Journal of Advanced Concrete Technology Vol. 4, No. 1, 3-17, February 2006 / Copyright © 2006 Japan Concrete Institute3

Invited paper

Tensile Characteristics Evaluation Method for Ductile Fiber-Reinforced
Cementitious Composites
Toshiyuki Kanakubo1
Received 30 September 2005, revised 1 December 2005

Abstract
This paper presents a brief overview of the tensile test methods for concrete and cementitious composites. Comparisonsof uniaxial tension test results for a round robin test conducted as part of a project of the Japan Concrete Institute Technical Committee (JCI-TC) for Ductile Fiber-Reinforced Cementitious Composites (DFRCC) are introduced. Four typesof tensile test methods for four types of DFRCC were used in this round robin test. The results differ according to thetesting method and compacting direction of DFRCC. The relationships between the tensile test results and tensile characteristics calculated from bending test results are discussed.
The possibility of establishing a standard test method for the evaluation of the tensile characteristics of DFRCC has been
discussed by the Japan Concrete Institute Standard Committee. This discussion was based on the report of the JCI-TC andthe results of the round robin test. Items that were discussed in further detail were (a) difficulties of uniaxial tension test asa standard test method, (b) treatment of DFRCC that does not have a strain hardening branch in tension, (c) adaptability ofstrain-based evaluation for cracked materials, and (d) relationship between uniaxial tensile characteristics and bending
characteristics. The Standard Committee proposed the standard test method using the 4-point bending test to obtainbending moment–curvature curves. An evaluation method for the tensile strength and ultimate strain of DFRCC was
added as an appendix of non-mandatory information. This method is considered to be one of the evaluation methods forthe tensile characteristics of DFRCC.

1. Introduction
Ductile Fiber-Reinforced Cementitious Composites(DFRCC) are defined as cementitious composite material reinforced with fiber, which show multiple cracking
characteristics under bending stress and feature drastically improved ductility during bending, tension andcompression failures (JCI-DFRCC Committee 2003).
High Performance Fiber-Reinforced Cementitious
Composites (HPFRCC), which show a strain hardening
branch and multiple cracking under uniaxial tensile stress,
are included in DFRCC. It is important to evaluate andexpress the characteristics of DFRCC with suitable
methods to enable the use of DFRCC for actual applications taking advantages of the merits of these composite
materials.
Table 1 lists examples of DFRCC use in actual applications and the required characteristics. In the future,additional applications will emerge. At present, however,
DFRCC use is largely confined to Japan. The slab
strengthening method is an example of the effective
application of the tensile characteristics of DFRCC. Thismethod requires not only tensile strength but also tensile
deformation capacity. On the other hand, tensile capacity
is not directly required in the surface protection method.
In this case, multiple cracking behavior featuring for
1

Associate Professor, Institute of Engineering Mechanics
and Systems, University of Tsukuba, Japan.
E-mail: kanakubo@kz.tsukuba.ac.jp

example cracks with a width of less than 0.1 mm is more
important. It is a well-known that the multiple cracking
behavior is the result of high tensile performance.
However, very small crack widths are only required in
actual situations. In the area of seismic strengthening, it
is still not clear which performance characteristics of
DFRCC are really required for the realization of highperformance strengthening members. It is a fact that thehigh tensile strength and tensile deformation capacity of
DFRCC produce ductile members. However, the confinement effect for the core of members is also important,and non-falling of the cover concrete leads good performance of members. Moreover, the tensile deformation
capacity of DFRCC is not such an important factor forthe shear performance of members. Fig. 1 shows acomparison of beam shear test results underanti-symmetrical bending moment loading. Mortar
without fiber (Shimizu et al. 2005), ultra high strength
concrete (UFC: DuctalTM) (Ujiie et al. 2005) and
PVA-ECC (Shimizu et al. 2005) are used for the upper,
middle and lower specimens, respectively. The amountof main bar and stirrup ratio are the same for the three
specimens. PVA-ECC with 2.0% volume percentage offiber has almost 2% strain deformation capacity andmultiple cracking behavior under uniaxial tensile stress.
UFC has a very small strain hardening branch with asingle crack. The crack behavior of beam specimens does
not differ greatly between UFC and PVA-ECC specimens. Since UFC has compressive strength almost fivetimes that of PVA-ECC, the maximum shear strength of

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T. Kanakubo / Journal of Advanced Concrete Technology Vol. 4, No. 1, 3-17, 2006

the UFC specimen is 1.7 times that of the PVA-ECC
specimen.
Demands for DFRCC vary according to the type of
application. Thus, the evaluation method must bechanged to match the application. In other words,
evaluation of the tensile characteristic of DFRCC without considering its intended use is meaningless. The
main point is how to best use DFRCC making the most of
their merits.
This paper reports the results of comparisons of direct
tensile test results for a round robin test conducted for
DFRCC. This round robin test was conducted as part of a
project of the Japan Concrete Institute Technical Committee for DFRCC (chaired by Prof. Rokugo of Gifu
University). Following the completion of that project,
JCI worked to standardize the evaluation method for thetensile properties of DFRCC. In the end, only the loading
method using the 4-point bending test was established as
the standard test method. The evaluation method for thetensile characteristics of DFRCC has been added as anappendix of the standard. The standard test method andthe evaluation method are introduced in this issue of the
Journal of Advanced Concrete Technology.

