Page 176 - Handbook of Materials Failure Analysis

172 CHAPTER 7 Investigation of failure behavior of tubular components

different levels of applied displacements in order to achieve different amounts of crack
growth. The initial crack lengths as well as the final crack lengths after the fracture tests
have been measured on the fracture surface.

6 RESULTS AND DISCUSSION
In this section, the load-displacement results as obtained directly from the experi-
ments with two different test setups are presented. The method to derive the fracture
resistance behavior of the axially cracked fuel-lad tube in terms of J-R curve is pre-
sented. Initially, the results of test setup with conical loading mandrels are presented.
This is followed by the results which have been obtained from the test setup with a
pair of split semi-cylindrical mandrels. The type of axially cracked specimen remains
same for both the test setup with different types of loading mandrels. However, the
first test setup uses specimen with 50 and 100 mm length, whereas the second setup
uses specimen with 13 mm length. The diameter and thickness of the specimens are
same for both the test setups.

6.1 RESULTS OF THE TEST SETUP WITH CONICAL-TYPE
LOADING MANDREL
The load-displacement behavior for the axially cracked specimens with different
values of a 0 /W is shown in Figure 7.10. As the specimen with higher a 0 /W ratio
has less stiffness, the load corresponding to same axial displacement of the mandrel
is less. It was also observed that for the same value of applied displacement, spec-
imens with smaller initial crack lengths absorb more energy due to extensive plastic
deformation.
For calculation of plastic deformation energy, the frictional dissipation needs to
be subtracted from the total energy applied on the specimen. Frictional dissipation is
calculated from the area under the frictional force F f versus the applied displacement
curve. The force of friction can be evaluated from the equilibrium condition and is
given as follows.
μF
F f ¼ (7.1)
sin θ + μcos θ
where μ is the coefficient of friction, θ is the half cone angle, F is the applied load.
The coefficient of friction between stainless steel mandrel and Zircaloy-4 (with
lubrication between the surfaces) has been taken as 0.08. The absorbed plastic defor-
mation energy versus crack extension data was observed to be nearly independent of
the a 0 /W ratios of the specimens as shown in Figure 7.11. This may be attributed
to the dependence of plastic deformation energy (required for ductile crack growth)
on the formation of an intense localized plastic deformation zone ahead of the crack-
tip, which is independent of the actual remaining ligament of the specimen. In order
to compare the fracture resistance behavior of axially cracked fuel-clad specimens,