Page 179 - Handbook of Materials Failure Analysis

6 Results and Discussion 175

with η and γ are the geometric factor and the correction factor, respectively, for a
growing crack situation. The η factor is defined as a nondimensional parameter that
takes into account of the effect of geometry and loading condition at the crack-tip of a
cracked specimen on the differential energy that is required for crack growth. For a
growing crack, the solution for J pl is corrected with a γ factor. It is defined as a non-
dimensional parameter that accounts for correction in the J-integral calculation due
to crack propagation, which is otherwise defined for a stationary crack.
For the axially cracked specimen loaded with conical mandrel, the state of stress
ahead of crack-tip is predominantly tensile with dominant mode-I crack growth.
Hence, the η and γ factors (taken from Ref. [28]) corresponding to the middle tension
“M(T)” specimen has been used here for evaluation of plastic part of J-integral
accordingly as described in Equation 7.5. For the case of the fuel-clad specimen with
100 mm total length (W), the value of initial crack length a 0 varies from 10 to 50 mm,
respectively, and hence, the initial remaining ligament varies from 90 to 50 mm,
respectively. In case of the specimen with 50 mm total length (W), the minimum
value of remaining ligament is 25 mm and the maximum value is 45 mm. The crack
growth measured in this work is of the order of 1.5-2 mm. The extent of crack growth
and the stressed region is small compared to the actual remaining ligament and
hence, the whole remaining ligament doesn’t participate in the plastic dissipation
process of ductile crack growth.
The actual remaining uncracked ligament length is very large compared to the
stressed region ahead of crack-tip for all the specimens with different initial crack
length values. In case of this specific loading geometry (i.e., longer fuel-clad spec-
imens loaded with conical mandrel), only a small region of the specimen, which is
very close to crack-tip, will be subjected to tensile stress and hence, this region will
offer resistance to crack propagation. This zone is termed here as the effective
remaining ligament. This length is calculated by FE analysis and it has been found
to be of the order of 20 mm. When this effective ligament length is used in the cal-
culation of the J-R curve in Equation 7.5, the results of fracture resistance are found
to be more or less similar for different values of a 0 /W ratios of the axially cracked
fuel-clad specimens.

6.2 FE ANALYSIS OF THE TEST SETUP WITH CONICAL-TYPE
LOADING MANDREL
FE analysis was carried out for the test setup with conical loading mandrel in order to
understand the load-displacement behavior of the axially cracked specimen and to
determine the effective ligament length. Due to symmetry, 1/4th of the test setup
was modeled and the 3D FE mesh of the test setup is shown in Figure 7.13.For
the elastic-plastic FE analysis of the test setup, the material true stress versus plastic
strain data for Zircaloy-4 as shown in Figure 7.14 was used. Tests were carried out at
room temperature with displacement-controlled mode and the state of von Mises
equivalent stress (in MPa) and equivalent plastic strain at the crack-tip are shown
in Figures 7.15 and 7.16, respectively, for an applied mandrel displacement of