2. Tensile test for concrete andcementitious composite
This chapter provides a brief overview of the tensile test
and bending test methods and evaluation methods forconcrete and cementitious composites. Information
about these tests and evaluation methods is helpful forunderstanding test and evaluation methods for DFRCC.
In the case of ordinary concrete, tensile characteristics
are not important in the design procedures of concrete
structures and thus standardization of tensile test andevaluation methods is not a necessity. Furthermore, it isdifficult to perform uniaxial tension tests because suchtests require special molds and loading jigs. Usually, asplitting test and 3-point bending test are carried out
instead of a uniaxial tension test.
2.1 Uniaxial tension test
The uniaxial tension test requires special devices forloading. Fig. 2 shows some examples of end shapes ofuniaxial tension test specimens (Kasai and Ikeda 1993).
The main points here are the load transmitting mecha-

MortarUFC

PVA-ECC

Fig. 1 Comparison of shear test results for beamnism (stress concentration) and boundary condition(moment transmission).
Failure at the end of a specimen or grip portion is observed in the case of specimens with a uniform crosssection. It is also difficult to establish the gage length formeasuring deformation (crack width). In the case of
specimens with a large cross section at the specimen ends,
failure occurs at the point where the cross sectional size
varies because of stress concentration. The same phenomenon is observed when anchors are set into thespecimens ends. Anchors should be shaped with sharp
tips to reduce the stress concentration effect.
Three conditions, pin-pin, pin-fix, and fix-fix, can beconsidered as the boundary conditions. “Uniaxial tensilestress” may be considered as the ideal. Non-uniformityof material itself, the precision of specimen shapes,
stiffness of the loading machine, setup conditions ofspecimens, etc., all contribute to bending moment occurrence. The pin-pin condition reduces the bending
moment effect. However, cracking occurs from one sideof specimens, and secondary moment is produced after
cracking. The bending moment effect causes large errors
in strength evaluation.

Table 1 Examples of actual applications and demands for DFRCC.

Application

MethodSlab strengthening

Spray up

Surface protection
Seismic strengthening

PCa,
Cast in situ,
Spray up
PCa,
Cast in situ

Demands
Tensile capacity,
Fatigue resistance, ･･･
Decrement of crack width,
Reduction of penetration, ･･･Strength capacity,
Confinement for axial load, ･･･

5T. Kanakubo / Journal of Advanced Concrete Technology Vol. 4, No. 1, 3-17, 2006

(a)

(b)

(c)

(d)

(w)
(e)

Fig. 2 Examples of end shapes for direct tensile test (Kasai and Ikeda, 1993).

Akita et al. have introduced an interesting uniaxial
tension test method in which bending moment is applied
to the specimens in order to eliminate the secondary
moment by controlled DC motors to obtain a uniaxial
tensile field. (Akita et al. 2005) This means that controlled bending moment is essential to realize uniaxial
tension.
In general, there are scale effects in element tests.
Smaller specimens, not only cementitious composites but
also common materials, show higher strength. Especiallyin the case of concrete, the size of defects such as air
voids, drying shrinkage and material segregation, is
considered to affect strength. Furthermore, the ratio offiber length to specimen dimensions and compacting
direction has an influence in the case of fiber-reinforced
concrete.
2.2 Splitting tensile test
A splitting tensile test is generally carried out to obtainthe tensile strength of concrete. The stress field in the
splitting tensile test is actually a biaxial stress field withcompressive stress three times greater than tensile stress.
From the previous study results, the tensile strength
obtained by the splitting tensile test is in good agreementwith the results obtained by the uniaxial tension test.
In the case of fiber-reinforced cementitious composites, specimens after first cracking do not separate unlikein the case of concrete failure. After fast cracking, aspecimen is subjected to compressive loading, and tensile strength cannot be observed. Previous studies havereported setting strain gages or LVDTs at the end surfaceof the specimen and obtaining first cracking strengthfrom the point at which displacement in the tensile direction increases remarkably.
2.3 Bending test
A modulus of rupture obtained by a bending test is generally used for concrete materials because of the easinessof making specimens and loading. However, the modulus
of rupture is considered not to represent material char-acteristics. Because the bending test is one of the structural tests, some considerations such as assumptions ofstrain and stress distribution are necessary in order tohave relationships between structural characteristics andmaterial ones.
It is difficult to measure deformation across a crack inthe case of 4-point bending test. Therefore, the 3-point
bending test is conducted for notched specimens in orderto obtain the fracture energy or softening curve of theconcrete. The Japan Concrete Institute and the Japan
Society for Civil Engineers have already established astandard test method using a bending test to evaluate thefracture toughness of fiber-reinforced concrete.
The scale effect, drying shrinkage and material segregation all affect bending characteristics as in the case of
the uniaxial tension test. Furthermore, slope of the strain
distribution causes large difference between the modulus
of rupture and tensile strength because of a reduction ofsoftening curve contribution. Especially in the case offiber-reinforced concrete, which has large fracture energy in the softening branch, slope of the strain distribution has a large effect on bending characteristics.
2.4 Affecting factor in tensile characteristics
evaluation
In the case of concrete, a uniaxial compression test iscommonly carried out to evaluate concrete characteristics. However, the results obtained by the compression
test may differ depending on the specimen dimensions,shape, boundary condition, and so on. It may be considered that smaller load in the case of tensile test thancompression test causes larger effect on those factors.
Especially for the case of fiber-reinforced cementitious
composites, fiber orientation and fiber length defined byrelative scale to specimen size (2-dimensional or
3-dimensional orientation) has an effect on the characteristics of cementitious composites. The affecting factors in testing of cementitious composites are listed inTable 2.
The important points for these affecting factors are to6

T. Kanakubo / Journal of Advanced Concrete Technology Vol. 4, No. 1, 3-17, 2006

Table 2 Affecting factors in material testing.

