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Flexural behaviour of arch-type steel fibre reinforced cementitious composites
Accepted Manuscript Flexural Behaviour of Arch-type Steel Fibre Reinforced Cementitious Composites Jong-Pil Won, Jae-Ho Lee, Su-Jin Lee PII: DOI: Reference:
S0263-8223(15)00785-0 http://dx.doi.org/10.1016/j.compstruct.2015.08.092 COST 6797
To appear in:
Composite Structures
Please cite this article as: Won, J-P., Lee, J-H., Lee, S-J., Flexural Behaviour of Arch-type Steel Fibre Reinforced Cementitious Composites, Composite Structures (2015), doi: http://dx.doi.org/10.1016/j.compstruct.2015.08.092
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Flexural Behaviour of Arch-type Steel Fibre Reinforced Cementitious Composites Jong-Pil Won*, Jae-Ho Lee, Su-Jin Lee Department of Civil & Environmental System Engineering, Konkuk University, Seoul, 143-701, Republic of Korea
ABSTRACT We investigated the flexural performance of arch-type steel fibre reinforced cementitious composites. We used arch-type steel fibres with a bend length of 1.5 mm and a radius of curvature of either 25 mm or 35 mm. The flexural performance of the two arch-type steel fibres with different radii of curvature was characterised in accordance with ASTM C1609, where the tensile strength of the steel fibre (i.e., 1100 or 1300 MPa) was also varied. With the 1100-MPa steel fibre reinforced cementitious composites, the composite with a radius of curvature of 35 mm exhibited higher flexural performance compared with the composite formed using the hooked-end-type fibres. The flexural tests of the 1300-MPa steel fibre reinforced cementitious composites formed using arch-type steel fibres with both radii of curvature revealed higher flexural performance compared with the composites formed using hooked-end type fibres. The flexural performance was characterised depending on volume fraction of fibres in accordance with EN 14652:2005 using the 1300-MPa arch-type steel fibres with a radius of curvature of 35 mm. The arch-type steel fibre reinforced
*
Corresponding author. Tel.: +82 2 450 3750; Fax: +82 2 2201 0907.
E-mail addresses: [email protected] (J.P. Won)
1
cementitious composites exhibited higher flexural strength and higher residual flexural tensile strength than those formed using the hooked-end-type steel fibre reinforcements at all volume fractions. Key words: Flexural performance, Residual flexural tensile strength, Toughness, Steel fibre
1. Introduction
The energy absorption capacity of brittle cementitious composites can be improved via the use of steel fibres, leading to ductile behaviour. The energy absorption capacity is increased due to the bridging effect of the reinforcing fibres across the cracks in the cementitious composite, which improves the mechanical properties [1–4]. The bond performance of steel fibres and cementitious composites is an important factor, and is closely correlated with the mechanical properties of steel fibre reinforced cementitious composites. Bond performance is influenced by the geometry of the steel fibre, the surface properties, and the tensile strength of the fibre. Of these factors, geometry affects bond strength most significantly, and so the shape of steel fibre is especially important [5–9]. Holschenmacher investigated how mechanical performance is affected by the geometry of steel reinforcements using flexural performance tests with hooked-end, straight, crimped, and crimped-flat-end steel fibre reinforcements, where the fibres had a tensile strength of 1100 MPa [10]. The results revealed that the hooked-end-type steel fibre exhibited the best flexural performance, and that the crimped and crimped-flat-end types exhibited an abrupt decrease in the load as the steel fibre began to be pulled out, and subsequently failed when the peak load was reached [10]. Hooked-end-type steel fibres exhibit constant energy absorption capacity and stable ductile behaviour in the post-crack behaviour of steel fibre reinforced cementitious
2
composites. These are the most widely used type of reinforcement, and are commonly used with both ends bent. However, with these fibres, the bond performance is substantially lowered and pull out resistance abruptly reduces at the time of pull out following the occurrence of cracks in the matrix. This occurs in the straight part of the fibres, rather than the hooked part, and limits the mechanical properties of the composite. To overcome this limitation, arch-type steel fibres have been developed. These have superior maximum bond strength and energy absorption capacity compared to hooked-end-type steel fibres, due to their smaller radius of curvature. However, they also exhibit fracturing due to excessive anchoring in the cement matrix. Here we investigate the flexural performance of two arch-type steel fibres with a bend length of 1.5 mm and radii of curvature of either 25 or 35 mm. These reinforcements have previously been shown to exhibit stable pull out and good bond performance. We compared the mechanical properties of composites formed using arch-type and hooked-end-type steel fibres. Notched-beam flexural tests were also carried out for reinforcements with different radii of curvature and volume fractions.
2. Materials and mix proportions
2.1 Arch-type steel fibres The flexural tests were carried out in accordance with the ASTM C1609 [14]. We used arch-type steel fibres with a bend length of 1.5 mm and radii of curvature of either 25 or 35 mm. These structures have been shown to pull out stably, and to exhibit good bond performance. Two fibres were investigated with tensile strengths of 1100 or 1300 MPa, and the results were compared with flexural tests on composites formed with hooked-end-type steel fibre reinforcements of the same tensile strength. Figure 1 shows photographs of the
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arch-type steel fibre reinforcements. Flexural tests were carried out in accordance with the EN 14651:2005 test method for metallic fibred concrete, where the fibre volume fraction was varied [15]. The specimens were named according to the specification, the steel fibre volume fraction and the tensile strength; for example, the name A25_30_1100 corresponds to arch-type fibres with a radius of curvature of 25 mm, a volume fraction of 30 kg/m3, and a tensile strength of 1100 MPa, and H_30_1100 corresponds to the hooked-end type fibres, with a volume fraction of 30 kg/m3 and a tensile strength of 1100 MPa.
2.2 Mix proportions Table 1 lists the composition of the cementitious composite used for the flexural tests. It consisted of type-I ordinary Portland cement with a specific gravity 3.15, fine aggregates with a specific gravity of 2.58, and coarse aggregates with a specific gravity of 2.69 and a maximum size of 25 mm. The mix was designed to have a compressive strength of 30 MPa. The target slump was 150±25mm, the air content was 2±1.5%, and the steel fibre volume fraction was 30 kg/m3. The cementitious composites used for the notched beam flexural tests employed the same materials as above, and Table 2 lists the mix proportions. The mix was designed to have a compressive strength of 42 MPa. The target slump was 50±15, the air content was 2±1.0%, and the volume fraction of steel fibre was varied through 20, 30, and 40 kg/m3.
