior of UHPCC. The impact of fiber orientation on the fiber bridging curve and flexural response of UHPCC was verified by Yoo et al. [21]. For this reason, all test beams in the current study were identically fabricated by placing concrete at one end of the mold and allowing it to flow. In order to prevent surface cracking caused by the high evaporation rate of water, the specimens were covered with plastic sheets immediately after casting and cured at room temperature for the first two days. Then, the specimens were demolded and heat cured at 90  C with steam for three days. After heat curing, all the specimens were stored at a room temperature until testing day. 2.2. Experimental setup and procedure 2.2.1. Compressive test (ASTM C 39) Fifteen cylinders (4 100 mm  200 mm) were fabricated using UHPCC and tested as per ASTM C 39 [22] to estimate the effects of the fiber aspect ratio and type on their compressive behavior. In order to ensure a parallel loading face, all cylindrical specimens were ground by a diamond blade before testing. A uniaxial load was applied by a universal testing machine (UTM) with a maximum capacity of 3000 kN at a rate of 0.1 mm/min. A compressometer equipped with three linear variable differential transformers (LVDTs) was installed to measure the average compressive strain and to calculate the elastic modulus and strain capacity. The detailed test setup for the compressive test can be found elsewhere [21]. 2.2.2. Four-point flexural test (ASTM C 1609) under quasi-static loading A total of fifteen prismatic specimens with a cross-sectional dimension of 100 mm  100 mm and a length of 400 mm were fabricated and tested according to ASTM C 1609 [23]. The clear span length used was 300 mm, and the uniaxial load was applied using the UTM with maximum capacity of 2500 kN through displacement control. The loading rate was 0.4 mm/min. In order to measure the net mid-span deflection excluding support settlement, a steel frame equipped with two LVDTs on both sides of the beam was

59

installed at the middle of the beam height, and the applied load was measured from the load cell affixed to the cross head. The detailed geometry and test setup for the flexural test are shown in Fig. 1.

2.2.3. Drop-weight impact test (three-point flexural test) A drop-weight impact test machine instrumented at the University of British Columbia was employed to provide high rates of flexural loading, as shown in Fig. 2. The impact load was applied to the midspan of the beams by dropping an 82-kg mass from two different drop heights of 600 and 1400 mm, which led to two different potential energies (Ep) of approximately 0.48 and 1.13 kJ, respectively. The incident impact velocities were found to be 3.43 and 5.24 m/s, respectively, by ignoring friction. A total of thirty prismatic beams (three beams for each variable) were fabricated and tested, and their dimensions and clear span lengths were identical to those used in quasi-static loading tests. According to a previous study [24], it is difficult to obtain an accurate reaction load versus midspan deflection curve with small beam specimens when using a potentiometer under drop-weight impact loading because the reaction load reacts very quickly to the impact. Therefore, the midspan deflection was measured using an accelerometer with a maximum capacity of ±5000 g, similar to previous studies [1,24]. The accelerometer was attached to the midspan of the beams using L-shaped aluminum plates, and very high strength epoxy was used to prevent the detachment of the accelerometer before the completion of testing. The deflection history was obtained by integrating the velocity, which was determined by integrating the acceleration with respect to time, as follows:

_ uðtÞ ¼

Z

Z uðtÞ ¼

€ uðtÞdt

(1)

_ uðtÞdt

(2)

€ _ where uðtÞ, uðtÞand uðtÞ are the acceleration, velocity, and midspan deflection, respectively. A drop hammer, called a “tup”, with a striking knife-edge end was used, and the impact load was measured from eight bonded strain gages mounted on the tup [25]. It is well known that the impact load measured from the tup includes the inertial load. Thus, two load cells were installed at both supports to measure the pure bending load excluding the inertial load. A simple support condition was used for all test beams, which was identical to that used in the quasi-static loading tests, and the detailed design of the support load cells used can be found elsewhere [26]. Data were collected at a rate of 100 kHz without filtering. A high-speed camera was also employed to capture images at 2200 frames/s. The high-speed images were used to evaluate the cracking behaviors of UHPCC beams during impact, and a trigger mechanism was installed to correlate the data obtained from the impact test machine with the images obtained from the high speed camera.

Table 3 Properties of steel fibers. Type of fiber

df (mm)

Lf (mm)

Aspect ratio (Lf/df)

Density (g/cm3)

fft (MPa)

Ef (GPa)

S65 S97.5 S100 T100

0.2 0.2 0.3 0.3

13.0 19.5 30.0 30.0

65.0 97.5 100.0 100.0

7.9 7.9 7.9 7.9

2788 2500 2580 2428

200 200 200 200

[Note] df ¼ fiber diameter, Lf ¼ fiber length, fft ¼ tensile strength of fiber, and Ef ¼ elastic modulus of fiber.

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Fig. 1. Four-point flexure test (ASTM C1609); (a) test picture, (b) specimen geometry and test setup (unit: mm).

Fig. 2. Drop-weight impact test machine.

3. Results and discussion

Table 4 Summary of compressive test results.

3.1. Compressive behavior The average parameters obtained from the compressive tests are summarized in Table 4, based on three specimens for each variable. In the case of the specimen NF, the compressometer was only used up to a stress of about 100 MPa to calculate the elastic modulus, and the ultimate strength was measured after removal of the compressometer. Although the steel fibers were included, a catastrophic failure was observed (a sudden drop of stress immediately after reaching the peak strength) for all tested cylinders. The elastic modulus was calculated based on the stressestrain relationships as per ASTM C 469 [27], by using the following equation: Ec ¼ (0.4fc'f1)/(ε2-0.00005), where fc' is the compressive strength, f1 is the stress corresponding to a strain of 50  106, and ε2 is the

NF S65 S97.5 S100 T100

fc' (MPa)

εu (mm/mm)

Ec (GPa)

