1. Chapter 4
FRAC
TURE
TOUGHNESS

2. The Fundamentals
Fracture = separation of body into two or more pieces due to
application of static stress
Tensile,
Compressive
Shear or torsional
FAST FRACTURE _
In a balloon energy is stored:
Compressed gas
Elastic energy of Rubber membrane
If more energy released than
is absorbed crack advances
Fails by fast fracture even
though below yield stress
Explosion of boilers,
collapse of bridges

3. Modes of fracture
DUCTILE
BRITTLE
Transgranular
vs. intergranular fracture

4. ‘’stress concentration’’y x
Stress trajectories
Professor Inglis (1913)
The birth of the term
‘’stress concentration’’
Large structures

5.  Griffith and his Energy criterion Crack propagates when favorable,
i.e. system reduces its total energy
Relaxed material behind crack =
Elastic strain energy released
Crack having surface energy (s) a 
a = edge crack or 1/2 central crack

6. What about ductile materials
But for v. ductile materials p >>> s
Define the strain energy release rate Gc
(IRWIN 1950)
Hence
Toughness or Strain energy release rate
(Energy absorbed per unit area of crack)

7. Modes of fracture Fast fracture occurs when K=Kc
Condition for fast fracture (for crack through center of a wide plate)
Comes up a lot
Hence give it symbol, K,
Stress intensity factor
Fast fracture occurs when K=Kc
Modes of fracture

8. Stress intensity factor
AND =

9. What about ductile materials  consider y (i. e
What about ductile materials  consider y (i.e. y means direction not yield)
Plastic zone

13. From: H.L.Ewalds, and R.J.H. Wanhill, Fracture Mechanics, 1991

14. From: H.L.Ewalds, and R.J.H. Wanhill, Fracture Mechanics, 1991

15. To be plane strain
Plane strain fracture toughness

17. Critical flaw size (microns)
Design using fracture mechanics
Example:
Compare the critical flaw sizes in the following metals subjected to
tensile stress 1500MPa and K = 1.12 a.
KIc (MPa.m1/2) Al
Steel
Zirconia(ZrO2)
Toughened Zirconia
Critical flaw size (microns)
7000
280
0.45 16
Where Y = Substitute values
SOLUTION

18. COMPRESSED AIR TANKS FOR A SUPERSONIC WIND TUNNEL
From, M. Ashby, Engineering Materials 1, 2nd edition, 1996
COMPRESSED AIR TANKS FOR A SUPERSONIC WIND TUNNEL
Supersonic wind tunnels in an Aerodynamic Lab, are powdered by a bank of large
cylindrical pressure vessels. How can we design and check pressure
vessels to make sure that they are safe?
Vessels must be safe from
plastic collapse or fail by fast fracture
Also must not fail by fatigue
Hoop stress in the wall of a cylindrical pressure vessel containing gas at pressure p:
Provided that the wall is thin (t<<r)
For general yielding
For Fast Fracture

19. Yield before fracture
Fracture before Yield
Fatigue or stress corrosion
Increases crack size to critical value

20. Easy to detect 10mm critical
crack but not 1mm as for Al

21. If critical flaw size is less than thickness fast fracture NO WARNING
For critical crack size 2a

22. R-curve behavior
From: Brian Lawn, Fracture of brittle solids, 2nd edition, Cambridge university press) p.210, 1993