35 / 352
31
2
K K
J
K K K
E E
σ
ε
= = ⋅
= ⋅
(22)
On the basis of total strains can this proposed relationship, achieved based on elastic
solution, be generalised by including the plastic deformation too
e
pl
ε
ε
ε
= +
(23)
It is obvious that any solution for the conditions at the crack tip must include, behind
the solution for stress state, the strain state too, as the
J
- integral does.
Although the standards for the material testing based on
J
-integral exist, at this point
will be useful, showing the way how to treat experimental results for the evaluation of
J
-
integral, to be familiarized with the these basic characteristics of the material.
Results of testing specimens are critical value of
J
Ic
–integral and
J-R
curve, defined as
the
J
vs. crack extension,
Δ
a
, over defined range of validity. The integral values can,
dependent on material, considerable exceed the critical values (
J
Ic
). During the test
measured are the pairs of
J
and
Δ
a
values and plotted in the diagram. The results are
sensitive to the initial crack size
a
0
. To ensure that the initial crack length is accurate, the
standard calls for
a
0
to be adjusted by fitting a third order polynomial to the
J
vs.
Δ
a
data:
2
3
0
2
Q
Y
J
a a
BJ CJ
σ
= + + +
and extracting an adjusted new calculated
a
0
, called
a
oQ
. If the new value differs from the
measured by more than
0.01W
the data are invalid. If not, the new diagram should be
designed where all points are corrected by new values
Δ
a =
a
0Q
− a
(Fig. 12). Even with
no visible physical crack growth, the crack will appear to have grown due to crack tip
blunting. To account for this, the ”blunting line” is drawn given by
J
= 2
σ
Y
Δ
a
Then the exclusion lines are defined parallel to the blunting line, at 0.15 and 1.5 mm
offset. Critical value is evaluated (
J
Q
=
J
Ic
, if the requirements are met), however, in cut
of the parallel line shifted at the 0.2 mm offset with results line. If all test conditions are
met the data between limits (1.5 mm) should be interpolated by exponential curve
J
=
C
1
Δ
a
C2
Slope that defines the increase of resistance above
J
Q
depends on many factors,
considered later on. Although this increase can be used the safest application is based on
critical value that defines initiation of real crack growth.
Fracture mechanics based on
J
- integral application certainly has advantages in
relationship to
K
. Moreover, this is also true concerning fatigue crack growth analysis,
taking in consideration that between the both parameters the direct dependence in linear
range exists. However, this means, at the same time, that the introduction of
Δ
J
at the
place of
Δ
K
does not have strong reasons. Even though is well known that
Δ
J
application
can extend the range of linear log-log dependence out of
Δ
K
(Fig. 13), regime of high
crack growth rates do not have large importance for the calculation of total number of
cycles to the fracture or the contribution within of the total life. Moreover, taking in
consideration that
J
is based on deformation theory that does not consider cyclic loading
(unloading), the main question is if this parameter is „better“ than
K
. In the same time, the
evaluation of small cracks (with high stresses) is not sufficient examined in this respect.