MethodCompression
test

Affecting factor
Dimensions ofspecimen
Specific surface areaof specimen
Length of test
regionEnd condition(Capping)
Stiffness of loadingmachineBoundary condition

Tensiletest

Dimensions ofspecimens
Specific surface areaof specimen
Length of test
regionEnd shape

Large
Small
Large
Small
Long
Short
Hard
Soft
Large
Small
Fix
Pin
Large
Small
Large
Small
Long
Short

Boundary condition
Pin

DFRCC

Casting direction(Fiber orientation)

Softening curve
Softening curve

Tensile strength
Tensile strain
Tensile strength
Tensile strain
Tensile strength
Tensile strain
Straight Tensile strength
Tensile strain
Other Multiple crack
Fix

Ratio of fiber length
to specimen
dimension

TargetCompressive strength
Elastic modulus
Compressive strength
Elastic modulus
Compressive strength
Elastic modulus
Ultimate strain
Compressive strength
Elastic modulus

Large
Small

Tensile strength
Tensile strain
Multiple crack
Tensile strength
Tensile strain

Vertical Tensile strength
Tensile strain
Horizon Multiple crack

know their existence and the possibility of relativeevaluation. The accumulation of additional data throughfurther research is strongly hoped for.

3. Round robin test for DFRCC
The Japan Concrete Institute established a TechnicalCommittee (JCI-TC) on DFRCC research that operated
from 2001 to 2004. In the first term of the JCI-TC, theround robin testing for DFRCC was conducted in orderto understand mechanical performance in a wide range of
DFRCCs, to evaluate DFRCC performance using consistent standards, and to establish consistent testing
methods to evaluate DFRCC performance (Matsuo andKanda 2002). The main focus of this round robin testing
was the comparison of DFRCC performance for several
types of fiber, mixing design, and so on. Uniaxial tension
tests were conducted only for two types.
In the following term of JCI-TC activities, a WG on
the tensile performance of DFRCC was organized for the
purpose of evaluating tensile characteristics and establishing a standard test method for DFRCC. Uniaxial

EffectSmaller
LargerSmaller
LargerSmaller
LargerLargerSmaller
Measurable
Not measurable
Measurable
Not measurable
Smaller
LargerSmaller
LargerSmaller
LargerStressconcentration
Smaller
Measurable
LargerNot measurable
LargerSmaller
Depend on
DFRCC

tension tests for several types of DFRCC were also
executed by this WG. Four types of tensile tests werecarried out in order to compare differences among testing
methods.
3.1 Outline of round robin test
3.1.1 Testing method
Four types of uniaxial tension test, compression test andbending test were performed for the round robin test.
These testing methods are summarized in Table 3 and thetensile test methods are shown in Fig. 3. The uniaxial
tension tests are named T1, T2, T3 and T4. The T1
specimen is plate type specimen with a 30 x 13 mm crosssection (Kanda and Li 1999). This specimen is commonly used for the tensile test of ECC. However, it isanxiety to use plate type specimen with 2-dimensional
fiber orientation considering structural application in
actual elements in which fiber orientation shows
3-dimension. Specimens T2, T3 and T4 have been developed to improve the effect of fiber orientation withlarge sectional size of specimens, in which the fiber has
3-dimensional orientation. Specimen T2 is a rectangle

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T. Kanakubo / Journal of Advanced Concrete Technology Vol. 4, No. 1, 3-17, 2006

Table 3 Test method of round robin test.

Test method

Uniaxial tension

Compression
Bending

ID
T1
T2-H
T2-V
T3
T4
C
B-H
B-V

Casting direction
Horizontal
Horizontal
VerticalVerticalVerticalVerticalHorizontal
VerticalShape of specimen
30 x 13 mm plate

Loading condition
Pin-Fix

100 x 60 mm dogbone

Pin-Fix

φ 70 mm dogbone
φ 100 mm cylinder
φ 100 mm cylinder

Pin-Fix
Fix-Fix
Fix-Fix
Four-point
bending

100 x 100 x 400 mm
Rectangle

T2

T1

T3

T4

LVDT
60

φ100

100

R48.3
φ70

200

70

200

100

400

80 40
60

Glass fiber sheet

Actuator

R350

30
330

100

t=13
Steel
plate

Universal
joint

Steel
plate
Steel
plate

Grip device

Fig. 3 Uniaxial tensile test method of round robin test.

Fig. 5 Mold for T3 tensile test.
Fig. 4 Mold for T2-H tensile test.

section measuring 100 x 60 mm, which is made using a
100 x 100 x 400 mm mold with curved plates as shown in
Fig. 4 (Shimizu et al. 2004). Specimen T3 has a 70 mm
circular section, which is shaped using a cylinder mold asshown in Fig. 5 (Furuta et al. 2003). For Specimen T4
and the compression test, ordinary cylinder specimens
were used (Sato et al. 2001). For specimen T2 and thebending test specimen, DFRCC was compacted in thehorizontal and vertical casting direction.
Support conditions are one of the important factors for
conducting uniaxial tension tests for cementitious materials. In actual loading, it is impossible to perform “puretension” because of the non-uniformity of the material
itself and variations in specimen shapes and setup con-ditions. The “pin-fix” ends condition was selected for T1,
T2 and T3 loading to decrease the effect of eccentricity
moment of tensile load and secondary moment after
cracking.
The bending test was carried out by 4-point loading
using spans of 100 mm. LVDTs were set on both sides ofthe specimen in order to measure deflection and curvature at the pure bending section as shown in Fig. 6.
3.1.2 Testing DFRCC
Four types of DFRCC were tested. Used fiber for eachtype of DFRCC is listed in Table 4. A steel mold wasused for specimens T1, T2-H and B-H. A tin mold wasused for specimens T3, T4 and C. A composite wooden
panel was used for the molds for T2-V and B-V. In principle, the number of specimens was three for each

