FRACTURE

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FRACTURE

• Brittle Fracture
• Ductile to Brittle transition

Fracture Mechanics T.L. Anderson CRC Press,
Boca Raton, USA (1995)
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Continuity of the structure
Welding instead of riveting
Residual stress
BreakingofLiberty Ships
Microcracks
Cold waters
High sulphur in steel
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Ductile
Fracture
Brittle
Temperature
Factors affecting fracture
Strain rate
State of stress
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Behaviour described Terms Used Terms Used
Crystallographic mode Shear Cleavage
Appearance of Fracture surface Fibrous Granular / bright
Strain to fracture Ductile Brittle
Path Transgranular Intergranular
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Tension
Torsion
Fatigue
Conditions of fracture
Creep
Low temperature Brittle fracture
Temper embrittlement
Hydrogen embrittlement
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Types of failure
Low Temperature
Promoted by
High Strain rate
Triaxial state of State of stress

• Brittle fracture
• Little or no deformation
• Observed in single crystals and polycrystals
• Have been observed in BCC and HCP metals but not
  in FCC metals

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Slip plane

• Shear fracture of ductile single crystals
• Not observed in polycrystals

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• Completely ductile fracture of polycrystals ?
  rupture
• Very ductile metals like gold and lead behave
  like this

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• Ductile fracture of usual polycrystals
• Cup and cone fracture
• Necking leads to triaxial state of stress
• Cracks nucleate at brittle particles (void
  formation at the matrix-particle interface)

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Theoretical shear strength and cracks

• The theoretical shear strength (to break bonds
  and cause fracture) of perfect crystals (E /
  6)
• Strength of real materials (E / 100 to E
  /1000)
• Tiny cracks are responsible for this
• Cracks play the same role in fracture (of
  weakening) as dislocations play for deformation

Cohesive force
Applied Force (F) ?
r ?
a0
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Characterization of Cracks

2a
a

• Surface or interior
• Crack length
• Crack orientation with respect to geometry and
  loading
• Crack tip radius

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Crack growth and failure

• Brittle fracture

Griffith

• Global
• Thermodynamic

Energy based
Crack growth criteria

• Local
• Kinetic

Stress based
Inglis
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It should be energetically favorable
For growth of crack
Sufficient stress concentration should exist at
crack tip to break bonds
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• Brittle fracture ? ? cracks are sharp no
  crack tip blunting ? No energy spent in plastic
  deformation at the crack tip

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Griffiths criterion for brittle crack propagation

• When crack grows

?U ?
c ?
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Increasing stress
?U ?
c ?
Griffith
By some abracadabra
At constant c ( c ? crack length)when ?
exceeds ?f then specimen fails
At constant stresswhen c gt c by instantaneous
nucleation then specimen fails
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To derive c we differentiated w.r.tc keeping ?
constant
c ?
Fracture
stable
?0
?0
? ?

• If a crack of length c nucleates
  instantaneously then it can grow with
  decreasing energy ? sees a energy downhill
• On increasing stress the critical crack size
  decreases

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Stress criterion for crack propagation

• Cracks have a sharp tip and lead to stress
  concentration

?0

• ?0 ? applied stress
• ?max ? stress at crack tip
• ? ? crack tip radius

For a circular hole
? c
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Work done by crack tip stresses to create a
crack (/grow an existing crack) Energy of
surfaces formed
After lot of approximations
Inglis

• a0 ? Interatomic spacing

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Griffith versus Inglis
Inglis
Griffith
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Rajesh Prasads Diagrams
Validity domains for brittle fracture criteria
Blunt cracks
Validityregion for StresscriterionInglis
? c
Validityregion for EnergycriterionGriffith
c ?
Sharp cracks
? gt c
a0
3a0
? ?
Approximate border for changeover of criterion
Sharpest possible crack
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Safety regions applying Griffiths criterion alone
c ?
Unsafe
c
Safe
? ?
a0
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Safety regions applying Ingliss criterion alone
c ?
Safe
Unsafe
? ?
a0
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Griffith unsafeInglis unsafe? unsafe
Griffith unsafeInglis safe? safe
c ?
c
Griffith safeInglis unsafe? unsafe
Griffith safeInglis unsafe? safe
Griffith safeInglis safe? safe
? ?
a0
3a0
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Ductile brittle transition

• Deformation should be continuous across grain
  boundary in polycrystals for their ductile
  behaviour ? 5 independent slip systems
  required (absent in HCP and ionic materials)
• FCC crystals remain ductile upto 0 K
• Common BCC metals become brittle at low
  temperatures or at v.high strain rates

• Ductile ? ?y lt ?f ? yields before fracture
• Brittle ? ?y gt ?f ? fractures before
  yielding

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Griffith
?y
Inglis
?f
?f , ?y ?
Ductile
Brittle
T ?
DBTT
Ductile ? yields before fracture
Brittle ? fractures before yield
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?f
?f , ?y ?
?y (BCC)
?y (FCC)
T ?
DBTT
No DBTT
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Griffith versus Hall-Petch
Hall-Petch
Griffith
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Grain size dependence of DBTT
gt
T1
T2
T2
T1
?f
T1
?y
T2
?f , ?y ?
Finer size
Large size
d-½ ?
DBT
Finer grain size has higher DBTT ? better
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Grain size dependence of DBTT- simplified version
- ?f ?? f(T)
gt
T1
T2
T1
?f
T1
?y
T2
?f , ?y ?
Finer size
d-½ ?
DBT
Finer grain size has lower DBTT ? better
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Protection against brittle fracture

• ?? ? ?f ? ? done by chemical adsorbtion of
  molecules on the crack surfaces
• Removal of surface cracks ? etching of
  glass (followed by resin cover)
• Introducing compressive stresses on the
  surface ? Surface of molten glass solidified by
  cold air followed by solidification of the
  bulk (tempered glass) ? fracture strength can
  be increased 2-3 times ? Ion exchange method ?
  smaller cations like Na in sodium silicate
  glass are replaced by larger cations like K on
  the surface of glass ? higher compressive
  stresses than tempering ? Shot peening ?
  Carburizing and Nitriding ? Pre-stressed concrete

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• Cracks developed during grinding of ceramics
  extend upto one grain ? use fine grained
  ceramics (grain size 0.1 ??m)
• Avoid brittle continuous phase along the grain
  boundaries ? path for intergranular fracture
  (e.g. iron sulphide film along grain boundaries
  in steels ? Mn added to steel to form spherical
  manganese sulphide)

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Ductile fracture

• Ductile fracture ? ? Crack tip blunting by
  plastic deformation at tip ? Energy spent in
  plastic deformation at the crack tip

?y
Schematic
? ?
r ?
Blunted crack
Sharp crack
r ? distance from the crack tip
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Orowans modification to the Griffiths equation
to include plastic energy
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