expansion to the axial compression. Equation 2-6 assumes that the Poisson's ratio is
constant and some testing has shown that the Poisson's ratio for HMA is frequency
dependent.
Master Curves and Shift Factors
The master curve of an asphalt mixture allows comparisons to be made over
extended ranges of frequencies and temperatures. Master curves are generated using the
time-temperature superposition principle. This principle allows for test data collected at
different temperatures and frequencies to be shifted horizontally relative to a reference
temperature or frequency, thereby aligning the various curves to form a single master
curve. The procedure assumes that the asphalt mixture is a thermo-rheologically simple
material, and that the time-temperature superposition principle is applicable.
The shift factor, a(T), defines the shift at a given temperature. The actual
frequency is divided by this shift factor to obtain a reduced frequency,f, for the master
curve,
f=- f or log(fr) = log(f) log[a(T)] (Eq. 2-7)
a(T)
The master curve for a material can be constructed using an arbitrarily selected
reference temperature, TR, to which all data are shifted. At the reference temperature, the
shift factor a(T) = 1. Several different models have been used to obtain shift factors for
viscoelastic materials. The most common model for obtaining shift factors is the
Williams-Landel-Ferry (WLF) equation (Williams, Landel, Ferry, 1955).
When experimental data are available, a master curve can be constructed for the
mixture. The maser curve can be represented by a nonlinear sigmoidal function of the
Equation 2-8.