Crack Paths 2006

'K IIth

ModeII fatigue crack growth threshold

In order to decide ModeII fatigue crack growth threshold 'KIIth in air and in a vacuum,

the relationship between ModeII fatigue crack length and 'KII were investigated by the

finite element method (FEM).

Figure 5(a) shows the shape and dimensions of F E Mmodel. Material properties are

Q = 0.3. The ModeII crack lengths a

Young’s modulus, E = 206GPaand Poisson ratio,

P during Mode II

are 0.3, 0.6, 2.0 and 5.0 m mand the assumed friction coefficient

fracture surfaces are 0.0, 0.2, 0.4, 0.6, 0.8 and 1.0.

Figure 5(b) shows the variation of KII in terms of crack length a. KII were calculated

by stress distribution singularity at the ModeII crack tip. ModeII stress intensity factor

KII decreases as the ModeII crack length a increases. And, the KII decreases as friction

P increases. In order to decide the ModeII crack growth threshold 'KIIth by

coefficient

P must be

F E Mresults and the Mode II fatigue crack length, the friction coefficient

determined. The friction coefficient in air was set to P = 0.6 considering the results of

the preview studies [8].The friction coefficient in a vacuum is unknown. W eneed to

estimate it. The friction coefficient in a vacuum is higher than that in air. Moreover, in

ModeI crack, 'KIth in a vacuum is higher than that in air [3]. The crack length for Mode

II fatigue threshold in a vacuum is shorter than that in air. Considering all these data, the

friction coefficient in a vacuum could be assumed to be P § 0.7. Thus, the values of

'KIIth in a vacuumwas determined to be P = 0.7.

Table 4 shows the ModeII crack length a and 'KIIth in air and in a vacuum. The Mode

II threshold stress intensity factor ranges in a vacuumwere higher than those in air. The

values of 'KIIth for crack growth perpendicular to the rolling direction (Transverse

crack) were higher than those for crack growth parallel to the rolling direction

(Longitudinal crack). The reason for higher values of 'KIIth in a vacuum is due to the

lack of oxidation at crack surfaces in a vacuum. It is presumed that new surfaces of the

ModeII fatigue crack tip in a vacuum may be easily re-adhered.

123505050

Crack length at branching (ModeII threshold), Longitudinal Transverse

P+S

w = 0

Contact area (P = 0) S

u, v, w = 0

)

P = 600kgf (5.88kN) S=108 gf 10.58kN)

P=0

Crack length

P=0.2

P=1.0

Contact area

P=0.4

Vacuum

Air

P=0.6

P=0.7

P=0.8

0

1

2

3

4

5

6

20 node tetrahedron element

Crack length a (mm)

(a) Analysis model and boundary condition.

(b) Relationship between ModeII crack length a

and ModeII stress intensity factor KII.

Figure 5. F E Mmodel and analysis result.