200.9 211.8 209.7 209.7 232.1

-a 4.53 4.84 4.58 5.28

45.3 46.7 46.9 46.8 47.0

(11.515) (5.710) (2.846) (1.482) (8.503)

(0.175) (0.281) (0.236) (0.249)

(2.464) (0.469) (0.169) (0.669) (2.705)

[Note] fc' ¼ compressive strength, εu ¼ strain at the peak load, Ec ¼ elastic modulus, and items in parentheses ¼ standard deviation. a Data is not available.

longitudinal strain produced by a stress at 40% of fc'. All cylindrical specimens exhibited very linear compressive stressestrain curves up to the peak strength and then failed in a brittle manner. The applied load abruptly dropped to almost zero

D.-Y. Yoo et al. / Cement and Concrete Composites 86 (2018) 57e71

immediately after reaching the peak strength because of the extremely high compressive strength and brittleness of the UHPCC matrix. Thus, the addition of 2 vol% of steel fibers was ineffective in improving the post-peak ductility under compression, relative to that under tension. Similarly, a previous study [24] reported no enhancement of compressive toughness of ultra-high-strength concrete by containing 2 vol% of hooked-end steel fibers. However, no fragmentation was observed for UHPCC with steel fibers due to the fiber confinement effect, as shown in Fig. 3. The UHPCC with fibers exhibited slightly higher compressive strength and elastic modulus than the NF without fiber, which is attributed to its proper fluidity and viscosity, which allowed the steel fibers to be well dispersed in the cylinders. Thus, the positive effects of adding fibers, such as the crack inhibition, were predominant as compared with the negative effects, such as fiber ball and high air content. The highest compressive strength and strain capacity were found to be 232.1 MPa and 0.00528 for specimen T100. The compressive strength of T100 was approximately 16% higher than that of NF (200.9 MPa). On the other hand, the elastic modulus was insignificantly affected by the fiber aspect ratio and type, and the average elastic modulus was found to be 46.8 GPa. 3.2. Quasi-static flexural behavior 3.2.1. Flexural performance with consideration of fiber distribution characteristics The average flexural loadedeflection curves are shown in Fig. 4,

Fig. 3. Typical compressive failure mode of UHPCC with fibers.

while the average parameters from flexural tests are summarized in Table 5. In order to obtain a precise average stressestrain curve, an averaging procedure, which was adopted by a previous study [9], was used for the simplicity. In this study, the mid-span deflection was assumed to increase in 0.01 mm increments, as shown in Fig. 5. As compared to the compressive behavior, the flexural loadedeflection curves varied quite largely, because the postcracking flexural behavior (both hardening and softening regions), closely related to fiber bridging capacity rather than matrix cracking strength, was strongly influenced by fiber orientation. Although identical placement method is applied, the fiber orientation can be changed due to several uncertainties, such as fiberfiber interaction, gradient of flow velocity, worker performance, etc. The flexural stress was obtained with the equation, f ¼ PL/bh2, where P is the applied load, L is the span length, b is the beam width, and h is the beam height. The first cracking properties, such as the first-cracking strength fLOP, the deflection at first cracking dLOP, and the toughness at first cracking ToughLOP, were insignificantly affected by the fiber aspect ratio and the fiber type. This is because the first cracking properties are more strongly influenced by the matrix tensile cracking rather than the fiber bridging capacity. Yoo et al. [21] denoted that the first cracking strength of UHPCC is insignificantly changed with fiber length and orientation, relative to the post cracking strength. In contrast, the post-cracking flexural performance, including the post-cracking flexural strength fMOR, the deflection capacity dMOR, and the toughness at the peak ToughMOR, was substantially improved by adding steel fibers. For instance, specimen S97.5 exhibited a flexural strength of 40.8 MPa, approximately 167% higher than that of NF. This is because the excellent fiber bridging capacity after matrix cracking leads the flexural stress to increase continuously with the deflection, which is known as the “deflection-hardening” response (fLOP < fMOR). For the same reason, a much higher deflection capacity was also observed for UHPCCs with steel fibers than that without fiber. The use of straight steel fibers with a higher aspect ratio and twisted steel fibers resulted in an improvement in the flexural performance compared to that of S65, which is a type of commercially available UHPCC in North America [17]. Among the specimens, specimen S97.5 provided the highest flexural strength, followed by S100 and T100; thus, the order of quasi-static flexural strength was obtained as follows: S97.5 > S100 > T100 > S65 > NF. However, specimen T100 exhibited the highest deflection capacity of 1.87 mm, approximately 2467%, 124%, 23%, and 20% higher than that of NF, S65, S97.5, and S100, respectively, because the un-twist mechanism

Normalized deflection (mm/mm)

0.001

90

0

0.0015 40

30 20

60

10

30

0

0 0

0.1

0.2

0.3

0.4

0.5

0.005

0.01

0.015

0.02

0.025

150 NF S65 S97.5 S100 T100

120

Load (kN)

120

Load (kN)

0.0005 NF S65 S97.5 S100 T100

Equivanlent flexural stress (MPa)

0

90

40

30 20

60

10

30

0

0 0

2

4

6

Deflection (mm)

Deflection (mm)

(a)

(b)

Fig. 4. Average flexural load-deflection curves; (a) initial behavior, (b) global behavior.

8

Equivanlent flexural stress (MPa)

Normalized deflection (mm/mm) 150

61

62

D.-Y. Yoo et al. / Cement and Concrete Composites 86 (2018) 57e71

Table 5 Summary of quasi-static flexure test results.

