Page 70 - Mechanics of Asphalt Microstructure and Micromechanics

Microstructure Characterization 63

Homogeneity—If the specimen is completely homogenous, then any random sec-
tioning (or sampling) would reveal the same statistical information. However, since
most materials are not completely homogenous, the section orientation should be per-
pendicular to the direction in which the feature (such as phase distribution) has the
largest gradients.
Anisotropy—Anisotropy in this scenario may mean two aspects: the anisotropy of
the morphology of particles or voids and the anisotropy of the orientation distribution
of these entities.
Accessible parameters versus inaccessible parameters—Stereology should provide
an unbiased estimate of the properties of higher dimensions from the observations made
on lower dimensions. Some parameters can be estimated without bias (with no assump-
tions) and some cannot (an assumption must be made on the distributions). Volume frac-
tions are one of the accessible parameters, while particle size, volume per particle, and
number of particles per unit volume cannot be estimated without some assumptions.

3.2.1 Volume Fraction
In Figure 3.5, if dots are randomly scattered on the image and then counted within the
various phases, it can be shown that if enough dots are used and the phase distribution
is random, the dot density is equal to line segment fraction, the area fraction, and the
volume fraction (Equation 3-3). This relationship is exact when the average is over the
entire volume. Nevertheless, sampling over the entire specimen would take tremen-
dous effort. Data based on sampling a portion of the specimen, however, are not accu-
rate and depend on the uniformity of the microstructure.
N L A V
P = α = α = α = α (3-3)
P N L A V
T T T T

Testing Line

Intersecting
Point

If the dots (points) represent pixels, P P = A A (point fraction is equal to area fraction)
FIGURE 3.5 Testing line, testing dots, and intersecting points.