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T. Kanakubo / Journal of Advanced Concrete Technology Vol. 4, No. 1, 3-17, 2006

P/2

P/2

Front

P/2

ε1

Back
70

100

P/2

ε2
δ3 δ2 δ1
100

100

100

Fig. 6 Bending test method.
Table 4 Testing DFRCC for round robin test.

Fiber characteristic
Tensile
DFRCC
LengthDiameterstrength
(mm)
(mm)
(MPa)
PVA
46%
PVA
1.9%
12
0.04
1600
PE
30%
PE
1.5%
12
0.012
2600
PE
1.0%
15
0.012
2600
HB*1
45%
Steel
1.0%
32
0.405
2700
DCT*2
22%
Steel
2.0%
15
0.2
2500
*1: Hybrid DFRCC involving both PE and steel fiber *2: UFC (DuctalTM)
Water /
binder
ratio

Fiber
type

Fiber
volumecontent

Elastic
modulus
(GPa)
40
73
73
200
210

Table 5 Compression test results.

DFRCC
PVA
PE
HB
DCT

Unit
weight(kg/m3)
1,788
1,958
1,997
2,490

Compressive strength
Average
SD
COV
(MPa)
(MPa)
(%)
31.3
0.8
2.7
67.3
1.8
2.7
43.6
2.7
6.3
198.0
3.7
1.9

Strain at strength
Average
SD
COV
(%)
(%)
(%)
0.555
0.045
8.0
0.463
0.027
5.8
0.442
0.065
14.6
0.430
0.005
1.2

DFRCC and specimen type. In the case of some tensile
test specimens, the number was 5 or 6. When the mixer
capacity was insufficient for making all the specimens,
the same batch of DFRCC was dispersed to each type of
specimens.
3.2 Test results
3.2.1 Compression test result
The compression test results are summarized in Table 5.
The coefficient of variation (COV) of compressive
strength ranges from 2 to 6%.
3.2.2 Uniaxial tension test result
The uniaxial tension test results of T1 are summarized inTable 6. Figure 7 shows the tensile stress–tensile strain
curves. The tensile strain was obtained by displacement
measured by LVDTs divided by gage length.
The T2 tensile test results and tensile stress–tensile
strain curves are shown in Table 7 and Fig. 8, respectively. The tensile strain is calculated from the displacement measured by LVDTs. Although loading was
carried out for three specimens for each type of DFRCC,
one or two of these specimens failed outside the contact
points of LVDT. In the case of the DCT specimens,
loading could not be completed for any of the specimens

1/3 secant modulus
Average
SD
COV
(GPa)
(GPa)
(%)
13.7
0.1
1.1
21.0
0.5
2.5
17.4
1.2
7.0
52.8
0.9
1.8

because of delamination of the steel plates.
Some differences between horizontal compacting(T2-H) and vertical compacting (T2-V) specimens arerecognized. However, this tendency differs according to
the DFRCC type, i.e., T2-H specimens show larger
strength and strain than T2-V specimens in the case of
PVA and HB, and the opposite tendency is observed in
the case of PE specimens.
The T3 tensile test results and tensile stress–tensile
strain curves are shown in Table 8 and Fig. 9, respectively. Tensile strain is calculated from the displacement
measured by LVDTs. In the case of the DCT specimens,
loading could not be completed for two specimens because of delamination of the steel plates.
The T4 tensile test results and tensile stress–tensile
strain curves are shown in Table 9 and Fig. 10, respectively. The tensile strain is calculated from the displacement measured by LVDTs. The first cracking point
could not be recognized clearly. The reason for this isthought to be the existence of the large level of bending
moment caused by the fix-fix condition.
3.2.3 Bending test result
The bending test results are summarized in Table 10.
Figure 11 shows the bending moment–curvature rela-9T. Kanakubo / Journal of Advanced Concrete Technology Vol. 4, No. 1, 3-17, 2006

Table 6 T1 tensile test results.

6

PVA-T1
Tensile stress (MPa)Tensile stress (MPa)DFRCC
First crack strength
First crack strain
Tensile strength
Strain at max.
(speciCOV Average SD
COV Average SD
COV Average SD
COV
Average SD
men(MPa) (MPa) (%)(%)(%)(%) (MPa) (MPa) (%)
(%)
(%)
(%)
number)PVA(6) 3.72
0.84
22.5 0.021 0.003 16.5
5.00
0.47
9.4
2.697 0.657 24.3
PE(3)
3.01
0.54
17.9 0.015 0.006 40.0
4.85
0.52
10.7 1.283 0.309 24.1
HB(3)
2.32
0.17
7.3
0.015 0.003 16.4
4.37
0.63
14.3 0.705 0.299 42.4
DCT(3) 13.69 0.93
6.8
0.032 0.012 37.4 15.27 1.03
6.7
0.528 0.265 50.2

42First crack
Max. stress
0

1

2
3
Tensile strain (%)

4

5

6

PE-T1

4
2

0

1

2
3
Tensile strain (%)

4

5

2
3
Tensile strain (%)

