1. FRACTURE
Fracture is the separation, or fragmentation, of a solid body into two or more parts under the action of stress.
Process of fracture- with two components-
CRACK INITIATION CRACK PROPAGATION
FRACTURE
DUCTILE BRITTLE

2. Fracture Behavior of Bulk Crystalline Materials
Fundamentals of Fracture
Ductile Fracture
Brittle Fracture
Crack Initiation and Propagation
Fracture Mechanics
Fracture Toughness
Design

3. Fundamentals of Fracture
A separation of an object into two or more pieces in response to active stresses far below the melting temperature of the material.
Atoms on the surface of a material give rise to a surface energy
Stems from the open bonds on the outer atoms
Grain boundaries also contain a surface energy due to the large number of open bonds
Two steps in the process of fracture:
Crack initiation
Propagation

4. Fundamentals of Fracture
Simple fracture may occur by one of two methods, ductile or brittle
Dependent upon the plastic deformation of the material
Properties which influence the plastic deformation of a material
Modulus of elasticity
Crystal structure

5. Fundamentals of Fracture
(a) Highly ductile fracture
(b) Moderately ductile fracture with necking
Called a cup-and -cone fracture
Most common form of ductile fracture
(c) Brittle fracture
No plastic deformation occurring

6. Fundamentals of Fracture
(a) Highly ductile fracture
(b) Moderately ductile fracture with necking
Called a cup-and -cone fracture
Most common form of ductile fracture
(c) Brittle fracture
No plastic deformation occurring

7. Ductile Fracture
Involves a substantial amount of plastic deformation and energy absorption before failure.
Crack propagation occurs very slowly as the length the crack grows.
Often termed a stable crack, in that it will not grow further unless additional stress is applied
The fracture process usually consists of several stages

8. Ductile Fracture
(a) Initial necking
(b) Cavity formation
(c) Cavities form a crack
(d) Crack propagation
(e) Final shear
occurs at an angle of 45°, where shear stress is at a maximum

9. Brittle Fracture
Exhibits little or no plastic deformation and low energy absorption before failure.
Crack propagation spontaneous and rapid
Occurs perpendicular to the direction of the applied stress, forming an almost flat fracture surface
Deemed unstable as it will continue to grow without the aid of additional stresses
Crack propagation across grain boundaries is known as transgranular, while propagation along grain boundaries is termed intergranular

10. Dimple size depends largely on the number of inclusion sites.
Ductile fracture
A pure and inclusion free metal can elongate under tension to give approx. 100% RA and a point fracture.
The central fracture surface consists of numerous cup-like depressions generally called dimples.
Dimple size depends largely on the number of inclusion sites.
(a) Stages in ductile fracture from inclusions
(b) Fracture toughness v/s thickness

11. Cleavage patterns in HS steel fracture (x12000)
Dimples in a ductile fracture of mild steel (x5000)
Intergranular fracture in low alloy steel (x1500)
Fatigue striations in Nimonic 80A (x7000)(A.Strang)

12. (a) Yield and cohesive stress curves
(b) Slow notch bend test
(c) Effect of temperature on the Izod value of mild steel

13. Cohesive stress-strain curves, B, N, and F.
If the two curves intersect at Y, brittle fracture occurs preceded by plastic deformation, which decreases as the cohesive strength curve becomes lower with respect to the yield stress-strain curve.
Orowan has shown that if the yield stress is denoted by Y, the strength for brittle fracture by B (both Y and B depend on the plastic strain), and the initial value of Y (for strain = 0) by Y0
The following are the relationships:
The material is brittle if B < Y0;
The material is ductile but notch-brittle if Y0 < B < 3Y0
The material is not notch-brittle if 3Y < B.

14. Brittle fracture
Brittle fracture is characterised by the very small amount of work absorbed and by a crystalline appearance of the surfaces of fracture, often with a chevron pattern pointing to the origin of fracture, due to the formation of discontinuous cleavage cracks which join up

15. It can occur at a low stress of MPa with great suddenness; the velocity of crack propagation is probably not far from that of sound in the material in this type of fracture plastic deformation is very small, and the crack need not open up considerably in order to propagate, as is necessary with a ductile failure.

