Materials and Design 54 (2014) 32–42

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Materials and Design

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Mechanical behavior of hybrid steel-fiber self-consolidating concrete:Materials and structural aspects

0261-3069/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.matdes.2013.08.014

⇑ Corresponding author. Tel.: +55 (21) 2562 8493x48; fax: +55 (21) 2562 8484.E-mail address: fsilva@coc.ufrj.br (Flávio de Andrade Silva).

Dimas Alan Strauss Rambo, Flávio de Andrade Silva ⇑, Romildo Dias Toledo FilhoCivil Engineering Department, COPPE, Universidade Federal do Rio de Janeiro, P.O. Box 68506, CEP 21941-972, Rio de Janeiro, RJ, Brazil

a r t i c l e i n f o

Article history:Received 24 April 2013Accepted 5 August 2013Available online 14 August 2013

Keywords:Hybrid reinforcementRound panel testCrack formationSteel fiberSelf-consolidating concrete

a b s t r a c t

This work presents the preliminary results of an experimental investigation on the mechanical behaviorof self-consolidating concrete reinforced with hybrid steel fibers in the material and structural scale.Straight and hooked end steel fibers with different lengths and diameters were used as reinforcementin fiber volume fractions of 1.0 and 1.5%. In the fresh state the concrete was characterized using theslump flow, L-box and V-funnel tests. To determine the effect of the hybrid reinforcement on the plasticviscosity and shear yield stress a parallel plate rheometer was used. Following, the mechanical responsewas measured under tension and bending tests. In the flexural test, the movement of the neutral axis wasexperimentally determined by strain-gages attached to compression and tensile surfaces. Furthermore,the mechanical response of the material under bi-axial bending was addressed using the round paneltest. During the test the crack opening was measured using three linear variable differential transformers(LVDT’s). The cracking mechanisms were discussed and compared to that obtained under four pointbending and direct tension. The obtained results indicated that the fiber hybridization improved thebehavior of the composites for low strain and displacement levels increasing the serviceability limit stateof the same through the control of the crack width. For large displacement levels the use of the longerfibers led to a higher toughness but with an expressive crack opening. Due to its structural redundancythe round panel test allowed the formation of a multiple cracking pattern which was not observed in thefour point beam tests. Finally, the obtained material’s properties were used in a nonlinear finite elementmodel to simulate the round panel test. The simulation reasonably agreed with the experimental testdata.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

The first works on fiber reinforced concrete (FRC) were real-ized in the 1950s and 60s decades of the last century with theaim of understanding the mechanical behavior of steel fiber rein-forced concrete [1,2]. Since that period, other fibers have beenevaluated as reinforcement in concrete elements, but steel is stillthe most used fiber. Its popularity is associated with the fact thatsteel presents a good affinity with concrete, the ease of use, thehigh toughness and resistance to static and dynamic loads [3].Several categories of fiber reinforced concrete have been devel-oped over the past three decades presenting different mechanicalproperties. Conventional FRC presents an increase in the ductilitywhen compared with the plain matrix showing a strain softeningbehavior after the appearance of the first crack. On the otherhand the high performance fiber reinforced cementitious com-posites (HPFRCC) exhibit a deflection hardening behavior and

can also present a strain-hardening type of response accompa-nied by multiple cracking in tension which leads to an improve-ment in strength and toughness compared to the non-reinforcedmatrix [4–6].

In the last few decades significant improvements in the devel-opment of cement based materials have been achieved resultingin high performance concrete that can present uniaxial compres-sive strength ranging from 150 to 400 MPa [5,7,8]. Theseimprovements were only possible due to developing techniquesof cement paste microstructure densification using efficientsuperplasticizing chemical additives and ultra-fine particles. Theproduction of hybrid fiber reinforced self-consolidating concretesaims to combine the mechanical properties of two or more differ-ent fibers to the rheological characteristics of self-consolidatingmatrices. Hybrid reinforcement systems can be used in order totake advantage of each individual fiber properties [9], which de-pend on the shape, type, size and the volume fraction of the usedfibers [1]. These composite systems can improve not only flexuraland tensile strength, but can also lead to a change in the crackingmechanisms. The manufacturing, the fiber dispersion and the fi-ber orientation are very important to improve the post-cracking

D.A.S. Rambo et al. / Materials and Design 54 (2014) 32–42 33

response of the fiber reinforced concrete [10]. Thus, the rheolog-ical properties of the matrices should be suitable for the fiberaddition [11]. It is worth noticing that most of the research per-formed on FRC systems found in the literature uses in the mixdesign matrices that do not contain coarse aggregates, but in-stead, fine aggregates [12–14].

Kim et al. [14] studied the flexural performance of hybrid ultrahigh performance FRC using one micro (L = 13 mm) and four typesof macro (L = 30 and 62 mm) high strength steel fibers. The resultsshowed an improvement in deflection and toughness for hybridsystems in comparison to systems reinforced by micro fibers only.

Akcay and Tasdemir [15], produced four different HSFRSCC’s(hybrid steel fiber reinforced self-compacting concrete) and re-ported that it is possible to add a volume fraction of fibers up to1.5% without affecting its workability. The mechanical behaviorshowed that the fiber hybridization increased the concrete fractureenergy and ductility.

