Crack Paths 2012

600

The method operates by selecting,

low-cycle fat. energy approach based onR-Omodel Steel 1045 a

along the iteration process, the best

Figure 4. S-N curves corresponding to the p=0 andp=0.90for the steel 1045.

solution among different possibilities,

trying to fulfil as better as possible the

required value of the objective function,

a

b

w

here identified as the known ratio

V y =382 MPa

V V

r

7 9 . 1 ) / ( 2 # ' ' w b for both the

cycles,N

initial and the final crack sizes.

Numberof p= 0 %

234500

After a short number of iterations, the

p=90%

sought values for

and

are

bia,

wia,

obtained. The G A process produces a

stable result for the two above quantities,

-4

namely

10 12682.2 ˜

m and

b i a

,

m, irrespectively of

10 80701.3 ˜

w i a

-4

,

the stress range and the final number

of cycles

L N adopted (see Eq.(8)).

1

(a)

(b)

1000

a

ai,b

ai,w

V

MPa

0

ai (m)

N

=100K

L

N

=500K

L

N

= 2 M

L

N

= 1 0 M

L

a

a

N

100

i,w

i,b

L

1.0E-004

1.0E-003

Initial crack size, ai (m)

Figure 5. Kitagawa-Takahashi diagram for the steel 1045 for different values of cycles

to failure

L N (a) with probability distribution related to the finishing surface state (b).

Finally, the generalised Kitagawa-Takahashi diagram has been obtained by

integrating the Donahue equation starting from the initial crack size up to the fulfilment

Ic K N a K' ' ) , ( ) for a given number of cycles L i I

of the critical condition (

L N to

failure; the initial crack size

ia has been assumed to be simply uniformly distributed in

the interval

bia,-wia,. As can be observed in Fig. 5, the initial crack size to be

1047