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FRACTURE. Brittle Fracture Ductile to Brittle transition. Fracture Mechanics T.L. Anderson CRC Press, Boca Raton, USA (1995). Continuity of the structure. Welding instead of riveting. Residual stress. Breaking of Liberty Ships. Microcracks. Cold waters. High sulphur in steel.

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slide1

FRACTURE

  • Brittle Fracture
  • Ductile to Brittle transition

Fracture Mechanics

T.L. Anderson

CRC Press, Boca Raton, USA (1995)

slide2

Continuity of the structure

Welding instead of riveting

Residual stress

BreakingofLiberty Ships

Microcracks

Cold waters

High sulphur in steel

slide3

Ductile

Fracture

Brittle

Temperature

Factors affecting fracture

Strain rate

State of stress

slide5

Tension

Torsion

Fatigue

Conditions of fracture

Creep

Low temperature Brittle fracture

Temper embrittlement

Hydrogen embrittlement

slide6

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
slide7

Slip plane

  • Shear fracture of ductile single crystals
  • Not observed in polycrystals
slide8

Completely ductile fracture of polycrystals → rupture

  • Very ductile metals like gold and lead behave like this
slide9

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)
slide10

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

slide11

Characterization of Cracks

=

2a

a

  • Surface or interior
  • Crack length
  • Crack orientation with respect to geometry and loading
  • Crack tip radius
slide12

Crack growth and failure

  • Brittle fracture

Griffith

  • Global
  • ~Thermodynamic

Energy based

Crack growth criteria

  • Local
  • ~Kinetic

Stress based

Inglis

slide13

It should be energetically favorable

For growth of crack

Sufficient stress concentration should exist at crack tip to break bonds

slide14

Brittle fracture → ► cracks are sharp & no crack tip blunting ► No energy spent in plastic deformation at the crack tip

slide16

Increasing stress

U →

c →

Griffith

By some abracadabra

At constant c (= c* → crack length)when  exceeds f then specimen fails

At constant stresswhen c > c*by instantaneous nucleation then specimen fails

slide17

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
slide18

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

slide19

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
slide21

Rajesh Prasad’s Diagrams

Validity domains for brittle fracture criteria

Blunt cracks

Validityregion for

StresscriterionInglis

 = c

Validityregion for

EnergycriterionGriffith

c →

Sharp cracks

 > c

a0

3a0

→

Approximate border for changeover of criterion

Sharpest possible crack

slide24

Griffith unsafeInglis unsafe unsafe

Griffith unsafeInglis safe safe

c →

c*

Griffith safeInglis unsafe unsafe

Griffith safeInglis unsafe safe

Griffith safeInglis safe safe

→

a0

3a0

slide25

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 < f yields before fracture
  • Brittle  y > f fractures before yielding
slide26

Griffith

y

Inglis

f

f , y→

Ductile

Brittle

T→

DBTT

Ductile  yields before fracture

Brittle  fractures before yield

slide27

f

f , y→

y(BCC)

y(FCC)

T→

DBTT

No DBTT

slide28

Griffith versus Hall-Petch

Hall-Petch

Griffith

slide29

Grain size dependence of DBTT

>

T2

T1

T2

T1

f

T1

y

T2

f , y→

Finer size

Large size

d-½→

DBT

Finer grain size has higher DBTT  better

slide30

Grain size dependence of DBTT- simplified version - f  f(T)

>

T2

T1

T1

f

T1

y

T2

f , y→

Finer size

d-½→

DBT

Finer grain size has lower DBTT  better

slide31

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
slide32

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)
slide33

y

→

r→

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