fatigue and creep

1. BITS Pilani
Pilani Campus
MATERIALS SCIENCE AND ENGINEERING

2. Creep
Creep may be defined as a time-dependent
deformation at elevated temperature and
constant stress
• Occurs when material supports a load for very long
period of time, and continues to deform until a
sudden fracture or usefulness is impaired
sudden fracture or usefulness is impaired
• Is only considered when metals and ceramics are
used for structural members or mechanical parts
are subjected to high temperatures
• Other materials (such as polymers & composites)
are also affected by creep without influence of
temperature

3. *3.7 FAILURE OF MATERIALS DUE TO CREEP & FATIGUE
Creep
• Stress and/or temperature significantly affects the
rate of creep of a material
• Creep strength represents the highest initial stress
the material can withstand during given time
Mechanical Performance of Materials
the material can withstand during given time
without causing specified creep strain
Simple method to determine creep strength
• Test several specimens simultaneously
– At constant temperature, but
– Each specimen subjected to different axial stress

4. *3.7 FAILURE OF MATERIALS DUE TO CREEP & FATIGUE
Creep
Simple method to determine creep strength
• Measure time taken to produce allowable strain or
rupture strain for each specimen
• Plot stress vs. strain
Mechanical Performance of Materials
• Plot stress vs. strain
• Creep strength inversely proportional to
temperature and applied stresses

5. *3.7 FAILURE OF MATERIALS DUE TO CREEP & FATIGUE
Creep
Schematic creep curve for a constant load; a plot of the change
in length verses time. The weight or load on the specimen is
held constant for the duration of the test.

6. *3.7 FAILURE OF MATERIALS DUE TO CREEP & FATIGUE
Creep
Creep deformation occurs by grain-boundary
sliding. That is, adjacent grains or crystals move
as a unit relative to each other

7. *3.7 FAILURE OF MATERIALS DUE TO CREEP & FATIGUE
Creep
There are four portions of the curve
that are of interest:
•An initial steep rate that is at least partly of
elastic origin, from point "0" to point "A" in
Figure.
• This is followed by a region in which the
elongation or deformation rate decreases with
time, the so-called transient or primary creep,
from region "A" to "B". The portion from point
from region "A" to "B". The portion from point
"0" to point "B" occurs fairly quickly.
• The next portion of the creep curve is the area of engineering interest,
where the creep rate is almost constant. The portion from "B" to "C" is
nearly linear and predictable.
• The fourth portion of the creep curve, beyond the constant-creep-rate or
linear region, shows a rapidly increasing creep rate which culminates in
failure. Even under constant-load test conditions, the effective stress may
actually increase due to the damage that forms within the microstructure.

8. Fatigue
Fatigue is the lowering of strength or the failure of a
material due to repetitive stress, which may be above
or below the yield strength.
Mechanical Performance of Materials
Many engineering materials such as those used in
cars, planes, turbine engines, machinery, shoes, etc
are subjected constantly to repetitive stresses in the
form of tension, compression, bending, vibration,
thermal expansion and contraction or other stresses.

9. FATIGUE
Fracture surface which usually exhibits:
Smooth areas -correspond to the gradual crack
growth stage, and
Rough areas-correspond to the catastrophic
fracture stage.
The smooth parts of the fracture surface usually
The smooth parts of the fracture surface usually
exhibit beach marks which occurs as a result of
changes in the magnitude of the fluctuating
fatigue load.
9

10. Fatigue Failures Are Often Easy To Identify
10

11. *3.7 FAILURE OF MATERIALS DUE TO CREEP & FATIGUE
Method to Determine Fatigue
Fatigue behavior of materials is usually described by
means of the S-N diagram which gives the number
of cycles to failure, N as a function of the max
applied alternating stress.
• Subject series of
specimens to specified
Fatigue
specimens to specified
stress and cycle to failure
• Plot stress (S) against
number of cycles-to-
failure N
(S-N diagram) on
logarithmic scale

12. DESIGNING AGAINST FATIGUE
S-N curve is a graphical representation of the maximum
applied stress versus the number of stress cycles N before
the fatigue failure on a semi-log graph. For ferrous metals
like steel the curve becomes asymptotic at 106 cycles.
The completely reversed stress which a material can
withstand 106 cycles without failure is called ENDURANCE
12
withstand 106 cycles without failure is called ENDURANCE
LIMIT of the material.
For non ferrous materials, the curve slopes gradually even
after 106 cycles. These materials do not have a limiting
value of endurance in true sense. In these cases endurance
limit is expressed as a function of number of cycles.

13. Fatigue
Fatigue Limit:
• For some materials such as BCC steels and Ti alloys, the S-N
curves become horizontal when the stress amplitude is
decreased to a certain level.
• This stress level is called the Fatigue Limit, or Endurance
Limit, which is typically ~35-60% of the tensile strength
for steels.
for steels.
• In some materials, including steels, the endurance limit is
approximately half (50%) the tensile strength, given by:
5
.
0
strength
tensile
limit
endurance
ratio
Endurance ≈
=

14. The S-N curves for a tool steel and an aluminum alloy showing the number of cycles to
failure

15. DESIGNING AGAINST FATIGUE
In the majority cases, the reported fatigue strength or
endurance limits of the materials are based on the test of
carefully prepared small samples under laboratory
condition.
Such values cannot be directly used for design purposes
because the behavior of a component or structure under
fatigue loading does depend not only on the fatigue or
endurance limit of the material used in making it, but also
an several other factors including :
endurance limit of the material used in making it, but also
an several other factors including :
Size and shape of the component or structure
Type of loading and state of stress
Stress concentration
Surface finish
Operating temperature
Service environment
Method of fabrication 15

