Study of P-h Curves on Nanomechanical
Properties of Steel Fiber Reinforced Mortar
S.F. Lee, J.Y. He, X.H. Wang, Z.L. Zhang, and S. Jacobsen1
Abstract. Steel fiber reinforced mortars with w/b 0.3 and 0.5 with and without
10% silica fume by cement weight were investigated using a Hysitron Triboin®
denter with Berkovich tip, indenting in the interfacial transition zone (ITZ) between steel fiber and matrix, and also on the steel fiber and aggregate using 5mN
maximum force to obtain P-h (Load-Displacement) curves for elastic modulus and
hardness analysis. Different P-h curves were generated at different points in the
ITZ region, steel fiber and aggregate. The P-h curves in the ITZ reached the
maximum force at larger displacement than those of aggregate and steel fiber, revealing that the microstructures in ITZ are loosely packed together. The unit structures in steel fiber are mainly bound together in regular way by covalent bond;
therefore, it reached the maximum force earlier than that of the actual igneous
granitic aggregate. Varying irregular P-h curves were observed, mostly in the ITZ,
and reasons for this are discussed; voids in microstructure, weak zone, possible
voids beneath the indented point, indenting in varying unhydrated and hydrated
phases, possible leaching/washing out of binder during polishing of non-epoxyreinforced samples.
1 Introduction
Steel fiber reinforced mortar consists of four phases: steel fiber, ITZ, matrix and
aggregate. The ITZ, which maximum thickness ranges from 15µm up to 50µm
[1, 2], is the region that has high porosity compared to the matrix [3]. It is formed
due to the so called wall effect where the cement packs more loosely against the
relatively large aggregate’s and steel fiber’s surface, and this also increases the local w/c ratio. Furthermore, it is also considered as a weakest link in the mechanical behavior of concrete [4].
S.F. Lee, J.Y. He, Z.L. Zhang, and S. Jacobsen
Department of Structural Engineering, Norwegian University of Science and Technology
(NTNU), Trondheim, Norway
X.H. Wang
Department of Civil Engineering, Shanghai Jiaotong University, Shanghai, China
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S.F. Lee et al.
In the past few years, nanoindentation on the cement paste [5, 6] was carried
out in order to understand properly the nanomechanical properties of the microstructures, so that the macroscopic properties of concrete can be controlled and
improved.
In this paper, nanoindentation was performed on the ITZ, steel fiber and aggregate. The P-h curves, elastic modulus and hardness obtained were compared and
related to the intrinsic property of each phase.
2 Experimental Procedures
2.1 Materials
Steel fiber reinforced mortars with w/b 0.3 and 0.5 with and without 10% silica
fume (sf) by cement weight were made with 0.3 vol% straight high carbon steel
fibers were added in each mix. The mix proportion is stated in ref. [7]. Norcem
Anlegg cement (an Ordinary Portland cement in Norway), silica fume with >90%
SiO2, limestone filler, granitic sand with 4mm maximum size, polycarboxylate
polymers superplasticizer, straight steel fibers with L13mm and D0.16mm were
used. The fresh mortars were casted into 40x40x160mm moulds and vibrated on
the vibrating table for 3 seconds. The mortars were then covered with plastic bags,
demoulded after 24 hours and cured in water at 20°C for 28 days.
2.2 Sample Preparation for Nanoindentation
Small cubes with 16x16x16mm dimension were cut out from the centre of the
mortar using a diamond saw at low speed with water as lubricant. The cubes were
dried at room temperature before epoxy mounting, followed by grinding and polishing. A Struers grinding and polishing machine together with the MD-grinding
discs and MD-polishing cloths were used. Ultrasonic cleaning in water to remove
grit and an examination of the polished surface under the transmitted light microscope were performed at each step of grinding and polishing. The specimens were
plane ground on the diamond discs of 68µm, 30µm
m and 14µm,
m, fine ground with
9µm
m diamond suspension, polished with 3µm
m and 1µm
m diamond suspension, and
finally done with oxide polishing, so that the surface flatness less than 1µm could
be achieved. The forces and durations used in the grinding and polishing can be
found in ref. [7].