LOPa

PLOP fLOP

dLOP ToughLOP d0.5

Pd0.5 fd0.5

dd0.5 Toughd0.5 b

MOR

PMOR fMOR

dMOR ToughMOR d2

Pd2 fd2

dd2 Toughd2 d4

Pd4 fd4

dd4 Toughd4 d8

Pd8 fd8

dd8 Toughd8

Unit

NFc

S65

S97.5

S100

T100

kN MPa mm kN$mm

51.0 (10.47) 15.3 (3.14) 0.073 (0.022) 1.92 (0.813)

50.4 (8.76) 15.1 (2.63) 0.073 (0.010) 1.87 (0.434)

49.7 (2.40) 14.9 (0.72) 0.062 (0.013) 1.61 (0.378)

45.6 (1.99) 13.7 (0.60) 0.062 (0.001) 1.48 (0.073)

53.1 (0.33) 15.9 (0.10) 0.073 (0.008) 2.03 (0.173)

kN MPa mm kN$mm

-d

84.3 (16.28) 25.3 (4.88) 0.5 31.73 (5.820)

110.0 (5.95) 33.0 (1.79) 0.5 41.69 (1.287)

96.6 (4.48) 29.0 (1.34) 0.5 36.15 (1.201)

86.9 (1.88) 26.06 (0.56) 0.5 33.43 (0.493)

kN MPa mm kN$mm

51.0 (10.47) 15.3 (3.14) 0.073 (0.022) 1.92 (0.81)

89.4 (16.49) 26.8 (4.95) 0.836 (0.024) 60.53 (10.92)

136.0 (16.03) 40.8 (4.81) 1.523 (0.217) 170.95 (38.27)

121.6 (5.53) 36.5 (1.66) 1.558 (0.572) 155.38 (68.23)

114.0 (7.14) 34.2 (2.14) 1.874 (0.237) 173.27 (30.89)

kN MPa mm kN$mm

-d

70.3 (12.26) 21.1 (3.68) 2.0 153.38 (28.65)

129.1 (17.68) 38.7 (5.30) 2.0 232.37 (18.31)

115.0 (9.87) 34.5 (2.96) 2.0 204.92 (4.36)

109.7 (10.96) 32.9 (3.29) 2.0 186.32 (3.89)

kN MPa mm kN$mm

-d

40.3 (7.31) 12.1 (2.19) 4.0 259.84 (47.64)

83.0 (13.54) 24.9 (4.06) 4.0 442.83 (46.84)

89.2 (15.16) 26.8 (4.55) 4.0 409.44 (32.92)

70.9 (13.18) 21.3 (3.96) 4.0 364.43 (30.74)

kN MPa mm kN$mm

-d

12.1 (1.81) 3.6 (0.54) 8.0 351.29 (61.76)

28.4 (3.36) 8.5 (1.01) 8.0 646.87 (71.05)

43.8 (10.69) 13.2 (3.21) 8.0 660.92 (84.22)

31.8 (6.76) 9.5 (2.03) 8.0 553.51 (68.08)

[Note] P ¼ applied load, f ¼ flexural stress, d ¼ deflection, Tough ¼ toughness, and (x.xxx) ¼ standard deviation. a LOP ¼ limit of proportionality (first-cracking point). b MOR ¼ modulus of rupture (peak point). c Parameters of NF at MOR are identical to those at LOP. d Data is not available.

along the fiber length maintains the pullout resistance of the twisted steel fibers up to much larger slips, compared to those of straight steel fibers [28]. Interestingly, specimen T100 exhibited slightly different hardening behavior as compared with others including straight fibers: slightly steeper increase of flexural stress with deflection was observed for the specimen T100 at near the peak strength. This might be attributed to the activation of un-twist moment, however, it is difficult to draw a certain conclusion due to its complicated bond components such as adhesion, friction, and mechanical anchorage. Slightly steeper increase of stress at near the peak strength was also observed by Wille et al. [29] for UHPCC with twisted steel fibers under tension. If a crack is normal to the loading direction and fibers are circular in cross section, the postcracking strength of UHPCC can be calculated by the following equation [30]: atVfLf/df, where a is the product of several coefficients considering the efficiency factor of fiber orientation, group reduction factor, snubbing coefficient, etc., t is the equivalent bond strength, Vf is the fiber volume fraction, Lf is the fiber length, df is the fiber diameter, and VfLf/df is the fiber reinforcing index. Thus, if the product of a and t is assumed to be marginally influenced by the aspect ratio of straight steel fibers, the post-cracking flexural strength of UHPCC is directly related to the fiber reinforcing index and aspect ratio at identical volume fraction. Consequently, the specimens S97.5 and S100 exhibited higher flexural strength, fMOR, than the specimen S65, because of their higher aspect ratios. In addition, the main reason that specimen S97.5 showed the higher fMOR compared to the specimens S100 and T100 is as follows. Since the steel fibers were included by volume fraction, the number of S97.5 fibers (32.6  106 number/m3) was approximately 3.5 times higher than the number of S100 and T100 fibers (9.4  106 number/ m3). However, the surface areas of S100 fiber (28.3 mm2) and T100 fiber (36.2 mm2) were only 2.3 and 2.9 times higher than that of S97.5 fiber (12.3 mm3). Thus, the total bonding area between the

fiber and the matrix was theoretically higher for specimen S97.5 than for S100 and T100. In order to verify these explanations and quantitatively analyze the relationship between the flexural performance and the fiber distribution characteristics, image analysis was performed by using the images obtained near the localized crack, as shown in Fig. 6. With the assumption that steel fibers in the half of the beam depth from the bottom surface crucially affect the flexural properties, only the half image was taken with a high resolution camera and used in the image analysis. Typical images obtained for all test series are illustrated in Fig. 7, while the average parameters for the fiber distribution characteristics are given in Table 6. The parameters were calculated by using the following equations [31].

sP ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 ðxi  1Þ2 5 af ¼ exp4  nf 2

ðfiber dispersion coefficientÞ (3)

Fn ¼

nf A

Fc ¼

Aob Ac

ðnumber of fibers in unit areaÞ

ðpacking densityÞ

(4)

(5)

qmax Z

pðqÞcos2 qdq

hq ¼

ðfiber orientation coefficientÞ

(6)

qmin

where nf is the total number of fibers in an image, xi is the number of fibers in the i th unit, which is a square portion allocated to the i th fiber by assuming perfect homogeneity of the fiber dispersion, A

D.-Y. Yoo et al. / Cement and Concrete Composites 86 (2018) 57e71

63

Table 6 Average parameters for fiber distribution characteristics. Name

af

Fn (number/cm2)

Fc

hq

S65 S97.5 S100 T100

0.378 0.382 0.362 0.377

37.07 37.84 19.41 20.39

0.790 0.803 0.789 0.767

0.655 0.679 0.657 0.630

[Note] af ¼ fiber dispersion coefficient, Fn ¼ number of fiber in unit area, Fc ¼ packing density, and hq ¼ fiber orientation coefficient.

