Fatigue
Fatigue is failure that occurs in structures that undergo repeated cyclic stress, for
example bridges and connecting rods.
In fatigue it is possible for failure to occur at stresses much lower than the yield
strength.
Fatigue is responsible for about 90% of all metallic component failures, and it is also
possible for polymers and ceramics to fail by fatigue.
It is catastrophic in that it occurs without warning because it is a brittle fracture (with
little or no plastic deformation) that occurs in materials that are normally ductile.
There are three different modes of fatigue loading, shown below:
Reversed stress cycle
Repeated stress cycle
Random stress cycle
There are a number of fatigue parameters used to characterise the fluctuating stress
cycle, shown below:
Mean stress
Stress range
Stress ratio R
A common method of testing fatigue resistance is the Wohler rotating rod test. One
end of the specimen is mounted in a rotating chuck and a load suspended from the
other end. The specimen experiences cyclic forces, from tension to compression in a
sinusoidal cycle, as it rotates.
After a number of cycles, the specimen may fail.
Generally, a number of specimens are tested at different applied stresses and the
number of cycles to failure is recorded.
These results are then plotted on a graph of stress, S, versus the number of cycles to
failure, N. This graph is termed an S-N curve.
Fatigue testing always gives a scatter in test results. Therefore, many points are
needed to give a best fit curve.
There are two different types of S-N curves.
Fatigue strength: the maximum stress a material can withstand without failing by
fatigue for a given number of cycles
Fatigue life: the number of stress cycles that will cause fatigue failure at a given
stress
Fatigue limit: the largest stress at which the fluctuating stress will not cause fatigue
failure indefinitely.
For some ferrous and titanium alloys, the S-N curve becomes horizontal at higher N
values - there is a limiting stress level below which fatigue failure will not occur.
Fatigue Life
There are three steps in fatigue failure:
1. Crack initiation - a small crack forms
2. Crack propagation - the crack grows slowly, each
stress cycle lengthening the crack a small amount
3. Final failure - occurs by fast fracture
when a>ac (as calculated earlier)
Cracks usually initiate at a stress concentration, such as surface scratches, fillets,
keyways, threads or dents. Initial flaws can be detected using non-destructive testing.
To determine design life, a number of laws can be used for different conditions to
estimate the total fatigue life. If it is assumed that the crack initiation stage is small or
cracks are pre-existent, then the crack growth rate can be used to estimate fatigue
life. This is the technique we will use in this module.
The growth rate will change throughout the life of the component. Short cracks grow
slowly, but larger cracks grow quickly. Therefore, to predict the life of a component
under fatigue conditions, the crack growth rate is required.
The crack growth rate is a function of the stress level, the crack size and material
properties. The relationship is expressed in terms of the stress intensity factor K:
where A and m are constants for the material, dependent on environment and stress.
Typical fatigue crack growth behaviour is shown in the graph.
Region 1:
Non-propagating cracks and slow crack growth. These
are initial cracks that form on slip planes.
Region 2:
Steady crack growth: power-law relationship (shown
above)
Region 3:
Rapid unstable crack growth K~Klc
To predict fatigue life, we take the initial crack length, a0, and the critical crack
length ac:
The number of cycles to failure due to stage II crack growth:
This expression is the fatigue life of a component.
However, it should be remembered that this expression is only valid in the crack
propagation stage and does not include crack initiation or rapid fracture and therefore
the fatigue life calculated should be taken as an estimate of fatigue life.
This expression also assumes that is constant
There are a number of factors that affect the fatigue life of a component:
1. Stress Level
Fatigue life is highly dependent on and R
2. Surface Effects
Surface finish is important because in fatigue, cracks usually start at the surface.
Design: Notches, discontinuities, grooves, holes, threads increase the stress
concentration, and the sharper the discontinuity the more severe the stress
concentration. Therefore, to design against fatigue, avoid irregularities and use
rounded fillets where possible.
Surface treatment: Machining introduces scratches and grooves, therefore polishing a
machined surface will increase fatigue life. Fatigue life can be improved by
introducing a compressive residual stress on the surface layer (shot peening and
case hardening).
3. Environment
Thermal fatigue: Fluctuating temperatures can cause thermal stresses due to thermal
expansion of the components.
Corrosion fatigue: If the component is exposed to a corrosive environment, pits
caused by corrosion can act as initiation sites and corrosion can also increase the
crack growth rate.
Problem
A component is made of a steel for which:
Kc=54 MPa m1/2. Non-destructive testing showed that the component contains cracks of up to 0.2 mm in
length.
Tests have shown that the crack growth rate is given by:
where A=4x10-13 (MPa m) and n=4. The component is subjected to an alternating stress of Δσ=180 MPa,
with a mean stress of Δσ/2.
Calculate the number of cycles to failure, then take the stress concentration factor Y=1.
Solution
Catastrophic failure will occur when:
Now integrate from a0= 0.1 to ac= 29 mm:
Therefore, the fatigue life of the component is 2.4 x 106 cycles to failure.