2.3 Nanoindentation
®
A Hysitron Triboindenter with a Berkovich diamond tip (a three-sided pyramidal
diamond with included angle of 142.3°) was used to indent on the steel fiber, ITZ
and aggregate. The maximum indentation load was 5mN. A series of P-h curves
Study of P-h Curves on Nanomechanical Properties of Steel Fiber Reinforced Mortar
283
indenting on the steel fiber, ITZ and aggregate were collected and analyzed. An
average of 10 indents was performed on the steel fiber and aggregate and nearly
40 indents were on the ITZ. The testing was repeated on two different areas of
each specimen. Elastic modulus, E, and hardness, H, of each phase is calculated
using the following equation:
1 (1 − v 2 ) (1 − vi2 )
=
+
Er
E
Ei
(1)
Pmax
A
(2)
H=
where Er and A are the reduced modulus and the projected area of the elastic contact respectively, v is the Poisson’s ratio of the phase, Ei and vi are the elastic
modulus and the Poisson’s ratio of the tip with 1140GPa and 0.07, respectively.
The reduced modulus, Er, can be calculated as below:
S=
dP
2
Er A
=
dh
π
(3)
where S = dP/dh is the stiffness of the upper portion of the unloading curve [8].
3 Results and Discussion
In nanoindentation, the maximum load is determined so that the tip will stop indenting when the maximum load is reached, and thus, a P-h curve is obtained.
This is different from the macromechanical test where the strength of the specimen is roughly estimated first before a machine is chosen. In nanoindentation, it is
important to have a surface flatness less than 1µm for the ease of nanoindentation,
and the nanomechanical properties calculated from the P-h curve for each phase
could be compared effectively. In order to minimize the error caused by the washing out of binder during polishing all specimens were polished under the same
preparation procedures in our study. The irregular P-h curves that possibly depicted material defect or tip slipping were discarded from being used so that the
intrinsic property of each phase could be studied as close as possible.
Fig. 1 shows the typical P-h curves of steel fiber, aggregate, cement paste and
some irregular P-h curves obtained during nanoindentation on the specimens. Fig.
1(b), an irregular P-h curve of steel fiber, shows a slight increase in load at the beginning of the displacement and followed by a very clean loading and unloading
curve. This depicted that the feature indented had a well-arranged structure but
with a local uneven surface. Fig. 1(d) shows that on unloading, some coarse grains
might attach to the indenter, and with their irregular shapes, interlocking between
coarse grains happened and stopped the load from decreasing smoothly with the
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S.F. Lee et al.
(a) Typical P-h curve of steel fiber
(b) Irregular P-h curve of steel fiber
5000
5000
4000
Load P (μN)
Load P (μN)
4000
3000
2000
3000
2000
1000
1000
0
0
0
50
100
150
200
0
50
Displacement h (nm)
100
150
200
250
300
Displacement h (nm)
(c) Typical P-h curve of aggregate
(d) Irregular P-h curve of aggregate
5000
5000
4000
3000
Load P(μN)
Load P (μN)
4000
2000
1000
3000
2000
1000
0
0
0
50
100
150
0
200
50
150
200
250
(f) Irregular P-h curve of cement paste
5000
5000
4000
4000
Load P (μN)
Load P (μN)
(e) Typical P-h curve of cement paste
3000
2000
1000
3000
2000
1000
0
0
0
50
100
150
200
250
300
350
0
Displacement h (nm)
50
100
150
200
250
300
Displacement h (nm)
(g) Irregular P-h curve of ITZ
(h) Irregular P-h curve of ITZ
5000
5000
4000
4000
Load P (μN)
Load P (μN)
100
Displacement h (nm)
Displacement h (nm)
3000
2000
1000
3000
2000
1000
0
0
0
1000
2000
3000
Displacement h (nm)
4000
5000
0
100
200
300
400
500
600
700
800
Displacement h (nm)
Fig. 1 Typical and irregular P-h curves found on the steel fiber, aggregate cement paste in
the and ITZ
displacement. The same interlocking phenomenon shown in the nanoindentation
on the microstructures in the cement paste, see Fig. 1(f). Fig. 1(g) and 1(h) reveals
that there could be large voids underneath the microstructure as the load stopped
Study of P-h Curves on Nanomechanical Properties of Steel Fiber Reinforced Mortar
285
increasing after a period of time of loading and remained the same even though
the indenting depth increased. Possibly also leaching during polishing may have
affected the results.