Fig. 5. Procedure of obtaining average flexural load-deflection curve (S97.5).

is the image area, Aob is the area of the object (¼ pdfl/4), Ac is the area of its circumscribed circle (¼ pl2/4), df is the diameter of the fiber, l is the length of the major axis of the detected fiber image, and p(q) is the probability density function of the fiber orientation.

Herein, af ¼ 1 represents homogeneous dispersion of the fibers, and, conversely, af ¼ 0 indicates significantly biased dispersion. In addition, hq ¼ 1 indicates that all fibers are aligned parallel to the tensile direction, whereas hq ¼ 0 indicates that all fibers are aligned perpendicular to the tensile direction. As given in Fig. 7 and Table 6, specimens S65 and S97.5 exhibited much higher numbers of fibers at the crack surface than S100 and T100 because many more fibers were included in the mixture for S65 and S97.5 than their counterparts. For instance, the number of fibers in a unit area for S97.5 was found to be 37.84 number/cm2, approximately 95% and 86% higher than that of S100 and T100, respectively. It is worth noting that, even though more fibers were included in S65 than in S97.5, similar values of the number of fibers in a unit area were obtained each other, which is consistent with

Fig. 6. Schematic view of cutting surface for image analysis.

Fig. 7. Typical image of cutting surface at near localized crack; (a) S65, (b) S97.5, (c) S100, (d) T100.

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the findings from Yoo et al. [21]. This is because the probability of the presence of fibers at the crack surface increases with the fiber length for identical diameters, and a slightly better fiber orientation, leading to a higher number of detected fibers, was somehow obtained for S97.5 than S65. The difference in the numbers of fibers detected in the cutting surface between specimen S97.5 and specimens S100 and T100 was lower than the difference in the numbers of fibers included in the mixture because of the higher probability of the presence of the fibers at the crack surface. Thus, the benefits of theoretically higher bonding area for S97.5 than for S100 and T100 might be reduced. However, specimens S100 and T100 showed lower post-cracking flexural strengths than S97.5, as a result of their poor fiber orientations, i.e., a lower fiber orientation coefficient was obtained in specimens S100 and T100 (Table 6), mainly caused by a fiber-fiber interaction. As the fibers are significantly inclined to a tensile load direction, their pullout resistance is greatly reduced. In addition, when the fresh UHPCC mixture was placed at the end of prismatic mold, it was flowed due to its selfconsolidating property. Because of a friction between side surfaces of the mold and UHPCC (called wall effect), a parabolic gradient of flow velocity is obtained [32], and thus, randomly oriented fibers become aligned in the flow direction from a toque, generated by the flow velocity gradient. However, for the long fibers (S100 and T100), the fiber rotation was disturbed by the fiberfiber interaction, and consequently, they provided poorer fiber orientation than the specimen S97.5. As the fibers are significantly inclined in the tensile load direction, a lower number of fibers is detected at crack surfaces [33]. Therefore, the poor fiber orientation normally results in deteriorated post-cracking tensile or flexural performance. For these reasons, although the specimens S97.5 and S100 have similar aspect ratios, the S97.5 gave higher flexural strength than the S100. 3.2.2. Toughness Since UHPCC with steel fibers exhibited deflection-hardening behavior, the energy absorption capacity (toughness) was determined by the area under the load-deflection curve up to first cracking (limit of proportionality, LOP) and peak load (modulus of rupture, MOR). Furthermore, four other deflection points were also considered in the current study because of the excellent load carrying capacity of UHPCC up to very large deflections as follows; d0.5: point at a net deflection equal to 1/600 of the span, d2: point at a net deflection equal to 1/150 of the span (recommended by ASTM C 1609 [23]), d4: point at a net deflection equal to 1/75 of the span, and d8: point at a net deflection equal to 1/37.5 of the span. The toughness values are summarized in Table 5. In order to compare the energy absorption capacity (toughness) and load carrying capacity (flexural strength) according to the test variables, the flexural strength ratio based on S65 was also investigated, as given in Fig. 8. The toughness and flexural strength at the LOP were all insignificantly influenced by the fiber aspect ratio, and the fiber shape. In contrast, both the toughness and the flexural strength after d0.5 noticeably increased with the inclusion of long straight steel fibers and twisted steel fibers. It is interesting to note that specimen S97.5 generally showed the highest flexural strength and toughness up to the points of d2 and d4, respectively. However, at very large deflection (after d4), specimens S100 or T100 exhibited higher flexural strength than S97.5 because of their longer embedment lengths, which led to a higher post-peak ductility. The highest toughness ratio was obtained at the point dMOR regardless of the aspect ratio or type of fibers because both the peak load and the deflection capacity increased with the use of long straight and twisted steel fibers. In addition, the highest toughness at dMOR was obtained for T100, attributed to the fact that its un-twist mechanism along the fiber length led to a much higher deflection

