Page 244 - Mechanics of Asphalt Microstructure and Micromechanics

236 Ch a p t e r Sev e n

Bilinear Model
Bilinear form in a cohesive zone model is described by:
δ 0 ≤ δ ≤ 1
σ = − δ 1 ≤ δ ≤ 2
2
0 2 ≤ δ (7-105)

The separation work is f = 1.
Parabolic Model
The parabolic cohesive zone model is described by:
−
2 δδ 2 0 ≤ δ ≤ 2
σ = { (7-106)
0 2 ≤ δ

The separation work is φ = 4 = 133. .
3
Sinusoidal Model
The sinusoidal cohesive zone model is described by:
πδ
sin( ) 0 ≤ δ ≤ 2
σ = { 2 (7-107)
0 2 ≤ δ

4
The separation work is φ = = 1 273 .
.
π
The Exponential Model
The exponential cohesive zone model is described by:
σ = δe 1 − δ 0 ≤ δ (7-108)

1
2
The separation work is φ ==e exp( ) ≅ .718 .
7.11.2 Cohesive Zone Models used in Modeling Fracture of AC
As mentioned before, cohesive zone models are widely used as a tool to investigate the
fracture of materials. They have been used in AC simulations in recent years. Kim (2008)
used a clustered discrete element method (DEM) as a tool to investigate fracture mech-
anisms in AC at low temperatures. The bilinear cohesive zone model was implemented
into the DEM to enable simulation of crack initiation and propagation in AC. Song et al.
(2005, 2006) used both the bilinear and the exponential cohesive zone models to de-
scribe cracking in AC. Cohesive elements are generated by means of a user subroutine

of the ABAQUS software and calibrated by simulation of the double cantilever beam
test. Song et al. (2008) conducted another study to investigate an important parameter
of the cohesive zone model, softening shape, which becomes very important as the
relative size of the fracture process zone compared to the structure size increases. The
parabolic cohesive zone model was used in that study. Liu (2008) incorporated the dig-
ital image processing techniques and finite element method to simulate the indirect
tension test in the lab. The fracture mechanism is described by a cohesive zone model.