Crack Paths 2009

as a maximumvalue of dissipation of a static energy component on plastic strain

(Γ=Wsmax), which initiates a proces of fracture without participation of energy for cyclic

strain changes (Wc=0) [5]. After elementary transformation (5) and considering (6) the

general form of the crack surface propagation the equation is as below:

S

∂ c ∂

W / N

∂

( ) / N W S s = ∂ ∂ Γ − ∂ (7)

In order to obtain the expression based on which the experimental diagram of fatigue

fracture kinetics is to be created, the simplified forms of (8) and (9) are to be used,

without considering the change in the function of length in crack opening δ:

∂

ΓS

fcplfεσ

(8)

=

∂

W

f p l f ε σ

S

∂ = S

(9)

max

Determining the exact forms of (8) and (9) has been presented in the work [5], based on

the Dugdale – Panasiuk model. Considering the (8) and (9), the expression being the

denominator of (7) can be obtained:

σ ε

σ ε σ ε

∂ −

ε

ε

Γ SW

(

)

(1

)

fc

max S p l f pflffc plffc

f

max

= −

(10)

∂

=

−

The equation (10) can also be presented somewhat differently:

2 ) ( 1 ) ) ( f S p l f f c p l f f c p l f f c f c fc Γ W K S K ε σ ε σ ε σ ε σ ε ∂ − = − = − ∂ (11) max Imax max 2 (

)1(

By designating

as a quantity of plastic strain energy dissipation ahead

W N W c c ∂ ∂/ =

of the crack tip for one load cycle we obtain:

)1(

c WK K

(12)

) / 1 ( d / d S maxI N − = ε σ

f c f c p l f

The equation of fatigue crack growth rate assumes the form of:

α

∆

da

H

=

(13)

σ ε

dN plffc

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