capacity, even though the peak load was slightly lower than those of S97.5 and S100. However, specimen T100 exhibited lower flexural strength and toughness at large deflections than S100, even though they had the same fiber length of 30 mm and aspect ratio of 100. This observation was due to the higher slope in the descending part of the load-deflection curve for T100 than S100, and a similar result was reported in a previous study [34]. A steeper decrease in the post-peak load carrying capacity versus deflection was obtained for T100, because of split cracks generated in surrounding matrix when the twisted fibers are pulled out [8]. Once the split cracks occur in the surrounding matrix, the fibers are easily pulled out even at low pullout force and a steep decrease in the fiber pullout resistance is obtained after the peak. Given these observations, it was briefly concluded that using the long straight fibers with higher aspect ratios and the twisted steel fibers (i.e., S97.5, S100, and T100) was effective in improving both the flexural strength and the toughness after the first cracking compared to the specimen with short straight steel fibers (S65), and their effectiveness was higher at large deflections. 3.2.3. Cracking behavior The cracking behaviors of UHPCC beams with steel fibers are shown in Fig. 9. Specimen NF failed with a single crack, while specimens with 2 vol% steel fibers exhibited multiple micro-cracks and one specific localized crack, which is known as the crack localization phenomenon. Long straight and twisted steel fibers produced more micro-cracks and smaller average crack spacing than short steel fiber (S65) in the same manner as the flexural performance, i.e., higher flexural strength, deflection capacity, and toughness. For instance, the average number of cracks produced in S97.5 was 22, approximately 100% more than that in S65. The main reason why long fibers produced more micro-cracks than short fibers is that higher tensile force was transferred from the fiber to the surrounding cement matrix because of the higher fiber pullout resistance, and it caused more tensile cracks in the matrix. Specimen T100 exhibited the highest number of micro-cracks and the smallest average crack spacing, which was also because the higher fiber pullout resistance of twisted steel fibers was maintained up to larger slips than that of straight fibers [28]. This observation is closely related to the much higher deflection capacity of T100, leading to a higher energy absorption capacity up to the peak strength than that of other beams. In addition, S97.5 exhibited a slightly higher number of cracks and a smaller average crack spacing than S100, but the differences were insignificant. 3.3. Flexural behavior under drop-weight impact loading 3.3.1. Inertial effect It is well known that specimen inertia plays a significant role under impact loading because the rate of loading is high. To investigate the effect of specimen inertia on the impact response of UHPCC beams, the typical loads measured from the tup and two supports over time were analyzed, as shown in Fig. 10. The initial behavior of load measured from the tup, called the impact load, was completely different from that of load taken as the summation of the two support reaction measurements, called the reaction load (Fig. 10(a)), which was caused by the inertia effect. The first sinusoidal impact-time curve was mostly attributed to the beam inertia, and thus, the peak value of the impact load was almost identical to the peak inertial load. Therefore, it was noted that the impact load included the inertial load and was not a pure bending load stressing the beams. Thus, only the reaction load was used for data analysis in the current study. The magnitude of the inertial load clearly decreased with time because the acceleration of the beam was reduced by the resistance to deflection and crack opening due to

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65

Fig. 8. Parameter ratio based on S65; (a) flexural strength, (b) toughness.

Fig. 9. Cracking behaviors under quasi-static loading condition; (a) average number of cracks and crack spacings, (b) picture of failure.

the fiber bridging effect. This resistance led to a decrease in the slope of the midspan deflection-time curve over time. Thus, the impact load-time history became similar to the reaction load-time history after approximately 1 ms, as shown in Fig. 10(b).

3.3.2. Deflection-hardening of UHPCC beams containing steel fibers under impact loading In order to investigate the effect of steel fibers on the postcracking flexural behavior under impact loading, the typical load versus midspan deflection curves of specimens NF and S100 at

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300

10

10

6

150 4

100 Inertial load (I–R)

50

2

0

0 0

0.4

0.8

1.2

Impact load (I)

250

1.6

Time (ms)

Load (kN)

Reaction load (R)

200

8

Midspan deflection

Deflection (mm)

250

Load (kN)

300

Impact load (I)

8

Reaction load (R)

200

6

150

Midspan deflection

4

100

Deflection (mm)

66

2

50

0

0 0

1

2

3

4

5

Time (ms)

(a)

(b)

Fig. 10. Impact load, reaction load, inertial load, and midspan deflection behaviors according to time (S97.5 at Ep ¼ 0.48 kJ); (a) initial behavior, (b) overall behavior.

Ep ¼ 0.48 kJ were compared, as shown in Fig. 11. Before the first cracking, an almost linear load-deflection response was obtained and the impact response was insignificantly influenced by the steel fibers. In contrast, the post-cracking responses in the beams with and without fibers were entirely different. Specimen NF exhibited a steep decrease in reaction load immediately after cracking, and an almost zero load carrying capacity was maintained thereafter. As shown in Fig. 12(a), a single visible crack occurred in the descending branch of the load-deflection curve, and the crack width increased very rapidly without any increase in the load. In the case of specimen S100, the load also decreased sharply after cracking until it reached approximately 24% of the first peak load, whereas thereafter, the load increased again up to the midspan deflection of approximately 2.9 mm because of its excellent fiber bridging capacity. In this deflection-hardening zone, only microcracks were observed without any localized cracks (Fig. 12(b)). After the postcracking peak load, the load carrying capacity decreased gradually with an increase in the specific crack width (crack localization), and a part of the stored energy released caused a rebound with decreases in the load and deflection after reaching a deflection of approximately 6.3 mm. 3.3.3. Load versus midpan deflection curve It was important to obtain a precise average reaction loademidspan deflection curve. In order to average the data, an averaging procedure that was identical to that used in static flexural

Normalized deflection (mm/mm) 0.005

0.01

0.015

0.02

0.025 90

200 Deflection hardening

Load (kN)

160

Softening with crack localization

75

First cracking

120

60 45

80

30

40

15

0

0 0

2

4

6

Equivanlent flexural stress (MPa)

0

Spec._1 (NF) Spec._1 (S100) (N1) …. (N3) (S1) …. (S4)

8

Deflection (mm) Fig. 11. Typical load-deflection curves of NF and S100 (Ep ¼ 0.48 kJ).

