51
the shift factors simultaneously with the coefficients of the sigmoidal function through
nonlinear regression, without assuming any functional form of a(T) versus temperature.
The nonlinear regression was performed using the Solver Function in a Microsoft Excel
spreadsheet.
The resulting shift functions and master curves for GA-C3 and GA-F1 are
presented in Figures 4-18 through Figure 4-21 below. The tails on the predicted master
curves are extrapolated. In a few cases, depending on the mixture properties, the tails of
the predicted mastercurve did not follow an S-shape. Rather, the mastercurve showed a
slight concave-down curvature. Figures 4-22 and 4-23 show the shift function and
predicted mastercurve for mixture GA-C1, respectively. The predicted mastercurve for
GAC 1 does not show an S-shape. It shows a slight concave-down curvature, indicating
that for this particular mixture, higher and lower temperature results are needed to define
the tails of the mastercurve adequately. Future testing at higher and lower temperatures
would help in defining the tails better.
4
y = -P.0614x + 4.9497
R2= 0.9872
2
-2
-4
0 20 40 60 80 100 120
TemperatureeF)
Figure 4-18. Shift function for coarse-graded GAC3 mixture.