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Understanding
the fatigue process is important for the analysis of fatigue properties of
engineering structures. Fatigue may occur when a structure is subjected to
repeated cyclic loadings (due to action of fluctuating stress, according to
(Professor Dan Dubina). Fluctuating stresses will cause structures to fail
(fracture) at stress levels which are much lower than the ultimate strength or
even yield strength of materials in some cases. Fatigue can occur inside and on
the surface of structures in the form of cracks. Railway tracks operate under
very arduous tribological conditions. Loads exerted by rail bogies are very
high and the contact between the rail and the wheels is usually unlubricated.

According to (R.S.
Dwyer-Joyce) when the train is in motion each passage of the wheel causes an
increment of plastic shear strain in the rail head. This strain accumulates in
the near surface region and is known as ratchetting. Ratchetting motion
continues to occur until such a point where the ductility of the material is
exceeded and subsequently rapture occurs. This is thought to be the point where
crack initiation occurs. Figure 12 shows how ratcheting motion from a) to c)
leads to eventual rapture in d).

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Figure 19.
Schematic of Fatigue Crack Initiation Subsequent Growth Corresponding and
Transition from Mode II to Mode I

Crack growth occurs
through various stages leading to failure and this can be best explained using
Fracture Mechanics. The presence of a cracks in components or structures can
reduce their life spans by great deal. It is common for structures to have
micro cracks which can be induced by manufacturing processes. Depending on the
application it may be possible to operate some structures safely for a given
period with small cracks present in them. However, in safety critical
applications such as the aerospace, and gas installations rail tracks and
wheels etc. Cracks are unacceptable as they may have unforeseen consequences to
the integrity of structures and the people who use them.  There are three modes of crack growth which
can occur as shown in Figure 13. (Ali Fatemi).

Figure 20. Modes of failure

·        
Mode I – 
Is the crack opening mode associated growth on the plane of maximum
tensile stress. It is the most common mode that is encountered in engineering
structures.

·        
Mode II – 
Is a shear type crack growth.

·        
Mode III – Is the stage where the growth of the crack
is influenced by torsional forces.

The general mode
of fatigue-crack growth in metallic materials and the manner in which it is
described using fracture mechanics can be brie?y summarised by the schematic
diagram in Figure 14 showing the variation in crack growth rate (da/dN) with
the nominal stress-intensity range (?K = Kmax?Kmin). Realistically,
the growth rates depend upon numerous factors other than ?K, although this is
the primary variable in metal fatigue (R.O. RITCHIE, 1999).

Figure 21. Crack Growth as a
function of stress intensity factor.

The stress-intensity factor (K) is used to
determine the fracture toughness of most materials. A Roman numeral subscript
indicates the mode of fracture and the three modes of fracture as illustrated in
Figure 13. Mode I fracture is the condition where the crack plane is normal to
the direction of largest tensile loading. The stress intensity factor is a
function of loading, crack size, and structural geometry. The stress intensity
factor may be represented by the following equation:

·        
KC is
the fracture toughness in MPa?m

·        
? is
the applied stress in MPa

·        
a is
the crack length in meters

·        
? (or Y) is a crack length and component
geometry factor that differs for each specimen, and is dimensionless.

When cracks are present within structures is important to
understand how they propagate and eventually become detrimental to the
integrity of their hosting structures. It is widely understood that cracks
propagate occurs when the magnitude of a tensile stress at the tip of one of these
flaws exceeds the value of this critical stress ?C. When that happens a crack forms and then propagates
through the material, leading to failure. Therefore, conditions for crack
propagation are given by: Stress Intensity factor  Fracture toughness.

The critical stress can be obtained
using: 

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