FRACTURE

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

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

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

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

6. 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

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

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 Cohesive force Applied Force (F) → r → a0

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

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

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

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 U → c →

16. 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

17. 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

18. 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

19. 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

20. Griffith versus Inglis Inglis Griffith

21. 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

22. Safety regions applying Griffith’s criterion alone c → Unsafe c* Safe → a0

23. Safety regions applying Inglis’s criterion alone c → Safe Unsafe → a0

24. Griffith unsafeInglis unsafe unsafe Griffith unsafeInglis safe safe c → c* Griffith safeInglis unsafe unsafe Griffith safeInglis unsafe safe Griffith safeInglis safe safe → a0 3a0

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

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

28. Griffith versus Hall-Petch Hall-Petch Griffith

29. 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

30. 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

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. 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

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