3. Experimental
3.1 Flexural tests The flexural tests were carried out in accordance with ASTM C1609. Two 150×150×550
4
mm prismatic specimens that had been aged for 28 days were used for each test. Following curing in water at a constant temperature of 23±2ºC, the specimens were set up as shown in Fig. 2. A 250-kN displacement-controlled universal testing machine (UTM) (SH-250, Shimadzu, Japan) was used for tests, which were carried out with the rate of increase of the net deflection as specified by ASTM C1609; i.e., 0.1 mm/min until a deflection of L/900, and 0.3 mm/min thereafter. The flexural strength was calculated as follows [14]:
=
∙ ∙
,
(1)
where is the peak load, = 450 mm is the span length, = 150 mm is the average
width of the specimen at fracture, and = 150 mm is the average depth of the specimen at fracture. The equivalent flexural strength ratio is given by: , =
∙
∙∙
∙ %,
(2)
where
is the equivalent flexural strength (i.e., the area under the load vs. net deflection curve form 0 to L/150).
3.2 Notched-beam flexural tests The notched-beam flexural tests were carried out in accordance with EN 14651:2005. Two 150×150×550 mm prismatic specimens were used, and the test was repeated. Twenty-four hours before the flexural performance evaluation, a notch (25 mm deep) was cut from the lower central part of the specimen, and a jig was attached to fix a gauge. The crack mouth opening displacement (CMOD) was measured using a clip gauge (UB-5, Tokyosokki, Japan) installed at the notch. After curing for 28 days in water at 23±2ºC, the specimens were set up as shown in Fig. 3. The tests were carried out using a UTM (SH-250, Shimadzu, Japan). In
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accordance with EN 14651:2005, the loading rate was 0.05 until a CMOD of 0.1 mm, and was 0.2 until a CMOD of 4 mm. The limit of proportionality (LOP) was calculated as follows:
, =
∙ ∙
∙∙
,
(3)
where is the load corresponding to the LOP, = 500 mm is the span length, = 150 mm is the width of the specimen, and = 125 mm is the distance between the tip of the notch and the top of the specimen. The residual flexural tensile strength is given by:
, =
∙ ∙
∙∙
,
(4)
so that , is the residual flexural tensile strength corresponding to CMOD = CMODj or = (j=1, 2, 3, 4), and is the load corresponding with CMOD = CMODj or = (j=1, 2, 3, 4).
4. Results and discussion
4.1 Flexural performance of the arch-type steel fibres Figures 4 and 5 show load–displacement curves from the flexural tests for cementitious composites formed using the arch-type steel fibres with tensile strengths of 1100 and 1300 MPa, respectively. Figure 6 shows the flexural strength and Fig. 7 shows the equivalent flexural strength of the two composite materials. For the composites formed with arch-type reinforcements with a tensile strength of 1100 MPa and a radius of curvature of 25 mm (i.e., sample A25_30_1100), the equivalent flexural strength was lower by 20.4% than the
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equivalent composite formed with hooked-end type reinforcements (i.e., sample H_30_1100). In contrast, sample A35_30_1100 (with a radius of curvature of 35 mm) exhibited a 25.8% larger flexural strength than sample H_30_1100. For the steel fibres with a tensile strength of 1300 MPa, the equivalent flexural strengths of samples A25_30_1300 (with a radius of curvature of 25 mm) and A35_30_1300 (with a radius of curvature of 35 mm) were both greater than that of sample H_30_1300 (by 6.8% and 10.2%, respectively). In the load–displacement curves obtained from flexural performance evaluation, the constant load (i.e., with no abrupt decrease in the load) following cracking indicated that the steel fibres formed a bridge across the cracked surface and did not fracture, but rather were pulled out slowly. Hence, regardless of the tensile strength of the steel fibre, cementitious composites formed using the arch-type fibres with a radius of curvature of 35 mm (i.e., samples A35_30_1100 and A35_30_1300) exhibited favourable flexural performance. This result can be explained by considering the theoretical number of steel fibres in the fracture plane [12, 13]. This calculation is based on the number of steel fibres per unit area, considering boundary conditions due to the specimen specification and three-dimensional random directivity. The orientation factor is given by:
∙ !"#$ ∙ %
( ∙ )1.56 + 0.766 ∙ 1 2 , 34 ℎ ≤ 89
C α= < >1? @ 0.098 ∙ 1∙ + 0.2 ∙ 89 ∙ 1∙ + 0.405, 34 ℎ > 89
√'∙
(5)
where b = 150 mm is the average width of the specimen at fracture, h = 150 mm is the
average depth of the specimen at the fracture, and 89 is length of the steel fibre. The number of fibres per unit cross-sectional area is given by:
n = α∙
G
H
,
(6)
where I9 is the volume fraction of fibre and J9 is the cross-sectional area of the steel fibre. 7
Table 3 lists the resulting orientation factor α and the number of steel fibres on the
fracture plane. For fibres with a radius of curvature of 25 mm, the aspect ratio was l/d = 66,
whereas it was l/d = 72 in the case of the fibres with a radius of curvature of 35 mm. In other words, as the radius of curvature increased, so did the length of the fibre, as well as α,
which resulted in an increase in the number of steel fibres forming an effective bridge across the crack. Increasing the number of steel fibres in the fracture plane is expected to increase the pull-out resistance. With the hooked-end-type steel fibres, the straight-line length from end to end of the fibres was 60 mm; therefore, after forming the hooks, the fibre length will decrease. With the arch-type fibres, the straight-line length before processing was also 60 mm; however, the curved fibres will be shorter, and the smaller the radius of curvature, the shorter the fibre. Because of this, arch-type steel fibres have a smaller orientation factor, and we may expect fewer fibres in the fracture plane than with the hooked-end type fibres. However, as the arch-type fibres were curved, the total length of the fibre in the cementitious composite provides frictional resistance to pull out, in contrast to the hooked-end type steel fibres, whereby only the hooked parts resist pull out. This is evidenced by the fact that the two arch-type steel fibres with differing radii of curvature exhibit improved flexural performance, despite the lower aspect ratio and orientation factor than the hooked-end-type fibres.
4.2 Notched-beam flexural tests The flexural tests of composites formed using the arch-type steel fibres with tensile strengths of 1100 and 1300 MPa and radii of curvature of 25 and 35 mm revealed that sample A35_30_1300 exhibited superior performance. The flexural performance was then characterised for fibre volume fractions of 20, 30, and 40 kg/m3 for arch-type steel fibres with a tensile strength of 1300 MPa and radius of curvature of 35 mm. Figure 8 shows
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load–CMOD curves obtained from notched beam flexural tests. Tables 4–6 list the limit of proportionality 4KL,M and the residual flexural tensile strength 4N,O . 9
With a volume fraction of 20 kg/m3, the results revealed that 4KL,M was 0.2% greater than 9
with the hooked-end type fibres, and the residual flexural tensile strengths 4N,$ , 4N,P , 4N,Q
and 4N,R , were 3.1, 18.2, 25.1, and 33.0% greater than with the hooked-end type fibres,
respectively. With a volume fraction of 30 kg/m3, 4KL,M was 1.4% greater than with the 9
hooked-end type fibres, and the residual flexural tensile strengths 4N,$ , 4N,P , 4N,Q and 4N,R , were 7.7, 12.0, 27.2, and 37.4% greater than with the hooked-end type fibres, respectively.
