Crack Paths 2009

direction where its growth rate is maximum.This generalises the idea of Hourlier et al

[6] who promoted it, under the restrictive assumption that mode I would necessary

prevail. The potential growth rates in corresponding directions are then estimated as:

da

l

f ≈

(1)

dN

()lN

Prediction of crack path and growth rate in fully reversed modeII

Figure 5 compares the potential crack growth rate in fully reversed modeII predicted by

Findley’s criterion and that of a branch crack, in modeI, according to S W T bfor various

amplitudes. These computations were performed for a smooth, frictionless crack. Coplanar growth is predicted for ∆KIIeffective higher than 15Mpa√m,which is consistent

with the threshold found by Pinna [1]. The predicted mode II crack growth rate is

correct above 25Mpa√m,but a bit too small below that value. This can be improved by

introducing a damage cumulation, to take into account the smaller cycles before the

crack tip touches the element whose fatigue life is computed. This will be reported

elsewhere, for lack of space.

1,E-0876 876

branch crack, m o d eI

maincrack, m o d eI

1,E-09

fit ofexperimental M o d eI data

1,E-10

∆KIIeffective (MPa√m)

10

100

Figure 5: Potential crack growth rate in reversed modeII predicted by Findley’s

criterion and that of a branch crack, in modeI, according to SWTb.

a)

b)

0,2

0,6 0, 0

0,4 friction coefficient h = 5 microns 1 mi rons 5 0 , ct ie 5 ns 1150m ron 0, , c i 550 oon 0,8

0,012 0 012 012

1

0,81

il

ilna

0,6 Kon m Ko

?

0,4 ?KIe ff / 0 ?KI ff /

h=5 microns

h=10 microns

0,2

h=15 microns

0

0

0,2

0,4

0,6

0,8

1

friction coefficient

Figure 6: Influence of crack roughness and friction coefficient on

effective

effective

a) ∆KI and b) ∆KII

in reversed modeII.

412