Griffith proposed that brittle materials contain fine cracks that concentrate stress below the theoretical strength, causing fracture. When a crack propagates, the new surface area requires energy from the released elastic strain energy of the material. Griffith established that a crack will propagate when the decrease in elastic strain energy is equal to or greater than the energy required to create the new surface. The stress intensity factor describes the stress near a crack tip and is used to predict crack propagation. Fracture toughness is the material property describing a material's resistance to crack propagation.

2. Griffith’s theory of brittle fracture
• Griffith proposed ideas that did have a great influence on the thinking
about the fracture of metals.
• He proposed that a brittle material contains a population of fine cracks
which produces a stress concentration of sufficient magnitude so that the
theoretical cohesive strength is reached in localized regions at a nominal
stress which is below the theoretical value.
• When one crack starts spreads into a brittle fracture , it produces an
increase in the surface area of the sides of the crack.
• This requires energy to overcome the cohesive force of the atoms , or
when expressed in another way , it requires an increase in the surface
energy.
• The source of the increased surface energy is the elastic strain energy
which is released as the crack spreads.

3. • Griffith established the following criterion
for the propagation of a crack.
• “A crack will propagate when the decrease in elastic
strain energy is at least equal to the energy required to
create the new surface.”
• This criterion can be used to determine the
magnitude of the tensile stress which will
just cause a crack of a certain size to
propagate as a brittle fracture.
• The elastic strain energy required per unite
of the plate thickness is equal to :
• Ue=-((c^2)(^2))/E
• Where =Tensile stress acting normal to the crack
of length 2a
• A negative sign is used because growth of the
crack releases elastic strain energy.

4. Stress Intensity Factor
• The stress intensity factor ,”K” , is
used in fracture mechanics to predict
the stress state ("stress intensity")
near the tip of a crack caused by a
remote load or residual stresses.
• The magnitude of ”K” depends on
sample geometry, the size and
location of the crack, and the
magnitude and the modal
distribution of loads on the material.
• The stress intensity factor for the
crack as show in the following figure
is given as :
K=(a)

5. • For a general case the stress intensity factor is written by the following
formula :
• K=(a)
• Where  is a parameter that depends on the specimen and crack
geometry.
• For example , a plate of width “w” loaded in tension with a centrally
located crack of length “2a” the stress intensity factor is given by the
following formula :
• K=(a){w/(a)*tan((a)/w)}
•

6. Fracture toughness
• Fracture toughness is a property which
describes the ability of a material
containing a crack to resist fracture ,
and is one of the most important
properties of any material for virtually
all design applications.
• The linear-elastic fracture toughness of
a material is determined from
the Stress intensity factor (K) at which
a thin crack in the material begins to
grow.
• The Fracture toughness is entirely a
material property like Ultimate stress of
a material , and hence the fracture
toughness is independent of the crack
length , geometry , or loading system
and depends only on the nature of the
material.
• They are generally represented as “Kic”.

7. Ductile-to-Brittle Transition
• The ductile to brittle transition is a very
important engineering phenomenon which
causes the “ductile to brittle” transition in
fracture behavior , which commonly occurs
with decrease in temperate as in the case of
steel and the other bcc materials as well.
• Consider the equation derived by Cottrell.
(iD+k’)k’=Gs
• i-The resistance of the lattice to dislocation
movement.
• k’-release of dislocations from a pile-up
• s-The effective surface enegry and plastic
deformations
• -Ratio of shear stress to normal stress

8. • By analysis we find that if the LHS of the equation is smaller than the RHS ,
a micro-crack is formed which is non propagative , but cannot grow.
• When the LHS of the equation is bigger than the RHS , a propagating
brittle fracture can be produced at a shear stress equal to the yield stress.
• Thus the before equation governs the ductile to brittle transition.
• The temperature that governs the transition of the fracture from ductile to
brittle is known as the transition temperature as shown in the previous
diagram.
• Key features :
– High frictional resistance would always lead to a brittle fracture .
– When the surface energy is large then the brittle fracture is suppressed.
As seen in the following diagram ,
(a) Brittle fracture
(b) Ductile fracture
(c) Completely Ductile fracture

9. Creep
• “Creep” is referred to the progressive
deformation of the material at a
constant stress.
• A plot of the strain of the material
upon applying a constant load and a
constant temperature , against the
time gives you the “creep curve” as
shown.
• The rate at which the strain changes
with respect to time is called as the
Creep rate.
• During the initial load the creep rate
decreases with time then essentially
reaches a steady state in which the
creep rate changes little with time, and
finally the creep rate increases rapidly
with time until fracture occurs.

10. • There are 3 stages to the creep curve .
• Primary creep :In this stage that the creep
rate gradually decreases with time , and the
above occurs as a consequence of the creep
resistance due to the material deformation
under the load .
• Secondary creep :In this stage , the creep
rate is almost nearly a constant .The above is
possible due to the balancing effects of
strain hardening and recovery acting as
competing processes.
• Tertiary creep :In this stage, occurs in
constant load creep tests carried out at high
temperatures ,at high stresses. This occurs
as a consequence of the “necking” of the
metal before it undergoes the fracture .
• The third stage is often associated with
metallurgical changes recrystallization etc.