4

5

6

DCT-T1
Tensile stress (MPa)Tensile stress (MPa)

20
HB-T1

4

10

2

0

1

2
3
Tensile strain (%)

4

5

0

1

Fig. 7 T1 tensile test results.

tionships. The curvature was calculated from the measured strain obtained by two LVDTs set at the purebending moment region. Some specimens failed at theoutside of the LVDTs. These specimen data were excluded from the results. “Deflection hardening” behavior
can be observed in all the tested specimens. Generally
speaking, the maximum moment and curvature at the
maximum moment obtained for the horizontal compacting specimens (B-H) are larger than those of thevertical compacting specimens (B-V).
3.3 Comparisons of test results
3.3.1 Comparisons of tensile test results
The test results of first crack strength and strain, tensile
strength and strain at maximum stress obtained by eachtensile test method are compared in Fig. 12. The plot
symbols are distinguished by the type of DFRCC andhorizontal axis indicates test method. The vertical lines
extending from the plot symbols indicate the range ofstandard deviation.
A clear tendency for the first crack strength and strain

cannot be recognized in the case of the tensile test
method. The tensile strength is observed to increase in
the order of T1>T2-H>T2-V=T3>T4, except for PE
specimens. The tensile strain at the maximum stressobtained by T1 and T2-H is larger than other test methods.
The tensile characteristics can be seen to differ for thefour types of test method and compacting direction. As
expected, the tensile strength and tensile strain at
maximum stress obtained from T1 specimens show ahigher level than for other test methods. This tendency is
considered to be due to the 2-dimensional fiber orientation. Comparing the compacting direction, specimen
T2-H has higher strength and strain than specimen T2-V.
The reason for the difference in compacting direction isthought to be due to the fact that the fiber orientation isaffected by the flowing direction during casting. The
coefficient of variation for tensile strength ranges from
5% to 15%, the same range as in the case of the compression test. The coefficient of variation for strain shows
scattering greater than that of tensile strength. It can be10

T. Kanakubo / Journal of Advanced Concrete Technology Vol. 4, No. 1, 3-17, 2006

Table 7 T2 tensile test results.

PVA-T2-H

First crack
Max. stressTensile stress (MPa)

6
4
2

1

6

PE-T2-H

2
3
Tensile strain (%)

4

5

Tensile stress (MPa)

0

4
2

0

1

6

HB-T2-H

2
3
Tensile strain (%)

4

5

Tensile stress (MPa)Tensile stress (MPa)Tensile stress (MPa)Tensile stress (MPa)DFRCC
First crack strength
First crack strain
Tensile strength
Strain at max.
(Specimen Average SD
COV Average SD
COV Average SD
COV Average SD
COV
number)(MPa) (MPa) (%)(%)(%)(%) (MPa) (MPa) (%)
(%)
(%)
(%)
H(2) 2.47
0.12
5.00.015 0.002 14.5
4.18
0.20
4.9
2.380 0.417 17.5
PVA
V(1) 2.51
0.006
2.87
0.769
H(1) 3.86
0.018
3.86
0.018
PE
V(2) 5.02
0.56
11.2 0.024 0.002
7.4
5.06
0.50
9.8
0.253 0.322 127.4
H(2) 3.42
0.66
19.2 0.018 0.001
4.8
3.54
0.50
14.1 0.217 0.182 84.0
HB
V(2) 2.51
0.36
14.3 0.012 0.005 39.8
2.51
0.36
14.2 0.017 0.012 69.4
H
DCT
Delamination of end plate
V

4
2

0

1

2
3
Tensile strain (%)

4

5

6

PVA-T2-V

4
2

0

1

6

PE-T2-V

2
3
Tensile strain (%)

4

5

2
3
Tensile strain (%)

4

5

2
3
Tensile strain (%)

4

5

4
2

0

1

6

HB-T2-V

4
2

0

1

Fig. 8 T2 tensile test results.

said that it is impossible to evaluate the tensile characteristics of materials that show 100% or larger scatteringin COV. Furthermore, it may be said that strain at
maximum stress is not suitable for expressing the tensile
deformation capacity of DFRCC.

3.3.2 Comparisons of bending test results
The test results of first crack moment and curvature,maximum moment and curvature at maximum moment
obtained by the bending test are compared in Fig. 13.
The plot symbols are distinguished by the type of

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T. Kanakubo / Journal of Advanced Concrete Technology Vol. 4, No. 1, 3-17, 2006

Table 8 T3 tensile test results.

6

PVA-T3First crack
Max. stress

4
2

0

1
Tensile strain (%)

Tensile stress (MPa)Tensile stress (MPa)DFRCC
First crack strength
First crack strain
Tensile strength
Strain at max.
(Specimen Average SD
COV Average SD
COV Average SD
COV Average SD
COV
number) (MPa) (MPa) (%)(%)(%)(%) (MPa) (MPa) (%)
(%)
(%)
(%)
PVA(5)
3.17
0.81 25.5 0.021 0.005 23.1
3.38
0.44
13.1 0.071 0.108 151.6
PE(3)
5.08
0.66 13.0 0.025 0.004 16.9
5.56
0.31
5.6
0.196 0.293 149.4
HB(3)
2.70
0.60 22.3 0.013 0.003 23.1
2.84
0.80
28.1 0.122 0.192 156.9
DCT(1)
9.38
0.017
12.41
0.089
-

2

6

PE-T3

4
2

0

1
Tensile strain (%)

2

1
Tensile strain (%)

2

6

DCT-T3Tensile stress (MPa)Tensile stress (MPa)

20
HB-T3

4
2

0

1
Tensile strain (%)

2

10

0

Fig. 9 T3 tensile test results.