A multi-scale reinforced cement composite was developed byRossi et al. at the Laboratoire Central des Ponts et Chausses (LCPC)[16]. Two types of materials were developed by using the multi-scale concept. A cement based compositewhich was reinforcedby 7% of two metal fibers of different geometries, and the CEM-TECmultiscale

�that was reinforced by 11% of three classes of steel fi-

bers [17,18]. Both materials present a tension hardening behaviorbut the MSCC can achieve up to 15 MPa under direct tension whilethe CEMTEC up to 20 MPa.

The mechanical behavior of fiber reinforced concrete is usuallyevaluated using bending tests, mostly performed in small prisms.This type of test does not represent the real structural behavior be-cause it results in a different cracking mechanism and normallyleads to a higher dispersion on experimental results [10,19–21].Structural or quasi-full scale tests as ASTM: C-1550, however, havegreater representation in relation to the concrete volume, failuremechanisms and toughness. As reported by Bernard [20] themechanical tests need to reflect the material variations and notvariations associated to the test method. Round panel tests wereperformed in steel fiber reinforced concretes with different dimen-sions. Results indicate that the main advantage of this test is to al-low the detection of a multiple crack pattern which is not observedin tests with small beams. Bernard [22] investigated the influenceof support conditions on flexural and shear behavior of steel fiberreinforced concrete slabs. According to the author, bending testsperformed on panels supported on three points show a consistentfailure mode and allows a more reliable measure of the concreteperformance when compared to alternative methods of support.Minelli and Plizzari [19] performed a comparison between roundpanel and flexural beam tests. Results reported that the geometryand fracture area involved in round panel tests leads to a lower dis-persion resulting in a better representation of the real structuralbehavior.

The effects of the steel fiber hybridization on the rheologicaland mechanical properties of self-consolidating FRC are addressedin the present work. Two different hybrid FRC systems were pro-duced, using straight and hooked end steel fibers with differentlengths, in fiber volume fractions of 1.0% and 1.5%. The self consol-idating concrete matrix was designed and produced based on thecompressible packing model. A parallel plate rheometer was usedto determine the influence of fiber hybridization on the plastic vis-cosity and shear yield stress. Furthermore, empirical rheologicaltests were performed. Mechanical tests were carried out in thestructural and materials scale and the changes in the crackingmechanisms were investigated. Direct tension and four pointbending tests were performed in the materials scale while theround panel tests for the structural testing. A non-linear finite ele-ment model was used to simulate the mechanical behavior of thestudied FRC system in the structural scale.

2. The compressible packing model

The compressible packing model (CPM) was developed by deLarrard and his collaborators and used in this research to designthe matrix of the self-consolidating fiber reinforced concrete[23,24]. Composite materials like concrete are made up of grainsembedded in a matrix. The aim of the design is to use the least pos-sible amount of binder by combining these grains in order to min-imize the concrete porosity [23]. The equation representing thevirtual packing density of a granular mix containing n classes ofgrains, ordered in such a way that its diameters ared1 � d2 � . . . di � diþ1 � . . . � dn, when the class i is dominant, isexpressed by the following equation:

cðiÞ ¼ bi

1�Xi�1

j¼1

yj 1� bi þ bi;jbi 1� 1bj

� �� ��Xn

j¼iþ1

yjð1� ai;jbibjÞ

ð1Þ

where c(i) is the virtual packing density when the ith class is dom-inant; yi is the volumetric fraction of the ith class; bi is the virtualpacking density of the ith class; it represents the volume of grainscontained in an unitary volume, compacted with an ideal compac-tion energy that would correspond to a maximum virtual packing;ai,j and bi,j represent the loosening effect and the wall effect exertedby the grains, respectively; they can be determined either experi-mentally or by the following formulas:

ai;j ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� ð1� dj=diÞ1:02

q

bi;j ¼ 1� ð1� di=djÞ1:50ð2Þ

The virtual compactness of the mix can be found by using theformula:

c ¼ inf ðcðiÞÞ ð3Þ

where inf indicates the least value.The actual compactness depends on three main parameters: the

size of the grains, the shape of the grains, and the method of pro-cessing the packing. The compressible packing model allows mak-ing the transition from virtual compactness, which cannot beobtained in practice, to the actual compactness of the mix, whichdepends on the energy being applied at the time of placing. A scalarK called compaction index enables connecting the virtual compact-ness (c) with the actual compactness (/). This scalar is strictlydependent on the protocol implemented for the particular mix.As K tends to infinity, the compactness / tends to the virtual com-pactness c.

The general shape of the compaction index equation, for n clas-ses of grains, is as follows:

K ¼Xn

i¼1

yi=bi

1=/� 1=cðiÞð4Þ

where / is the actual compactness of the granular mix.The values of index K are calculated from the binary mixes for

each placing processes. K assumes a value of 4.5 when the compac-tion process is the simple pouring, 6.7 for water demand and 9when the placing process is vibration plus 10 kPa compression[23].

If the actual compactness for a single granular class i (/i) isexperimentally determined, by means of a compaction processhaving compaction index K, it is possible to use Eq. (5), derivedfrom Eq. (4), to determine the virtual compactness of the granularclass i.

bi ¼/i

Kð1þ KÞ ð5Þ

Table 1Mix composition of concretes.

