1. UNIT – 3: Syllabus
Fracture: Type I, Type II and Type III.
Creep: Description of the phenomenon with examples. three stages of creep, creep properties, stress relaxation.
Fatigue: Types of fatigue loading with examples, Mechanism of fatigue,
fatigue properties, fatigue testing and S-N diagram.

2. What is fracture?
Fracture is the separation (fragmentation) of a part into two, or more pieces under a stress
The stress could be tensile, compressive, shear, or torsional
When the materials fail under cyclic load, it is called fatigue fracture, whereas the materials under service at high temperature can fail due to creep fracture

3. Fundamentals of fracture
Any fracture can be considered to be made up of two steps:
Crack initiation and
Crack propagation
Fracture in engineering materials can be broadly divided into
Ductile fracture
Brittle fracture

4. The mode of fracture is highly dependent on the mechanism of crack propagation
A ductile fracture is characterized by substantial plastic deformation prior to and during propagation of the crack
In ductile fracture crack resists any further extension unless there is an increase in stress
That is why the crack is stable in ductile fracture
A brittle fracture in metals is characterized by a fast rate of crack propagation with no macro-deformation and very little micro-deformation

5. Crystallographic mode Appearance of Fracture surface
The process of plastic deformation, such as necking of a section, gives enough warning to allow preventive measure to be taken
But brittle fracture doesn’t give any warning
The tendency to brittle to ductile fracture increases with the fall of temperature
Behaviour described
Terms Used
Crystallographic mode
Shear
Cleavage
Appearance of Fracture surface
Fibrous
Granular / bright
Strain to fracture
Ductile
Brittle
Path
Transgranular
Intergranular

6. Types of fracture
Though we classify fracture as ductile and brittle but based on crystallographic mode we have shear fracture and cleavage fracture (breaking bonds)
A shear fracture is promoted by shear stress
A cleavage fracture is promoted by tensile stress
A shear fracture appears, at low magnification, as grey and fibrous, and is termed as ductile
A cleavage fracture occurs along definite crystallographic planes in the individual grains
Cleavage fracture appears bright or granular as the flat cleavage surfaces reflect the light and named as brittle fracture

7. Fracture-based upon metallographic examination
Transgranular (Intragranular) Fracture
Intergranular fracture

8. If the crack propagates along the grain boundaries, it is named as Intergranular fracture
If the fracture crack pass through the grains, it is named as Transgranualr (Intragranular) fracture
A cleavage fracture is transcrystalline

9. Ductile Fracture
Ductile fracture surfaces will have their own distinctive features on both macroscopic and microscopic levels
It is characterized by extensive deformation in the vicinity of an advancing crack
Highly ductile fracture in which the specimen necks down to a point
Moderately ductile fracture after some necking
Brittle fracture without any
plastic deformation

10. The most common type of tensile fracture profile for ductile metals is that represented in Figure
Initial necking.
Small cavity formation.
Coalescence of cavities to form a crack.
Crack propagation.
Final shear fracture at a 45 angle relative to the tensile direction.

11. The fracture process normally occurs in several stages
When there is reduction in cross-sectional area, necking begins
After necking begins, small cavities, or microvoids, form in the interior of the cross section
Next, as deformation continues, these microvoids enlarge, come together, and coalesce to form an elliptical crack, which has its long axis perpendicular to the stress direction
The crack continues to grow in a direction parallel to its major axis by this microvoid coalescence process
Finally, fracture ensues by the rapid propagation of a crack around the outer perimeter of the neck

12. Cup and cone fracture in aluminum

13. Ductile to Brittle transition Temperature (DTBT)
At low temperatures some metals that would be ductile at room temperature become brittle. This is known as a ductile to brittle transition.
The ductile to brittle transition temperature is strongly dependant on the composition of the metal.
Steel is the most commonly used metal that shows this behaviour.
For some steels the transition temperature can be around 0°C, and in winter the temperature in some parts of the world can be below this.
As a result, some steel structures are very likely to fail in winter

14. DTBT

15. The ductile-brittle transition is exhibited in bcc metals, such as low carbon steel, which become brittle at low temperature or at very high strain rates.
FCC metals, however, generally remain ductile at low temperatures.
Dislocation movement remains high even at low temperatures and the material remains relatively ductile