DFRCC and the horizontal axis indicates the compacting
direction. The vertical lines extending from the plot
symbols indicate the range of standard deviation.
Clear tendencies in first crack moment and curvaturecannot be recognized for the compacting direction. The
maximum moments obtained for the B-H specimens area little larger than those of the B-V specimens. The curvatures at the maximum moment obtained for the B-H
specimens show remarkably larger values than thoseobtained for the B-V specimens. The same tendency isevidenced through the tensile test for the compacting
direction.
3.3.3 Comparisons between tensile test results
and bending test result
The stress distribution assumption is essential for a discussion of the comparisons between tensile characteristics and bending characteristics. In the case of cementitious composites, which have compressive strength asten or more times greater than their tensile strength, andseveral percent tensile strain capacity, maximum momentin the pure bending field can be determined by tensile

strain at maximum tensile stress. At the maximum moment, compressive strain is smaller than the strain at
maximum compressive stress. Two types of stress distribution are assumed as shown in Fig. 14 for the purposeof inverse analysis from bending test results to tensile
characteristics. In Case 1, first crack tensile strength andmaximum tensile strength is determined from the moment at first crack and at maximum moment, respectively.
In Case 2, stress distribution is supposed to be uniform in
the tensile side, and only tensile strength is calculated
from the maximum moment. In both cases, tensile strain
at maximum tensile stress (ultimate strain) is determinedby the curvature at the maximum moment. The compressive stress distribution is supposed to have an elastic
region.
Table 11 and Table 12 show the calculation results inCase 1 and Case 2, respectively. Comparing the calculated values between Case 1 and Case 2, no remarkabledifference is recognized in tensile strength and ultimate
strain except for the DCT specimens. Because bending
test specimens have the same sectional dimensions as T2
tensile test specimens, it is proper to compare the calcu-

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T. Kanakubo / Journal of Advanced Concrete Technology Vol. 4, No. 1, 3-17, 2006

Table 9 T4 tensile test results.

6

PVA-T4Max. stress

4
2

0

1
Tensile strain (%)

Tensile stress (MPa)Tensile stress (MPa)DFRCC
Tensile strength
Strain at max.
(Specimen Average SD
COV Average SD
COV
number) (MPa) (MPa)
(%)
(%)
(%)
(%)
PVA(3)
1.78
0.22
12.2
0.320 0.234
73.1
PE(3)
4.18
0.07
1.7
0.833 0.287
34.5
HB(3)
2.15
0.27
12.3
0.437 0.076
17.3
DCT(2)
7.18
0.44
6.1
0.045 0.049 110.0

2

6

PE-T4

4
2

0

1
Tensile strain (%)

2

1
Tensile strain (%)

2

6

DCT-T4
Tensile stress (MPa)Tensile stress (MPa)

20
HB-T4

4

10

2

0

1
Tensile strain (%)

20

Fig. 10 T4 tensile test results.

lated values with T2 tensile test results. Comparing Table 11, Table 12 and Table 7, differences between thetype of DFRCC and compacting directions show thesame tendencies as those observed in the tensile test
results. In these test results, the difference between tensile test results and calculated values is in the data scattering range.

4. Modeling of tensile stress–tensile strain
relationshipSome examples of tensile stress–tensile strain relationship models for DFRCC are shown in Fig. 15. The
modeling aims are identification of DFRCC and the useof models for analysis and design of DFRCC members
and structures. In principle, a suitable model should be

Table 10 Bending test results.

First crack
Maximum load
DFRCC
MomentCurvature
MomentCurvature(specimenSD
Average SD COV Average SD COV Average
COV Average SD COV
number)(kN･m) (kN･m) (%) (µ/mm) (µ/mm) (%) (kN･m) (kN･m) (%) (µ/mm) (µ/mm) (%)H(3) 0.442 0.137 30.9
4.7
1.8 38.5 1.535
0.145
9.4
349.2
96.3 27.6
PVA
V(3) 0.461 0.157 34.0
4.5
2.9 64.4 1.333
0.243 18.2
173.9 119.5 68.7
H(1) 0.519
3.3
2.212
269.6
PE
2.8
0.1
5.1
1.468
0.686 46.7
137.6
96.8 70.4
V(2) 0.436 0.089 20.3
H(3) 0.400 0.065 16.2
5.9
4.1 68.8 1.531
0.531 34.7
213.4 147.6 69.2
HB
V(2) 0.288 0.026 9.0
1.9
0.7 37.2 1.013
0.313 30.9
90.0
63.1 70.1
H(2) 2.154 0.088 4.1
5.0
0.1
2.8
4.518
0.117
2.6
141.2
24.1 17.1
DCT
V(3) 2.331 0.095 4.1
6.7
4.1
61.0 3.243
0.615 19.0
72.0
39.5 54.9

13

200

400
600
Curvature (µ/mm)

PE-B-H

1

2

200

400
600
Curvature (µ/mm)

00

HB-B-H

200

6

3
2
1
200

400
600
Curvature (µ/mm)

2

200

800

400
600
Curvature (µ/mm)

800

400
600
Curvature (µ/mm)

800

400
600
Curvature (µ/mm)

800

400
600
Curvature (µ/mm)

800

PE-B-V

1

2

200

HB-B-V

1

200

6

DCT-B-H

4

0
0

1

0
0

800

Moment (kNm)

5

400
600
Curvature (µ/mm)

