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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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)1

(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