G.J. Parra-Montesinos, H.W. Reinhardt, and A.E. Naaman (Eds.): HPFRCC 6, pp. 373–380. © RILEM 2012

Characterization of Bending and Tensile Behavior of Ultra-High Performance Concrete Containing Glass Fibers

S. Rigaud, G. Chanvillard, and J. Chen

Lafarge Centre de Recherche, Saint Quentin Fallavier, France

Abstract. Ultra High Performance Concrete (UHPC) is used to design structural elements with unique combinations of aesthetic, lightness, self-placing and ductil-ity properties. The difficulty to design such a ductile composite is obtaining an optimum compromise between reinforcements, cementitious matrix strengths, rheology and costs.

An ultra high performance reinforced concrete containing glass fibers (GF-UHPRC) is described for thin plate geometries. Including complete mechanical characterization, based on four point bending tests, and reverse analyses to extract the post-cracking behavior in tension (e.g. the tensile strength versus strain rela-tionship of the glass fibers). The results of accelerated aging tests in 50°C water showed that its durability and ductility were maintained.

1 Introduction

Ultra-high performance fiber reinforced concrete allows the design of complex and very thin structural elements by combining aesthetic, lightness, self-placing and ductility properties. The difficulty to design such a ductile composite is ob-taining an optimum compromise between reinforcements, matrix strengths, rheol-ogy and costs.

The purpose of this paper is to present an ultra high performance reinforced concrete containing glass fibers (called here GF-UHPRC) for thin-plate applica-tions. The mechanical performances of such material were evaluated in bending tests. A reverse analysis method was used, based on the mechanical equilibrium of the cracked cross section to obtain the direct tensile behavior. An important point in all glass fiber reinforced cementitious composites is a loss of ductility due to wet aging. This phenomenon is attributed to the growth of portlandite at the glass/fiber mortar interface [2, 7]. Results showed that the ductility was main-tained after accelerated aging tests.

374 S. Rigaud, G. Chanvillard, and J. Chen

2 Glass Fibers and Ultra-High Performance Concrete

From a rheological perspective, the aim is to design a GF-UHPRC with self-placing capability. The glass fiber used is a bundle of numerous microfilaments held together by a sizing. An appropriate choice of sizing is needed to ensure good fluidity and adequate bonding between the fiber and the matrix. The mechanical results shown in this paper are based on commercially available hydrophilic fibers. The physical characteristics of the glass fibers are shown below.

- Young´s modulus: 72 GPa - Tensile strength: 1200 MPa–1700 MPa - Length: 6 mm - Diameter: 0.15 mm–0.2 mm - Slenderness: 30-40 - Density: 2.6 g/cm3

Two other aspects must be taken into account to design a ductile GF-UHPRC. The cementitious matrix strength must be adapted to the tensile strength and aspect ra-tio of the glass fibers to avoid an early failure of the composite. The composites in this study have a W/C ratio from 0.25 to 0.30, a compressive strength of 120-140 MPa after 28-day hydration at ambient temperature, and up to 170 MPa after acce-lerated aging at 50°C. The volume content of glass fibers must ensure an adequate mean spacing of the fibers compatible with the maximum sand size of the matrix to ensure good rheological properties and efficient crack bridging. Moreover, each fiber must have sufficient mobility, without forming clusters. The volume content of glass fibers in GF-UHPRC is thus limited to 2%-2.5% to ensure a self-placing composite (Fig. 1).

3 Characterization Tests

The tensile behavior was characterised by reverse analysis carried out on four point bending tests. The specimens were 450 x 145 x 20 mm3 plates cut from a larger plate (Fig. 1) after demolding at 24 hours. The samples were stored in a room at 20°C and 100% HR for 28 days. A device fixed to the plate measured the real deflection (Fig. 2). The latter was controlled during the test by a LVDT sensor at a rate of 0.1 mm/min. Fig. 4 shows two series of tests performed on composites with varying glass fiber contents and matrix strengths.