Constituent Mixtures

Matrix C1.0%H C1.0% C1.5%H C1.5%

Coarse aggregate (G) (kg/m3) 494 468 468 454 454Sand (S1) (kg/m3) 830 830 830 830 830

34 D.A.S. Rambo et al. / Materials and Design 54 (2014) 32–42

Eq. (4) is an implicit equation in / and allows the determination ofthe actual compactness since the other variables are all known.

To use the model it was determined the virtual compactness,size grading distributions and specific gravity of the constituentsas well as the cement contribution to compressive strength andthe saturation dosage of the chemical additive.

*Sand (S2) (kg/m3) 100 100 100 100 100Silica mesh 325 (kg/m3) 70 70 70 70 70Cement (kg/m3) 360 360 360 360 360Fly ash (kg/m3) 168 168 168 168 168Silica fume (kg/m3) 45 45 45 45 45Superplasticizer (kg/m3) 45.1 45.1 45.1 45.1 45.1Viscosity modifier (kg/m3) 0.36 0.36 0.36 0.36 0.36Water (kg/m3) 150 150 150 150 150Straight fiber (SF1) (kg/m3) 0 39 0 39 0Hooked end fiber (SF2) (kg/

m3)0 39 78 78 117

Superplasticizer (%) 4 4 4 4 4Water/binder ratio 0.50 0.50 0.50 0.50 0.50

* Sand (S2): sand (S1) with diameter less than 0.85 mm.

3. Materials and processing

The matrix was designed following the CPM routine describedin Section 2. For the fiber addition the rheological behavior of thematrix was adjusted through the use of superplasticizer and a vis-cosity modifier. The materials used in the self-consolidating con-crete composition were a Brazilian slag cement type CPIII 40with a 28 days compressive strength of 40 MPa, river sand withtwo classes of particle size: one ranging from 0.15 mm to 4.8 mmand the other from 0.15 mm to 0.85 mm, coarse aggregates withmaximum diameter of 9.5 mm, fly ash, silica flour (ground quartz),silica fume, and a polycarboxilate superplasticizer with solid con-tents of 31.2%. The water/cementitious material ratio of the self-compacting composite was 0.32. Fig. 1 shows the grain size distri-bution of the used binder materials and aggregates.

Two steel fiber types, one straight (SF1) and one with hookedends (SF2), were used as reinforcement. The straight fiber pre-sented a tensile strength of 1100 MPa, elastic modulus of200 GPa and a density of 7.85 g/cm3, and the fiber with hookedends (SF2) a tensile strength of 1150 MPa, elastic modulus of200 GPa and a density of 7.85 g/cm3. The length and aspect ratioof the SF1 fiber were 12 mm and 67 and those presented by SF2were 35 mm and 65, respectively. The SF1 fiber was produced witha brass coating providing the fiber a relatively smooth surface.

Five concrete mixtures, with the proportions presented in Ta-ble 1 were produced. One control mixture without steel fibers,two mixtures with a fiber volume fraction of 1.0% (78 kg/m3)named as C1.0% (1.0% of SF2) and C1.0%H (0.5% of SF1 + 0.5% ofSF2) and two mixtures with a fiber volume fraction of 1.5%(117 kg/m3) named as C1.5% (1.5% of SF2) and C1.5%H (0.5% ofSF1 + 1.0% of SF2).

The concretes were produced in a room with controlled temper-ature of 21 �C ± 1 �C using a planetary mixer (previously mois-tured) of 100 l capacity. The cementitious materials werehomogenized by dry mixing for 60 s prior to the addition of sand.The dry ingredients were mixed for an additional 60 s prior to addi-tion of superplasticizer and water. The mixture was blended for8 min.

Fig. 1. Particle size distribution of (a) the used

For the production of the samples, the concrete mixtures wereplaced in the steel molds in one layer. The round panel forms weremade using a thin steel sheet and a wood base with thickness of20 mm. After consolidation, the round panel surfaces were leveledwith a steel plate. The samples did not suffer any kind of vibration.The specimens were covered in their molds for 48 h prior to moistcuring for 28 days in a cure chamber with 100% RH and 23 ± 1 �C.

4. Rheological tests

The effect of the hybrid reinforcement on the plastic viscosityand shear yield stress was measured with a parallel plate rheome-ter developed at the LCPC [25]. Ten rotation speeds ranging from0.2 rev/s to 0.8 rev/s were used to perform the tests. These speedscorrespond to strain rates of 0.25 s�1 and 6.0 s�1.

The tests with V funnel were performed in an apparatus withrectangular top and bottom sections of 515 mm� 75 mm and65 mm� 75 mm (length and width), respectively [26]. Through thistest the elapsed time (in seconds) between the opening of the bot-tom and the time when all the concrete flows through the lower sec-tion can be determined in order to measure the concrete flow ability.

The L box test was used to measure the filling and passing abil-ity of the studied concretes [27]. Three different configurations ofbars (12 mm of diameter) were used. The space between barswas 94 mm (one bar), 58.66 mm (two bars) and 41 mm (threebars).

cementitious materials and (b) aggregates.

D.A.S. Rambo et al. / Materials and Design 54 (2014) 32–42 35

Finally, the slump flow test was used to describe the flow abilityof the fresh mixtures in unconfined condition [28]. The determina-tion of the concrete spread was performed by the arithmetic aver-age of two measurements of the perpendicular concrete massdiameter.

