Fatigue Crack Paths 2003

the maximumstress and the corresponding nominal stress in the notched cross-section)

is univocally related to the loading condition applied. An axisymmetric finite element

analysis with an increasing number of elements (h-convergence test) has been carried

out in order to obtain the asymptotic

tK values for uncracked notched bars under

tension. The relative notch radius

dρ has been assumed to be equal to 0.1, 0.2, 0.5, 0.7

(blunt notch) and ∞ (unnotched bar), where such notch configurations correspond to t K va es equal to about 2.83, 2.19, 1.70, 1.58 and 1.0 in the case oftension loadi g.

Then, an external surface crack is assumed to exist in the notched cross-section of the

structural component. Such a flaw presents an elliptical-arc shape (Fig.1). The crack

= D a / ξ of the

configuration being examined is described by the relative crack depth

deepest point A on the defect front (with

8.0 1.0 ≤ ≤ ξ ), and the flaw aspect ratio

b a / = α(with 2 . 1 0 ≤ ≤)α, whereas the generic point P along the crack front is

identified by the dimensionless coordinate h / * ζ ζ = (Fig.1).

STRESSINTENSITFYA C T OERV A L U A T I O N

A finite element model has been adopted to determine the SIF values along the crack

front. Due to the symmetry of the problem, only a quarter of the bar has been modelled

by 20-node isoparametric finite elements. Quarter-point wedge finite elements have

been used along the crack front in order to model the stress field singularity. A total

number of 3186 finite elements and 14367 nodes have been employed. The SIF values

have been obtained from the displacements of the wedge finite elements, measured in

correspondence to the quarter-point nodes.

X M σ

Dimensionless SIFs, normalised with respect to the reference stresses

F σ and

for tension and bending, respectively, are defined as follows:

π

K

K a F F I

K

K

F I

X M I

X MX M I

=

=

(1)

*

*

,

,

,

,

π σ

σ

a

where

32 π

DF

M

02

M X

X

F

σ π =

σ

=

(2)

03

4

D

The t K parameter is very important especially in presence of cracks, since it heavily

affects the SIF results. The dimensionless SIFs along the crack front, determined

through the above finite element analysis, are displayed for both tension and bending

(

)1.0 = d ρ

values equal to 2.83

and 1.0

loading in Figs 2 and 3, respectively, for

tK

( )∞= d ρ . Different values of ξ

α are considered. The effect of the stress

and

concentration on the SIFs can be observed. For instance, the dimensionless SIFs for

d ρ

d ρ

= 1.0

are greater than those for

∞ = , the values of the other parameters being the