1. 3 – Fracture of Materials

2. Part of the top of an Aloha Airlines jet peeled of during the flight

3. Liberty Ship failures involved both brittle fractures and fatigue fractures.
Of 2700 ships built, 400 suffered hull and deck fractures. 90 were considered serious and in 20 ships fracture was essentially total with 10 ships breaking in half without warning.

5. Outline Fracture of Materials Types of Fracture Brittle Fracture
Ductile Fracture
Brittle to Ductile Transition
Fracture Mechanics
Stress Concentration
LEFM
K & G Kc
Appendix - Griffith Theory

6. Fracture
Fracture: separation of a body into pieces due to stress, at temperatures below the melting point.
Steps in fracture:
Crack formation
Crack propagation
Depending on the ability of material to undergo plastic
deformation before the fracture two fracture modes can be defined - ductile or brittle

7. Ductile fracture - most metals (not too cold):
Extensive plastic deformation ahead of crack
Crack is “stable”: resists further extension unless applied stress is increased
Brittle fracture - ceramics, ice, cold metals:
Relatively little plastic deformation
Crack is “unstable”: propagates rapidly without increase in applied stress
Ductile fracture is preferred in most applications

8. Brittle vs. Ductile Fracture
Ductile materials - extensive plastic deformation and
energy absorption (“toughness”) before fracture
Brittle materials - little plastic deformation and low
energy absorption before fracture

9. Brittle vs. Ductile Fracture
Brittle fracture; (b) Shearing fracture in single crystal
(c) Completely ductile (d) Ductile fracture

10. Ductile Fracture Necking, (b) Cavity Formation,
(c) Cavity coalescence to form a crack,

11. Ductile Fracture
(d) Crack propagation, (e) Fracture

12. (Cap-and-cone fracture in Al)
Ductile Fracture
(Cap-and-cone fracture in Al)

13. Ductile Fracture
Scanning Electron Microscopy: Fractographic studies at high resolution. Spherical “dimples” correspond to micro-cavities that initiate crack formation.

14. Brittle Fracture No appreciable plastic deformation
Crack propagation is very fast
Crack propagates nearly perpendicular to the direction of the applied stress
Crack often propagates by cleavage – breaking of atomic bonds along specific crystallographic planes (cleavage planes)

15. Brittle Fracture
Brittle fracture in a mild steel

16. Brittle Fracture
Transgranular fracture: Fracture cracks pass through grains. Fracture surface have faceted texture because of different orientation of cleavage planes in grains.
Intergranular fracture: Fracture crack propagation is along grain boundaries (grain boundaries are weakened or embrittled by impurities segregation etc.)

17. Brittle Fracture

18. Ductile-to-Brittle Transition
Ductile-to-Brittle Transition: As temperature decreases a ductile material can become brittle
Alloying usually increases the ductile-to-brittle transition temperature.
FCC metals remain ductile down to very low temperatures.
For ceramics, this type of transition occurs at much higher temperatures than for metals.

19. Ductile-to-Brittle Transition
DBTT: Ductile-Brittle Transition Temperature

20. Fracture Mechanics & Fracture Toughness
Stress Concentration
Energy Release Rate
Crack Tip Plasticity
Fracture Toughness

21. Stress Concentration

22. Stress Concentration m  2 (a/)1/2
For a long crack oriented perpendicular to the applied stress the maximum stress near the crack is:
m  2 (a/)1/2
(1)
where σ is the applied external stress, a is the half-length of the crack, and ρ the radius of curvature of the crack tip. (note that a is half-length of the internal flaw, but the full length for a surface flaw).

23. Stress Concentration Factor
The ratio of the maximum stress and the nominal applied tensile stress is denoted as the stress concentration factor, Kt, where Kt can be calculated by Equation 1. The stress concentration factor is a simple measure of the degree to which an external stress is amplified at the tip of a small crack.

24. Stress Concentration
The stress distribution at the crack tip in a thin plate for an elastic solid is given by:
(2)

25. Stress Concentration K: Stress Intensity Factor (3)
Unit of K: psiin, MN/(m3/2), or MPam

26. Stress Concentration
Substitute K into Equation (3):
(4)

27. Stress Concentration Opening In-plane Shear Out-of-Plane Shear
Fracture Modes

28. Energy Release Rate G = - dU/dA
Energy Release Rate: In 1956, Irwin defined an energy release rate, G, which is a measure of the energy available for an increment of crack extension:
G = - dU/dA
Since G is obtained from the derivative of a potential, it is also called the crack extension force or crack driving force

29. Energy Release Rate Griffith Approach: G = 2a/E
Where  is the nominal stress, a is half-length of crack, E is Young’s Modulus

30. Relationship between K and G
Mode I
Plain Stress:
G = KI2/E
Plain Strain:
G = KI2(1-2)/E

31. Plain Stress vs. Plain Strain

32. Crack Tip Plasticity
Irwin Approach

33. Crack Tip Plasticity
Irwin Approach

34. Crack Tip Plastic Zone Shape

35. Fracture Toughness
Kc: If we assume a material fails locally at some combination of stresses and strains, then crack extension must occur at a critical K value. This Kc value, which is a measure of fracture toughness, is a material constant that is independent of the size and geometry of the cracked body.

36. Fracture Toughness Measurement
MEASURE STRENGTH WITH A CRACK OF KNOWN LENGTH
SHARP CRACK
LINEAR ELASTIC?
SMALL PROCESS ZONE RULES
ASTM STANDARDS: E-399

37. SUMMARY Types of Fracture: Brittle Fracture Ductile Fracture
Ductile Fracture: Crack initiation, crack growth, fracture, fractography
Brittle Fracture: Intergranular & Transgranular (Cleavage)
Brittle to Ductile Transition: DBTT

38. SUMMARY – Cont’d Stress Concentration
Stress distribution in front of the crack tip Stress concentration factor
Linear Elastic Fracture Mechanics
K: Stress Intensity Factor
G: Energy Release Rate
Relationship between K & G
Crack tip plasticity
Fracture Toughness

39. Appendix - Griffith Theory for Brittle Fracture
For defect-free material:
sth ~ E/10 is orders of magnitude higher than usually observed
Where E – Young’s modulus
g – specific surface energy
a0 – lattice parameter
sth – theoretical strength of the material

40. Energy criterion for brittle fracture (Griffith Theory)
Energy criterion: when rate of change of the release of elastic energy with respect to crack size  rate at which energy is consumed to create new surfaces, fracture occurs
Onset:
Where s – Griffith’s stress (the critical stress)
gs – surface energy/per unit area

41. Griffith Equation
Griffith equation is only for glasses & ceramics – brittle fracture, no plastic deformation occurs prior to fracture
Metals and polymers  plastic deformation occurs before fracture  modified Griffith equation (Orowan equation)