Page 45 - Mechanics of Asphalt Microstructure and Micromechanics

T
38 Ch a p t e r w o

F is compression load; A is aspect ratio of the film; 2h is thickness of the film; a is
width or diameter of the plate; and l is length of the plate.
For small changes in the thickness of the film, both h and a can be assumed constant.
Therefore, the deformation behavior of a plane strain contact in compression can be
expressed as:
⎡ n+1 ⎤ 1
·
⎛ σ ⎞ ⎢ ⎛ n ⎞ 1 ⎛ A ⎞ n ⎛ ε ⎞ n
⎥
n
⎜ ⎝ σ ⎠ ⎟ = ⎜ ⎢ ⎢ ⎟ ( n + 2) n ⎜ ⎟ ⎠ ⎥ ⎜ · n ⎟ ⎠ (2-11)
⎝ ε
⎢ ⎣ ⎝ 2 n + ⎠ 1 ⎝ 3 ⎥ ⎦ 0
· ·
Where s n = F/4al is the nominal compressive stress and e n =−h/h is the nominal
compressive strain rate.
For larger changes in the thickness of the film, h and a can no longer be assumed
constant.
If the initial dimensions of the contact are denoted by h 0 and a 0 , the change of these
dimensions can be assumed to be a constant volume process.The governing equation
can be expressed as:
n ⎛ ⎞ n+1 ⎛ n
dh =− hε · ⎛ 1 ⎞ ⎛ 2 n + ⎞ 1 3 ⎟ F F /4 ⎞ (2-12)
al
⎟ ⎜
⎠ ⎝
dt 0 ⎜ ⎝ n + ⎠ ⎝ n ⎟ ⎜ A ⎠ ⎜ ⎝ σ 0 ⎟ ⎠
2
For a viscoelastic contact in which both the elastic and the viscous constitutive
properties of the film material are to be included, the exact constitutive equation can be
obtained by using a spring in series with a non-linear dashpot (Cheung and Cebon,
1997b).
2.1.9 Characterization of Mechanical
Properties of Asphalt Binders and Mastics
This section presents the methods for characterizing the mechanical properties of as-
phalt binder and mastics. Only brief descriptions are given for readers as convenient
referencing.

2.1.9.1 Absolute (Dynamic) Viscosity (Pa.s or Poise)
Viscosity is the resistance to flow of a fluid. The viscosity grading of asphalt binders is
based on measurements at 60°C. This temperature was selected for testing due to the
fact that it is the assumed maximum asphalt pavement temperature during summer in
the United States. Two capillary tube viscometers are used to perform viscosity tests.
They are the Cannon-Manning and Asphalt Institute vacuum viscometers (Roberts et
al., 1996; Asphalt Institute, 2007). These viscometers measure the asphalt consistency at
60°C using a procedure described in ASTM D2171. They are placed in a thermostatically
controlled water/oil bath at constant temperature (60°C) and their tubes are filled with
binder that is forced to flow by applying a partial vacuum. The time in seconds required
for it to flow between two timing marks is measured and then multiplied by the calibra-
tion factor of the viscometer tube to obtain the viscosity in poises. These test methods
were introduced in the early 1960s by the FHWA, AASHTO, State DOTs, and Industry.

2
2.1.9.2 Kinematic Viscosity (cm /s or Stoke)
Kinematic viscosity is equal to the absolute viscosity divided by density (for asphalt it is
3
1 g/cm ). It is a consistency measurement performed at 135°C using a Zeitfuchs Cross-