Characterization of Bending and Tensile Behavior 375

Fig. 1. Self-placing properties. The plates are sawn in the direction of casting after demolding

Fig. 2. Deflection measuring device

Fig. 3 illustrates very low dispersion for the elastic behavior or the first cracking stress, and the ductile nature of the composite. The limit of proportionality was reached at a deflection of 0.4 mm and 0.5 mm in both systems; the maximum load (modulus of rupture) corresponded to a deflection of approximately of 3.5 mm and 2.3 mm for the composites with 2.0% and 2.5% volume fibers, respectively. Such ductile behavior is due to fine multiple cracking (Fig. 4) in the area submitted to the highest flexural moment.

Four points bending tests on plates (450*145*20 mm3)

0

5

10

15

20

25

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Deflecion (mm)

Str

ess

(MP

a)

2% glass fibers2.5% glass fibers

Fig. 3. Flexural tests on two types of composites Fig. 4. Multiple cracking on the tensile face after the flexural test

The location of the main crack was established after the peak; the opening me-chanism depended directly on the anchoring of the fibers in the matrix and how well the fibers were located regarding the main crack. Fig. 3 shows a systematic failure of the fibers characterised on the curves by a steep slope just after the peak. It is important to highlight that the ultimate deflection obtained before the failure of the fibers is not a material but a structural property. As soon as a uniform crack distribution was established in the central area of the specimen, the ultimate de-flection was reached. Consequently, a longer plate would directly increase this de-flection and the multiple cracking. Table 1 summarizes the obtained mechanical properties. Young´s modulus (E) could be estimated with Eq. 1 from the elastic behavior and the real deflection measurement. It took into account the effect of shear stress occurring outside the central area of the plate. F represents the load, h the thickness of the plate, δ the deflection, I the inertia moment, ν the Poisson coefficient and for L and a see Fig. 2.

L

a

376 S. Rigaud, G. Chanvillard, and J. Chen

( ) ( )[ ]νδ

++−= 18.44348

222 haLI

FaE (1)

Table 1. Flexural results

E (GPa) Elastic limit σfe (MPa) Max stress(MPa)

Composite 1 - 2% glass fibers 45 13.5 17

Composite 2 - 2.5% glass fibers 47 16 20

The lower side of the sample is in tension during the flexural test. The limit of proportionality (σfe) in bending is known to not match the elastic limit in pure ten-sion. This is called the scale effect phenomena and arises from micro-cracking oc-curring above the crack front, leading to a higher apparent limit of proportionality compared to the real tensile strength. Models based on the cohesive crack concept [5] describe this phenomena very well; the CEB Model Code [3] is a simplified model describing the scale effect on beam-geometry given in Eq. (2). The coeffi-cient β depends on the type of matrix and varies between 1 and 2. Coefficient β increases with the brittleness of the matrix; and h (in mm) represents the height of the sample.

7.0

7.0

100.

100.1

.

+

=h

h

fet

β

βσσ (2)

Three 70 x 70 x 280 mm3 prisms were made for each system and tested in four-point bending test to illustrate the scale effect. The aim was only to obtain the elastic limit to apply the CEB Model Code and know the direct tensile strength of the two GF-UHPRC studied in this paper. The limit of proportionalities (σfe) were 13 MPa and 15 MPa for composites 1 and 2, respectively. It seems that β=2 is a good compromise for the GF-UHPRC systems. The direct tensile strengths of the two composites were 8 MPa and 9 MPa, respectively, when applying the relation (2). Additional mechanical tests would be necessary to evaluate these results more accurately.

4 Reverse Analysis

Calculations were done for a rectangular cracked section (height h, width b), loaded in flexure. This section is divided into two parts (Fig. 5). First, the compo-site has an elastic behavior in the compressive zone and at the beginning of the tensile zone. Second, the material is in tension and damaged by an unknown beha-vior law. The objective is to determine this tensile post-cracking behavior.

Characterization of Bending and Tensile Behavior 377

Neutral axis

zt

zc

z

0

Ela

stic

area

Dam

aged

area

h

α n.h

Neutral axis

zt

zc

z

0

Ela

stic

area

Dam

aged

area

h

α n.h

Fig. 5. Stress distribution in the section (zc: height of the compressive area; zt: height where the tensile strength is reached, before damage zt=h/2; αn: relative height of neutral axis, be-fore damage αn=0.5.)

