Crack Paths 2009

∞ annihilation occur, decreases as lGB increases, resulting in that the lowest σ

needed

yy min

to obtain crack growth is decreased whenlGB is increased.

1234505050 1234505050

σ ∞

=

MPa

20

yymin

12

numberof dislocations

yymaxσ ∞

numberof dislocations at na

at

10

σ ∞

=

MPa

40

d i s l o c a o n s t i

yymin

8

σ ∞

=

MPa

60

6

yymin

4

yyminσ ∞

σ ∞

=

MPa

80

2

yymin

10

0

2000 4000 6000 8000 10000 12000 14000 16000

2000 4000 6000 8000 10000 12000 14000

lGB [b]

lGB[b]

5

1.

2.

Figure 3. Numberof dislocations along the slip plane at yy σ∞

=40 M P aand

min

yy σ∞

=200MPaas functions of lGB. 2. Crack growth rate for different yy σ∞

as a

max

min

functions of lGB.

Crack growth rate as function of ∆ K

To compare the results from the simulations to typical behaviour for long cracks the

crack growth rate is calculated as a function of the stress intensity factor range, ∆K, [1].

∆ K is calculated according to Eq. 5, where no consideration to the mixed modeloading,

or influence of the free edge is taken into consideration. Thus ∆ Kis merely treated as a

way of measuring howcrack length and external load influences the stresses in front of

the crack.

(

)

(5)

yymax a σ σ π ∞ ∞ − yymin

K ∆ =

First da/dN as function of ∆K, with ∆ K increasing due to increasing a, was calculated with lGB1=5000b and yy σ∞ =200 M P afor different yy σ∞ with four different crack

max

min

lengths; a=10000b, 20000b, 40000b and 80000b, cf. Figure 4.1. It is found that, for all

but the lowest growth rates, the curves for the different load amplitudes show very good agreement. The discrepancies for the lowest loads are due to that at already yy σ∞ =40

min

MPa, the crack growth rate equals zero. Therefore, the first point, with yy σ∞

=60 M P a

min

σ ∞

and

=80 MPa, is not the limit for crack growth.

yy min

574