17. Example of Brittle Failure
Ductile fracture is always a preferred mechanism of failure.
Many cases have occurred through history where catastrophic failures have occurred as a result of brittle fracture.
The most infamous of these is the sinking of the Titanic.
The sinking of the titanic was caused primarily by the brittleness of the steel used to construct the hull of the ship.
In the icy water of the Atlantic, the steel was below the ductile to brittle transition temperature.
In these conditions even a small impact could have caused a large amount of damage.
The impact of an iceberg on the ship's hull resulted in brittle fracture of the bolts that were holding the steel plates together.
Nowadays engineers know more about this phenomenon and the composition of the steels used is much more controlled, resulting in a lower temperature at which the ductile to brittle transition occurs.

19. Theoretical cohesive strength of the metals
The strength of any material is due to cohesive forces that exist between atoms.
The strength required to break these forces is known as the theoretical cohesive strength
High cohesive forces are related to high melting points and small co- efficient of thermal expansion

20. Cohesive force as a function of the separation
The fig. shows the variation of the cohesive force between two atoms as a function of the separation between these atoms.
This curve is the resultant of the attractive and repulsive forces between the atoms.
The interatomic spacing of the atoms is the unstrained condition is indicated by ao.
If the crystal is subjected to a tensile load, separation between atoms will be increased.
The repulsive force decreases more rapidly with increased separation than the attractive force, so that a net force between atoms balances the tensile load.
Cohesive force as a function of the separation
between the atoms

21. Cohesive strength can be represented by a curve
Where 𝝈 max is the theoretical cohesive strength and x = a-ao is the displacement in atomic spacing in a lattice with wavelength 𝝀.
For small displacements, sin x ≈ x, and
Also, if we restrict consideration to a brittle elastic solid, then from Hooke’s law
From the above equations
If we make reasonable assumption that then

22. When fracture occurs in a brittle solid all of the work expended in producing the fracture goes into the creation of two new surfaces
Each of these surfaces has a surface energy of 𝜸s J/m2.
The work done per unit area of surface in creating the fracture is the area under the stress-displacement curve
But this energy is equal to the energy required to create new fracture surfaces
We know that

23. If we substitute in it gives
𝝈max∝ E when 𝜸s and ao are constants

24. What is creep?
Plastic deformation of a material (time dependent) that is subjected to a stress lower than its yield stress when that material is at a high homologous temperature.
Progressive deformation at constant load is also called creep
Creep occurs at temperatures greater than about 0.4Tm
absolute melting temperature = Tm
Creep is normally an undesirable phenomenon and is often the limiting factor in the lifetime of a part.

25. Instantaneous elastic strain = /E 90 % of life time spent in stage-II
Creep curve
To determine the engineering creep curve of a metal, a constant load is applied to a tensile specimen maintained at a constant temp
And the strain (extension) of the specimen is determined as a function of a time
Instantaneous elastic strain = /E
90 % of life time spent in stage-II
In the steady-state range,
the creep rate is constant

26. Curve ‘A’ in fig. illustrates the idealized shape of a creep curve
The slope of this curve ( 𝒅𝜺 𝒅𝒕 or 𝜺 ) is referred as the creep rate
Following an initial rapid elongation of the specimen, 𝜺o, the creep rate decreases with time, then reaches essentially a steady state in which the creep rate changes little with time, and finally the creep rate increases rapidly with time until fracture occurs
Creep curve has 3 stages. These 3 stages are distinguishable based upon the applied stress and temperature

27. In making an engineering creep test, it is usual practice to maintain the load constant throughout the test
Thus, as specimen elongates and decreases in cross-sectional area, the axial stress increases
If the creep rate is decreasing with time, its called as transient creep
Deformation is rapid at first but gradually it comes down with the time in transient creep
It is coming down because of strain hardening effect where deformation goes down
As time progresses, elongation becomes more and more difficult and the curve enters into the second stage

28. Stage-3 Stage-2 Stage-1 Stages of creep Creep rate decreases with time
Effect of work hardening more than recovery
Stage of minimum creep rate → constant
Work hardening and recovery balanced
Absent (delayed very much) in constant stress tests
Necking of specimen starts
Specimen failure processes set in

29. Effect of stress and temp on creep
Both temperature and the level of the applied stress influence the creep characteristics
At a temperature substantially below 0.4Tm, and after the initial deformation, the strain is virtually independent of time.
With either increasing stress or temperature, the following will be noted:
The instantaneous strain at the time of stress application increases
The steady-state creep rate is increased, and
The rupture lifetime is diminished.