5. Mechanical testing

5.1. Direct tensile test

Direct tensile tests were performed in a Shimadzu universaltesting machine model UH-F1000kN with a computer-controlledhydraulic servo system. The tests were controlled by the actuatordisplacement at a rate of 0.1 mm/min (strain rate of1.6 � 10�5 s�1). Four dumbbell shaped specimens measuring400 mm � 100 mm � 48.5 mm (length �width � thickness) weretested using a gage length of 100 mm with fixed-hinged boundaryconditions for each concrete mix produced. Fig. 2 shows the testingarrangement for the tensile test. Steel plates were glued on bothends of the specimen at the gripping regions. A set of mechanicalgrips were used. The tensile load and actuator displacement wererecorded.

5.2. Four point bending test

The bending tests were performed in the same Shimadzu uni-versal testing machine used in direct tensile tests. Three specimenswere produced for each concrete mix produced, with cross sec-tional dimensions of 100 mm � 100 mm (width � thickness) and

Fig. 2. Direct tensile test set-up.

length of 400 mm. The span used between supports was 300 mmlong and between the loading knives 100 mm. The tests were con-trolled by the actuator displacement at a rate of 0.5 mm/min. Thedeflections of the beams at the mid-span were measured usingone LVDT. The neutral axis movement was experimentally deter-mined by strain-gages (51.1 mm of length) attached to compres-sion and tensile surfaces. The crack opening in the bottomsample face of the beams was measured using one LVDT positionedon the mid-span and aligned with the length. Furthermore, thecracking development was also recorded during the loading cycleof the bending test at regular time intervals for posterior imageanalysis. A Nikon D90 digital camera with an AF Micro Nikkor60 mm lens (f/2.8D) and frame grabber captured images of4288 � 2848 pixels in resolution at 60 s intervals. The images wereused to measure the crack width during bending tests.

6. Round panel test

Structural tests were performed through round panel testsbased on the ASTM: C-1550. The nominal diameter and the thick-ness of all tested specimens were 750 mm and 75 mm, respec-tively. Three symmetrically arranged pivots (40 mm of diameter)were used to support the samples (see Fig. 3). Three round panelspecimens were tested to failure in a Shimadzu servo-controlledtesting machine for each concrete mix produced. The load was ap-plied using a rigid steel cylinder (50 mm of diameter) onto theupper surface of the specimen at an actuator displacement rateof 0.5 mm/min. The deflection response (until 40 mm) was mea-sured using a LVDT positioned at the central part of the bottomsurface of the specimens. During the tests the crack opening, inthe bottom surface, was measured using a triangle shaped systemof three LVDT’s with three equal sides of 190 mm.

7. Discussion and analyses

7.1. Rheological properties

Fig. 4 shows the influence of steel fibers on the self-compactingconcrete flow measured with the parallel plate rheometer used inthis study. It can be seen that while the unreinforced concrete be-haves linearly following the Bingham model the FRC curves arenon-linear. The rheological parameters of the fiber reinforced con-cretes were then calculated using the Herschel–Bulkley modelwhere, s0o a and b are characteristics material parameters that de-scribe the fresh behavior of concrete.

s ¼ s0o þ a _cb ð6Þ

To correlate the material parameters s00 and ‘‘a’’ of the Herschel–Bulkley model with the numerical parameters Co, A and b theexpressions derived by De Larrard and co-workers [29], shown inEqs. (7) and (8), were used. In those expressions R1 and R2 arethe internal and external sample radii of the rheometer (20 mmand 120 mm, respectively), and h is the height of the sample(100 mm).

s0o ¼3

2pðR32 � R3

1ÞCo ð7Þ

a ¼ 0;9ðbþ 3Þð2pÞbþ1

hb

ðRbþ32 � Rbþ3

1 ÞA ð8Þ

The plastic viscosity was determined using the equivalentparameters a and b using Eq. (9), which correlates the Herschel–Bulkley and Bingham models, where _cmax represents the maximumstrain rate used during the test ð _cmax ¼ 6 s�1Þ.

Fig. 3. Round panel test set-up: (a) details of the supports and LVDT’s and (b) detail of the crack opening measurement system.

Fig. 4. Influence of steel fibers on the self-compacting concrete flow of (a) concrete reinforced with 1.0% of steels fibers and (b) with 1.5%. The experimental points of the FRCwere adjusted by the Herschel–Bulkley model.

36 D.A.S. Rambo et al. / Materials and Design 54 (2014) 32–42

�l ¼ 3abþ 2

_cb�1max ð9Þ

From Fig. 4 and Table 2 it can be seen that, although a non-lin-ear (Herschel–Bulkley) behavior was noticed, the non-hybrid sys-tems presented a shear yield stress and viscosity lower than thatobserved in the unreinforced matrix. On the other hand the hybrid-ization of fibers (i.e. the addition of the 12 mm straight steel fiber)increased the viscosity of the mix. This behavior was more pro-nounced for the reinforcement ratio of 1.5%. Comparing the hybridsystem reinforced with 1.0% (Fig. 4a) to the one with 1.5% (Fig. 4b)it can be seen that the shape of the curves are different and that forspeeds above 0.5 rev/s the non-linearity increases in a differentrate. This behavior indicates that the shear yield strength increaseswhen increasing the fiber volume fraction of the hybrid systems.This was confirmed when computing the shear yield stress whichwas found to be 111 Pa for the mix reinforced with 1.0% and220 Pa for that reinforced with 1.0% of steel fiber.

