Page 208 - Mechanics of Asphalt Microstructure and Micromechanics

200 Ch a p t e r S i x

6.5.6.4 Micro Hardness Test
Hardness is a measurement of the stress defined as the ratio between indentation force
F
and the indentation area, H = i . Both theory analysis and experimental data indicate
S
i
this measurement is proportional to the yield stress or H = a(s y + R + X)(1 − D).
H
Therefore one may obtain: D =−1 (6-182)
H *
Where H is measured hardness for damaged materials, H* corresponds to the hard-
ness measured on the undamaged material for low-cycle fatigue (Lamaitre, 1996).
6.5.6.5 Other Methods
There are other approaches that can be used to measure the degree of damage. They
include plastic strain variation method due to cyclic stress, electrical resistance method,
tertiary creep rate method, and acoustic emission method. Table 6.2 (Lamaitre, 1996)
presents a summary of these methods that may be used for AC.
In the AC modeling studies, the major methods rest on the elasticity modulus deg-
radation approach.

6.5.7 Validity of the Above Relationships
For fatigue tests of AC, a criterion to judge whether the material has reached failure is to
use the modulus. When the modulus is reduced to 50% of the original modulus, the
material is considered being failed. Obviously, at this stage, D = 0.5, or the cross-section

Low- High-
cycle cycle
Methods Damage Brittle Ductile Creep fatigue fatigue

/
Density ⎛ ρ ⎞ ∼ 23 ** * *
⎜
D = 1 − ⎟
⎝ ρ ⎠
∼
Elasticity D =− E ** *** *** ***
modulus 1
E
2 ∼
Ultrasonic V L *** ** ** * *
1
waves D =−
V 2
L
Cyclic stress D =− Δ σ * * ** *
amplitude 1 Δ σ *
Tertiary creep ε ⎛ * ⎞ 1/N * *** *
D =− p ⎟
1 ⎜
⎜ ε ⎟
⎝ p ⎠
Electrical D =− V * ** ** * *
resistance 1 ∼
V
TABLE 6.2 Damage assessment methods (from Lamaitre, 1996) *Not sure, **Good,
***Very good).