Straight high carbon steel fiber consists of mainly atom Fe, 0.7% C and some
other compositions bound together in covalent bonds in a well-arranged structure.
During loading, dislocation happened in the steel fiber. During unloading, the
bonds between the layers of atoms are so strong that the dislocation was hardly
disturbed by the uplifting indenter. Thus, the load dropped to zero at a small displacement on unloading. The similar unloading curves were shown in metals such
as aluminum and tungsten [8]. However, if the surface of the steel fiber was not
polished properly, the irregular P-h curve shown in Fig. 1(b) was commonly seen.
The igneous granitic aggregate consists of mainly coarse mineral crystals of
quartz, feldspar and mica packed tightly together. From the P-h curves, see
Fig. 1(a) and Fig. 1(c), it was found that the load reached the maximum at nearly
the same displacement for the steel fiber and aggregate, and the hardness calculated was also nearly the same for both, see Table 1. This could attribute to the
tightly-packed-together structure shown in both. Although the coarse minerals in
aggregate have crystalline structures, they are packed together in week bonds.
Therefore, the orderly arranged atomic structure with covalent bonds in the steel
fiber could be responsible for its high elastic modulus when compared to the aggregate and microstructures in the ITZ.
The hydration products, such as calcium silicate hydrate (C-S-H), calsium hydroxide (CH), ettringite and monosulphate, found in the ITZ and bulk matrix have
crystalline structures. However, see Fig. 1(e), a typical P-h curve of ITZ shows
that the load reached the maximum at a displacement larger than that of steel fiber
and aggregate, which means a lower elastic modulus and hardness in the ITZ than
that of steel fiber and aggregate. The weak bonds between heterogeneous microstructures in the ITZ in fact were often found between the coarse minerals in the
aggregate, however, the coarse minerals in the aggregate packed more tightly than
the heterogeneous microstructures in the ITZ. The more porous characteristic of
ITZ due to locally lower cement packing caused by wall effect and high w/c in
ITZ than in bulk matrix, voids right under the indented surface and possible washing out of non-epoxy reinforced polished paste could be also additional reasons for
the lower elastic modulus and hardness shown in the ITZ than in the aggregate and
steel fiber. Hu et al. [3] revealed that with computer simulation, a higher volume
fraction of hydration products were found in the ITZ than in the matrix, mainly
due to the disproportional high rate of hydration in the ITZ, however, the packing
discontinuity due to the wall effect caused the higher porosity in the ITZ than in
the matrix for a matured concrete. Furthermore, irregular P-h curves with possible
large voids were mostly found in the ITZ in our study.
Mondal et al. [5] performed nanoindentation on cement paste with w/c 0.5 and
revealed that for unhydrated cement grain, the elastic modulus was 110GPa; for
cement paste matrix was 21GPa, and for ITZ was 18GPa. Comparing our results,
see Table 1, with Monda et al. [5] and Sorelli et al. [9], a high value of elastic
modulus found in w/b 0.3 could be from the indentation either fully on the unhydrated cement grains or partially on the unhydrated cement grains and hydration
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products. In general, the hydrated microstructures in the ITZ have lower elastic
modulus and hardness than the steel fiber and aggregate for both w/c studied.
4 Conclusions
The results of the nanoindentation revealing the microstructures in the ITZ had
lower elastic modulus and hardness than steel fiber and aggregate greatly supports
the wall effect and more porous characteristic in the ITZ of steel fiber and aggregate. This also possibly supports the assumption that ITZ is a weak link in the mechanical properties of the steel fiber reinforced mortar.
Table 1 Elastic modulus, E, and hardness, H, of steel fiber, aggregate and microstructures
in the ITZ at a distance of 10 to 50µm from the steel fiber, and aggregate
Steel fiber
w/b0.3, sf0%
E (GPa)
H (GPa)
285-310
7.2-8.5
ITZ (10-50µm)
Aggregate
E (GPa)
H (GPa)
E (GPa)
H (GPa)
14-50
0.3-1.8
48-85
6-10.5
105-160
2.3-3.6
w/b0.3, sf10%
250-310
7.8-9.8
2-85
0.1-4
60-115
6.5-15
w/b0.5, sf0%
240-280
7.8-9.8
6-38
0.2-1.3
65-95
6-12
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