16. Endurance-limit modifying factors
se = kakbkckdkekfkgkhse’
Where se = endurance limit of component
se’ = endurance limit experimental
ka = surface finish factor (machined parts have different finish)
kb = size factor (larger parts greater probability of finding
defects)
DESIGNING AGAINST FATIGUE
defects)
kc = reliability / statistical scatter factor (accounts for random
variation)
kd = operating T factor (accounts for diff. in working T & room T)
ke = loading factor (differences in loading types)
kf = stress concentration factor
kg = service environment factor (action of hostile environment)
kh = manufacturing processes factor (influence of fabrication
parameters)
16

17. DESIGNING AGAINST FATIGUE
ka = Surface finish factor
17

18. DESIGNING AGAINST FATIGUE
kb = Size factor
Large engineering parts have lower fatigue
strength than smaller test specimen
Greater is the probability of finding metallurgical
flaws that can cause crack initiation
Following values can be taken as rough guidelines :
kb = 1.0 for component diameters less than 10
mm
kb = 0.9 for diameters in the range 10 to 50 mm
kb = 1 – [( D – 0.03)/15], where D is diameter
expressed in inches, for sizes 50 to 225 mm.
18

19. DESIGNING AGAINST FATIGUE
kc = Reliability factor
Accounts for random variation in fatigue
strength.
The following value can be taken as
guidelines
guidelines
kc = 0.900 for 90% reliability
kc = 0.814 for 99 % reliability
kc = 0.752 for 99.9 % reliability
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20. DESIGNING AGAINST FATIGUE
kd = Operating temperature factor
Accounts for the difference between the test
temperature and operating temperature of the
component
For carbon and alloy steels, fatigue strength not
affected by operating temperature – 45 to
affected by operating temperature – 45 to
4500C kd = 1
At higher operating temperature
kd = 1 – 5800( T – 450 ) for T between 450 and
550oC, or
kd = 1 – 3200( T – 840 ) for T between 840 and
1020oF 20

21. DESIGNING AGAINST FATIGUE
ke = Loading factor
Different type of loading, give
different stress distribution
ke = 1 for application
ke = 1 for application
involving bending
ke = 0.9 for axial loading
ke = 0.58 for torsional loading
21

22. DESIGNING AGAINST FATIGUE
kf = Fatigue stress concentration factor
Accounts for the stress concentration
which may arise when change in cross-
section
kf = endurance limit of notch-free part
kf = endurance limit of notch-free part
endurance limit of notched part
Low strength, ductile steels are less
sensitive to notch than high-strength
steels
22

23. DESIGNING AGAINST FATIGUE
kg = Service environment factor
Accounts for the reduced fatigue strength
due to the action of a hostile environment.
23

24. DESIGNING AGAINST FATIGUE
kh = Manufacturing process factor
Accounts for the influence of fabrication
parameter
Heat treatment, cold working, residual
stresses and protective coating on the
stresses and protective coating on the
fatigue material.
It is difficult to quantify, but important to
be included.
24

25. Fatigue Failures
Types of stresses for fatigue tests include,
axial (tension – compression)
flexural (bending)
torsional (twisting)
From these tests the following data are generated.
σ
σ +
By convention, tensile stresses are positive and compression stresses are
negative.
max
min
min
max
r
min
max
a
min
max
m
Ratio,
Stress
Range,
Stress
2
Amplitude,
Stress
2
Stress,
Mean
σ
σ
σ
σ
σ
σ
σ
σ
σ
σ
σ
=
−
=
−
=
+
=
R

26. Fatigue Failures
Examples of stress
cycles where a) shows
the stress in
compression and
tension, b) shows
a
tension, b) shows
there’s greater tensile
stress than
compressive stress
and in c) all of the
stress is tensile.
b
c

27. Fatigue Failures
As the mean stress, σ
σ
σ
σm, increases, the stress amplitude, σ
σ
σ
σa,
must decrease in order for the material to withstand the
applied stress. This condition is summarized by the
Goodman relationship:














−
= m
fs
a 1
Amplitude,
Stress
σ
σ
σ
σ
Where σ
σ
σ
σ fs is the desired fatigue strength for zero mean
stress and σ
σ
σ
σ TS is the tensile strength of the material.







 TS
fs
a
σ

28. Fatigue Failures
Crack Growth Rate
To estimate whether a crack will grow, the stress intensity
factor (∆
∆
∆
∆K), which characterizes the crack geometry and
the stress amplitude can be used.
Below a threshold ∆
∆
∆
∆ K a crack doesn’t grow.
For somewhat higher stress intensities, the cracks grow
slowly.
slowly.
For still higher stress-intensities a crack grows at a rate
given by:
Where C and n are empirical constants that depend
on the material.
When DK is high, the cracks grow in a rapid and
unstable manner until fracture occurs.
( )n
K
C
dN
da
∆
=

29. Fatigue Failures

30. Fatigue Failures
if we integrate between the initial size of a crack and the
crack size required for fracture to occur, we find that the
number of cycles to failure is given by
( )n
K
C
dN
da
∆
=
From the steady state crack growth relationship of
number of cycles to failure is given by
where C and n are empirical constants that depend on the
material.
[ ]
2
/
2
/
)
2
(
2
/
)
2
(
)
2
(
)
(
)
(
2
n
n
n
n
i
n
c
Cf
n
a
a
N
π
σ
∆
−
−
=
−
−