As showed in Table 2, even with the incorporation of steel fi-bers, all concretes had adequate viscosity and deformability under

Table 2Results of rheological tests.

Mixtures Spread (mm) V-funnel (s) L-box (H2/H1)

I

Matrix 620 18.15 0.95C1.0%H 705 18.39 0.95C1.0% 720 19.28 1.00C1.5%H 620 BL 0.53C1.5% 700 19.56 0.86

BL = congestion of flow section.I, II, III = number of steel bars.

their own weight. All studied concretes can be classified as self-compacting as they presented values of slump flow consistent withthe lower limit given by EFNARC 2005 [30] (P550 mm). The slumpflow diameter values ranged from 620 to 700 mm. The unrein-forced matrix and the concretes produced with 1.0% of fibers(C1.0% and C1.0%H) also meet the EFNARC specification for viscos-ity (V funnel) and passing ability (L-box). The concrete reinforcedwith 1.5%H was blocked in the V funnel and in the L-box with 2bars. All the fiber reinforced concrete mixes were blocked in theL-box test with three bars. This occurs due to the small spacing be-tween the bars that is not common in structures where such fiberreinforcement dosages (1.0% and 1.5%) and aspect ratios are used.

7.2. Mechanical behavior

Fig. 5 presents one representative curve obtained in the directtensile test for each material investigated in the present work.The results of evaluation of all curves are given in Table 3. A smallbranch of hardening was only observed for the mixtures C1.5% and

Viscosity (Pa s) Shear yield stress (Pa)

II III

0.90 0.85 187 1830.90 BL 230 1110.86 BL 157 178BL BL 341 2200.50 BL 156 131

Fig. 5. Influence of the steel fiber reinforcement ratio in the direct tensile behaviorof the self-consolidating concretes.

D.A.S. Rambo et al. / Materials and Design 54 (2014) 32–42 37

C1.5%H. The composites reinforced with 1.0% of steel fiber pre-sented a strain softening behavior. The tensile curves were de-picted in 3 distinct phases. Phase I corresponds to the elastic-linear range where both matrix and the fiber behave linearly.Due to low volume fraction of fibers (61.5%) the stiffness of thecomposite is dominated by matrix properties and this zone is lim-ited to strain measures of up to 0.016%. This was confirmed by theelastic modulus value of approximately 30 MPa computed for allconcretes. Phase II is marked by the bend over point (BOP) whichcorresponds to the formation of matrix cracking. Phase III wascharacterized by a strain softening behavior for composites rein-forced with 1.0% and strain hardening for 1.5% of reinforcement.The addition of the 12 mm fibers did not affect the ultimate tensilestrength (UTS) and rBOP. The maximum UTS of 4.46 MPa was ob-

Table 3Average results of the direct tensile test. Standard deviation values are presented in paren

Mixtures Tensile strength, deformation and modulus

rBO (MPa) eBOP (%) Et (GPa) rUTS (MPa) eUTS

Matrix 2.19 (0.57) 0.0097 (0.0022) 28.93 (1.56) – –C1.0% 3.75 (0.49) 0.0163 (0.0087) 30.40 (1.33) 3.89 (0.59) 0.08C1.0%H 3.74 (1.31) 0.0162 (0.0048) 30.53 (2.43) 3.85 (1.31) 0.06C1.5% 3.89 (0.59) 0.0113 (0.0016) 32.07 (3.28) 4.46 (0.36) 0.17C1.5%H 3.09 (0.25) 0.0142 (0.0024) 31.11 (3.53) 3.74 (0.22) 0.25

Fig. 6. Influence of the steel fiber reinforcement in the mechanical behavior of the self-cozoom in (a) up to 0.4 mm of displacement.

served for the C1.5%. The strain hardening was marked by the for-mation of only one visible cracking. This crack was able to widenfrom 0.1% to 0.3% of deformation where a strain softening behaviorstarted.

Fig. 6a presents one representative curve obtained in the four-point bending tests for each reinforcement ratio and hybridizationinvestigated in the present work. The results of evaluation of allcurves are given in Table 4. All fiber reinforced concretes presenteda deflection hardening behavior with a single cracking formationsurrounded by ramifications. The curves can be divided in fourmain phases. The phase I corresponds to the linear elastic regionwhere both matrix and fiber behave linearly. In this region bothcompression and tension strains are compatible. The limit of pro-portionality (LOP) delimit the phase II. The LOP increased withthe addition of fiber reinforcement from 7.58 MPa (unreinforcedmatrix) to 10.70 MPa (C1.0%H) (see Fig. 6b). This can be explainedby the action of the 12 mm fibers that bridges the micro-cracks.When further increasing the reinforcement ratio to 1.5% it was no-ticed a tendency of decreasing in LOP probably due to an increasein the matrix porosity. The post LOP range (phase III) is character-ized by a deflection hardening behavior but with the formation ofone single crack. Phase IV is characterized by the strain softeningresponse due to the widening of the crack. The highest flexuralbehavior was observed for the composite C1.5% which presentedstrength of 17.66 MPa. This represents an increase of 2.3 times incomparison to the unreinforced matrix. It seems that the fiberhybridization did not influence the flexural strength. The tough-ness computed as the total area under the load displacement curveshowed to be sensitive to the hybridization of fibers. At low levelsof displacement (i.e. 0.2 mm) the hybrid composites (C1.0%H andC1.5%H) showed a higher efficiency on energy absorption capacityin comparison with non-hybrid systems (C1.0% and C1.5%). Forexample, the concrete C1.0%H presented a toughness of 6.72 Jwhile the C1.0% 5.61 J. This can be attributed to the ability of the

theses.

