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IBRACON Structures and Materials Journal • 2012 • vol. 5 • nº 3
Nanotechnology and Construction: use of nanoindentation measurements to predict macroscale elastic
properties of high strength cementitious composites
the level II porosity. Image analysis was employed on segmented
back-scattered (BSE) electron and optical images (OI). The seg-
mentation was performed on the thresholded binary images as il-
lustrated in Figure 9.
The medium size porosity (10µm to 1mm) was assessed from
25× magnification BSE images, see Figure 10. Fifteen different
BSE images were analyzed and the results averaged. The analysis
yielded 8.92% (Table 8). The
pores larger than 1 mm (mainly
entrapped air pores) were as-
sessed similarly also from OI
with 10× magnification, see
Figure 11. As indicated in Ta-
ble 8, the analysis resulted with
0.31% of porosity. The results
obtained for the homogenized
elastic modulus and the Pois-
son’s ratio by using the Mori-
Tanaka method are shown in
Table 8 for the level II.
4. Verification of the results
The verification of the results is based on the comparison of the
elastic modulus obtained from the level II homogenization (Table 8)
and the macroscopic tests (Table 5). These results are summarized
in Table 9. The relative error between the results obtained from the
macroscale elastic modulus tests and homogenized values is within
the order of tens of percent.
As mentioned in section 2.4.1,
evaluation of nanoindentation
tests is not error-free. In the
case of HPCC, which consists
in a dense matrix, in which sev-
eral phases of different stiffness
occur, the interaction between
the matrix and these different
phases can affect the nanoin-
dentation results. Therefore, it
can be assumed that the error
presented in Table 9 is caused
Figure 9 – Mercury intrusion porosimetry: (a) incremental porosity curve;
(b) cumulative porosity curve
A
B
Table 8 – Mechanical properties of level II obtained by homogenization
Phase
Elastic
modulus [GPa]
n
Volume
fraction [%]
level-II
E
hom
[GPa]
level-II
hom
n
[GPa]
Level I - homogenized matrix
45.9
0.20
46.2
0.18
Aggregate (0.10-1.25mm)
71.8
0.17
Capillary pores >10µm –1mm
(BSE)
–
–
Large air pores >1mm (OI)
–
–
47.6
43.2
8.92
0.31
Table 9 – Elastic modulus:
Homogenization vs. Macroscale tests
Elastic
modulus
homogenization
[GPa]
Elastic modulus
macroscopic
level-static
[GPa]
Error
[%]
46.2
39.0
18.5