Page 119 - Mechanics of Asphalt Microstructure and Micromechanics

Experimental Methods to Characterize the Heterogeneous Strain F ield 111

The average engineering shear strain (tangent strain) in the mastic is:
Δu − ω − ω r
r
γ = t i i j j (4-12)
H
Where r i is the distance from the center of the particle to a crossing point such as A;
w i is the rotation of the particle (counter-clockwise rotation as positive); H is the dis-
tance between A and B.
As the vector connecting the centroids of two particles is not necessarily normal to
the particle surface at crossing points such as A and B, the displacement normal to the
vector, and therefore the shear strain, is only an approximation. Both direct and shear
strain are average values between A and B. It should be noted that in the above formu-
lations there is an implied assumption that there is no discontinuity between the parti-
cle and the mastic.
An interesting implication of the above formulation is that Equations 4-11 and 4-12
are related to particle translation and rotation (particle kinematics), respectively.

4.2.6 Experimental Results and Analysis
The above procedure was implemented to estimate the strains in the mastic for the
eight images previously analyzed. The normal strains and the tangent strains for one of
the images (Image 10) are presented in Figure 4.10. The micro-strain values for the same
triangle whose macro-strain values are presented in Table 4.3 are presented in Table 4.4.
From the results, several observations are made:

a. The mastic strain is very localized. The magnitude varies by several orders and
is typically much larger than global strains.
b. In the zone dominated by compression, tensile strain does take place. This is
consistent with the material properties of AC and with doublet mechanics
predictions.
c. At a very large magnitude of strain, the interface between particles and the
mastic might debond. The actual strain in the mastic may be smaller, however,
before debonding the mastic likely was subjected to much larger strains than
estimated using the conventional approach of measuring global strains. This
has important implications in material property evaluations in that consistent
strain levels should be used in experiments to evaluate the mechanical properties
of AC.
The evolution of the mastic/solid area ratio indicated that the zone under the wheel
demonstrated dilatancy, whereas the zone away from the wheel demonstrated contrac-
tion. The measured permanent strain field demonstrated strong localism. Thus, direct
strains, shear strains, and volumetric strains all demonstrated particle configuration
dependency.
The permanent strain in the mastic was also evaluated. It was found that this strain
is generally much larger than the macro-strain. This measurement has important impli-
cations in the evaluation of rutting and fatigue resistance of AC because deformations
in the mastic are the source of rutting and fatigue development and are related to par-
ticle rotations.