tests was adopted [19]. The typical averaged loadedeflection curves of S100 at two potential energies are shown in Fig. 13. A higher variation in the test results was generally obtained at higher potential energies (or at higher impact velocities). Although the test results were fluctuated highly, the shapes of the loadedeflection curves obtained from three specimens were quite consistent. Therefore, the averaged loadedeflection curve was used for all test series in this study to compare the flexural response under impact loading. Fig. 14 shows the average loadedeflection (or flexural stressenormalized deflection) curves for all test series, and several important parameters obtained from the impact tests are summarized in Table 7. Unrealistic test data were obtained for NF at a high potential energy Ep of 1.13 kJ, because the applied potential energy was too high to obtain reliable data for the beams with a very brittle matrix without fibers (NF); the NF beams broke into several pieces by impact, and thus, the accelerometer was detached from the beam, and a much low reaction load was obtained. Thus, specimen NF at an Ep of 1.13 kJ was not compared in Fig. 14(b). After the impact, the reaction load increased almost linearly and similar first peak flexural strengths were found for all test specimens with and without fibers. In accordance with the images obtained from the high speed camera (Fig. 12(b)), the first peak strength was closely related to the matrix cracking, and thus, it was only marginally influenced by the steel fibers, similar to the value of fLOP under quasi-static loading. The first peak strength, called the firstcracking flexural strength or fLOP,D, hereafter, increased noticeably with an increase in the potential energy. For instance, the average value of fLOP,D was found to be 78.1 MPa at an Ep of 1.13 kJ, approximately 57% higher than that at an Ep of 0.48 kJ. Subsequently, the load dropped to nearly zero for specimen NF because of the occurrence of flexural cracks and the lack of stress transfer at the crack surface. However, UHPCC beams with steel fibers showed another increase in the load after a steep load drop occurred due to the occurrence of flexural cracks and the downward acceleration of the hammer. The post-cracking load-deflection response was clearly affected by the fiber type. For example, specimens S97.5 and S100 exhibited a deflection-hardening response at an Ep of 0.48 kJ, generating a higher load carrying capacity after first cracking (fMOR,D > fLOP,D), but specimens S65 and T100 showed deflectionsoftening behavior at the same potential energy. Even though all test series exhibited deflection-softening behavior (fMOR,D < fLOP,D) at high potential energy (Ep ¼ 1.13 kJ), specimens S97.5 and S100 provided higher post-cracking strength than specimens S65 and T100, which was consistent with the test results at the lower

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67

Fig. 12. Cracking behaviors during impact (Ep ¼ 0.48 kJ); (a) NF, (b) S100 (Note: d ¼ midspan deflection).

Fig. 13. Average load-deflection curves of S100; (a) Ep ¼ 0.48 kJ, (b) Ep ¼ 1.13 kJ.

potential energy. According to these observations, it was noted that long straight steel fibers are more effective in improving the impact resistance of UHPCC than short straight and twisted steel fibers. It is consistent with the results of static flexural tests that long straight fibers provided a better flexural response as compared with short straight fibers. However, twisted steel fibers led to worse impact resistance than long straight steel fibers (S97.5 and S100) and

similar resistance to short straight steel fibers (S65), which is inconsistent with the static flexural test results. The reduction in the tensile performance of UHPCC containing twisted steel fibers under high rate loadings was also reported by Tran et al. [9], which was attributed to the breakage of twisted steel fibers before pullout at high rate loadings. However, in this study, no breakage of twisted fibers was observed, but instead, they were all completely pulled

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Fig. 14. Average load-deflection curves under impact loading; (a) Ep ¼ 0.48 kJ, (b) Ep ¼ 1.13 kJ.

Table 7 Summary of impact flexure test results. Name Velocitya (m/s) Strain rateb (1/s) Strain ratec (1/s) fLOP,D (MPa) fMOR,D (MPa) Energy absorption, Ua (J) b  100 (%) Ratio of fLOP,D/fLOPd Ratio of fMOR,D/fMORd NFe S65

3.43 3.43 5.24 S97.5 3.43 5.24 S100 3.43 5.24 T100 3.43 5.24

32.2 32.0 49.5 30.5 48.4 29.4 48.2 33.3 46.7

e 19.4 26.0 20.5 21.3 15.9 30.6 17.1 29.6

47.6 50.0 76.4 49.3 79.9 49.0 78.0 52.7 82.9

(0.86) (16.18) (1.74) (7.04) (9.42) (8.72) (14.7) (14.14) (19.93)

47.6 48.9 49.4 73.1 73.1 71.1 77.0 60.1 61.9

(0.86) (5.29) (12.91) (15.35) (14.76) (10.25) (14.56) (7.49) (11.85)

52.3 (4.02) 298.1 (56.52) 357.0 (41.19) -f 593.6 (139.91) -f 634.0 (157.67) 331.4 (99.22) 423.9 (58.47)

10.9 62.1 31.6 -f 52.5 -f 56.1 69.0 37.5

3.11 3.31 5.06 3.31 5.36 3.58 5.70 3.31 5.21

e 1.82 1.84 1.79 1.79 1.95 2.11 1.76 1.81

[Note] fLOP,D ¼ dynamic first-cracking flexural strength, fMOR,D ¼ dynamic post-cracking flexural strength, Ua ¼ absorbed energy by the specimen, and b ¼ normalized energy dissipation rate (Ua/Ui). a Velocity is calculated by 1/2mv2 ¼ Ep. b Average value of strain rate at first peak flexural strength. c Average value of strain rate at post-cracking flexural strength. d Ratio is average value. e Flexural strength of NF at MOR is identical to that at LOP, and test data at Ep of 0.48 kJ is only available. f Data is not available because specimens did not completely break.