With a volume fraction of 40 kg/m3, 4KL,M was 4.6% greater than with the hooked-end type 9
fibres, and the residual flexural tensile strengths 4N,$ , 4N,P , 4N,Q and 4N,R , were 2.8, 11.5, 17.3, and 26.3% greater than with the hooked-end type fibres, respectively.
The flexural strength of the arch-type steel fibre reinforced cementitious composites was higher than the equivalent composite formed using the hooked-end type steel fibres. However, the strengths of both types were similar, and furthermore both increased as the volume fraction of steel fibres increased. The residual flexural tensile strength was higher for the composites formed using the arch-type steel fibre than for the composites formed using the hooked-end-type steel fibres at all volume fractions, and both increased as the CMOD increased.
4.3 Predicted flexural strength Previous reports of calculations of the flexural strength of arch-type steel fibre reinforced cement composites have considered only the reinforcing index and volume fraction of steel fibre [16–21]. However, with the arch-type steel fibres, an empirical equation with various
9
design strength and fibre volume fraction should be used, as the matrix strength is particularly important [22]. Using the experimental data reported here, we developed the following expression for the flexural strength of concrete composites formed using arch-type steel fibre reinforcements: S9 T = 0.86>4 U KV @W.X − 515Z4 U KV [
W.X
\] + 3339.5\],
(7)
where f ' cu is the 28-day compressive strength of the concrete, and RI is the product of the aspect ratio and volume fraction of the fibres. Figure 9 shows the results of this expression together with the experimental data; the coefficient of determination was R2 = 0.973.
5. Conclusion
We investigated the flexural performance of arch-type steel fibre reinforced cementitious composites. Previously reported flexural tests have shown that arch-type steel fibres pull out stably, and exhibit good bonding performance with a bend length of 1.5 mm and a radius of curvature of 25 mm or 35 mm. We carried out flexural tests and found that the arch-type steel fibre reinforcements with a tensile strength of 1300 MPa and a radius of curvature of 35 mm exhibited the best performance. Notched beam flexural tests were performed with this fibre with volume fractions of 20, 30, and 40 kg/m3. Tests were also carried out using composites formed with hooked-end-type steel fibres of the same tensile strength. The major results of this study can be summarised as follows.
(1) Arch-type steel fibre reinforced cementitious composites exhibited higher flexural performance to composites formed using hooked-end type steel fibres. The
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composites formed using arch-type steel fibres with a tensile strength of 1300 MPa and radius of curvature of 35 mm exhibited the best performance overall, with a 10.2% higher
equivalent
flexural
strength
than
composites
formed
using
the
hooked-end-type steel fibres. This can be explained by considering that the radius of curvature of the arch-type steel fibres increases as the dimension in the length direction increases, and hence the orientation factor also increases. However, the arch-type steel fibres have a lower aspect ratio and orientation factor than the hooked-end type steel fibres, and the number of fibres in the fracture plane was smaller. Despite this, the arch-type steel fibres exhibited improved flexural strength because the whole of the fibre length exhibits frictional resistance to pull out, due to the curved geometry.
(2) The notched-beam flexural tests revealed that the arch-type steel fibre reinforced cementitious composites exhibited high flexural strength at all volume fractions, as well as high residual flexural tensile strength depending on the CMOD.
(3) We developed an empirical relation describing the flexural strength of the arch-type steel fibre reinforced cementitious composites, which had a coefficient of determination of R2 = 0.973.
Acknowledgements
This research was supported by KOSTEEL Co. from South Korea. The authors are grateful for this support.
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References
[1] Bentur, A. and Mindess, S. Fibre reinforced cementitious composites. ELSEVIER APPLIED SCIENCE. 1990:33-210. [2] Prisco, M. Plizzari, G. and Vandewalle, L. Fibre reinforced concrete: new design perspectives. Mater Struct 2009;42(9):1261-81 [3] Shah, S.P. and Rangan, V. Fibre reinforced concrete properties. Am. Concr. Inst. 1971;68(2):126-35 [4] Balaguru, P.N. and Shah, S.P.. Fibre-Reinforced Cement Composite. McGraw-Hill, Inc., New York. 1992:17-100. [5] Robins, P.J. Austin S.A. and Jones, P.A. Pull-out behavior of hooked steel fibres. Mater STRUCT 2002;35(7):434-42 [6] Soulioti, D.V. Barkoula, N.M. Koutsianopoulos, F. Charalambakis, N. and Matikas, T.E. The effect of fibre chemical treatmet on the steel fibre/cementitious matrix interface. Construction and Building Materials. 2013;40:77-83 [7] Krasnikovs, A. Kononova, O. Khabbaz, A. Machanovsky, E. and Machanovsky, A. Post-cracking behavior of high strength fibre concrete prediction and validation. World Academy of Science. Engineering and Technology. 2011;59:988-92 [8] Laranjeira, F. Molins, C. and Aguado, A. Predicting the pullout response of inclined hooked steel fibres. Cement and Concrete Research. 2010;40:1471-87 [9] Naaman, A. E. Engineered Steel Fibres with Optimal Properties for Reinforcement of Cement Composites. Journal of Advanced Concrete Technology. 2003;1(3):241-52 [10] Holschemacher, K. Influence of fibre type on hardened properties of steel fibre reinforced concrete. In: Procs. of 2nd International Balkans Conference on Challenges of Civil Engineering(BCCCE2013) 23-25 May 2013.Tirana, Albania.
12
[11] Choi, O.C. and Lee, C. Flexural performance of ring-type steel fibre-reinforced concrete. Cement and Concrete Research. 2003;33:841-49 [12] Soroushian, P. Lee, C. Distribution and Orientation of Fibres in Steel Fibre Reinforced Concrete. ACI Materials Journal. 1990;87(5):433-39 [13] Lee, C. and Kim, H. Orientation factor and number of fibres at failure plane in ring-type steel fibre reinforced concrete. Cement and Concrete Research. 2010;40:8210-19 [14] ASTM C1609. Standard test method for flexural performance of fibre-reinforced concrete. American Standard Test Method International, PA, USA, 2010. [15] EN 14651. Test method for metallic fibreed concrete-Measuring the flexural tensile strength(limit of proportionality(LOP)). British Standards Institute Staff, 2005
[16] Song, H. W., and Hwang, S. Mechanical properties of high strength reinforced concrete. Constr. Build. Mater., 2004:18;669–673. [17] Ghosh, S., Battacharya, C., and Ray, S. P. Tensile strength of steel fibre reinforced concrete. Institute of Engineers (India). 1989:69(1); 222–227. [18] Agrawal, R., Singh, A. K., and Singhal, D. Effect of fibre reinforcing index on compressive strength and bond strength of steel fibre reinforced concrete. Institute of Engineers (India). 1996:(77)1; 37–40. [19] Gao, J., Sun, W., and Morino, K. Mechanical properties of steel fibre reinforced high strength light weight concrete. Cem. Concr. Compos., 1997:19; 307–313. [20] Padmarajaiah, S. K. Influence of fibres on the behavior of high strength concrete in fully/partially prestressed beams: an experimental and analytical study. Ph.D. thesis, Indian Institute of Science, Bangalore, India. 1999;904
[21] Won, J.P., Hong, B. T., Choi, T. J., Lee, S. J., and Kang, J. W. Flexural behavior of amorphous
micro-steel
fibre-reinforced
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composites.
