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CHAPTER 5
Uniaxial Tension Results and Analyses
The testing performed at the University of New Hampshire Dynamic Modulus and Phase Angle
(UNH) includes complex modulus, monotonic, and fatigue Master Curves
tests in uniaxial tension. Analysis of the data is done using
Uniaxial complex modulus tests were performed on at least
viscoelastic and continuum damage mechanics principles to
three specimens from each mixture. The testing was done at the
identify the fatigue endurance limit of the PG 67-22 opti-
following five temperatures: -10C, 0C, 10C, 20C, and 30C
mum, PG 67-22 optimum plus, PG 76-22 optimum, and
and at eight frequencies: 0.1, 0.2, 0.5, 1, 2, 5, 10, and 20 Hz.
PG 76-22 optimum plus mixtures. Frequency sweeps at var-
The dynamic modulus and phase angle values at each
ious temperatures are run to measure the complex dynamic
frequency and temperature were calculated from stresses
modulus of each mix. The dynamic modulus and phase angle and LVDT measured strains. The individual dynamic mod-
master curves are then constructed from these data and the ulus curves were shifted along the frequency axis to construct
relaxation master curve is obtained through linear viscoelas- the dynamic modulus master curve using the time-temperature
tic conversion. The damage characteristic curve of each mix superposition principle. The reference temperature was selected
is obtained by running uniaxial monotonic tests to failure or as 20C. The resulting master curve for dynamic modulus (|E|)
by running constant amplitude fatigue tests to failure. The is expressed by the following sigmoidal equation:
characteristic damage curve is used to predict the number of
cycles to failure at different strain amplitudes to determine b
log E = a + (19)
the fatigue endurance limit of the mixture. 1 + exp ( -c - d log fr )
Fatigue tests with increasing strain amplitude are run in uni-
axial tension to directly identify the fatigue endurance of the where,
mixtures. The testing and analysis procedures are described in a, b, c, and d are positive regression coefficients.
the following sections, starting with the dynamic modulus
tests, followed by monotonic tests, fatigue tests, and finally the The term fr represents the reduced frequency, given by
prediction of endurance limit.
log fr = log f + log aT (20)
Test Specimens where,
aT is the shift factor which is a function of temperature and
A summary of the air void content and testing performed f is the actual frequency at which the individual curves are
on each specimen at UNH is shown in Table 5.1. All test spec- obtained.
imens were fabricated at NCAT using an SGC and shipped to
UNH, where they were cut and cored to 75-mm diameter, The solver function in Microsoft Excel is used to simul-
150-mm tall specimens. Steel plates were glued to the ends of taneously determine the sigmoidal fit coefficients and the
the uniaxial specimens using plastic epoxy glue in a gluing jig shift factors for the individual specimens using error min-
designed to align the specimen vertically. Four LVDTs spaced imization. An overall mixture master curve is determined
90 apart around the circumference of the specimen were by fitting the sigmoidal function in Equation 19 to all of the
attached to the surface of the specimen using a 100-mm gage individual specimen master curves. Figures 5.1 through 5.4
length. show the individual and overall dynamic modulus master

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Table 5.1. Summary of specimens and tests conducted.
Specimen Air |E*| Monotonic
Mix Fatigue Test Comments
No. Voids % Test Test
(After
Constant Increasing
Core and
Amplitude Amplitude
Cut)
1 8.6 Broke
during |E*|
testing
2 7.0 X
3 7.3 Broke
during |E*|
testing
4 7.3 X
5 7.5 X
6 6.8 X
7 7.7 X
8 7.2 X
PG 67-22,
Optimum 9 7.7 X
10 7.5 X
11 7.7 X X
12 7.0 Broke
during |E*|
testing
13 7.7 X X
14 6.9 X
15 6.9 X
16 6.7 X
17 6.7 X
18 6.6 X
1 6.5 Broke
during |E*|
testing
PG 76-22, 2 6.9 X X
Optimum 3 6.1 X X
4 7.0 X X
5 6.2 X X
1 2.2 X X
2 1.5 X X
3 2.2 X X Monotonic
test data not
usable
4 1.3 X X
5 2.1 X X
PG 67-22, 6 3.6 X X
Optimum+ 7 3.6 Broke
during |E*|
testing
8 2.7 X X
9 3.0 Broke
during |E*|
testing
10 3.0 X X
1 1.5 X X
2 1.3 X
3 1.9 X X
4 1.2 X X
5 1.0 Broke
PG 76-22, during |E*|
Optimum+ testing
6 3.1 X X
7 3.2 X X
8 2.7 X X
9 3.7 X X
10 2.8 X X

