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44 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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45 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 20C 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 20C 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 20C 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 20C 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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48 60 Master Curve at 20C 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 20C 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.