Compos.
Struct.,
2012;94(4):1443-9. [22] Thomas, J., Ramaswamy, A. Mechanical properties of steel fibre-reinforced concrete. J Mater Civ Eng ASCE, 2009;19 (5):385–92.
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List of Tables
Table 1 Mix proportions of cementitious composites used in flexural tests. Table 2 Mix proportions of cementitious composites used in notched-beam flexural tests. Table 3 Orientation factor and number of fibres in the failure plane. Table 4 Limit of proportionality (LOP). Table 5 Residual flexural tensile strength of cementitious composites formed using hooked-end-type fibres. Table 6 Residual flexural tensile strength of cementitious composites formed using arch-type fibres.
15
Table 1 Mix proportions of cementitious composites used in flexural tests.
*
fck
Gmax
Slump
Air
W/C
S/a
(MPa)
(mm)
(mm)
(%)
(%)
(%)
30
25
150±25
2±1.5
47.1
48
Unit weight (kg/㎥) W
C
S
G
AD*
173
367
818
924
1.84
superplasticizer
Table 2 Mix proportions of cementitious composites used in notched-beam flexural tests.
*
fck
Gmax
Slump
Air
W/C
S/a
(MPa)
(mm)
(mm)
(%)
(%)
(%)
42
25
50±15
2±1.0
33.8
39.1
Unit weight (kg/㎥) W
C
S
G
AD*
135
400
744
1159
8.0
superplasticizer
Table 3 Orientation factor and number of fibres in the failure plane. Steel fibre type
89 (mm)
Aspect ratio
Orientation
(d/l)
factor (α)
Number of fibres at failure plane
Hooked-ends-type
60
80
0.581
118.2
Arch-type R25mm
49.78
66
0.549
111.8
Arch-type R35mm
54.17
72
0.562
114.5
16
Table 4 Limit of proportionality (LOP). Limit of proportionality, 4KL,M 9
Fibre volume Steel fibre type
fraction
(MPa)
(kg/m3)
batch #1
batch #2
5.564
5.814
5.975
5.462
6.037
5.620
5.709
6.090
6.000
5.909
6.169
5.802
5.108
6.435
5.136
6.172
5.720
6.095
5.780
6.184
5.445
6.835
5.838
6.866
20
Hooked-ends-type
5.704
30
5.864
40
5.970
20
Arch-type R35mm
avg.
5.713
30
5.945
40
6.246
17
Table 5 Residual flexural tensile strength of cementitious composites formed using hooked-end-type fibres. Residual flexural tensile strength, 4N,O (MPa)
Fibre
volume 4N,$
fraction (kg/m3)
batch 2.990 #1
#1
batch 2.251 #2
#2
batch 4.834 #1
#1
batch 4.194 #2
#2
batch 7.954 #1
#1
batch 6.758 #2
4.779
#1
#2
#1
2.470
4.010
#2
18
2.146
batch 4.166
3.058
batch 4.580
4.145
2.234
#2
2.725
4.870 batch 5.332
1.903
batch 2.429
batch 5.149
3.800
6.331
#1
2.212
2.702
#2
3.850
1.336
batch 2.458
batch 2.773
batch 6.203
5.834
40
#1
batch 3.521
5.782
#2
1.545
3.484
1.206 batch 1.071
batch 3.096
2.632
4.480
1.360
1.440
#2
batch 3.933
3.108
#1
batch 1.311
1.847
3.254
avg.
batch 1.056
1.637
1.802 batch 1.637
2.443
30
#1
4N,R
avg.
batch 1.268
1.944
2.645
4N,Q
avg.
batch 1.779
2.897
20
4N,P
avg.
3.329 batch 4.035 #2
2.645
Table 6 Residual flexural tensile strength of cementitious composites formed using arch-type fibres. Residual flexural tensile strength, 4N,O (MPa)
Fibre
volume 4N,$
fraction (kg/m3)
batch 2.972 #1
#1
batch 2.495 #2
#2
batch 5.734 #1
batch 4.423 #1
4.850
3.885
4.823 batch 4.966 #2
#2
batch 5.006 #1
#1
#2
7.648
batch
4.111
#1
3.324
#1
batch 7.010
batch 3.706 #1
3.070
#2
3.020
batch 3.728 #1
3.268
2.723
4.702
#2
19
2.940
batch 2.614
3.271
batch 5.945
6.338
2.693
3.438
5.432
#2
#2
batch 4.145
3.729
6.511 batch 7.935
2.942
#2
batch 4.650
5.453
40
#2
1.604 batch 1.387
batch 3.045
3.546
1.175
1.801
3.902 batch 3.753
3.740
#1
batch 1.567
3.297
5.449
avg.
batch 1.159
1.322
2.130 batch 1.859
3.600
30
#1
4N,R
avg.
batch 1.374
1.637
2.726
4N,Q
avg.
batch 1.727
1.837
20
4N,P
avg.
4.203 batch 5.444 #2
4.918
List of Figures
Figure 1 Photographs of arch-type steel fibres. Figure 2 Setup for flexural tests. Figure 3 Setup for notched-beam flexural tests.
Figure 4 Load–deflection curves obtained from flexural tests with 4_ = 1,100 `a!. Figure 5 Load–deflection curves obtained from flexural tests with 4_ = 1,300 `a!. Figure 6 Results of flexural tests with 4_ = 1,100 `a!. Figure 7 Results of flexural tests with 4_ = 1,300 `a!.
Figure 8 Load–CMOD curves obtained from the notched-beam flexural tests. Figure 9 Measured flexural strength as a function of RI together with the empirical relation in Eq. (7).
20
(a) R=25mm
(b) R=35mm Figure 1 Photographs of arch-type steel fibres.
21
Figure 2 Setup for flexural tests.
22
Figure 3 Setup for notched-beam flexural tests.
Figure 4 Load–deflection curves obtained from flexural tests with 4_ = 1,100 `a!.
Figure 5 Load–deflection curves obtained from flexural tests with 4_ = 1,300 `a!.
Figure 6 Results of flexural tests with 4_ = 1,100 `a!.
Figure 7 Results of flexural tests with 4_ = 1,300 `a!.