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46
50000
Master Curve at 20°C
Dynamic Modulus, MPa
40000
Individual Specimens
30000
20000
10000
0
1.E-03 1.E-01 1.E+01 1.E+03 1.E+05 1.E+07
Reduced Frequency, Hz
Figure 5.1. Dynamic modulus master curves for PG 67-22 optimum.
50000
Individual Specimens
Dynamic Modulus, MPa
40000 Master Curve at 20°C
30000
20000
10000
0
1.E-03 1.E-01 1.E+01 1.E+03 1.E+05 1.E+07
Reduced Frequency, Hz
Figure 5.2. Dynamic modulus master curves for PG 76-22 optimum.
50000
Master Curve at 20°C
40000 Individual Specimens
Dynamic Modulus, MPa
30000
20000
10000
0
1.E-03 1.E-01 1.E+01 1.E+03 1.E+05 1.E+07
Reduced Frequency, Hz
Figure 5.3. Dynamic modulus master curves for PG 67-22 optimum plus.

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47
50000
Mix Master Curve at 20°C
Dynamic Modulus, MPa
40000
Individual Specimens
30000
20000
10000
0
1.E-03 1.E-01 1.E+01 1.E+03 1.E+05 1.E+07
Reduced Frequency, Hz
Figure 5.4. Dynamic modulus master curves for PG 76-22 optimum plus.
50000
67-22, Opt
76-22, Opt
Dynamic Modulus, MPa
40000
67-22, Opt+
30000 76-22, Opt+
20000
10000
0
1.E-03 1.E-01 1.E+01 1.E+03 1.E+05 1.E+07
Reduced Frequency, Hz
Figure 5.5. Dynamic modulus master curves for all mixes tested.
curves obtained for the four mixtures. Figure 5.5 shows the curve for each specimen. The phase angle master curves are
overall dynamic modulus curves (obtained from fit) for all fit with a sigmoidal function of the form in Equation 19. Fig-
four mixtures together. ures 5.6 through 5.9 show the individual and overall phase
The shift factors determined from the dynamic modulus angle master curves for individual mixtures. Figure 5.10 shows
master curves were then used to shift the individual phase angle the overall phase angle master curves for all four mixtures
curves at each temperature to obtain the phase angle master together.
60
Combined Mix
Individual Specimens
Phase Angle, Degree
40
20
0
1.E-03 1.E-01 1.E+01 1.E+03 1.E+05 1.E+07
Reduced Frequency, Hz
Figure 5.6. Phase angle master curves for PG 67-22 optimum.

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60
Master Curve at 20°C
Phase Angle, Degree
Individual Specimens
40
20
0
1.E-03 1.E-01 1.E+01 1.E+03 1.E+05 1.E+07
Reduced Frequency, Hz
Figure 5.7. Phase angle master curves for PG 76-22 optimum.
60
Master Curve at 20°C
Phase Angle, Degree
Individual Specimens
40
20
0
1.E-03 1.E-01 1.E+01 1.E+03 1.E+05 1.E+07
Reduced Frequency, Hz
Figure 5.8. Phase angle master curves for PG 67-22 optimum plus.
60
Individual Specimens
Phase Angle, Degree
Master Curve
40
20
0
1.E-03 1.E-01 1.E+01 1.E+03 1.E+05 1.E+07
Reduced Frequency, Hz
Figure 5.9. Phase angle master curves for PG 76-22 optimum plus.