out after impact loading. This is because, according to Tai and ElTawil [11], the inclined twisted steel fibers exhibited the DIF on pullout resistance below 1 at the impact loading rate, meaning that the pullout resistance was rather decreased with an increase in the loading rate, caused by more sever matrix spalling at the exit than that of straight fibers. Thus, the deteriorated impact resistance of specimen T100 might be caused by the reduced pullout resistance of inclined twisted steel fibers under drop weight impact and not by the fiber breakage in this study. With an increase in the potential energy from 0.48 kJ to 1.13 kJ, the load decreased more significantly immediately after reaching fLOP,D, owing to the higher downward acceleration of the hammer; thus, the load at the point (at the midspan deflection ranging from 1 to 2 mm) where the load increased again was lower at a higher potential energy (Ep ¼ 1.13 kJ). The post-cracking strength, fMOR,D, was only slightly influenced by the potential energy as compared with fLOP,D, as summarized in Table 7 and shown in Fig. 15. The differences in fMOR,D according to the potential energy were within 8% for all test series. This is because the effect of strain rate on fMOR,D was mitigated by decreasing the downward velocity of beams, leading to a lower strain rate (Table 7) due to the resistance to deflection and the fiber bridging effect at crack surfaces, which inhibited crack opening. In addition, the sensitivity to the strain rate on fLOP,D, which was related to matrix cracking, was higher than that to the

strain rate on fMOR,D, which was related to the fiber pullout. The latter explanation was verified by analyzing the effect of strain rate effect on the DIF, as reported in the following section.

Fig. 15. Effect of potential energy on flexural response under impact (S97.5).

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3.3.4. Energy absorption capacity The total input energy provided by the potential energy of the drop-weight hammer was mainly composed of the energy absorbed by the specimen, the energy remaining in the system after impact, and the energy dissipated by friction as follows:

Ui ¼ mgh ¼

1 mv2 þ Uf ¼ Ua þ Ur þ Uf 2

(7)

where Ui is the input energy, m is the mass of the drop-weight hammer, g is the acceleration due to gravity, h is the drop height, v is the hammer velocity, Uf is the energy dissipated by friction during the impact event, Ua is the energy absorbed by the specimen, and Ur is the energy remaining in the system after impact. The energy absorbed by the specimen, Ua, is a part of the kinetic energy and can be defined as the enclosed area of the loaddeflection curve. Dey et al. [35] proposed a parameter called the normalized energy dissipation rate to quantitatively investigate the efficiency of the material used to absorb a part of input energy during impact as follows:

b¼

Ua Ui

(8)

The average values of the absorbed energy, Ua, and the normalized energy dissipation rate, b, are summarized in Table 7. Since specimens S97.5 and S100 were not completely broken by impact loading at an Ep of 0.48 kJ, the absorbed energy could not be calculated. It was obvious that the specimens with steel fibers absorbed much more input energy by impact than the specimen without fiber because of their excellent capacity for post-cracking fiber bridging. Specimen S100 exhibited the highest energy absorption capacity of 634 J at an Ep of 1.13 kJ, approximately 78%, 50%, and 7% higher than those of specimens S65, T100, and S97.5, respectively, at the identical Ep. Thus, it was noted that the use of long steel fibers is also more effective in improving the energy absorption capacity of UHPCC than the use of short steel fibers. A comparison of the absorbed energies at an Ep of 1.13 kJ with Toughd8 in Table 5 shows that the energy absorption capacity of specimen T100 was much lower under impact loading than under quasi-static loading compared to those of specimens containing straight steel fibers (S65, S97.5, and S100). For example, the ratio of Ua at Ep of 1.13 kJ and Toughd8 was found to be 0.77 (¼ 423.9/553.5 J/J) for T100, which is much smaller than 1.02, 0.92, and 0.96 for S65, S97.5, and S100, respectively. Therefore, it is concluded that the straight steel fibers were more favorable for UHPCC under high rate loading than the twisted steel fibers. The value of b decreased noticeably with the potential energy, which is attributed to the fact that the increase in potential energy only influenced the first half of the sinusoidal loadedeflection curve, leading to a higher fLOP,D, and the post-cracking impact behavior was insignificantly affected by the potential energy (Fig. 15) because of the reduced downward velocity of the beams and its lower sensitivity to the strain rate on the DIF.

Fig. 16 shows the typical initial stress, midspan deflection, and strain rate versus time curves under impact loading. The strain rate was not constant with time and exhibited behavior similar to that of the reaction load initially, which is consistent with the finding from Pyo and El-Tawil [7]. The strain rates at the first and postcracking peak strengths were adopted in this study because these values were used to analyze the DIF. The calculated strain rates are summarized in Table 7, and the relationship between the DIF and the strain rate is shown in Fig. 17. The strain rate increased with an increase in the potential energy (or impact velocity) for all test series. For instance, the strain rates at first peak strength ranged from 29.4 to 33.3 s1 for Ep ¼ 0.48 kJ and from 46.7 to 49.5 s1 for Ep ¼ 1.13 kJ, respectively. In order to compare the effect of strain rate on the DIF according to the concrete strength, the relationships between the DIF and the strain rate for the normal-, high-, and ultra-high-strength concretes were adopted from previous test results performed by Yoo et al. [24]. The concretes with a higher strength were less sensitive to the strain rate than those with a lower strength. This is consistent with the findings from Bentur et al. [37] and Yoo et al. [24], but contrary to the findings from Bishoff and Perry [38]. The relationship between the DIF on fLOP and the strain rate was insignificantly influenced by the steel fibers because fLOP is more affected by matrix cracking rather than fiber bridging. Thus, all specimens made with an ultra-high-strength matrix, i.e., UHPCC and UHSC from Yoo et al. [24], exhibited a similar DIF on fLOP versus strain rate relationship (Fig. 17). The DIF on fMOR was lower than that on fLOP at identical strain rates, which indicates that a lower sensitivity to the strain rate on DIF was obtained for fMOR than for fLOP. Because of the lower sensitivity to strain rate at the post-cracking strength, the ratios of the postcracking flexural strengths obtained from impact and static loadings, fMOR,D/fMOR, were approximately 45e67% lower than the ratios at first-cracking strengths, fLOP,D/fLOP, as given in Table 7. This is consistent with the findings from Wille et al. [8] that slightly higher DIF on first-cracking strength was generally obtained than that on post-cracking strength. In particular, specimen T100 exhibited the lowest DIF on fMOR at identical strain rate, because of its limited strength increase with the strain rate, whereas similar DIFs on fMOR were obtained for all test specimens with straight steel fibers (S65, S97.5, and S100), as shown in Fig. 17. This is because the increase of bond strength of twisted steel fibers was much less sensitive to the strain rate as compared to that of straight steel fibers. Tai and ElTawil [11] experimentally verified the deteriorated pullout resistance of inclined twisted steel fibers embedded in UHPCC under higher loading rates (i.e., a DIF below 1). Consequently, the poor post-cracking flexural performance of specimen T100 under impact