Figure 8 Load–CMOD curves obtained from the notched-beam flexural tests.
Figure 9 Measured flexural strength as a function of RI together with the empirical relation in Eq. (7).
S0263-8223(15)00785-0 http://dx.doi.org/10.1016/j.compstruct.2015.08.092 COST 6797
To appear in:
Composite Structures
Please cite this article as: Won, J-P., Lee, J-H., Lee, S-J., Flexural Behaviour of Arch-type Steel Fibre Reinforced Cementitious Composites, Composite Structures (2015), doi: http://dx.doi.org/10.1016/j.compstruct.2015.08.092
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Flexural Behaviour of Arch-type Steel Fibre Reinforced Cementitious Composites Jong-Pil Won*, Jae-Ho Lee, Su-Jin Lee Department of Civil & Environmental System Engineering, Konkuk University, Seoul, 143-701, Republic of Korea
ABSTRACT We investigated the flexural performance of arch-type steel fibre reinforced cementitious composites. We used arch-type steel fibres with a bend length of 1.5 mm and a radius of curvature of either 25 mm or 35 mm. The flexural performance of the two arch-type steel fibres with different radii of curvature was characterised in accordance with ASTM C1609, where the tensile strength of the steel fibre (i.e., 1100 or 1300 MPa) was also varied. With the 1100-MPa steel fibre reinforced cementitious composites, the composite with a radius of curvature of 35 mm exhibited higher flexural performance compared with the composite formed using the hooked-end-type fibres. The flexural tests of the 1300-MPa steel fibre reinforced cementitious composites formed using arch-type steel fibres with both radii of curvature revealed higher flexural performance compared with the composites formed using hooked-end type fibres. The flexural performance was characterised depending on volume fraction of fibres in accordance with EN 14652:2005 using the 1300-MPa arch-type steel fibres with a radius of curvature of 35 mm. The arch-type steel fibre reinforced
*
Corresponding author. Tel.: +82 2 450 3750; Fax: +82 2 2201 0907.
E-mail addresses: [email protected] (J.P. Won)
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cementitious composites exhibited higher flexural strength and higher residual flexural tensile strength than those formed using the hooked-end-type steel fibre reinforcements at all volume fractions. Key words: Flexural performance, Residual flexural tensile strength, Toughness, Steel fibre
1. Introduction
The energy absorption capacity of brittle cementitious composites can be improved via the use of steel fibres, leading to ductile behaviour. The energy absorption capacity is increased due to the bridging effect of the reinforcing fibres across the cracks in the cementitious composite, which improves the mechanical properties [1–4]. The bond performance of steel fibres and cementitious composites is an important factor, and is closely correlated with the mechanical properties of steel fibre reinforced cementitious composites. Bond performance is influenced by the geometry of the steel fibre, the surface properties, and the tensile strength of the fibre. Of these factors, geometry affects bond strength most significantly, and so the shape of steel fibre is especially important [5–9]. Holschenmacher investigated how mechanical performance is affected by the geometry of steel reinforcements using flexural performance tests with hooked-end, straight, crimped, and crimped-flat-end steel fibre reinforcements, where the fibres had a tensile strength of 1100 MPa [10]. The results revealed that the hooked-end-type steel fibre exhibited the best flexural performance, and that the crimped and crimped-flat-end types exhibited an abrupt decrease in the load as the steel fibre began to be pulled out, and subsequently failed when the peak load was reached [10]. Hooked-end-type steel fibres exhibit constant energy absorption capacity and stable ductile behaviour in the post-crack behaviour of steel fibre reinforced cementitious
2
composites. These are the most widely used type of reinforcement, and are commonly used with both ends bent. However, with these fibres, the bond performance is substantially lowered and pull out resistance abruptly reduces at the time of pull out following the occurrence of cracks in the matrix. This occurs in the straight part of the fibres, rather than the hooked part, and limits the mechanical properties of the composite. To overcome this limitation, arch-type steel fibres have been developed. These have superior maximum bond strength and energy absorption capacity compared to hooked-end-type steel fibres, due to their smaller radius of curvature. However, they also exhibit fracturing due to excessive anchoring in the cement matrix. Here we investigate the flexural performance of two arch-type steel fibres with a bend length of 1.5 mm and radii of curvature of either 25 or 35 mm. These reinforcements have previously been shown to exhibit stable pull out and good bond performance. We compared the mechanical properties of composites formed using arch-type and hooked-end-type steel fibres. Notched-beam flexural tests were also carried out for reinforcements with different radii of curvature and volume fractions.
2. Materials and mix proportions
2.1 Arch-type steel fibres The flexural tests were carried out in accordance with the ASTM C1609 [14]. We used arch-type steel fibres with a bend length of 1.5 mm and radii of curvature of either 25 or 35 mm. These structures have been shown to pull out stably, and to exhibit good bond performance. Two fibres were investigated with tensile strengths of 1100 or 1300 MPa, and the results were compared with flexural tests on composites formed with hooked-end-type steel fibre reinforcements of the same tensile strength. Figure 1 shows photographs of the
3
arch-type steel fibre reinforcements. Flexural tests were carried out in accordance with the EN 14651:2005 test method for metallic fibred concrete, where the fibre volume fraction was varied [15]. The specimens were named according to the specification, the steel fibre volume fraction and the tensile strength; for example, the name A25_30_1100 corresponds to arch-type fibres with a radius of curvature of 25 mm, a volume fraction of 30 kg/m3, and a tensile strength of 1100 MPa, and H_30_1100 corresponds to the hooked-end type fibres, with a volume fraction of 30 kg/m3 and a tensile strength of 1100 MPa.
2.2 Mix proportions Table 1 lists the composition of the cementitious composite used for the flexural tests. It consisted of type-I ordinary Portland cement with a specific gravity 3.15, fine aggregates with a specific gravity of 2.58, and coarse aggregates with a specific gravity of 2.69 and a maximum size of 25 mm. The mix was designed to have a compressive strength of 30 MPa. The target slump was 150±25mm, the air content was 2±1.5%, and the steel fibre volume fraction was 30 kg/m3. The cementitious composites used for the notched beam flexural tests employed the same materials as above, and Table 2 lists the mix proportions. The mix was designed to have a compressive strength of 42 MPa. The target slump was 50±15, the air content was 2±1.0%, and the volume fraction of steel fibre was varied through 20, 30, and 40 kg/m3.
