325 / 352
321
and with the fractal geometry taken into account. Thus, our most advanced model
incorporates the discrete nature of fracture process and its fractal geometry at the same
time. Two new variables enter the theory:
(1) fracture quantum
a
0;
(2) fractality degree, measured by the fractal dimension
D
or by the fractal exponent
α
.
It is noteworthy that each of the successive models listed in Fig. 6 predicts for a given
level of the applied load successively larger cohesive zone, namely
f
Dd D LEFM
Dd
R R R R
≥ ≥ ≥
The interpretation of the subscripts is as follows:
f
- fractal,
Dd
– Dugdale discrete,
D
–
Dugdale. Of course, the LEFM value of
R
is zero, but using the
K
c
value obtained from
the tests specified by ASTM one could, in a
hindsight, define an equivalent length
R
that
could be associated with a LEFM crack.
At the micro- and nano-scale the size of the Neuber particle, or process zone in a
more updated nomenclature, becomes important not only for mathematical treatment of
the problem, but also for the physical interpretation of the decohesion phenomenon at the
atomistic scale.
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