Page 241 - Mechanics of Asphalt Microstructure and Micromechanics

Models for Asphalt Concrete 233

materials in an axial compression experiment, and the damage evolution in elastic sol-
ids under an indirect tensile test were simulated. The simulation results agree well with
the theoretical solutions and show excellent promise in predicting cracking patterns in
the indirect tensile test.

7.10.6 Surface Energy-Related Model
Based on Schapery’s fundamental law of fracture mechanics and Lytton et al.’s healing
model, Cheng et al. (2002) derived the following cohesive fracture law for cyclic fatigue
testing, which is the equivalent of Paris’s law.
1
Δ t f m f
dc = ∫ ∫ K α( D E J ) dt − dh (7-92)
R ν
f 1
d
dN 1 dN
0 m f
(2Γ − DE J )
f 0 f R υ
Where dh/dN = the rate of crack healing per load cycle; dc/dN = the rate of cracking
−1
per load cycle; Γ f = fracture surface energy density of a crack surface (FL ); a = the
length of the fracture process zone before the crack surface; E R = reference modulus
used to represent a nonlinear viscoelastic material as equivalent nonlinear elastic (FL );
−2
mf
D 0f , D 1f , m f = creep compliance coefficients of the power law; D f (t) = D 0 f + D 1 f t ; K f =
constants that depend on the value of m, the slope of the log creep compliance versus
log time curve (a common value is one-third); and J v = strain energy (this is the rate of
change of dissipated energy per unit of crack growth area from one tensile load cycle to
−1
the next) (FL ).
Cohesive fracture and healing were treated in this model as a special case of adhe-
sive fracture and healing. Asphalt pavement fatigue failure occurs at the interface be-
tween asphalt and aggregate, which is caused by adhesive bonding failure. For adhe-
sive fracture, the following, more general, equations hold:
Γ + Γ − Γ = ED t J()
1 2 12 R f α V
Γ + Γ − Γ = ED t H()
1 2 12 R h α V
1
Δt f m f
dc K α( D E J ) dh
R ν
= ∫ dt − (7-93)
f
f 1
dN 1 dN
N
0 0 m f
(Γ + Γ − Γ − DE J )
1 2 12 0 f R υ
Where Γ 1 = surface energy of the asphalt, Γ 2 = surface energy of the aggregate, and
Γ 12 = energy of interaction between the asphalt and the aggregate.
7.10.7 Dissipated Energy-Based Model
Based on the relationship between total dissipated energy and the number of cycles up
to fatigue or fracture, the following energy model was developed by van Dijk (1975):
π SSinφ 1 2
N = ( fat ) z−1 ε z−1 (7-94)
A ϕ 0

Where N is the number of load applications to fatigue; S fat is initial stiffness modu-
lus; f-phase angle between stress and strain; and z and A are material constants.