3. Experimental
3.1 Flexural tests The flexural tests were carried out in accordance with ASTM C1609. Two 150×150×550
4
mm prismatic specimens that had been aged for 28 days were used for each test. Following curing in water at a constant temperature of 23±2ºC, the specimens were set up as shown in Fig. 2. A 250-kN displacement-controlled universal testing machine (UTM) (SH-250, Shimadzu, Japan) was used for tests, which were carried out with the rate of increase of the net deflection as specified by ASTM C1609; i.e., 0.1 mm/min until a deflection of L/900, and 0.3 mm/min thereafter. The flexural strength was calculated as follows [14]:
=
∙ ∙
,
(1)
where is the peak load, = 450 mm is the span length, = 150 mm is the average
width of the specimen at fracture, and = 150 mm is the average depth of the specimen at fracture. The equivalent flexural strength ratio is given by: , =
∙
∙∙
∙ %,
(2)
where
is the equivalent flexural strength (i.e., the area under the load vs. net deflection curve form 0 to L/150).
3.2 Notched-beam flexural tests The notched-beam flexural tests were carried out in accordance with EN 14651:2005. Two 150×150×550 mm prismatic specimens were used, and the test was repeated. Twenty-four hours before the flexural performance evaluation, a notch (25 mm deep) was cut from the lower central part of the specimen, and a jig was attached to fix a gauge. The crack mouth opening displacement (CMOD) was measured using a clip gauge (UB-5, Tokyosokki, Japan) installed at the notch. After curing for 28 days in water at 23±2ºC, the specimens were set up as shown in Fig. 3. The tests were carried out using a UTM (SH-250, Shimadzu, Japan). In
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accordance with EN 14651:2005, the loading rate was 0.05 until a CMOD of 0.1 mm, and was 0.2 until a CMOD of 4 mm. The limit of proportionality (LOP) was calculated as follows:
, =
∙ ∙
∙∙
,
(3)
where is the load corresponding to the LOP, = 500 mm is the span length, = 150 mm is the width of the specimen, and = 125 mm is the distance between the tip of the notch and the top of the specimen. The residual flexural tensile strength is given by:
, =
∙ ∙
∙∙
,
(4)
so that , is the residual flexural tensile strength corresponding to CMOD = CMODj or = (j=1, 2, 3, 4), and is the load corresponding with CMOD = CMODj or = (j=1, 2, 3, 4).
4. Results and discussion
4.1 Flexural performance of the arch-type steel fibres Figures 4 and 5 show load–displacement curves from the flexural tests for cementitious composites formed using the arch-type steel fibres with tensile strengths of 1100 and 1300 MPa, respectively. Figure 6 shows the flexural strength and Fig. 7 shows the equivalent flexural strength of the two composite materials. For the composites formed with arch-type reinforcements with a tensile strength of 1100 MPa and a radius of curvature of 25 mm (i.e., sample A25_30_1100), the equivalent flexural strength was lower by 20.4% than the
6
equivalent composite formed with hooked-end type reinforcements (i.e., sample H_30_1100). In contrast, sample A35_30_1100 (with a radius of curvature of 35 mm) exhibited a 25.8% larger flexural strength than sample H_30_1100. For the steel fibres with a tensile strength of 1300 MPa, the equivalent flexural strengths of samples A25_30_1300 (with a radius of curvature of 25 mm) and A35_30_1300 (with a radius of curvature of 35 mm) were both greater than that of sample H_30_1300 (by 6.8% and 10.2%, respectively). In the load–displacement curves obtained from flexural performance evaluation, the constant load (i.e., with no abrupt decrease in the load) following cracking indicated that the steel fibres formed a bridge across the cracked surface and did not fracture, but rather were pulled out slowly. Hence, regardless of the tensile strength of the steel fibre, cementitious composites formed using the arch-type fibres with a radius of curvature of 35 mm (i.e., samples A35_30_1100 and A35_30_1300) exhibited favourable flexural performance. This result can be explained by considering the theoretical number of steel fibres in the fracture plane [12, 13]. This calculation is based on the number of steel fibres per unit area, considering boundary conditions due to the specimen specification and three-dimensional random directivity. The orientation factor is given by:
∙ !"#$ ∙ %
( ∙ )1.56 + 0.766 ∙ 1 2 , 34 ℎ ≤ 89
C α= < >1? @ 0.098 ∙ 1∙ + 0.2 ∙ 89 ∙ 1∙ + 0.405, 34 ℎ > 89
√'∙
(5)
where b = 150 mm is the average width of the specimen at fracture, h = 150 mm is the
average depth of the specimen at the fracture, and 89 is length of the steel fibre. The number of fibres per unit cross-sectional area is given by:
n = α∙
G
H
,
(6)
where I9 is the volume fraction of fibre and J9 is the cross-sectional area of the steel fibre. 7
Table 3 lists the resulting orientation factor α and the number of steel fibres on the
fracture plane. For fibres with a radius of curvature of 25 mm, the aspect ratio was l/d = 66,
whereas it was l/d = 72 in the case of the fibres with a radius of curvature of 35 mm. In other words, as the radius of curvature increased, so did the length of the fibre, as well as α,
which resulted in an increase in the number of steel fibres forming an effective bridge across the crack. Increasing the number of steel fibres in the fracture plane is expected to increase the pull-out resistance. With the hooked-end-type steel fibres, the straight-line length from end to end of the fibres was 60 mm; therefore, after forming the hooks, the fibre length will decrease. With the arch-type fibres, the straight-line length before processing was also 60 mm; however, the curved fibres will be shorter, and the smaller the radius of curvature, the shorter the fibre. Because of this, arch-type steel fibres have a smaller orientation factor, and we may expect fewer fibres in the fracture plane than with the hooked-end type fibres. However, as the arch-type fibres were curved, the total length of the fibre in the cementitious composite provides frictional resistance to pull out, in contrast to the hooked-end type steel fibres, whereby only the hooked parts resist pull out. This is evidenced by the fact that the two arch-type steel fibres with differing radii of curvature exhibit improved flexural performance, despite the lower aspect ratio and orientation factor than the hooked-end-type fibres.
4.2 Notched-beam flexural tests The flexural tests of composites formed using the arch-type steel fibres with tensile strengths of 1100 and 1300 MPa and radii of curvature of 25 and 35 mm revealed that sample A35_30_1300 exhibited superior performance. The flexural performance was then characterised for fibre volume fractions of 20, 30, and 40 kg/m3 for arch-type steel fibres with a tensile strength of 1300 MPa and radius of curvature of 35 mm. Figure 8 shows
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load–CMOD curves obtained from notched beam flexural tests. Tables 4–6 list the limit of proportionality 4KL,M and the residual flexural tensile strength 4N,O . 9
With a volume fraction of 20 kg/m3, the results revealed that 4KL,M was 0.2% greater than 9
with the hooked-end type fibres, and the residual flexural tensile strengths 4N,$ , 4N,P , 4N,Q
and 4N,R , were 3.1, 18.2, 25.1, and 33.0% greater than with the hooked-end type fibres,
respectively. With a volume fraction of 30 kg/m3, 4KL,M was 1.4% greater than with the 9
hooked-end type fibres, and the residual flexural tensile strengths 4N,$ , 4N,P , 4N,Q and 4N,R , were 7.7, 12.0, 27.2, and 37.4% greater than with the hooked-end type fibres, respectively.
