Fatigue Crack Paths 2003

M o d eI

M o d eII

M o d eIII

M o d eI+II+III

Figure 4. Different types of crack growth under MixedModeloading.

The basis for all concepts are the near-field-solution for the stress distribution at the

crack front:

or I ‘kl/<2’? {5 cos[%] — cos[3?(p]} — 4 % {Sin[5%] — 3 Sinfgj}

(1a)

o,p I —4\I/<2I_m{3 cos[%] + cos[3?(p]} — 4 % {sin[3%] + 3 sin[%)}

(1b)

-

14%) +set +e100 -we)

K111 ~ [(1)] In I — s 1— n

(1d)

-\/21tr

2

K111 C O S F P )

Z I

_

(18)

R0 \I21tr

2

62 I v(c5r + ow) I 4 % { KcosI[%) —KII sin[%)}

(1f)

Eqs 1a-1c are valid for plane stress, while Eqs ld-lfg have to be added for a spatial

stress state. All those stress field equations are based in a cylindrical co-ordinate system

with the co-ordinates r, (p and 2 (Figure 5). For r 9 0 all stress fields becomesingular.

The parameters K1, K H and K111 are the stress intensity factors for the three fracture

modes (Figure 1). They describe the loading situation at the crack tip and can be used to

estimate the risk of fracture as well as for the description of the fatigue crack growth.