16. The work required to propagate a crack is given by
Griffith`s formula:
σ = tensile stress required to propagate
a crack of length c γ = surface energy of fracture faces E = Young`s modulus
Orowan modified the Griffith theory to include
a plastic strain energy factor, p

17. Initiation and propagation portions of fatigue life

18. Location of local stresses near a crack tip in cylindrical coordinates

19. Mode 1:
Opening or tensile mode (the crack faces are pulled apart)
Mode 2:
Sliding or in-plane shear (the crack surfaces slide over each other)
Mode 3:
Tearing or anti-plane shear (the crack surfaces move parallel to the leading edge of the crack and relative to each other)

20. Most alloys contain second phases which lose cohesion with the matrix or fracture and the voids so formed grow as dislocations flow into them.
Coalescence of the voids forms a continuous fracture surface followed by failure of the remaining annulus of material usually on plane at 45° to the tension axis.
The central fracture surface consists of numerous cup-like depressions generally called dimples.
The shape of the dimples is strongly influenced by the direction of major stresses-circular in pure tension and parabolic under shear

21. Behaviour described Terms used Crystallographic mode
Appearance of Fracture
Strain to Fracture
Shear
Fibrous
Ductile
Cleavage
Granular
Brittle
Ref: M.Gensamer

22. Stress intensity factor for
(a) Center-cracked plate loaded in tension,
(b) Edge-cracked plate loaded in tension,
(c) Double-edge-cracked plate loaded in tension
(d) Cracked beam in pure bending

23. Plane stress and plane strain conditions

24. Monotonic plastic zone size
Plane stress
plane strain
Monotonic plastic zone size

25. plane stress
plane strain

26. Reversed plastic zone size

27. TYPICAL FATIGUE STRESS CYCLES
(a) REVERSED (b) REPEATED (c ) IRREGULAR OR RANDOM

28. Atomistic Simulation of Brittle Fracture
Image of simulated brittle fracture
Mode I fracture

29. Crack Initiation and Propagation
Cracks usually initiate at some point of stress concentration
Common areas include scratches, fillets, threads, and dents
Propagation occurs in two stages:
Stage I: propagates very slowly along crystallographic planes of high shear stress and may constitute either a large or small fraction of the fatigue life of a specimen
Stage II: the crack growth rate increases and changes direction, moving perpendicular to the applied stress

30. Crack Initiation and Propagation

31. Crack Initiation and Propagation
Double-ended crack simulations

32. Fracture Mechanics
Uses fracture analysis to determine the critical stress at which a crack will propagate and eventually fail
The stress at which fracture occurs in a material is termed fracture strength
For a brittle elastic solid this strength is estimated to be around E/10, E being the modulus of elasticity
This strength is a function of the cohesive forces between the atoms
Experimental values lie between 10 and 1000 times below this value
These values are a due to very small flaws occurring throughout the material referred to as stress raisers

33. Fracture Mechanics
If we assume that the crack is elliptical in shape and it’s longer axis perpendicular to the applied stress, the maximum stress at the crack tip is:
Fracture will occur when the stress level exceeds this maximum value .

34. The ratio σm/ σ0 is known as the stress concentration factor, Kt :
Fracture Mechanics
The ratio σm/ σ0 is known as the stress concentration factor, Kt :
It is the degree to which an external stress is amplified at the tip of a small crack

35. Griffith Theory of Brittle Fracture
The critical stress required for crack propagation in a brittle material is given by:
E = modulus of elasticity
gs= specific surface energy
a = half the length of an internal crack
Applies only in cases where there is no plastic deformation present.

36. Fracture Toughness
Stresses near the crack tip of a material can also be characterized by the stress intensity factor, K,
A critical value of K exists, similar to the value sc, known as fracture toughness given by:
Y is a dimensionless parameter that depends on both the specimen and crack geometries.
Carries the unusual units of

37. Yielding near crack tip.
FRACTURE TOUGHNESS
Yielding near crack tip.

38. Plane Strain Fracture Toughness
Kc depends on the thickness of plate in question up to a certain point when it becomes constant
This constant value is known as the plane strain fracture toughness denoted by:
The I subscript corresponds to a mode I crack displacement
KIc values are used most often because they represent the worst case scenario
Brittle materials have low KIc values, giving to catastrophic failure
ductile materials usually have much larger KIc values
KIc depends on temperature, strain rate, and microstructure
Increases as grain size decreases

39. Fracture Toughness in Design
There are three crucial factors which must be considered in designing for fracture:
The fracture toughness (Kc or plane strain KIc)
the imposed stress (s)
and the flaw size (a)
It must be determined first what the limits and constraints on the variables will be
Once two of them are determined, the third will be fixed
For example, if the stress level and plane strain fracture toughness are fixed, then the maximum allowable flaw size must be:

40. Ductile Fracture
Involves a substantial amount of plastic deformation and energy absorption before failure.
Crack propagation occurs very slowly as the length the crack grows.
Often termed a stable crack, in that it will not grow further unless additional stress is applied
The fracture process usually consists of several stages

41. Fracture Mechanics
If we assume that the crack is elliptical in shape and it’s longer axis perpendicular to the applied stress, the maximum stress at the crack tip is:
Fracture will occur when the stress level exceeds this maximum value .