With a volume fraction of 40 kg/m3, 4KL,M was 4.6% greater than with the hooked-end type 9
fibres, and the residual flexural tensile strengths 4N,$ , 4N,P , 4N,Q and 4N,R , were 2.8, 11.5, 17.3, and 26.3% greater than with the hooked-end type fibres, respectively.
The flexural strength of the arch-type steel fibre reinforced cementitious composites was higher than the equivalent composite formed using the hooked-end type steel fibres. However, the strengths of both types were similar, and furthermore both increased as the volume fraction of steel fibres increased. The residual flexural tensile strength was higher for the composites formed using the arch-type steel fibre than for the composites formed using the hooked-end-type steel fibres at all volume fractions, and both increased as the CMOD increased.
4.3 Predicted flexural strength Previous reports of calculations of the flexural strength of arch-type steel fibre reinforced cement composites have considered only the reinforcing index and volume fraction of steel fibre [16–21]. However, with the arch-type steel fibres, an empirical equation with various
9
design strength and fibre volume fraction should be used, as the matrix strength is particularly important [22]. Using the experimental data reported here, we developed the following expression for the flexural strength of concrete composites formed using arch-type steel fibre reinforcements: S9 T = 0.86>4 U KV @W.X − 515Z4 U KV [
W.X
\] + 3339.5\],
(7)
where f ' cu is the 28-day compressive strength of the concrete, and RI is the product of the aspect ratio and volume fraction of the fibres. Figure 9 shows the results of this expression together with the experimental data; the coefficient of determination was R2 = 0.973.
5. Conclusion
We investigated the flexural performance of arch-type steel fibre reinforced cementitious composites. Previously reported flexural tests have shown that arch-type steel fibres pull out stably, and exhibit good bonding performance with a bend length of 1.5 mm and a radius of curvature of 25 mm or 35 mm. We carried out flexural tests and found that the arch-type steel fibre reinforcements with a tensile strength of 1300 MPa and a radius of curvature of 35 mm exhibited the best performance. Notched beam flexural tests were performed with this fibre with volume fractions of 20, 30, and 40 kg/m3. Tests were also carried out using composites formed with hooked-end-type steel fibres of the same tensile strength. The major results of this study can be summarised as follows.
(1) Arch-type steel fibre reinforced cementitious composites exhibited higher flexural performance to composites formed using hooked-end type steel fibres. The
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composites formed using arch-type steel fibres with a tensile strength of 1300 MPa and radius of curvature of 35 mm exhibited the best performance overall, with a 10.2% higher
equivalent
flexural
strength
than
composites
formed
using
the
hooked-end-type steel fibres. This can be explained by considering that the radius of curvature of the arch-type steel fibres increases as the dimension in the length direction increases, and hence the orientation factor also increases. However, the arch-type steel fibres have a lower aspect ratio and orientation factor than the hooked-end type steel fibres, and the number of fibres in the fracture plane was smaller. Despite this, the arch-type steel fibres exhibited improved flexural strength because the whole of the fibre length exhibits frictional resistance to pull out, due to the curved geometry.
(2) The notched-beam flexural tests revealed that the arch-type steel fibre reinforced cementitious composites exhibited high flexural strength at all volume fractions, as well as high residual flexural tensile strength depending on the CMOD.
(3) We developed an empirical relation describing the flexural strength of the arch-type steel fibre reinforced cementitious composites, which had a coefficient of determination of R2 = 0.973.
Acknowledgements
This research was supported by KOSTEEL Co. from South Korea. The authors are grateful for this support.
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References
[1] Bentur, A. and Mindess, S. Fibre reinforced cementitious composites. ELSEVIER APPLIED SCIENCE. 1990:33-210. [2] Prisco, M. Plizzari, G. and Vandewalle, L. Fibre reinforced concrete: new design perspectives. Mater Struct 2009;42(9):1261-81 [3] Shah, S.P. and Rangan, V. Fibre reinforced concrete properties. Am. Concr. Inst. 1971;68(2):126-35 [4] Balaguru, P.N. and Shah, S.P.. Fibre-Reinforced Cement Composite. McGraw-Hill, Inc., New York. 1992:17-100. [5] Robins, P.J. Austin S.A. and Jones, P.A. Pull-out behavior of hooked steel fibres. Mater STRUCT 2002;35(7):434-42 [6] Soulioti, D.V. Barkoula, N.M. Koutsianopoulos, F. Charalambakis, N. and Matikas, T.E. The effect of fibre chemical treatmet on the steel fibre/cementitious matrix interface. Construction and Building Materials. 2013;40:77-83 [7] Krasnikovs, A. Kononova, O. Khabbaz, A. Machanovsky, E. and Machanovsky, A. Post-cracking behavior of high strength fibre concrete prediction and validation. World Academy of Science. Engineering and Technology. 2011;59:988-92 [8] Laranjeira, F. Molins, C. and Aguado, A. Predicting the pullout response of inclined hooked steel fibres. Cement and Concrete Research. 2010;40:1471-87 [9] Naaman, A. E. Engineered Steel Fibres with Optimal Properties for Reinforcement of Cement Composites. Journal of Advanced Concrete Technology. 2003;1(3):241-52 [10] Holschemacher, K. Influence of fibre type on hardened properties of steel fibre reinforced concrete. In: Procs. of 2nd International Balkans Conference on Challenges of Civil Engineering(BCCCE2013) 23-25 May 2013.Tirana, Albania.
12
[11] Choi, O.C. and Lee, C. Flexural performance of ring-type steel fibre-reinforced concrete. Cement and Concrete Research. 2003;33:841-49 [12] Soroushian, P. Lee, C. Distribution and Orientation of Fibres in Steel Fibre Reinforced Concrete. ACI Materials Journal. 1990;87(5):433-39 [13] Lee, C. and Kim, H. Orientation factor and number of fibres at failure plane in ring-type steel fibre reinforced concrete. Cement and Concrete Research. 2010;40:8210-19 [14] ASTM C1609. Standard test method for flexural performance of fibre-reinforced concrete. American Standard Test Method International, PA, USA, 2010. [15] EN 14651. Test method for metallic fibreed concrete-Measuring the flexural tensile strength(limit of proportionality(LOP)). British Standards Institute Staff, 2005
[16] Song, H. W., and Hwang, S. Mechanical properties of high strength reinforced concrete. Constr. Build. Mater., 2004:18;669–673. [17] Ghosh, S., Battacharya, C., and Ray, S. P. Tensile strength of steel fibre reinforced concrete. Institute of Engineers (India). 1989:69(1); 222–227. [18] Agrawal, R., Singh, A. K., and Singhal, D. Effect of fibre reinforcing index on compressive strength and bond strength of steel fibre reinforced concrete. Institute of Engineers (India). 1996:(77)1; 37–40. [19] Gao, J., Sun, W., and Morino, K. Mechanical properties of steel fibre reinforced high strength light weight concrete. Cem. Concr. Compos., 1997:19; 307–313. [20] Padmarajaiah, S. K. Influence of fibres on the behavior of high strength concrete in fully/partially prestressed beams: an experimental and analytical study. Ph.D. thesis, Indian Institute of Science, Bangalore, India. 1999;904
[21] Won, J.P., Hong, B. T., Choi, T. J., Lee, S. J., and Kang, J. W. Flexural behavior of amorphous
micro-steel
fibre-reinforced
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2012;94(4):1443-9. [22] Thomas, J., Ramaswamy, A. Mechanical properties of steel fibre-reinforced concrete. J Mater Civ Eng ASCE, 2009;19 (5):385–92.
