1. FATIGUE FATIGUE Dr. Mohammed Abdulrazzaq
Materials Engineering Department

2. 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.
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.

3. Fatigue Fatigue failures are often easy to identify.
The fracture surface near the origin is usually smooth. The surface becomes rougher as the crack increases in size.
Microscopic and macroscopic examination reveal a beach mark pattern and striations.
Beach mark patterns indicate that the load is changed during service or the load is intermittent.
Striations are on a much finer scale and show the position of the crack tip after each cycle.

4. Fatigue
The most important fatigue data for engineering designs are the S-N curves, which is the Stress-Number of Cycles curves.
In a fatigue test, a specimen is subjected to a cyclic stress of a certain form and amplitude and the number of cycles to failure is determined.
The number of cycles, N, to failure is a function of the stress amplitude, S.
A plot of S versus N is called the S-N curve.

5. 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.
In some materials, including steels, the endurance limit is approximately half (50%) the tensile strength given by:

6. Factors necessary to cause fatigue failure
Sufficiently high maximum tensile stress
Factors necessary to cause fatigue failure
Large variation/fluctuation in stress
Sufficiently large number of stress cycles

7. Factors which play an important role in fatigue
Stress concentration
Corrosion
Temperature
Microstructure
Residual stress
Stress state

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

9. Fatigue Failures
As the mean stress, sm, increases, the stress amplitude, sa, must decrease in order for the material to withstand the applied stress. This condition is summarized by the Goodman relationship:
Where sfs is the desired fatique strength for zero mean stress and sTS is the tensile strength of the material.
Example, if an airplane wing is loaded near its yield strength, vibrations of even a small amplitude may cause a fatigue crack to initiate and grow. This is why aircraft have a routine inspection in order to detect the high-stress regions for cracks.

10. Fatigue Failures
Crack Growth Rate
To estimate whether a crack will grow, the stress intensity factor (DK), which characterizes the crack geometry and the stress amplitude can be used.
Below a threshold DK a crack doesn’t grow.
For somewhat higher stress intensities, the cracks grow 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.

11. Fatigue Failures

12. Completely reversed cycle of stress
Types of stress cycles and parameters characterizing them
Completely reversed cycle of stress
← Stress →
Cycles →
Tensile →
← Compressive a r

13. Cycles → m r
max
min
Tensile stress →
Purely tensile cycles

14. Random stress cycles
Tensile →
← Compressive
← Stress →
Cycles →

15. S-N Curve
Engineering fatigue data is usually plotted as a S-N curve [S: stress; N: number of cycles to failure (usually fracture), plotted as log(N)]
The stress plotted : a, max, min
Stress values plotted are nominal values (no account for stress concentrations)
Each plot is for a constant m, R or A
Most fatigue experiments are with m = 0 (rotating beam tests)
S-N curves deal with fatigue failure at a large number of cycles (> 105)
Stress < y but microscopic plasticity occurs
Stress   life 
For low cycle fatigue (N < 104 or 105 cycles) tests are conducted in controlled cycles of elastic + plastic strain (instead of stress control)

16. S-N Curve Bending stress (MPa) → Number of cycles to failure (N) →
400
300
Fatigue limit
Mild steel
Bending stress (MPa) →
200
No fatigue limit  fatigue strength is specified for and arbitary number of cycles (~ 108 cycles)
Aluminium alloy
100
105
106
107
108
Number of cycles to failure (N) →
Steel, Ti show fatigue limit
Al, Mg, Cu show no fatigue limit
Fatigue limit = Endurance limit

17. S-N Curve: Basquin equation
S-N curve in the high cycle region is described by the Basquin equation: a is the stress amplitude, p & C emperical constants
S-N curve is determined using 8-12 specimens
Starting with a stress of two-thirds of the static tensile strength of the material the stress is lowered till specimens do not fail in about 107 cycles
Usually there is considerable scatter in the results