312 / 392
1.2.1. Linear-elastic deformation behaviour
For linear-elastic deformation behaviour the crack tip loading can simply be deter-
mined by superposition of the
K
factor due to primary, and the
K
factor due to secondary
stress, provided the crack opening mode is identical:
I
I
I
p
s
K K K
= +
(1)
1.2.2. Elastic-plastic deformation behaviour
In the general case, assessment is more complicated since interaction effects between
primary and secondary stresses must be taken into account. Secondary stresses cannot
cause plastic collapse, however, they may well contribute to plastic deformation. If they
reach yield strength magnitude, the resultant crack tip loading is larger than
K
I
p
+
K
I
s
.
On the other hand, secondary stresses may be partly relieved due to relaxation effects
introduced by ligament yielding. The interaction effect is modelled by a correction term
ρ
, which is defined in the Fracture Assessment Diagram (FAD) approach as:
I
I
p
s
r
mat
K K
K
K
ρ
+
=
+
(2)
and in the Crack Driving Force (CDF) route as,
2
I
I
1
( )
p
s
r
K K
J
E f L
ρ
⎡
⎤
+
=
⎢
⎥
′
−
⎢
⎥
⎣
⎦
or
2
I
I
1
( )
p
s
Y
r
K K
E f L
δ
σ
ρ
⎡
⎤
+
=
⎢
⎥
′
−
⎢
⎥
⎣
⎦
(3,4)
The quantity
ρ
characterizes the difference between actual crack tip loading and crack
tip loading which would result from simple superposition of
K
I
p
and
K
I
s
. By using
p
ref
r
Y
L
σ
σ
=
(5)
it is dependent on the ligament of plasticity,
L
r
(which is a function on primary loading),
and on the magnitude of secondary stresses, and on the equation applied for
f
(
L
r
). There-
fore, it is possible to determine the correction term
ρ
from plot in Fig. 8.
Secondary stresses are not significant for analysis performed here, but they shall be
mentioned without going into details. Note, that the SINTAP procedure gives guidance
for the treatment of secondary stresses.
Figure 8. Determination of the correction term
ρ
on the treatment of secondary stresses
308