This approach is similar to the French recommendations for UHPFRC [1], without explicitly introducing the cracking concept. From the crack distribution in the con-stant moment zone, we propose a mechanical model based on the assumption of a constant curvature in this area. Consequently, the experimental deflection can be converted into a curvature using Eq. (3). This equation is considered valid until crack localization. The curvature (χ) was chosen to describe the yield strains in the section. All the calculations were done from the neutral axis; the sign convention was negative for tensile stresses and positive for compressive stresses.

223

216

Li

i

δχ = (3)

The mechanical equilibrium of the section led to the following Eq. (4). The sum of axial loads in the section is equal to zero; the sum of the moments was equal to the applied external bending moment (Mext).

0=+= de NNN deext MMM += (4)

Thus, in the elastic area, Eq. (6) was obtained by relation (5).

z.χε = (5)

( )( )

−==

−==

h

t

h

t

z

z tce

z

z tce

zzbE

dzzbM

zzbE

dzbN

33

22

3..

...

2..

..

χσ

χσ (6)

From geometry consideration, the heights zc and zt are given as:

( )nc hz α−= 1 χ2

06

Ebh

Mzt −= (7)

M0 corresponds to the bending moment required to reach the elastic limit on the bottom side, ε0 corresponds to the strain.

The same calculations were reproduced in the damaged zone. The obvious rela-tion dzd .χε = (from Eq. (5)) led to:

378 S. Rigaud, G. Chanvillard, and J. Chen

==−

0 ...

ε

εαε

χσσ

m

t

n

db

dzbNz

hd ==

−

0

2

.....

ε

εαε

χεσσ

m

t

n

db

dzzbMz

hd (8)

εm is the strain of the bottom side, hnm αχε .−= .

An incremental approach was used to calculate the integrals in Eq. (8) consider-

ing two successive loading stages. Stage i of loading is characterized by imε , iχ ,

inα , and introducing σi , the tensile stress associated to i

mε . This gives:

= 0 .ε

εε

χσ

im

db

Ni

id =

0

2

..ε

εε

χεσ

im

db

Mi

id hi

niim αχε .−= (9)

Equations (9) can be expressed between two successive steps as follows (10).

( ) ( )( ) ( )

( )111

11

12

11

1

11

11

1

.

.2

...

.2

.

+++

++

+

++

+

++

++

+

−=−

−++

=

−++

=

iiiiim

im

im

im

imi

imi

i

id

i

iid

im

im

ii

i

id

i

iid

h

bMM

bNN

αχαχεε

εεεσεσχχ

χ

εεσσχχ

χ

(10)

1+inα and σi+1 are unknown in each step; the reverse analysis consists of determin-

ing these two parameters to ensure the mechanical equilibrium of the section. The variables of step 0 were initialized to start the calculation:

00 =eN 6

.. 02

0 σhbM e −= feσσ =0 00 =dN 00 =dM 5.00 =nα

Thus, step-by-step and after a reasonable smoothing process of the experimental data to avoid numerical instabilities, the tensile behavior versus strain could be de-scribed (Fig. 7). An interesting plastic behavior before crack localization was ob-served, leading to the failure of the fibers.

Fig. 6 compares the bending moment, for the two composites from the first cracking, obtained experimentally and by direct modeling using the tensile beha-vior calculated by reverse analyses.

0

50000

100000

150000

200000

250000

0 0.5 1 1.5 2 2.5 3 3.5

Post elastic deflection (mm)

Ben

din

g m

om

ent

(N.m

m)

Composite 1- 2% glass fibers

Modeling composite 1

Composite 2-2.5 glass fibers

Modeling composite 2

0

2

4

6

8

10

12

0.E+00 5.E-04 1.E-03 2.E-03 2.E-03 3.E-03 3.E-03

Strains

Ten

sile

str

ess

(MP

a)

Composite 1 - 2% of glass fibersComposite 2 - 2.5% of glass fibers

Fig. 6. Comparison between experimental data and the modeling of the flexural test

Fig. 7. Tensile behavior obtained by reverse analysis

Characterization of Bending and Tensile Behavior 379

The elastic limit in bending was indeed submitted to a scale effect (§3) and does not equate with the direct tensile strength. Therefore, the first point σfe of the reverse analysis was corrected by the real tensile strength of the composite.

At this stage, it was interesting to compare the reverse analyses results with a simplified approach of the potential tensile strength [4], σp, of a fiber-reinforced concrete (11).