Tensile toughness

(%) T0.5mm (J) T1.0mm (J) T2.0mm (J) T3.0mm (J) T4.0mm (J)

– – – – –88 (0.12) 5.7 (1.1) 10.4 (2.9) 16.9 (5.7) 20.5 (7.5) 22.5 (8.1)50 (0.071) 5.8 (2.1) 9.9 (4.1) 15.0 (5.3) 18.5 (6.4) 20.3 (7.5)4 (0.092) 6.3 (1.4) 11.1 (2.8) 16.8 (4.7) 21.1 (6.1) 25.0 (9.2)7 (0.040) 5.7 (0.5) 12.3 (1.1) 19.2 (1.9) 23.8 (2.2) 26.1 (4.5)

nsolidating concrete in the materials scale: (a) stress vs. displacement curves and (b)

Tabl

e4

Ave

rage

resu

lts

ofth

efle

xura

lbe

amte

st.S

tand

ard

devi

atio

nva

lues

are

pres

ente

din

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Mix

ture

sFl

exu

ral

stre

ngt

han

ddi

spla

cem

ent

Flex

ura

lTo

ugh

nes

s

P LO

P(k

N)

rLO

P(M

Pa)

d LO

P(m

m)

P u(k

N)

MO

R(M

Pa)

d MO

R(m

m)

T 0.2

mm

(J)

T 1.0

mm

(J)

T 2.0

mm

(J)

T 3.0

mm

(J)

T 4.0

mm

(J)

Mat

rix

25.2

7(2

.51)

7.58

(0.7

5)0.

049

(0.0

07)

––

––

––

––

C1.

0%29

.60

(2.7

8)8.

88(0

.84)

0.05

9(0

.002

)43

.08

(11.

06)

12.9

3(3

.32)

0.83

(0.1

6)5.

61(0

.72)

38.5

7(2

.56)

71.2

5(4

.53)

95.2

4(7

.20)

112.

9(1

0.23

)C

1.0%

H36

.02

(3.3

1)10

.70

(1.0

1)0.

053

(0.0

07)

44.3

6(2

.97)

13.3

0(0

.89)

0.53

(0.2

2)6.

72(0

.56)

40.8

2(3

.73)

71.9

2(6

.56)

91.3

7(8

.90)

105.

28(1

1.02

)C

1.5%

34.9

5(2

.82)

10.4

8(0

.84)

0.05

6(0

.007

)58

.89

(4.4

9)17

.66

(1.3

4)0.

72(0

.07)

7.16

(0.1

5)49

.87

(2.1

1)97

.67

(5.4

1)13

3.60

(6.5

1)16

3.21

(6.9

5)C

1.5%

H31

.42

(3.2

9)9.

42(0

.98)

0.04

9(0

.007

)51

.46

(13.

35)

15.4

3(4

.00)

0.67

(0.0

5)7.

33(0

.26)

45.2

4(1

2.05

)87

.53

(24.

13)

117.

77(3

4.65

)14

0.68

(43.

71)

38 D.A.S. Rambo et al. / Materials and Design 54 (2014) 32–42

small fibers (SF1) to delay micro-cracks in the concrete matrix.However, for high displacement levels, the opposite occurs, andthe hybrid reinforced mixtures showed a more pronounced soften-ing branch and lower toughness values than that of the non-hybridreinforced mixtures. Kim et al. [14] performed a similar work andtheir results for bending tests of FRC’s reinforced with a mix ofhooked end and micro fibers resulted in an increase of bendingstrength and toughness. It should be noted that they have used ahigher fiber dosage and a fine mortar matrix which resulted inhigher efficiency of fiber–matrix stress transfer.

The data acquisition of strains from the compression and ten-sion faces during the bending test allowed the computation ofthe neutral axis, NA (normalized with specimen depth, h) as seenin Fig. 7a and b. During the bending test the section remains con-stant at the centroidal location (0.5 h) until the first crack forma-tion which happens at a deflection of about 0.05–0.06 mm. Asudden change of the NA to 0.3 h happens for the non-hybrid sys-tem and is observed after the formation of the first crack. This NAcontinues to reduce until the displacement of 0.1 mm to a value ofapproximately 0.23–0.25 h. This value indicates that assumingplane sections remaining plane, 76–78% of the sample cross sectionis in tension while the rest is in compression. For the hybrid sys-tems (in special the C1.5%H mixture) a gradual decrease in NA isobserved as a result of stress redistribution due to crack formation.This value reaches 0.3 h at a displacement of 0.1 mm indicatingthat the fiber hybridization was effective in mitigating the micro-crack development as previously indicated by the toughness re-sults calculated at low displacements.

