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Chapter 4
FRACTURE
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FAST FRACTURE
If more energy released than is absorbed crack advances
The FundamentalsFracture = separation of body into two or more pieces due to application of static stress
Tensile,CompressiveShear or torsional
Fails by fast fracture even though below yield stress
In a balloon energy is stored:1. Compressed gas
2. Elastic energy of Rubber membrane
Explosion of boilers, collapse of bridges
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Transgranular vs. intergranular fracture
Modes of fracture
DUCTILE
BRITTLE
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y
x
Stress trajectories
Professor Inglis (1913)
The birth of the term ‘’stress concentration’’
Large structures
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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
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What about ductile materials
But for v. ductile materials p >>> s
Define the strain energy release rate Gc
(IRWIN 1950)
HenceToughness or Strain energy release rate(Energy absorbed per unit area of crack)
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cEGa Condition for fast fracture (for crack through center of a wide plate)
Comes up a lotHence give it symbol, K,Stress intensity factor
Fast fracture occurs when K=Kc
Modes of fracture
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Stress intensity factor
AND =
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Plastic zone
What about ductile materials consider y (i.e. y means direction not yield)
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From: H.L.Ewalds, and R.J.H. Wanhill, Fracture Mechanics, 1991
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From: H.L.Ewalds, and R.J.H. Wanhill, Fracture Mechanics, 1991
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To be plane strain Plane strain fracture toughness
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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 250Steel 50 Zirconia(ZrO2) 2 Toughened Zirconia 12
Critical flaw size (microns)70002800.4516
Where Y = 1.12. Substitute values
SOLUTION
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COMPRESSED AIR TANKS FOR A SUPERSONIC WIND TUNNELSupersonic 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?
t
pr
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 y For Fast Fracture cKa
From, M. Ashby, Engineering Materials 1, 2nd edition, 1996
Vessels must be safe from plastic collapse or fail by fast fractureAlso must not fail by fatigue
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(a
Kc
Yield before fracture
Fracture before Yield
Fatigue or stress corrosionIncreases crack size to critical value
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Easy to detect 10mm critical crack but not 1mm as for Al
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For critical crack size 2a
If critical flaw size is less than thickness fast fracture NO WARNING
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R-curve behavior
From: Brian Lawn, Fracture of brittle solids, 2nd edition, Cambridge university press) p.210, 1993