Crack Paths 2009

point A increases for 3.0< ξ in the case of straight-fronted crack (Fig. 3c) and for

< 2.0 ξ

in the case of circular-arc crack (Fig. 3d).

0

s

3.0

ρd=

ρd=

Point A

PointAC

0.0

0

1.0

Point C

α=0.0 (a)

α=1.0

0.5

5

2.5

s

1.0

0.5

0

2.0

0.0

s

5

1.5

0.0.51.0

0.0

0.5

1.0

1.0

(b)

0.5

5

s

.0

ρd = 0.009

ρd = 0.009

10.05

PointAC

PoiintntCA

α = 1.0

α = 0.0

.5

3.0 2 5

0.0

s

.0

1.0 0.5 0.0

2.0

1.0.50.0

.5

1.5

.0

1.0

0.0.51.0

.5

(d)

(c)

0.5

0.1

0.2

0.3

0.4

0.5

.0

RELATIVEC R A C DKEPTH, ξ

0.2 RELATIVCE R A CDKEPTH, ξ 0.3 0.4

0.

0.1

0.5

Figure 3. Dimensionless total stress-intensity factor

against relative crack

)(*resFI K +

depth ξ , for different values of s : (a, b) unnotched round bar and (c, d) notched round

bar; (a, c) straight-fronted crack and (b, d) circular-arc fronted crack.

From the above discussion, it can be deduced that the effect of the residual stresses

on the SIFs is remarkable and, therefore, a significant change of the fatigue behaviour of

both unnotched and notched bars can also be expected by varying the value of the

parameter s. Since the present paper aims at investigating the effect of different

residual stress distributions on the fatigue behaviour of round bars under constant

amplitude cyclic tension, the actual stress ratio

a R needs to be evaluated:

][ ])(* 1 / ) ( *

[

)(

) ( s r s R r R resI resI F a σ σ + ⋅ = + ⋅ ) ( r

(5)

σ=

σ

where

F R is the nominal stress ratio of the cyclic tension, i.e.

/

, and

F R

m a x ) ( m i n ) ( F F

)(Frefσ in s (see just after Eq.(4)) is assumed to be equal to the maximumstress

m a x ) ( F σ .

1171