Fatigue Crack Paths 2003

curved increments of the crack path, the following first and second order finite element

representation of Irwin’s crack closure integral relations can be given for the crack clo

sure length Δa, Fig. 4:

() a1t2 a G i ( 1 ) I

()

u F

)1-i,11i,2 u F Δ + +

u F

)1-i,11i,1 u F Δ + +

(

(

i,2 = Δ Δ

(1)II G a

, i,1 = Δ Δ a1t2

2-i,2

i

2-i,1

() a1t2 a G i )2(I

u F u F u F Δ + Δ +

u F

(

) 1 i , 2 3 i , 2 − + , (8)

i,2 = Δ Δ

2-i,2 + − + + Δ 2i,2 3 i , 2 1 i , 2

4-i,2

u F

u F u F u F + − + Δ + Δ + Δ +

) 1 i , 1 3 i , 1 − + .

() i a1t2 a G )2(II

= Δ Δ

(

2 - i , 1 2 i , 1 3 i , 1 1 i , 1 4 - i , 1 i , 1

As the consequence of two calculations [9-11] with the same Δa and different ele

ment sizes h1>h2 in the neighbourhood of the crack tip the improved strain energy re

lease rates are obtained as

G

12 2 1 ) 2 ( I ) 1 ( I h 1 hh G G = −− ,

h h G G

IMPRI

−

2 1 ) 2 ( I I ) 1 ( I I

h

IMPRII

G

=

−

(10)

.

1 h

1

2

The essential feature of this technique is, that SIFs of higher accuracy can be ob

tained by comparatively coarse mesh divisions.

C U R V EFDA T I G UCE R A CGKR O W TEHSTS

In order to evaluate the validity and the efficiency of the proposed higher-order crack

path simulation method with respect to the well established basic strategies, experiments

of non-coplanar fatigue crack growth were carried out with a specially designed speci

menunder cyclic lateral force bending (LFB). The L F B Hspecimen was designed with a

hole in the centre in order to produce a non-homogeneous stress field (Fig. 5). Steel

E335 was selected as specimen material.

F 80 ∅ 2 0 ∅ 1 3

30 ∅ 2 1

60

40 225

∅ 2 1

6 0

Figure 5. Dimensions and definition of the

a 6

notch position aN of the L F B Hspecimens

(thickness t = 10 mm).

Crack initiation from notches at different positions aN along the tensile loaded edge

of these specimens is investigated to produce different crack interactions with the hole.

The notches have been manufactured with a width of 0.4 m mand a depth of 6 mm.