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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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Presentation on theme: "FRACTURE  Brittle Fracture  Ductile to Brittle transition Fracture Mechanics T.L. Anderson CRC Press, Boca Raton, USA (1995)"— Presentation transcript:

1 FRACTURE  Brittle Fracture  Ductile to Brittle transition Fracture Mechanics T.L. Anderson CRC Press, Boca Raton, USA (1995)

2 Breaking of Liberty Ships Cold waters Welding instead of riveting High sulphur in steel Residual stress Continuity of the structure Microcracks

3 Fracture Brittle Ductile Factors affecting fracture Strain rate State of stress Temperature

4 Behaviour describedTerms Used Crystallographic modeShearCleavage Appearance of Fracture surfaceFibrousGranular / bright Strain to fractureDuctileBrittle PathTransgranularIntergranular

5 Conditions of fracture Torsion Fatigue Tension Creep Low temperature Brittle fracture Temper embrittlement Hydrogen embrittlement

6  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 Types of failure Promoted by High Strain rate Triaxial state of State of stress Low Temperature

7  Shear fracture of ductile single crystals  Not observed in polycrystals Slip plane

8  Completely ductile fracture of polycrystals → rupture  Very ductile metals like gold and lead behave like this

9  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)

10 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 Applied Force (F) → r → a0a0 Cohesive force

11 = 2a a Characterization of Cracks  Surface or interior  Crack length  Crack orientation with respect to geometry and loading  Crack tip radius

12 Crack growth and failure  Brittle fracture Crack growth criteria Stress based Energy based  Global  ~Thermodynamic  Local  ~Kinetic Griffith Inglis

13 For growth of crack Sufficient stress concentration should exist at crack tip to break bonds It should be energetically favorable

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

15 Griffith’s criterion for brittle crack propagation  When crack grows c →  U →

16 c →  U → Increasing stress By some abracadabra At constant stress when c > c * by instantaneous nucleation then specimen fails At constant c (= c * → crack length) when  exceeds  f then specimen fails Griffith

17  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  → c → Fracture stable 00 00 To derive c * we differentiated w.r.t c keeping  constant

18 Stress criterion for crack propagation  Cracks have a sharp tip and lead to stress concentration 00   0 → applied stress   max → stress at crack tip   → crack tip radius  = c For a circular hole

19 Work done by crack tip stresses to create a crack (/grow an existing crack) = Energy of surfaces formed After lot of approximations Inglis  a 0 → Interatomic spacing

20 Griffith versus Inglis Inglis Griffith

21 Rajesh Prasad’s Diagrams Validity domains for brittle fracture criteria Sharpest possible crack Approximate border for changeover of criterion  → c → a0a0 3a 0 Validity region for Energy criterion Griffith Validity region for Stress criterion Inglis Sharp cracks Blunt cracks  > c  = c

22  → c → a0a0 c*c* Safety regions applying Griffith’s criterion alone Unsafe Safe

23 Unsafe Safe  → c → a0a0 Safety regions applying Inglis’s criterion alone

24  → c → a0a0 c*c* 3a 0 Griffith safe Inglis unsafe  safe Griffith unsafe Inglis safe  safe Griffith safe Inglis unsafe  unsafe Griffith unsafe Inglis unsafe  unsafe Griffith safe Inglis safe  safe

25 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

26  f,  y → yy T → ff DBTT Ductile Brittle Ductile  yields before fracture Brittle  fractures before yield Inglis Griffith

27  f,  y →  y (BCC) T → ff DBTT  y (FCC) No DBTT

28 Griffith versus Hall-Petch Griffith Hall-Petch

29  f,  y → yy d -½ → DBT T1T1 T2T2 T1T1 T2T2 ff Grain size dependence of DBTT Finer size Large size Finer grain size has higher DBTT  better T1T1 T2T2 >

30  f,  y → yy d -½ → DBT T1T1 T2T2 T1T1 ff Grain size dependence of DBTT- simplified version -  f  f(T) Finer size Finer grain size has lower DBTT  better T1T1 T2T2 >

31 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

32  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)

33  Ductile fracture → ► Crack tip blunting by plastic deformation at tip ► Energy spent in plastic deformation at the crack tip Ductile fracture  → yy r →  → yy r → Sharp crack Blunted crack Schematic r → distance from the crack tip

34 Orowan’s modification to the Griffith’s equation to include “plastic energy”

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