30. Effect of stress and temp on creep
When the T<0.4Tm
the instantaneous strain at the time of stress application increases,
(2) the steady-state creep rate is increased, and
(3) the rupture lifetime is diminished.

31. Mechanisms of creep deformation
Dislocation glide
Dislocation creep
Diffusion creep
Grain boundary sliding

32. Dislocation Creep Dislocation Glide
Involves dislocations moving along planes and overcoming barriers at high stress values 𝝈/𝑮>10-2
Involves the movement of dislocations which overcome barriers by thermally assisted mechanism involving the diffusion of vacancies or interstitials. Occurs 10-4<𝝈/G<10-2

33. Diffusion Creep (N-H Creep) Grain boundary sliding
Involves the flow of vacancies and interstitials through a crystal under the influence of applied stress. Occurs for 𝝈/G<10-4
This category includes Nabarro-Herring and Coble creep
Grain boundary sliding
Involves the sliding of grains past each other

34. What is fatigue?
Failures occurring under conditions of dynamic loading are called fatigue failures
This failure is observed only after considerable period of service
Fatigue is catastrophic and insidious (gradually and secretly causing harm), occurring very suddenly and without warning.
A fatigue failure is particularly dangerous because it occurs without any obvious warning
Fatigue failure is brittlelike in nature even in normally ductile metals, in that there is very little, if any, gross plastic deformation associated with failure.
Fatigue results in a brittle-appearing fracture, with no gross deformation at the fracture

35. Fracture
Crack propagation
Crack initiation

36. Fatigue failures occur when metal is subjected to a repetitive or fluctuating stress and it will fail at a stress much lower than its tensile strength

37. Different types of fluctuating stress
Stress cycles
Different types of fluctuating stress
Reversed stress cycle, in which the stress alternates from a maximum tensile stress (+) to a maximum compressive stress (-) of equal magnitude.

38. Repeated stress cycle, in which maximum and minimum stresses are asymmetrical relative to the zeros tress level; mean stress 𝞂m, range of stress 𝞂r , and stress amplitude 𝞂a.

39. Random stress cycle/irregular stress cycle

41. N increases with decreasing stress level
S – N Curve
The basic method of presenting engineering fatigue data is by means of the S-N curve, a plot of stress ‘S’ against number of cycles to failure ‘N’
The stress can be 𝝈a, 𝝈max, 𝝈min
The S-N curve is concerned chiefly with fatigue failure at high numbers of cycles (N>105 cycles) – High Cycle Fatigue (HCF)
N<104 or 105 – Low Cycle Fatigue (LCF)
N increases with decreasing stress level

43. RR Moore Fatigue test

44. RR Moore Fatigue test
Fatigue failures in engineering materials are observed by conducting the fatigue test which involves the plotting of an S-N diagram
One such test is RR Moore fatigue test
Specimens subjected to fatigue test are made to undergo fluctuating stresses
In the above fig, alternate tensile and compressive stresses are imposed on the specimen
A counter coupled to the motor counts the number of cycles to failure

45. Design for fatigue: Fatigue performance can be improved by avoiding the sharp corners
Fatigue cracks are usually initiated at the sharp corners
Good design
Bad design

46. Surface Treatment: During machining operations, small scratches and grooves are invariably introduced into the workpiece surface by cutting tool action.
These surface markings can limit the fatigue life.
It has been observed that improving the surface finish by polishing will enhance fatigue life significantly.
Introduce compressive stresses: Introducing compressive stress within the outer layer of the workpiece can reduce the external tensile stress.
But if the external stresses acting on the specimen is also compressive, this technique will not work
Case hardening is a technique by which both surface hardness and fatigue life are enhanced for steel alloys.
This is accomplished by a Carburizing or Nitriding process whereby a component is exposed to a carbonaceous or nitrogenous atmosphere at an elevated temperature.

47. Example for shot peening
Shot peening is a process where we introduce the compressive stresses on to the surface of a material/metal
This aids metal in getting good fatigue strength
Example for shot peening