PVA-B-V

0
0

800

1

2

0
0

800

Moment (kNm)

Moment (kNm)

200

Moment (kNm)

First crack
Max. moment

100

Moment (kNm)

PVA-B-H

Moment (kNm)

2

Moment (kNm)

Moment (kNm)

T. Kanakubo / Journal of Advanced Concrete Technology Vol. 4, No. 1, 3-17, 2006

5

DCT-B-V

4
3
2
1
0
0

200

Fig. 11 Bending test results.

selected for the purpose of suitable use. For structural
application and evaluation, bi-linear, elastic-plastic andrigid-plastic models are considered sufficient for expressing DFRCC characteristics. If detailed cracking
behavior such as crack width and crack intervals is required for analysis and design, tensile stress–strainmodels are not adaptable for evaluation. The tensile

strain gives the average value of multiplication of thecrack width and the reciprocal number of the crack interval.
As an extreme example, the rigid-plastic model issufficient for evaluating only the strength capacity of
DFRCC members such as beams, columns, walls andbeam-column joints. For the sake of evaluation and14

T. Kanakubo / Journal of Advanced Concrete Technology Vol. 4, No. 1, 3-17, 2006

Crack strength (MPa)

13.69

9.38

5
3

+σ

2

-σ

0

HB

T1

T2-H

T2-V

T3

0.02
0.01

T4

0

T1

15.27

4
3
2
T1

T2-H

T2-V

T2-V

T3

T4

3
Strain at max. (%)

Tensile strength (MPa)

7.18
12.41

5

0

T2-H

Tensile test method

Tensile test method
6

1

DCT

0.03

4

1

PE
0.04

Strain at first crack (%)

PVA

6

T3

T4

2

T1

T2-H

T2-V

T3

T4

1
0

Tensile test method

Tensile test method

Fig. 12 Comparisons of tensile test results.

PVA
2.154

+σ

0.4

-σ

0.3
0.2
0

8

2.331

0.5

0.1

PE

B-H

Curvature at first
crack (µ/mm)

Moment at first
crack (kN・m)

0.6

B-V

4
2
0

1.5
1
0.5
B-H

B-V

400

3.243

2

0

B-H
Bending test method

Curvature at max.
moment (µ/mm)

Max. moment (kN・m)

4.518

DCT

6

Bending test method
2.5

HB

B-V

Bending test method

300
200
100
0

B-H

B-V

Bending test method

Fig. 13 Comparisons of bending test results.

calculation simplicity, unknowns had better be not somany. It can be said that material characteristics haveinsensitive effect on structural performance in case ofcomplicated stress fields because of redistribution ofstress.

5. JCI proposal for tensile characteristics
evaluation method
The Japan Concrete Institute Standard Committee decided to discuss the possibility of setting up a standard

15

T. Kanakubo / Journal of Advanced Concrete Technology Vol. 4, No. 1, 3-17, 2006

Case 2

Case 1

D/2

φ u σ cr

xn

φ cr

Mmax

xn

φu

Mmax

Mcr
ε cr

σ cr

εu

At first crackεuAt maximum moment
E ⋅ b ⋅φu2

At first crackD ⋅ φ cr
ε cr =
2
6M cr
σ cr =
b⋅ D2

E=

σ max

At max. moment⋅ xn =2b⋅ (σ cr + σ max ) ⋅ ( D − x n )2
E ⋅ b ⋅φu
M max =⋅ xn 3 +
3

σ cr
ε cr

b
⋅ (σ cr + 2σ max ) ⋅ ( D − x n ) 2
6

σ max
At max. momentc E ⋅ b ⋅ φu

2

⋅ xn 2 =σ max ⋅ b ⋅ ( D − xn )M max = c

σ max ⋅ b
2

E ⋅ b ⋅ φu
⋅ xn3 +
3
⋅ ( D − xn ) 2

Fig. 14 Assumption of stress distribution.
Table 11 Tensile characteristics calculated from bending test results (Case 1).

First crack strength
DFRCC
PVA
PE
HB
DCT

H
V
H
V
H
V
H
V

Average SD(MPa) (MPa)
2.65
0.82
2.77
0.94
3.11
2.62
0.53
2.40
0.39
1.73
0.16
12.92 0.53
13.99 0.57

COV
(%)
30.9
34.0
20.3
16.2
9.0
4.1
4.1

First crack strength
Tensile strength
Ultimate strain/ strain
Average SD
COV Average SD
COV Average SD
COV(GPa) (GPa)(%) (MPa) (MPa) (%)
(%)
(%)
(%)
12.0
4.3
35.9
3.75
0.70
18.7
3.07
0.92
29.9
13.8
4.2
30.8
3.14
0.30
9.4
1.46
1.01
69.3
18.9
5.82
2.36
18.6
2.9
15.4
3.66
1.95
53.2
1.18
0.88
74.3
10.6
5.6
52.9
4.16
1.82
43.8
1.79
1.40
78.6
19.2
5.5
28.7
2.54
0.92
36.2
0.78
0.59
75.7
51.7
3.6
6.9
8.62
0.63
7.3
1.19
0.21
17.8
50.8
22.8
44.8
3.91
2.43
62.0
0.57
0.34
60.1

Table 12 Tensile characteristics calculated from bending
test results (Case 2).

