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49 60 67-22, Opt 76-22, Opt Phase Angle, Degree 67-22, Opt+ 40 76-22, Opt+ 20 0 1.E-03 1.E-01 1.E+01 1.E+03 1.E+05 1.E+07 Reduced Frequency, Hz Figure 5.10. Phase angle master curves for all mixes tested. Damage Characteristic Curve men data are fit using both a generalized power model and an exponential model (60, 61), given in Equations 21 and 22, The characteristic curve for a mixture describes the rela- respectively. tionship between C, which is normalized pseudo stiffness C = 1 - C11 ( S ) C12 calculated through viscoelastic theory, and S, which is the dam- (21) age parameter calculated from continuum damage mechanics C = e - kS (22) theory. Practically, C can be thought of as the material's integrity at any point in time and S as the level of damage over where, time. As the amount of damage in the material increases, the C11, C12, and k are regression coefficients (hereafter referred material integrity decreases. A mixture's characteristic curve to as damage curve coefficients) obtained by ordinary can be constructed from monotonic or cyclic tests. The steps least squares technique. involved in the construction of the characteristic curves are described in Appendix E. The generalized power law does a better job fitting the actual data obtained from the tests. Figures 5.15(a) and (b) show the characteristic curve fits for all mixtures obtained using the gen- Monotonic Testing eralized power model and exponential model, respectively. The Figures 5.11 through 5.14 show the characteristic curves behavior of the PG 76-22 optimum plus mixture appears to obtained from on-specimen LVDTs for each individual mix- be significantly different from the other mixtures; the curve for ture tested under monotonic loading. The individual speci- this mixture only represents one specimen, so more testing 1 Individual Specimens Generalized power model 0.75 Exponential model 0.5 C 0.25 0 0 0.5 1 1.5 2 2.5 3 S Figure 5.11. Characteristic curves using on-specimen LVDTs for different strain rates for PG 67-22 optimum.

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50 1 Individual Specimens Generalized power model 0.75 Exponential model 0.5 C 0.25 0 0 0.5 1 1.5 2 2.5 3 S Figure 5.12. Characteristic curves using on-specimen LVDTs for PG 76-22 optimum. 1 Individual Specimens Generalized power model 0.75 Exponential model 0.5 C 0.25 0 0 0.5 1 1.5 2 2.5 3 S Figure 5.13. Characteristic curves using on-specimen LVDTs for PG 67-22 optimum plus. 1 Individual Specimens Generalized power model 0.75 Exponential model 0.5 C 0.25 0 0 0.5 1 1.5 2 2.5 3 S Figure 5.14. Characteristic curves using on-specimen LVDTs for PG 76-22 optimum plus.

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51 1 67-22, opt 76-22, opt 0.75 67-22, opt+ 76-22, opt+ C1 0.5 0.25 0 0 0.5 1 1.5 2 2.5 3 S1 (a) Generalized power model 1 67-22, opt 76-22, opt 0.75 67-22, opt+ 76-22, opt+ 0.5 C 0.25 0 0 0.5 1 1.5 2 2.5 3 S (b) Exponential model Figure 5.15. Overall characteristic curves using on-specimen LVDTs for all mixtures tested under monotonic loading. must be done to determine if this is representative behavior or versus S curves will be different for the various strain rates. a problem with the one test specimen. Figures 5.16(a) and (b) show the C versus S curves at differ- Initially, specimens failed near the end plates during mono- ent strain rates measured using the on-specimen and plate- tonic tests, which is likely due to the presence of high air void to-plate LVDTs, respectively. It can be seen from these figures content at the ends of the specimens. The specimens were that the curves for the various strain rates fall on top of each shortened by cutting more material from the top and bottom. other except for the plate-to-plate curve for Specimen 10. This was successful in producing failure in the middle of the There are some issues related to the strain data obtained from specimens. In addition to making shorter specimens, LVDTs plate-to-plate LVDTs for this specimen. Thus, the data for the were located plate to plate along with the on-specimen LVDTs remaining specimens indicates that the effect of viscoplastic- during the monotonic tests (two on-specimen and two plate- ity in the monotonic test results is not significant. to-plate LVDTs). The advantage of using the plate-to-plate LVDTs is that the material response can be captured even if Fatigue Testing the specimens fail outside the on-specimen LVDT gage length. Monotonic tests performed at various strain rates can be A total of five specimens of PG 67-22 optimum were tested used to investigate whether there is any significant effect of under cyclic fatigue loading using four on-specimen LVDTs. plasticity in the mixture behavior. If there is a significant The testing was performed at 20C by controlling the cross- portion of viscoplastic strain in the material response, the C head displacements. Haversine waveforms were applied to the

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52 1 0.75 0.5 C 0.25 0 0 0.5 1 1.5 2 2.5 S rate=0.135/min (Spec #5) rate=0.135/min (Spec #6) 0.135/min (Spec #7) rate=0.02/min (Spec #9) rate=0.1/min (Spec #8) rate=0.0675/min (Spec #10) (a) On-specimen LVDTs 1 0.75 0.5 C 0.25 0 0 0.5 1 1.5 2 2.5 3 S rate=0.135/min (Spec #6) rate=0.135/min (Spec #7) rate=0.02/min (Spec #9) rate=0.1/min (Spec #8) rate=0.0675/min (Spec #10) (b) Plate to Plate LVDTs Figure 5.16. C versus S curves at different strain rates for PG 67-22 optimum specimens. specimen until failure occurred. Table 5.2 summarizes the fa- The fatigue tests are neither controlled strain nor con- tigue testing. Specimen 17 was the first specimen tested. The trolled stress tests, rather a mixed mode of loading occurs be- research team anticipated that the specimen would fail within cause the crosshead rate is controlled, but the on-specimen 10,000 cycles, so the test was halted after about 26,000 cycles strains are used for analysis. Figures 5.17(a) and (b) show typ- to determine what was happening. Due to machine compli- ical stress and strain history, respectively, recorded during a ance, the actual strains measured by the LVDTs were roughly constant amplitude fatigue test. The load continuously de- one-quarter of the applied crosshead strain, so the strain am- creases due to the development of damage, and decreases dra- plitude was increased for subsequent tests. matically at failure. The mean strain increases continuously Table 5.2. Summary of fatigue tests performed on PG 67-22 optimum specimens. Specimen ID Average On- Crosshead Nf Comments Specimen LVDT Strain, ms Strain, ms Specimen 14 242 1050 17,480 Failed in the middle Specimen 15 254 1017 10,728 Failed in the middle Specimen 16 n/a n/a n/a Failed at first cycle Specimen 17 134 1300 >26,687 Did not fail Specimen 18 223 1017 1731 Failed near top end plate