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List of Tables
Table 1 Mix proportions of cementitious composites used in flexural tests. Table 2 Mix proportions of cementitious composites used in notched-beam flexural tests. Table 3 Orientation factor and number of fibres in the failure plane. Table 4 Limit of proportionality (LOP). Table 5 Residual flexural tensile strength of cementitious composites formed using hooked-end-type fibres. Table 6 Residual flexural tensile strength of cementitious composites formed using arch-type fibres.
15
Table 1 Mix proportions of cementitious composites used in flexural tests.
*
fck
Gmax
Slump
Air
W/C
S/a
(MPa)
(mm)
(mm)
(%)
(%)
(%)
30
25
150±25
2±1.5
47.1
48
Unit weight (kg/㎥) W
C
S
G
AD*
173
367
818
924
1.84
superplasticizer
Table 2 Mix proportions of cementitious composites used in notched-beam flexural tests.
*
fck
Gmax
Slump
Air
W/C
S/a
(MPa)
(mm)
(mm)
(%)
(%)
(%)
42
25
50±15
2±1.0
33.8
39.1
Unit weight (kg/㎥) W
C
S
G
AD*
135
400
744
1159
8.0
superplasticizer
Table 3 Orientation factor and number of fibres in the failure plane. Steel fibre type
89 (mm)
Aspect ratio
Orientation
(d/l)
factor (α)
Number of fibres at failure plane
Hooked-ends-type
60
80
0.581
118.2
Arch-type R25mm
49.78
66
0.549
111.8
Arch-type R35mm
54.17
72
0.562
114.5
16
Table 4 Limit of proportionality (LOP). Limit of proportionality, 4KL,M 9
Fibre volume Steel fibre type
fraction
(MPa)
(kg/m3)
batch #1
batch #2
5.564
5.814
5.975
5.462
6.037
5.620
5.709
6.090
6.000
5.909
6.169
5.802
5.108
6.435
5.136
6.172
5.720
6.095
5.780
6.184
5.445
6.835
5.838
6.866
20
Hooked-ends-type
5.704
30
5.864
40
5.970
20
Arch-type R35mm
avg.
5.713
30
5.945
40
6.246
17
Table 5 Residual flexural tensile strength of cementitious composites formed using hooked-end-type fibres. Residual flexural tensile strength, 4N,O (MPa)
Fibre
volume 4N,$
fraction (kg/m3)
batch 2.990 #1
#1
batch 2.251 #2
#2
batch 4.834 #1
#1
batch 4.194 #2
#2
batch 7.954 #1
#1
batch 6.758 #2
4.779
#1
#2
#1
2.470
4.010
#2
18
2.146
batch 4.166
3.058
batch 4.580
4.145
2.234
#2
2.725
4.870 batch 5.332
1.903
batch 2.429
batch 5.149
3.800
6.331
#1
2.212
2.702
#2
3.850
1.336
batch 2.458
batch 2.773
batch 6.203
5.834
40
#1
batch 3.521
5.782
#2
1.545
3.484
1.206 batch 1.071
batch 3.096
2.632
4.480
1.360
1.440
#2
batch 3.933
3.108
#1
batch 1.311
1.847
3.254
avg.
batch 1.056
1.637
1.802 batch 1.637
2.443
30
#1
4N,R
avg.
batch 1.268
1.944
2.645
4N,Q
avg.
batch 1.779
2.897
20
4N,P
avg.
3.329 batch 4.035 #2
2.645
Table 6 Residual flexural tensile strength of cementitious composites formed using arch-type fibres. Residual flexural tensile strength, 4N,O (MPa)
Fibre
volume 4N,$
fraction (kg/m3)
batch 2.972 #1
#1
batch 2.495 #2
#2
batch 5.734 #1
batch 4.423 #1
4.850
3.885
4.823 batch 4.966 #2
#2
batch 5.006 #1
#1
#2
7.648
batch
4.111
#1
3.324
#1
batch 7.010
batch 3.706 #1
3.070
#2
3.020
batch 3.728 #1
3.268
2.723
4.702
#2
19
2.940
batch 2.614
3.271
batch 5.945
6.338
2.693
3.438
5.432
#2
#2
batch 4.145
3.729
6.511 batch 7.935
2.942
#2
batch 4.650
5.453
40
#2
1.604 batch 1.387
batch 3.045
3.546
1.175
1.801
3.902 batch 3.753
3.740
#1
batch 1.567
3.297
5.449
avg.
batch 1.159
1.322
2.130 batch 1.859
3.600
30
#1
4N,R
avg.
batch 1.374
1.637
2.726
4N,Q
avg.
batch 1.727
1.837
20
4N,P
avg.
4.203 batch 5.444 #2
4.918
List of Figures
Figure 1 Photographs of arch-type steel fibres. Figure 2 Setup for flexural tests. Figure 3 Setup for notched-beam flexural tests.
Figure 4 Load–deflection curves obtained from flexural tests with 4_ = 1,100 `a!. Figure 5 Load–deflection curves obtained from flexural tests with 4_ = 1,300 `a!. Figure 6 Results of flexural tests with 4_ = 1,100 `a!. Figure 7 Results of flexural tests with 4_ = 1,300 `a!.
Figure 8 Load–CMOD curves obtained from the notched-beam flexural tests. Figure 9 Measured flexural strength as a function of RI together with the empirical relation in Eq. (7).
20
(a) R=25mm
(b) R=35mm Figure 1 Photographs of arch-type steel fibres.
21
Figure 2 Setup for flexural tests.
22
Figure 3 Setup for notched-beam flexural tests.
Figure 4 Load–deflection curves obtained from flexural tests with 4_ = 1,100 `a!.
Figure 5 Load–deflection curves obtained from flexural tests with 4_ = 1,300 `a!.
Figure 6 Results of flexural tests with 4_ = 1,100 `a!.
Figure 7 Results of flexural tests with 4_ = 1,300 `a!.
Figure 8 Load–CMOD curves obtained from the notched-beam flexural tests.
Figure 9 Measured flexural strength as a function of RI together with the empirical relation in Eq. (7).