ωσσ ... kv ffp = (11)

vf is the volume content of the fibers (2.0% or 2.5%). σf is the direct tensile of the fibers (~1500 MPa). k is a coefficient for the orientation of the fibers in the matrix. The orientation coefficient is 0.5, 2/π or 1 for a 3D, 2D or 1D distribution, respec-tively. We assumed k=0.6 for an intermediate solution. ω is a coefficient representing the effectiveness of the fiber/matrix combination. All the fibers are therefore perfectly centered relative to the crack for a value equal to one (but in our case, ω=0.5).

Equation (10) gives an estimated tensile strength equal to 9 MPa for the com-posite with 2.0% fibers and 11 MPa for the composite with 2.5% fibers. These re-sults agree with the reverse analyses and show that the fibers’ tensile strength is fully exploited.

5 Durability

An accelerated aging method was used to assess the long-term performance of GF-UHPRC, using the common immersion in hot water method for various pe-riods. The following tests were carried out. The samples were stored in a humid chamber at 20°C-100%HR for one month, then placed in hot water at 50°C for three months after demolding at 24h.

0

5

10

15

20

25

0 0.5 1 1.5 2 2.5 3

Deflection (mm)

Str

ess

(MP

a)

Composite 2 - 28 days at 20°C-100%HRComposite 2 - After accelerated ageing

Fig. 8. Results of four-point bending test after accelerated ageing, composite 2

Fig. 8 illustrates the maintenance of ductility of this composite after wet aging. This aging resistance is due to the optimum use of a pozzolanic filler in the matrix, limiting the formation of portlandite at the fiber interface. Multiple cracking was

380 S. Rigaud, G. Chanvillard, and J. Chen

observed and the maximum bending strength was reached for a deflection of ~1.5 mm. According to previous remarks on structural ductility, this impact on the ultimate deflection should not be considered as a material property. Indeed, struc-tural ductility is largely governed by the length of the specimen. The limit of pro-portionality increased and was equal to 20 MPa; the elastic modulus remained unchanged. This was due to cement hydration and pozzolanic reactions, both of which increased during the accelerated aging. The compressive strength of the composite with 2.5% fibers was 170 MPa after the aging treatment.

6 Conclusions

A self-placing, ductile, ultra high performance reinforced concrete was designed containing glass fibers. Ductility was maintained on thin structural elements after accelerated aging tests by an optimum combination of types of fibers and matrix compositions. Reverse analysis of the flexural results was proposed to extract the mechanical behavior of the composite in direct tension after taking into account the scale effect. The curvature was used as a description parameter; the cracking concept is therefore not explicit. According to the presented model, the tensile be-havior is unique and could be used in codes to design thin structural elements. Considering the very high mechanical performance of this new GF-UHPRC, in terms of strength, ductility and durability, we firmly believe that innovative struc-tural elements could be developed with these composites, thereby facilitating the current drive in construction industries for more sustainable and energy-efficient practices.

References

[1] AFGC, Ultra High Performance Fibre Reinforced Concretes, Recommendations, AFGC Publication, France (January 2002)

[2] Bentur, A., Mindess, S.: Fibre reinforced cementitious composites, 2nd edn., vol. 15. Taylor & Francis, Abingdon (2007)

[3] CEB-FIP, Structural Concrete, textbook on behaviour, design and performance, up-dated knowledge of the CEB-FIP Model Code 1990 FIB Publication (1999)

[4] Chanvillard, G., Rigaud, S.: Complete characterization of tensile properties of Ductal® UHPFRC according to French recommendations. In: HPFRCC-4, June 16-18, p. 14. Michigan, Ann Arbor (2003)

[5] Hillerborg, A., Modéer, M., Petersson, P.E.: Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite element. Cem. Concr. Res. 6, 773–782 (1976)

[6] Leonard, S., Bentur, A.: Improvement of the durability of glass fiber reinforced cement using blended cement matrix. Cem. Concr. Res. 14, 717–728 (1984)

[7] Yilmaz, V.T., Glasser, F.P.: Reaction of alkali-resistant glass fibres with cement: part 1, review, assessment and microscopy. Glass Technol. 32, 91–98 (1991)