11. Deformation mechanism maps
• A deformation mechanism map is a way
of representing the dominant
deformation mechanism in a material
loaded under a given set of conditions
and thereby its likely failure mode.
Deformation mechanism maps consist of
some kind of stress plotted against some
kind of temperature axis.
• The various types of deformations or
creeps are mentioned in the map , each
separated by boundaries or lines.
• An example is as shown in the diagram
on the right hand side .

12. Fatigue
• Fatigue is the progressive and localized structural damage that occurs when
a material is subjected to cyclic loading.
• The nominal maximum stress values are less than the ultimate tensile
values.
• Fatigue results in a brittle-appearing fracture, with no gross deformation at
fracture.
• On macroscopic scales , the fatigue surface is normal to the direction of the
principle tensile stress.
• The fatigue failure is usually recognized with the presence of both smooth
hand rough regions.
• The smooth regions occur as a consequence of the rubbing action as the
crack propagated and the rough regions occur as a consequence of ductile
failure when the cross section is no longer able to carry the load.
• Failure usually occurs at points of stress concentration such as sharp corners
or notches .

13. There are three basic factors for the fatigue failure :-
• Maximum tensile stress of sufficiently high value
• A large variation or fluctuation in the applied
stress and
• A sufficiently large number of cycles of the
applied stress.
• In addition there are host of other variables like
corrosion , temperature , overload , stress
concentration , metallurgical structure.
• STRESS CYCLE :-
• A stress cycle is defined as a change in the force
distribution being applied upon the material at
regular intervals .
• They can be of many types such as reverse (a) ,
repeated (b), irregular or random stress cycles
(c) as well .
• The types are as shown in the figure .

14. High-cycle fatigue
• High cycle fatigue of the material is that failure
that occurs when the number of cycles that the
material undergoes in very high that is in the
order of 10,000 cycles etc.
• The following are the key features necessary for
the high cycle fatigue.
- Stress below yield strength
- Macroscopically brittle
- May be very long life

15. S-N Curves
• In high-cycle
fatigue situations,
materials
performance is
commonly
characterized by an
S-N curve, also
known as a Wöhler
curve . This is a
graph of the
magnitude of a
cyclic stress (S)
against the
logarithmic scale of
cycles to failure (N).

16. Mechanism involved
• There are three steps to the High cycle fatigue .
• Local yielding at a defect or in a stress
concentration (filet root, scratch, bend, hole)
• Dislocation pile up/ saturation
• Crack formation
• Crack propagation

17. Low cycle fatigue
• When fatigue occurs within lesser number of
cycles with stresses greater that yielding
strength is called as the low fatigue failure .
• The features are as follows :-
• Stress exceeds yield strength
• Very few cycles to failure
• Lots of plastic deformation

18. Mechanism involved
• There are 4 steps again
:-
• Sharp Crack – closed
• Stress opens crack
• Tip of crack blunts
• Crack closure/
sharpening
• Repeat

19. Fracture of non metallic materials
• In brittle fracture, no apparent
plastic deformation takes place
before fracture.
• In brittle crystalline materials,
fracture can occur by cleavage as
the result of tensile stress acting
normal to crystallographic
planes with low bonding
(cleavage planes).
• In amorphous solids, by
contrast, the lack of a crystalline
structure results in a special type
of fracture, with cracks
proceeding normal to the
applied tension.

20. Failure Analysis
• Failure analysis is process of obtaining information (as much as possible )
from the “failed” part itself along with the investigation of the conditions
at the time of failure .
• A component is said to have failed is the “unacceptable” deformation or
fracture, which is a relative term. (The term varies depending upon the
product description)
• The failure analysis has its fundamental use in the “Reliability” of the
product being manufactured that determines his popularity and the
extent to which customer satisfaction is achieved by the same .
• There various types of failures that occur , some of them are as follows :
– Fracture
– Fatigue
– Creep

21. Source of failure
• Failure causes are defects in design, process, quality, or part application, which are
the underlying cause of a failure or which initiate a process which leads to failure.
Where failure depends on the user of the product or process, then human error
must be considered.
• They include corrosion, welding of contacts due to an abnormal electrical current,
return spring fatigue failure, unintended command failure, dust accumulation and
blockage of mechanism, etc.
• The real root causes can in theory in most cases be traced back to some kind of
human error, e.g. design failure, operational errors.
• Some types of mechanical failure mechanisms are: excessive deflection, buckling,
ductile fracture, brittle fracture, impact, creep, relaxation, thermal shock, wear,
corrosion, stress corrosion cracking, and various types of fatigue.
• Each produces a different type of fracture surface, and other indicators near the
fracture surface(s).
• The way the product is loaded, and the loading history are also important factors
which determine the outcome. Of critical importance is design geometry because
stress concentrations can magnify the applied load locally to very high levels, and
from which cracks usually grow.

22. Procedure to Failure analysis
• They are of many steps :-
• Initial observation :
• -Make a detailed visual study of the actual component that failed.
• Record all details by photographs
• Interpretation must be made of deformation markings, fracture appearance,
deterioration etc.
• Background data :
• -Collect all data concerned with specifications and drawings, component
design, fabrication, repairs, maintenance and service use.
• Laboratory studies:
• -Verify the chemical composition of the material within specified limits.
• Other tests such as NDT(Non –destructive tests) , heat treatment are carried
out.
• Synthesis of Failure :
• Study all the positives and negatives of the situation and indicate a solution
to the problem of failure.