3.3.5. Strain rate effect on the DIF In order to analyze the DIF, the strain rate of a beam subjected to three-point flexural impact loading was first calculated by differentiating the strain with respect to time [35,36], as follows:

ε_ ¼

dε 6hv ¼ 2 dt L

(9)

where t is the time, h is the height of the beam, v is the velocity of the beam, and L is the span length.

69

Fig. 16. Stress, deflection, and strain rate responses according to time.

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decreased slightly by impact loading, whereas the residual loadedeflection curves provided similar behaviors with the loadedeflection curves of the virgin specimens without impact damage. This is attributed to the fact that any extra damage of the specimens was not caused by the impact loading, but the overall flexural damage by impact was generated corresponded to the maximum deflection [18]. Thus, the residual flexural performance of UHPCC beams can be simply determined by the maximum deflection by impact loading and the corresponding flexural stress of virgin specimens.

Fig. 17. Strain rate effect on DIFs of fLOP and fMOR.

loading was considered to be attributed to the less strain rate sensitivity to the bond strength or even lower bond strength of twisted steel fibers under impact loading, compared to those including straight fibers. 3.3.6. Residual performance The comparison of the average loadedeflection curves for specimens S97.5 and S100 with and without impact damage (Ep of 0.48 kJ) is illustrated in Fig. 18. The residual tests were performed in four-point flexure as per ASTM C1609 [23], which is consistent with the quasi-static flexural tests of virgin specimens. The residual loadedeflection curves were drawn by fitting the deflection at the peak strength to the point of average maximum deflection, dmax, by impact loading. The beams exhibited a significant deterioration in the flexural strength after impact damage because of the formation of severe flexural cracks. Interestingly, specimen S100 provided higher residual flexural strength and toughness than S97.5, even though its maximum deflection by impact was higher than its counterpart. For example, the average residual flexural strength of S100 was found to be 14.8 MPa (41% of fMOR), which is approximately 31% higher than that of S97.5. This is because the specimen with longer fibers can maintain higher load carrying capacity at large deflections than that with shorter fibers (Fig. 18). A slightly higher residual moment capacity of structural UHPCC beams with steel reinforcing bars was also obtained for longer straight steel fibers than for shorter fibers [39]. Thus, it can be noted that long steel fibers are effective in improving the residual performance after impact damage. The initial stiffness of the UHPCC beams

Fig. 18. Residual flexural response of S97.5 and S100 at Ep of 0.48 kJ.

4. Conclusions This study experimentally examined the rate dependent flexural behavior of UHPCC beams with various steel fibers. The primary objectives were to evaluate the effects of potential energy and steel fiber geometric properties (aspect ratio and shape) on the impact and residual performances of UHPCC beams, and the quasi-static flexural performance was also investigated for comparison. From the above discussions, several important findings were obtained, and the following conclusions could be drawn: 1) All cylindrical specimens made of UHPCC showed a very linear compressive stressestrain curve and brittle failure. The inclusion of 2 vol% steel fibers was ineffective in improving the compressive post-peak ductility, but it resulted in a slightly higher compressive strength and elastic modulus than the specimen without fiber. 2) Long straight and twisted steel fibers resulted in an improvement of the quasi-static flexural performance, including flexural strength, deflection capacity, toughness, and cracking performance, compared to short straight steel fibers (S65), and their effectiveness on the flexural performance was higher at large deflections. The highest flexural strength was obtained for specimen S97.5, while the highest deflection capacity and number of micro-cracks were observed for specimen T100. On the contrary, the flexural properties at the first-cracking point were insignificantly affected by the steel fibers because these properties depended on matrix cracking rather than fiber bridging. 3) The deflection-hardening behavior of UHPCC beams with long straight steel fibers under impact loading was captured at a potential energy of 0.48 kJ, and the micro-cracking response in the deflection-hardening zone was verified through images obtained with a high speed camera. The first peak strength by impact loading was marginally influenced by the steel fibers, whereas a higher post-cracking strength and energy absorption capacity by impact loading were clearly obtained for the specimens with long straight steel fibers (S97.5 and S100) than those including short straight and twisted steel fibers (S65 and T100). Thus, the use of long straight steel fibers was more favorable for UHPCC under impact loading than that of twisted steel fibers. 4) The strain rate was not constant with time and increased with the potential energy. The concrete with a higher strength was less sensitive to the strain rate on the first peak flexural strength than the one with a lower strength. In addition, a lower sensitivity to the strain rate on the DIF of fMOR was obtained than that on the DIF of fLOP. Specimen T100 showed the lowest DIF on fMOR at the same strain rate because of its limited strength increase with strain rate, but the DIF on fMOR was insignificantly affected by the aspect ratio of straight steel fibers. Long steel fibers were effective in improving the residual flexural strength and toughness after impact damage, and a simple method to predict the residual performance was introduced.

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Acknowledgements This research was supported by a Construction Technology Research Project (17SCIP-B128706-01) funded by the Ministry of Land, Infrastructure and Transport.

[19]

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