Crack Paths 2009

(2)

m K C d N d a ∆ = ,

in the term of the stress intensity factor range defined as

max K K K− = ∆ , where

min

m a x K and

respectively are the maximumand minimumstress intensity factors, C

m i n K

and m are empirical constants which a functions of both material properties and

microstructure and the loading parameters (R ratio for instance) as seen hereafter. This

formula predicted the Paris exponent of m ≈ 4 in agreement with experiments for most

metals. Since the crack growth kinetics is linked with the temporal ability of material to

the energy absorbing at the crack tip area the understanding of the saturation nature can be the key factor for the explanation of the 4th power universality. It was shown that the

saturation nature can be considered as a consequence of the anomaly of energy

absorbing in the course of structural-scaling transition in dislocation ensembles with the

creation of PSBs and long-range interaction of dislocation substructures due to the

internal stresses, which provide the “self-criticality”

scenario of structure evolution at

S σ value of external stress. The saturation plateau is very pronounced

some constant

feature of the structure controlled regime with the low sensitivity to the applied stress

starting from some critical value

S σ . Since the damage kinetics along the path D H F

leads finally to the nucleation of the crack hotspots after the second bifurcation point at

C δ δ = , the stress controlled regime corresponds to the set of states D,…H,…,F,... with

the kinetics of this path approaching to the 4th power of damage kinetics

4 ~ S A p σ & . This

result supports the phenomenological law proposed by Paris for the H C Fcrack growth

kinetics. It is interested to note that this channel (scaling transitions due to the

generation of the multiscale dislocation substructures similar to PSBs) is very powerful in the sense of the energy absorbing. For instance, similar to the Paris law, the 4th power

law

A σ , was established at

4 A A σ ε ≈ & for plastic strain rate

pε& on the stress amplitude

the steady-state plastic wave front for the wide class of shocked materials [24].

DISCUSSION

The Paris law has found multiple conformations for different materials and numerous

experimental data reveal the power 4 3 ~ m i−n an intermediate range of K∆. The

weak dependence of this power on material microstructure, loading ratio and

environmental conditions manifested some universality features of material responses

concerning damage evolution scenario providing the fatigue crack advance. There are

two deviations from the Paris law. The crack growth is decreased in the region, where

the stress intensity factor is below the threshold value

t h K ∆ that depends significantly

on the material microstructure and the loading ratio. The third area corresponds to the

stress intensity factor

1 K K → , where the Griffith-Irwin crack growth instability C1

appears.

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