Crack Paths 2009

(the

σ σ & ~ and correlation index ν

The stress signals, corresponding phase portraits

characteristics of dynamic system symmetry) are presented in Fig. 5,6. The scaling

properties as the above attractor were studied in the term of the correlation integral

phase pattern using the formula [17]

calculated

from the stress

r C

≈ − − , where j

m

)νrxxrH j i

i x, x are the coordinates of the points in

()

∑

(

2 1 l i m

=

m

∞ →

m

j1i = ,

the σ& ~σ space, (...)H is the Heaviside function. The existence of the scales

0 r> rwith

the stable correlation index was established for the regimes

C V V < and

C B V> V>.

V

The values of the correlation indexes show the existence of two scaling regimes with

4 . 0 , / 6 1 3 , 4 2 6 ≈ = ν s m V )

8 . 0 , / 2 0 0 ≈ = ν V s m ) and stochastic (

the deterministic (

dynamics. The extension of the portions with a constant indexes determines the scale of

the process zone

P Z L . The length of the process zone increases with the growth of the

crack velocity in the range

C B V> V>. NumeriVcal simulation of the damage kinetics in

the process zone allowed us to conclude that this scaling is the consequence of the

subjection of crack advance to the blow-up collective modes, which determines the

collective behavior of defects ensemble in the process zone [18,19].

,/MPasσµ&

,/MPasσµ&

σ,MPa

-05

-02

10

20

2 0

4 0

σ ,MPa

s m V / 2 0 0 =

s m V / 6 1 5 =

σ σ & ~ .

Figure 5. The phase portraits

() lnC r

-04

-6

-4

-2

0 . 8 ν =

0 . 4 ν =

P Z L Figure 6.

-200 m/s

+-613m/s

o-426 m/s

ln r

290