Page 174 - Mechanics of Asphalt Microstructure and Micromechanics

166 Ch a p t e r S i x

σ -Peak Strength
m
σ

σ -Yield Stress σ -Residual or
y Hardening Softening r
Fracture Strength
σ -Proportional Limit
p
II

III IV

I

ε

FIGURE 6.1 Typical stress-strain curve for metals and other materials.

point on, the material starts softening. This zone (Zone IV) might be better described by
continuum damage mechanics (CDM) or fracture mechanics.
Many materials may not follow the well defined behavior. In some cases certain
zones may not exist. For different stress modes, the behavior of the material may be-
come very complicated.
Elasticity comes from resilient deformation of perfect atom lattice or crystals. Wein-
er (1983) presents excellent explanation on elasticity and its atomistic scale reasons. Due
to the existence and movements of such as a point, line, surface, and volume defects,
and breaking up of bonds or fracture, plastic deformation, or irrecoverable deformation
occurs. The traditional plasticity considers dislocations as the resources of plastic defor-
mation. The limit forces exist that drive the dislocation to move. This explains the yield
strength of metals. For AC, scientifically valid and verified microscopic mechanisms
regarding yielding are needed.

6.1 Elasticity

6.1.1 Linear Elasticity
Generally speaking, the phenomenological modeling of the stress-strain relationship
using mathematic functions can be represented as a Taylor series:
ε ∂ ∂ 2 ε
ε = ε + ij σ + 1 ij σσ + .... (6-1)
0
∂
ij ij ∂ σ kl 2 ∂ σσ kl pq
kl kl pq
0
If there exists a state where zero stresses corresponds to zero strains, e ij = 0, which
means no residual strains (plastic strains, eigenstrains), then the material is elastic. If
the high order terms are neglected, then the following relationship holds:
ε ∂
ε = ij σ (6-2)
ij ∂ σ kl
kl