INDIAN INSTITUTE OF TECHNOLOGY KHARAGPUR
End Spring Semester 2022-23
Date of Examination: 25/04/2023 Session (FN/AN) AN
Duration 3 Hrs. Full Marks 50
Subject No. : ME60434 Subject:
FRACTURE MECHANICS
Department/Center/School: ME M. Tech. / DD (elective) + AE Ph.D.
Specific charts, graph paper, log book etc. required: NO
Special Instructions (if any): Question paper has 2 pages (both side printing)
and 6 questions. Answer at least 5 questions. Each question carries 10 marks.
If more than 5 questions are answered the marks of the 6th (bonus) question
will be added as long as the total marks obtained do not exceed 50.
____________________________________________________________
1. The Westergaard function for an infinite
plate with a crack of length 2a subjected to a
pair of forces P at x=b under mode I loading
is (see figure 1 (a) below) is given by
ZI 
P
a 2  b2
. The formula for
  z  b z2  a2
the stress intensity factor for mode I is
K I  lim 2 Z I where   z  a .
 0
Figure 1
Show
P
ab
. Using this result find the
a a  b
stress intensity factor if the loading in (a) is replaced by the triangular loading shown in in
figure 1 (b).
that the stress intensity factor for such a crack is K I 
2. The vertical displacement of the fictions crack face in the Dugdale model (figure 2) is
Figure 2
Find the crack width (Crack Tip Opening
Displacement) and the slope of the curve v(x) i.e.
dv/dx, at the tip of the actual crack (x=a).
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Figure 3
3. Assuming that the J integral
is path independent along a closed contour, show that
the J integral along the paths ABC (1) and FED (2)
shown in figure 3 are the same.
4. For a double cantilever beam of total
length L, with a>>2h and L>>2h subject
to moment loads as shown as shown in
figure 4, determine the strain energy
release rate (per unit area) G.
Figure 4
5. The Von Mises yeild criterion is given by

2 Y 2   xx   yy
2
2
2
            6 
yy
zz
zz
xx
2
xy

  yz 2   zx 2 .
For mode III loading in cracks the stresses are
  ,  yz  Re  Z III
  where Z III
 
 xx   yy   zz   xy  0, zx  Im  Z III
z
and  is the far
z 2  a2
 at the
field shear load. Use the transformation   z  a to obtain a simplified form of Z III
crack tip. Using this form and expressing   rei obtain the approximate shape of the
plastic zone. What is this shape?
6. Explain how either G or J can be determined using multiple specimens with different
crack lengths from their load vs displacement curves. Under what conditions will J and G be
equal? Under this (these) condition(s) what other fracture mechanics parameter can be related
with G and J?
.
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