Page 98 - Mechanics of Asphalt Microstructure and Micromechanics

Microstructure Characterization 91

X-ray cross-sectional image

FIGURE 3.22 Illustration of the determination of stereological fabric tensors.

same as that in another orientation and equals to the volume fraction of cracks or voids
in the specimen. Therefore, the damage tensor should be a field variable rather than a
state variable. In damage mechanics, it is convenient to define the damage tensor.
However, it is difficult to implement its quantification. For example, it is easy to define
dA
the area fraction as φ = d (where s represents the area fraction of defects; dA d repre-
dA
sents the area of defects on a cross-section; and dA represents the total cross-section
area of a representative cross-section), but how large should dA be in order to have a
reasonable evaluation of the determination of the area fraction? In this section, the
concept of a representative specimen is defined as a sphere centered at the point to be
evaluated. If a cylindrical specimen is used, the point under evaluation should be the
mass center of the cylinder and the diameter of the sphere should be equal to the diam-
eter of the cylinder. To quantify the damage tensor, which is symmetric and therefore