Fatigue Crack Paths 2003

60

50

40

c

30

20

5 5 V M 4

8 0 V G 9

10

0

10

20

30

40

a

Figure 7. Aspect ratio.

STRESSINTENSITFY A C T OERV A L U A T IFOON RT H EPIN

The first phase of the crack propagation was analysed by the model given in [2] for

semi-elliptical surface cracks in pipes subjected to either remote tension or bending

loads:

Q F a K N I ⋅ ⋅ = π σ

(1)

with:

65.1

a

464.11 ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ⋅ c

(2)

Q

+ =

in which:

- σN= bending nominal stress ;

a and c = main crack dimensions;

-

- Q = the shape factor for a semi-elliptical crack;

- F = the stress intensity boundary-correction factor.

The second phase of the crack propagation was analyzed by [3],[4] modelling the

pipe as a plate with a periodic series of aligned through cracks propagating along the

width (Fig.8). For this case , the weight function is available giving by [5] :

(3)

a W

with

f K I

π σ ⋅ ⋅ =

∫ ⋅

and

f

a d x a x a m x 0 ) , ( ) ( π σ σ

(4)

=

a a π π

tan

2

π

x

⎜ ⎝ ⎛

⋅⎟ ⎠ ⎞

2

2

) , ( x a m =

⋅

cos

(5)

x π π a

2

π

a

2

2

sin

−

sin

2

2