Fatigue Crack Paths 2003

expanded Kitagawa diagrams shown in Figure 4c and 4d may give a qualitative

explanation on this.The Kitagawa diagram [7] describes the correlation between the

critical crack length and the threshold value of the stress intensity factor range for crack

propagation or the fatigue limit. This concept may be used to determine the critical crack

length for Stage I cracking (crack initiation site) and Stage II cracking (“fish eye”), and is

given by the following equations.

Δ

K m a x

= σΔ

F max

π

a

and Δσmax=kΔσmax-surf

(1)

where ΔKmax is the maximumstress intensity factor range, F is the geometry factor, Δσmax

is the maximumstress amplitude at a given position in the rod section. , Δσmax-surf is the

maximumstress amplitude at the rod surface, k is the factor related to the stress decrease

in the rod,

1202468068

8

itioan

0

7

ey e " ( m

6

gair n s i n i n

5

S i z e o f " f i s h

4

e r o f

3

024 0 1 2 3 4 5 6 7 Distance from the surface (mm) N u m b

2

1

(a)

(b)

0

1

2

3

4

5

6

Distance from the surface (mm)

34560

Limit of stage II

56,0 0

100 ai (crack initiation size) (μμm) Limit ofstageI 200 300

400

10

4,0

3,0

2,0

20

01,0

(c)

(d)

0

2

4

6

8

af("fish eye" size) (mm)

Figure 4. Influence of location on the S N D C Oand “fish eye” size: (a).

S N D C Osize, (b). “fish eye” size, (c). Expanded Kitagawa diagram for

Stage I cracking, (d). Expanded Kitagawa diagram for Stage I cracking.

Crack Initiation and Propagation

As shown in Figure 2, the fatigue cracks started at initiation sites. A further S E M

investigation showed that cracks may have already been formed, and then propagated at

some angle to the fracture surface before the crack initiation sites were formed (Figure 5a

and 5b). This indicates that the crack propagation started with shear cracking, and then