Tensile strength

Ultimate strain
AverDFRCC Average SD COV
SD COVage(MPa) (MPa) (%)(%) (%)(%)
H 3.33 0.31 9.2
3.10 0.90 29.2
PVA
V 3.01 0.48 16.0 1.48 1.06 72.0
H 4.842.37
PE
V 3.27 1.48 45.3 1.18 0.86 72.5
H 3.37 1.11 33.0 1.86 1.35 72.6
HB
V 2.30 0.64 27.8 0.76 0.55 73.1
H 10.15 0.17 1.7
1.20 0.22 18.4
DCT
V 7.63 1.59 20.8 0.59 0.35 59.2
test method for the evaluation of tensile characteristics
for DFRCC and established a WG on the DFRCC standard test method for this purpose. The base of discussion

was the report of the Technical Committee for DFRCC
and the results of JCI’s round robin test described in
Chapter 3.
In the WG discussions, it was recognized anew that thetensile characteristics obtained from the uniaxial tension
test differ according to the test method and type of
DFRCC. The dimensions and shape of specimens,boundary conditions of loading, and compacting direction all influence the test results. The following items
were mainly discussed in this WG.
(a) Difficulties of uniaxial tensile test as a standard test
method(b) Treatment of the DFRCC that does not have strain
hardening branch(c) Adaptability of strain-based evaluation for cracked
materials(d) Relationship between direct tensile characteristics
and bending characteristics
In the discussions of the WG, it was pointed out that16

T. Kanakubo / Journal of Advanced Concrete Technology Vol. 4, No. 1, 3-17, 2006

Tensile stressTensile stressMulti-function model

Unknowns: any number

Multi-linear model

Unknowns: any number
Tensile strain
Tensile stress

Tri-linear model

Tensile stressTensile strain

Unknowns: 5

Bi-linear model

Unknowns: 4
Tensile strain

Tensile strain
Tensile stressTensile stress

Elastic-plastic model

Unknowns: 3

Rigid-plastic model

Unknowns: 2
Tensile strain

Tensile strain

Fig. 15 Tensile stress–strain models.

T2 Tensile test strength (MPa)the same results have to be obtained by using a standard
method in all cases, regardless of the testing machine andoperator. As mentioned in Chapter 2, the uniaxial tension
test requires special jigs and molds. Therefore, it is difficult to establish a standard test method using the uniaxial tension test without special techniques. In addition,
precise execution of the uniaxial tension test requires a
great deal of time and labor. An easier test method isrequired considering daily check for quality control at the
mixing plants as same as compression test of concrete.
6
5
4
3

PVA-H
PVA-V
PE-H
PE-V
HB-H
HB-V

0.7

2
1
0

1

2

3

4

5

6

Calculated tensile strength (MPa)Fig. 16 Comparison between calculated tensile strengthand T2 test results.

For a strain hardening-type DFRCC, the tensile
strength and ultimate tensile strain evaluated by inverse
analysis from the bending test results with the assumption of the stress–strain model of bi-linear or elastic–plastic generally correspond to the tensile stress andstrain at the maximum point obtained by the uniaxial
tension test, respectively. For a strain softening-type
DFRCC, the tensile strength and ultimate tensile strain
evaluated by these models vary depending on the extent
of softening branch. It is certainly clear that distinction
between hardening-type and softening-type DFRCC is
impossible based only on the bending test results.
Demands for DFRCC vary by types of applications, as
described in Chapter 1. Thus, the evaluation method
must be changed to match the application. In other words,
tensile characteristic evaluation without considering theintended use of DFRCC is meaningless.
As a result of discussions, only a test method for obtaining bending moment–curvature curves using a
4-point bending test was established. The applicablefiber-reinforced cementitious composites are limited tothose in which several separated plural cracks occur at
the pure bending region corresponding to discussion item(c). The evaluation method for tensile strength and ultimate strain was added as an appendix of non-mandatory

T. Kanakubo / Journal of Advanced Concrete Technology Vol. 4, No. 1, 3-17, 2006

information. The standard is designed from the standpoint that the evaluation method should be selected in asuitable way by each user. For example, these test andevaluation methods are suitable for quality control use
for DFRCC, which has a strain-hardening branch.
Figure 16 shows an example of evaluation using the
JCI standard method. The plotted values have alreadybeen shown in Table 7 and Table 12. The relationshipbetween the uniaxial tension test results and calculated
values from the bending test results may be considered tovary according to the type of DFRCC. To find out theanswer for discussion item (d), more data and further
research are necessary.
The JCI Standard titled “Method of test for bending
moment–curvature curve of fiber-reinforced cementitious composites” and its commentary are presented inthis issue of the Journal of Advanced Concrete Technology.

6. Conclusions
Four types of uniaxial tension test methods for four types
of DFRCC were performed in the round robin test as oneof the projects of the Japan Concrete Institute TechnicalCommittee (JCI-TC) on DFRCC. There are differencesin the obtained results according to the testing methodparameters, such as dimensions and shape of specimens,boundary conditions, and compacting direction of
DFRCC. The relationships between the tensile test results and tensile characteristics calculated from thebending test results are discussed. The Japan Concrete
Institute standard for the test method using the 4-point
bending test is introduced. This standard was evolved
through discussions of the JCI-TC and based on roundrobin test results. This method is considered to indicate
one example of evaluation method of DFRCC tensile
characteristics.
Demands for DFRCC vary according to the type of
application. An evaluation method suitable for the investigation of DFRCC characteristics to ensure that therequirements for the intended application are met should
be selected. Further research to enable the effective useof DFRCC for actual applications is hoped for.
Acknowledgement
The author wishes to acknowledge the members of theJapan Concrete Institute Technical Committee on
DFRCC and the DFRCC Standard WG.

17

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