Page 215 - Mechanics of Asphalt Microstructure and Micromechanics

Fundamentals of Phenomenological Models 207

FIGURE 6.17 First-order and =0
second-order estimates of
yy
plastic zone size (r y and r p , Elasti
respectively).
Y
Elastic-
S
r y
yx
u

r
r p

A more accurate estimation will need to account for the stress redistribution:
r y r y
YS p ∫
σ r = σ dr = ∫ K I dr
yy
0 0 2 πr
1 ⎛ K ⎞ 2
r = ⎜ I ⎟
p πσ YS ⎠
⎝
(6-209)
The meaning of some of the symbols are illustrated in Figure 6.17. There are more
accurate approaches to do the estimation (Irwin, 1961). Additional information will not
enhance the understanding of the tip plasticity concept and will not be presented.

6.6.8 Crack Tip Open Distance (CTOD)
Wells (1961) discovered that due to plastic deformation, the sharp crack will become
blunt around the tip. He found that the degree of blunting increased proportionally to
the toughness of the material. Wells then proposed the opening at the tip as a measure
of the fracture toughness. Irwin (1961) showed that the plasticity effect is equivalent to
a “longer” tip starting r y from the actual tip (Figure 6.17).
Therefore,
κ + 1 r
u = K y (6-210)
y 2 μ I 2 π

Considering the Irwin’s plastic zone correction, CTOD is:

4K 2
δ = 2u = I
y πσ E
YS (6-211)
It is related to the energy release rate by:
4 G
δ =
πσ YS (6-212)
G
δ =
m σ
YS (6-213)