Introduction to fatigue of materials, causes, identification by using S-N curve method.

1. Fatigue of materials

2. What is fatigue?
 It is a type of damage/failure in
materials;
◦ Which is caused by fluctuating or cyclic
stresses,
◦ Under the effect of fluctuating stress a
point comes where the material is
fractured. This level of stress is called
fatigue stress and the failure is called
fatigue failure.
◦ The fatigue stress is much lower than
the yield stress or tensile stress.

3.  Fatigue failure is caused by initiation
and propagation of cracks and fracture
surface is perpendicular to the
direction of an applied tensile stress.
 It is brittle like in nature even in ductile
materials (fracture without prior
indication).
Ductile fracture: the fracture caused after
plastic deformation.
Brittle Fracture: the fracture caused
without any appreciable plastic
deformation.

4. Cyclic stresses
 Three different stress-time modes are
possible.
 The stress can be axial (tension –
compression), bending or torsional in nature.
σm=mean stress
σm =
σmax + σmin
2
𝜎𝑟=range of stress
𝜎𝑟=𝜎 𝑚𝑎𝑥 − 𝜎 𝑚𝑖𝑛
𝜎 𝑎=amplitude of stress
𝜎 𝑎 =
𝜎𝑟
2
=
𝜎 𝑚𝑎𝑥 − 𝜎 𝑚𝑖𝑛
2
Type (a)
Type (b)
Type (c)

5.  Type (a) mode
◦ The amplitude is symmetrical about a
mean zero stress level.
◦ Alternating from a maximum tensile stress
to a minimum compressive stress of equal
magnitude.
◦ It is called a reversed stress cycle.

6. Reversed stress cycle
 Type (a) mode (reversed stress cycle.)
◦ Tensile Stress applied to a sample→ Released
→Compressive Stress Applied →Released. (One cycle
completes).
◦ Example: Bending load applied to a rotating shaft. (Axles of
vehicles)

7. Repeated stress cycle
 Type (b) mode
◦ The maxima and minima are asymmetrical relative to the
zero stress level.
◦ It is termed as repeated stress cycle.
◦ Example is cycling load on a cantilever beam, depending
upon the residual stresses inside the material.

8. SPECTRUM LOADING
 Type (c) mode
◦ The stress level vary randomly in amplitude and frequency.
 Suspension wires in a railroad bridge.
 Wires carry weight of bridge—under static tensile load.
 Additional load when a train is on bridge.

9. The S – N curve
 The specimen is subjected to the cyclic stress at a
large maximum stress amplitude.
 This large maximum stress is usually taken two
third of the static tensile strength.
 Finally the number of cycles to the failure is
counted.
 Then other specimens are taken of the same
material and dimensions. And are subjected to the
same procedure but at progressively decreasing
maximum stress amplitudes.
 Data are plotted as stress S versus the logarithm of
the number of cycles to failure for each specimen.
 The values of S are normally taken as stress
amplitude (𝜎 𝑎)or differently 𝜎 𝑚𝑎𝑥 or 𝜎 𝑚𝑖𝑛 values can
also be used.

10. The S – N curve
The higher the magnitude of stress the smaller the no. of
cycles the material is capable of enduring.

11. Fatigue limit
 For some ferrous and titanium alloys, the S –
N curve becomes horizontal at higher N
values. This is called fatigue limit or
endurance limit.
 This fatigue limit actually represents the
maximum value of cyclic stress below which
fatigue will not occur for an infinite no. of
cycles.
 For many steels the fatigue limit ranges
between 35% and 60% of the tensile strength.

12. Fatigue strength
 Many non ferrous alloys (Al, Cu, Mg) do
not have a fatigue limit.
 Their S – N curve continues downward
trend at increasing no. of cycles.
 Thus fatigue is inevitable for these alloys
regardless of the amplitude of the stress.
 The fatigue response of these materials is
specified by fatigue strength.
 It is defined as the magnitude of the stress
at which failure will occur for some
specified no. of cycles. (e.g., 107
)

13. Fatigue Life
 It is the number of cycles to cause
failure at specified stress level.

14. Fatigue surface