Crack Paths 2009

a R is plotted against the dimensionless radial

In Fig. 4, the actual stress ratio

coordinate *r. For both unnotched (Fig. 4a) and notched (Fig. 4b) bar, by increasing

the parameter s the actual stress ratio

a R increases in the outside part of the bar and

decreases in the inner part of the bar.

0.8

0.8

(b)

s 0.012 0.3

ρd= (a)

U A L S T R E S S R A T I O ,

0.4

s

0.0

0.0

0.1

0.2

0.4

0.3

0.0 0.2 0.4 0.6 0.8 1.0

0.45

0.4

A 0.04 C T

0.8

0.5

ρd = 0.009

1.2

0.0 0.2 0.4 0.6 0.8 1.0 DIMENSIONLESS RADIALCOORDINATE, r* -10.284

DIMENSIONLESS

RADIALCOORDINATE, r*

Figure 4. Actual stress ratio

a R against radial coordinate *r, for different values of s and

cyclic tension with

= 0.0 F R : (a) unnotched round bar; (b) notched round bar.

F A T I G UCE R A CPKR O P A G A T I O N

N o wthe fatigue behaviour under tension loading is examined through a two-parameter

theoretical model [15], by also using the Paris-Erdogan equation [17] modified by

means of the Walker relationship [8]. It has experimentally been observed [18] that the

coefficient C of the Paris-Erdogan equation is not only dependent on the material, but

also on the stress ratio of the applied cyclic loading. Many equations have been

proposed to take into account the stress ratio effect [8, 19-21]. The empirical Walker

equation modifies the Paris-Erdogan law as follows [8, 22]:

( ) m L L R C R C ) 1 ( 0 1 ) ( β − − = − (6)

[ ] I m

L K R C d N ⋅ dΔ a = ) ( /

with

where )(LRC is the effective Paris-Erdogan coefficient for a generic stress ratio L R ,

β is the Walker exponent. It has been found that, for

0 C is )(LRC for

L R = 0, and

positive stress ratio values, the exponent β

usually ranges from 0.3 to 0.8 (

= 3.0 β

and

produce a strong and a weak dependence on

= 8.0 β

L R , respectively). For negative

β can be set equal to zero because only

stress ratio values,

I (max) K drives the crack [22].

The parameters 0 C and m are here assumed equal to 101064.1−⋅ and 2 (with dNda/ in ]cycle[m 1−⋅ and I K Δ in ]mm[N2/3−⋅) [23], and the exponent β equal to 5.0.

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