Transcript Slide 1

Chapter 4
FRAC
ME 340: Materials & Design
4.1
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:
1.
Compressed gas
2.
Elastic energy of Rubber membrane
If more energy released than
is absorbed crack advances
Fails by fast fracture even
though below yield stress
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Explosion of boilers,
collapse of bridges
4.2
Modes of fracture
DUCTILE
BRITTLE
Transgranular
vs. intergranular fracture
ME 340: Materials & Design
4.3
Professor Inglis (1913)
The birth of the term
‘’stress concentration’’
Large structures
Stress trajectories
y
x
ME 340: Materials & Design
4.4
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
ME 340: Materials & Design
4.5
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)
ME 340: Materials & Design
4.6
Condition for fast fracture (for crack through center of a wide plate)
Comes up a lot
Hence give it symbol, K,
Stress intensity factor
 a  EGc
Fast fracture occurs when K=Kc
Modes of fracture
ME 340: Materials & Design
4.7
Stress intensity factor
AND
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=
4.8
What about ductile materials  consider y (i.e. y means direction not yield)
Plastic zone
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4.9
ME 340: Materials & Design
4.10
ME 340: Materials & Design
4.11
ME 340: Materials & Design
4.12
From: H.L.Ewalds, and R.J.H. Wanhill, Fracture Mechanics, 1991
ME 340: Materials & Design
4.13
From: H.L.Ewalds, and R.J.H. Wanhill, Fracture Mechanics, 1991
ME 340: Materials & Design
4.14
Plane strain fracture toughness
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To be plane strain
4.15
ME 340: Materials & Design
4.16
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)
Critical flaw size (microns)
Al
250
7000
Steel
50
280
Zirconia(ZrO2)
2
0.45
Toughened Zirconia
12
16
SOLUTION
Where Y = 1.12. Substitute values
ME 340: Materials & Design
4.17
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)
pr

t
For general yielding
For Fast Fracture
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 y
 a  Kc
4.18
Kc
1

( )
 a
Yield before fracture
Fracture before Yield
Fatigue or stress corrosion
Increases crack size to critical value
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4.19
Easy to detect 10mm critical
crack but not 1mm as for Al
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4.20
If critical flaw size is less than thickness fast fracture NO WARNING
For critical crack size 2a
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4.21
R-curve behavior
From: Brian Lawn, Fracture of brittle solids, 2nd edition, Cambridge university press) p.210, 1993
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4.22