The bending and tensile responses are compared in Fig. 8. Theinset plot shows the relationship between LOP vs. BOP and MOR(modulus of rupture) vs. UTS. It can be seen that under bending,loads associated with the formation of the first crack occur at stresslevels 2.5 times higher as those observed for the direct tensiontests. At these stress levels a similar response was observed forall composites. Although a greater variability was noticed at ulti-mate stress states, it can be concluded that values reported forMOR is approximately four times greater than that of the UTS.The localized strain measured from the electrical resistance gagepositioned at the tensile surface is also shown in Fig. 8. The resultsshow that strains corresponding to first crack formation (from0.01% to 0.016%) are in the same range for bending and tensileloads. It can also be seen that the strain response agrees well withthe LVDTs results until the crack appearance (LOP).

Fig. 9a shows one representative curve obtained in the roundpanel test for each studied material. Table 5 presents the resultsand calculations related to the tests. In the same way as that ob-served for the flexural beam tests the round panel test resultscan be divided in four phases. Phase I corresponds to the linearelastic region where the compressive and tensile strains are com-patible. The formation and propagation of the first crack delimitsthe second phase. During phase III all FRC’s exhibited a straindeflection behavior with the formation of three major axial cracks.Several multiple fine cracks (see the inset in Fig. 9a) were also no-ticed. The localization and widening of one major crack leads theFRC to failure which is followed by a strain softening behavior.While the unreinforced concrete presented the formation of onlythree major radial cracks all steel fiber reinforced concretes alsopresented a formation of multiple micro-cracks. A similar behaviorwas also reported by Bernard when testing FRC round panel spec-imens [20,22]. In a different manner than that observed for theflexural beam tests the fiber hybridization in the panels were ben-eficial in increasing the first crack and ultimate loads for both stud-ied reinforcement ratios. For example, for the reinforcement ratioof 1% the first crack and ultimate load increased from 29.76 to41.16 MPa and from 39.66 to 45.50 MPa, respectively. When look-ing at Fig. 9b it can be seen that for low displacements (i.e.

Fig. 7. Neutral axis computation: (a) non-hybrid and (b) hybrid systems.

Fig. 8. Comparative of flexural and tensile response. The curve in red shows thelocal strain measurement of the electrical gage positioned in the tensile surface ofthe flexural specimen.

D.A.S. Rambo et al. / Materials and Design 54 (2014) 32–42 39

<2.5 mm) the fiber reinforcement plays a major role in themechanical behavior of the FRC’s. For displacements at phase I(in the linear elastic region) it was observed that the hybridizationin the C1.5%H increased the load bearing capacity showing the

Fig. 9. Influence of steel fiber reinforcement on the round panel test: (a) load vs. displaresults up to 2.5 mm of displacement.

capacity of the short 12 mm fibers of bridging the micro-cracksand increasing the serviceability limit of the structure. The tough-ness values computed at 5 and 10 mm also confirmed this mecha-nism. At these displacements the energy absorption capacity wassuperior for hybrid concretes than that observed by the concretesreinforced only with the 35 mm hooked end fibers (refer toTable 5).

The crack opening was measured during the round panel andbeam flexural test for the concrete specimens reinforced with1.5% of the hooked end fibers. Fig. 10a shows one representativecurve along with the crack opening measurements of the three ma-jor cracks for the round panel and of the single crack for the flex-ural beam. Fig. 10b presents a detail plot of the crack openinguntil a central displacement of 6 mm. The crack opening develop-ment for the round panel can be divided in three phases. The firstphase corresponds to the linear elastic range. It can be seen thatthe three used LVDT’s only measured the matrix deformationwhich was linear elastic up to a deformation of 1.2 mm. At thispoint the several radial cracks start to form. At phase II, from thecentral displacement of 1.2 mm (0.73Pu) until 2.0 mm (0.89Pu),the originated cracks propagated across the radius of the round pa-nel specimen. At the end of phase II (0.89Pu) a crack opening of0.2 mm was measured. It should be noticed that codes and specifi-cations for design of most reinforced concrete structures establishthat the maximum allowable crack widths should range from 0.15to 0.38 mm. Phase III initiates at the displacement of 2 mm. Fromthis point and above the three cracks start a widening process

cement results and typical crack pattern at 40 mm for C1.5% and (b) a zoom in the

Table 5Average results of round panel test. Standard deviation values are presented in parentheses.

Mixtures First crack strength Flexural strength Toughness

P (kN) d (mm) P (kN) d (mm) T5.0mm (J) T10mm (J) T20mm (J) T30mm (J) T40mm (J)

Matrix 30.71 (3.72) 0.72 (0.05) – – – – – – –C1.0% 29.76 (2.66) 0.95 (0.08) 39.66 (3.86) 3.42 (0.26) 164 (13.1) 336 (40.3) 519 (111) 781 (150) 870 (280)C1.0%H 41.16 (0.61) 1.46 (0.25) 45.50 (1.97) 3.26 (0.54) 189 (13.2) 368 (15.1) 547 (25.9) 627 (98.5) 649 (170)C1.5% 40.25 (0.58) 1.23 (0.16) 53.82 (4.76) 5.30 (0.56) 207 (17.7) 481 (30.5) 841 (87.9) 1021 (144) 1077 (320)C1.5%H 46.36 (2.62) 1.16 (0.51) 63.38 (5.96) 5.23 (0.65) 255 (30.8) 549 (64.8) 612 (105) 1207 (250) 1303 (325)

Fig. 10. Crack opening measurements: (a) correlation of the crack opening measurements using three LVDT’s and the load vs. displacement curve obtained in the round paneland flexural beam test for the C1.5%; (b) Zoom in the crack opening measurements up to 6 mm.

