Fatigue Crack Paths 2003

have been substracted. As can be seen the FLEXmodel seems to be more accurate with

respect to the modified SERRmodel, assuming as reference the 3D calculation. As can

be seen especially the effects of tangential stresses due to torsion or shear forces cannot

be correctly represented by the modified SERRmodel.

0.14

0.12

r a d * 1 0 - 3 ]

[]m

0.10

amtcen

0.08

0.0246

R o ta t io n[

FLEX

ilsp

FLEX

-54321012.0 0 60 120 180 240 300 360 Degree [°] D S E R R

S E R R

0.00

3D

3D

0 60 120 180 240 300 360 Degree [°]

Figure 6. Bending and torsion, 50%crack depth, x displac. (left), ϑz rotation (right)

0.40

0.30

t[m ]

[ r a d * 1 0 -3 ]

0.20

0.10

a c e m e n

0.00

R o ta t io n

FLEX

-0.10

ips l

FLEX

-0.320

-1-208642024.0 0 60 120 180 240 300 360 Degree [°] D S E R R

S E R R

-0.40

3D

3D

0 60 120 180 240 300 360

Degree [°]

Figure 7. Bending and shear, 50%crack depth, x displacement (left), ϑx rotation (right)

T H ED Y N A M IBCE H A V I O UORFT H EC R A C K ER DO T A T I NSGH A F T

The model of a cracked shaft line is represented by the traditional 2.nd order matrix

differential equation, in which the mass and damping matrices are constant, whilst the

stiffness matrix has a variable part, which is function of the breathing behaviour, which

in turn is determined by the angular position of the crack with respect to the static and

dynamic loads.

When the breathing is mainly due to static loads (such as the weight of horizontal

rotors) then the equation is linear and the stiffness is only depending on the angular

position of the shaft with respect to the load. Steady state solutions can be found in the