Chemistry Reference
In-Depth Information
d
ef
surf
Further the fracture surface effective dimension
can be calculated
by analogy with the Eq. (1.12) as follows [55]:
12
φφφ
++
c
ef
ef
-
10
d
= =- ×
d
3
6, 44
10
cl
n
n
(7.19)
surf
f
SC
∞
Since the authors of Ref. [54] consider fracture process in Euclidean
space with dimension
d
= 2 (flat crack), then in assumption of crack propa-
gation direction independence it can be written [59]:
ef
d
ef
d
=
f
.
(7.20)
surf
2
The authors of Ref. [55] considered two main case of crack presentation:
by a stochastic self-affine fractal (coordinates quasihomogeneous tension
occurs at scaling) and by usual isotropic fractal. For the indicated cases it
can be written, respectively [54]:
1/ 2
ef
surf
d
-
1
K
~
(7.21)
Ic
ef
surf
2
-
d
and
1/ 2
ef
surf
d
-
1
.
(7.22)
K
~
Ic
ef
surf
2
-
d
where
K
Ic
is stress intensity critical factor, determined as follows [20]:
1/ 2
,
(7.23)
K
ps
=
Ic
f
where
a
is critical defect length, is
f
is fracture stress.
With the Eq. (7.23) appreciation the Eqs. (7.21) and (7.22) can be rewrit-
ten as follows [55]:
ef
surf
d
-
1
s
~
=
B
(7.24)
f
1
2
-
d
ef
surf