40 D.A.S. Rambo et al. / Materials and Design 54 (2014) 32–42

which for this specific specimen followed different rates. It was ob-served a mean crack opening of 1.5 mm at the displacement corre-sponding to the maximum load. During the strain softening regionthe cracks continued to open until the final measured central dis-placement of 40 mm. The final measured cracking opening was12 mm for LVDT 1 and 27 mm for LVDT’s 2 and 3.

In the flexural beam test the crack initiated at the mid-span dis-placement of 0.056 mm (0.6Pu). Results obtained from LVDT mea-surement and image analysis showed similar values. The crackopening was linear up to 2.0 mm (end of the strain softening

Fig. 11. Uniaxial compressive and tensile stress strain relationship used in the finiteelement simulation.

phase). Different from the round panel test it was not possible toidentify the point at which the crack crossed the specimen. Atthe modulus of rupture point a crack width of 1.5 mm was mea-sured (same value as reported for the round panel). It was observedthat for the same load ratios the crack width measured in the flex-ural beam test was higher. For example the crack width computedat 0.89Pu was found to be 0.36 mm in comparison to 0.2 mm ob-tained at the same load ratio for the round panel. From the resultsreported above it can be concluded that the 35 mm hooked end fi-ber is effective in bridging the major and localized cracks leading toa more stable crack propagation whereas the 12 mm fibers canlimit the initiation and propagation of microcracks. This behavioris only visible in the structural scale testing performed in the roundpanels.

7.3. Finite element analysis

A nonlinear simulation of the mechanical behavior of round pa-nel samples was performed in the finite element software ABAQUSusing the concrete damaged plasticity model [31]. The global ele-ment was created according with the dimension of the real sample.The round panel sample was discretized using 10404 shell ele-ments with reduced integration (S4R). These type of elements areusually employed in structures in which the thickness is approxi-mately 1/10 the overall size. The three supports were fixed in threemesh nodes spaced 120 �C radially in accordance with the testgeometry. Each support was modeled as hinges, unable to movein the load direction. The used constitutive material relationshipis shown in Fig. 11. The experimental results were obtained inthe present work and in the author’s previous work [32].

In order to determine the load–displacement curves, incremen-tal displacements were imposed at the central node and the reac-tion force was measured. Fig. 12 compares the experimentalresults with the simulation and shows the stress and displacement

Fig. 12. Comparison of finite element analysis and experimental tests for the C1.5% and the stress and displacement fields immediately after the initiation of the first crack.

D.A.S. Rambo et al. / Materials and Design 54 (2014) 32–42 41

fields of the FEA. The simulation results obtained from the finiteelement analysis showed a good correlation with the experimentalresults, as the model accurately predicted the load vs. displace-ment curve. The simulation at first crack reveals a maximum stressof 3.69 MPa in the central part as well as over the three majorcracks. These agree well with the mean first crack stress of3.89 MPa found in the direct tension tests. Central displacementand load corresponding to first crack were smaller than the meanvalues found in the experiments indicating that the modeledboundary conditions were stiffer than the real tests. The use ofround panel tests to validate the finite element model is importantfor further use in structural design. More research is needed to ver-ify the model with others fibers in order to be able to use thisknowledge for the material and structural design purposes. Theuse of the finite element analysis can be a powerful and uniquetool to design structural elements reinforced with fibers thus sav-ing enormous time in laboratory.

8. Conclusions

The following conclusions can be drawn from the present workon mechanical behavior of self-compacting concrete:

– The results obtained from the parallel plate rheometer showedthat while the unreinforced concrete behaves linearly followingthe Bingham model the FRC curves are non-linear followingHerschel–Bulkley. The hybridization of fibers increased the vis-cosity of the mix. Also for the hybrid system the increase in fibervolume fraction lead to an increase in the shear yield strength.

– The direct tensile tests did not show any improvements for fiberhybridization. Nevertheless for concretes reinforced with 1.5%of fibers a small strain hardening branch has been observed.

– The flexural beam tests showed that all concretes have a deflec-tion hardening behavior but with the formation of one macrocrack. The fiber hybridization was effective to increase thetoughness for central displacements up to 0.2 mm. The compu-tation of the neutral axis by means of electrical strain gagesshowed a gradual decrease when hybrid fibers are used in com-parison to a sudden drop at 0.3 h observed for the non-hybridsystems. Therefore, the fiber hybridization was effective in mit-igating the micro-crack formation during bending tests.

– All FRC’s used in the round panel tests were characterized by aformation of three major cracks and several micro-cracks. Thefiber hybridization was very effective in limiting the initiationand propagation of micro-crack thus increasing the first-crack

and ultimate loads. A comparison of crack width performed inthe materials (four point bending) and structural scale (roundpanel) showed that the widths related to same loading ratioare smaller in the panel tests. Furthermore, crack widths com-puted at up to 90% of the ultimate load were in the rangeallowed in most of the design codes for reinforced concrete.

Finite element analysis was performed for the round paneltests. The results showed a good correlation with the experimentaltests. Stresses at first crack were also similar in experimental FEsimulation and experiments. It seems that the boundary conditionsin the model are somehow stiffer than the ones used in the exper-iments leading to lower displacements at first crack.

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