Page 242 - Mechanics of Asphalt Microstructure and Micromechanics

234 Ch a p t e r Sev e n

Ghuzlan et al. (2000) proposed a dissipated energy model to model the fatigue
of AC. The following equation is used to calculate dissipated energy in the flexural
fatigue test:
W = πσ ε sin ϕ (7-95)
i i i i
Where W i = dissipated energy at load cycle I; s i = stress amplitude at load cycle I;
e i = strain amplitude at load cycle i; and f i = phase angle between stress and strain.
Then the total (cumulative) dissipated energy at failure will be as follows:
fat ∑
W = n W i (7-96)
i=1
Conventionally, fatigue life was related to the total dissipated energy in the fatigue
test as follows, where N is the number of cycles to failure and A, z are experimentally
determined coefficients:
W = A N z (7-97)
⋅()
fat
The conventional failure criterion in fatigue testing, 50% reduction in modulus,
however, was found not to provide a consistent indicator of the onset of failure when
different modes of loading are used. Dissipated energy, when examined as a change
between two load cycles, provides a more fundamentally correct indication of damage
from one load cycle to the next than does cumulative dissipated energy.
A new failure criterion has been presented for fatigue characterization based on the
premise that the change in dissipated energy from one load cycle to the next is the ap-
propriate indicator of the damage done to the material by that load cycle. The new
failure criterion was defined as the change in dissipated energy (ΔDE) between cycles a
and a + 1 (representative of the actual damage to the sample) divided by the total dis-
sipated energy (DE) to load cycle a. Because of equipment readout limitations, this
change was usually calculated approximately every 100 load cycles. The new failure
criterion is given as follows, where N is the number of cycles to failure and A, z are ex-
perimentally determined coefficients.
ΔDE = AN z (7-98)
()
DE
The damage accumulation ratio (ΔDE/DE) provides a consistent failure indicator
that appears to be independent of the mode of loading.
Bonnetti et al. (2002) performed fatigue tests on a set of unmodified and modified
binders and analyzed the test results using the dissipated energy ratio concept. The
number of cycles to crack propagation, N p , was used as the fatigue criterion for the
analysis. Using the initial dissipated energy per cycle (W i ) as the main independent
variable for modeling fatigue of binders appears to be a promising technique to normal-
ize some of the testing conditions. The parameter N p20 , defined as the number of cycles
at which the dissipated energy ratio shows 20% deviation from the no-damage ratio,
appears to be a promising parameter to define failure.
It was found that the most suitable means of evaluating the effect of modifiers in the
fatigue response of the binders is using the cumulative dissipated energy ratio (DER):
n
∑ W
DER = i=1 i (7-99)
W
n