Fatigue Index

Metal Fatigue and Endurance

Important note.. The information below is for guidance only . Evaluating the fatigue strength to be used for component design should be carried out using validated material information and with careful consideration of all factors relevant to the stress locations. The links below the table provide more detailed information on fatigue design.

Fatigue Modifying Factors

The load experience by a component subject to fatigue loading must not exceed the MODIFIED endurance limit divided by the Stress Concentration factor (Kf).    The Modified fatigue endurance limit for, ferrous materials and titanium, is the endurance strength ( S' e ) identified from the relevant S-N ( Wohler) curve modified by a number of factors

Max load (tension)   <   Se / K f = C s   x  C f   x  C l   x C t   x  C r   x   C m   x   S' e  /  K f

Max load (shear)   <   Ses / K f = C s   x  C f   x  C l   x C t   x  C r   x   C m   x  S'es  /  K f

Note: For metals which do not have a definite endurance limit e.g copper allows the endurance limts S'e, S'es etc are replaced by assumed endurance limits S'n, S'ns etc. etc...

SeModified endurance/fatigue limit. (Ferrous metals and titanium.)
SesModified endurance/fatigue limit (shear) (Ferrous metals and titanium.)
S'eTest specimen endurance/fatigue limit. (Ferrous metals and titanium.)
S'esTest specimen endurance/fatigue limit (shear) (Ferrous metals and titanium.)
SnModified fatigue limit (tensile) stress for which it is assumed that the material will never fail regardless of the number of cycles.
SnsThe maximum fatigue limit (shear)stress for which it is assumed that the material will never fail regardless of the number of cycles.
S'nThe maximum completely reversed (tensile) stress (from test specimen results) for which it is assumed that the material will never fail regardless of the number of cycles.
S'nsThe maximum completely reversed (shear)stress (from test specimen results) for which it is assumed that the material will never fail regardless of the number of cycles.
C sSize Factor
C fSurface Finish Factor
C lLoading Factor
C tTemperature Factor
C rReliability factor
C m Miscellaneous factor

All of the above factors have significant quantifiable negative effect on the fatigue strength of a metal.
Other factors can also have a significant non-quantifiable effect on the fatigue strength of metals.

Cs = Size Factor

The endurance limit of specimens have been observed to vary with their size.   This is possibly related to the probability of a high stress interacting with a critical flaw within a certain volume, i.e., when the volume is large there is a higher probability of failure.   Hence, when the size increases, the endurance decreases. Alternatively, since there appears to be a more pronounced size effect in reversed bending and/or torsion than in the reversed axial loading situation this suggests that the stress gradient at the surface is partially responsible for the size effect.

For circular components of diameter, d, an accepted relation illustrating the specimen size effect on the endurance limit for the reversed bending and torsion situations, is

  • Cs = 1 for d < 8 mm
  • Cs = 1.189 .d-0.097 for 8 mm < d < 250mm

C f = Surface Finish Factor

The specimens used in the laboratory to determine the fatigue strength curve or endurance limit of a particular material have a standard size and surface finish that are closely monitored prior to the test. As discussed previously, the initiation of microcracks is almost always associated with a free surface and, hence, the surface condition of the location being reviewed plays a crucial role in assessing the modified fatigue strength.

There are basically three reasons why manufacturing procedures influence the fatigue characteristics of a component:
1) surface irregularities...
2) the condition of the surface, i.e., whether it has been cold worked or softened by decarburization,
3) and the introduction of residual stresses into the surface by, for example, shot-peening.

While the first is due to the machining processes employed during the manufacture of the component, the latter two influence the yield and tensile strengths of the material in the neighbourhood of the surface.   The surface modifying factor therefore depends of the quality of the finish and the material strength characteristics.

Fatigue_surface Finish

The surface finish factor can be calculated using the equation derived from this graph as follows

Cf = a.Sutb

Sut = tensile stresss in MPa. a and b are factors listed in table below

Surface finish a (MPa)b
Ground 1,58-0,085
Machined or Cold Drawn 4,51-0265
Hot rolled 57,7-0,718
As Forged272 -0,995

C l = Load factor

The strength values obtained from the S-N (Wohler plot) result from a reversed bending load as the specimen is rotated. In the rotating-bending testing every element in the specimen diameter surface is subjected to a bend in one direction and then the other, with only a small region on the outer surface being subjected to the maximum stress level.   The reversed axial loading scenario is a much more arduous condition because the all of the section is subject to the full stress and not just the surface elements (The strength values reported for reversed axial loading has been reported at various ratios from 0,7 - 0,85 times that reported for reversed bending ).  Again in the reversed torsion scenario the loading is shear as opposed to bending.  To allow for these differences a loading factor is provided.

  • Cl =1,0 When the loading is reversed bending
  • Cl =0,71 When the loading is reversed axial
  • Cl = 0,6 when the loading is reversed torsional
C t = Temperature factor

Components are often required to endure temperatures different from those at which the mechanical properties of a material were obtained. For metals, the following relations may be applicable in certain situations.   A lower temperatures and higher temperatures a more detailed assessment will be required...

  • Ct =1,0 When the temperature is less than 450 deg C
  • Ct =1 - 5.8-3 (T-450 deg C) When the 450o C <   t   < 550oC
C r = Reliability factor

The basis of the concept of reliability is that a given component has a certain strength resisting capacity; if the stress induced by the operating conditions exceeds this capacity, failure results.   In themselves, design methods based solely on the use of factors of safety and margins of safety give little indication as to the failure probability of the component under cyclic loading.   Furthermore, design variables and parameters are random variables, a fact often ignored by conventional design methods.

In order to define an acceptable meaning of reliability, consider a large population of mechanical parts.   For a specific choice of the number of cycles to failure, n, (where n may also be identified with the number of cycles defining the endurance limit), a fatigue strength, Sn, and a stress action range, s amp, are associated with each location in the component being designed.

Owing to the statistical nature of S - N curves and the uncertainty in both the level and frequency of the loads being applied, there exists in their simplest form a mean value and a standard deviation for each of these variables that defines, for example, a normal distribution for each.

As illustrated in the figure below the forward 'tail' of the stress distribution may overlap the rearward 'tail' of the strength distribution, results in an interference which may be associated with the probability of failure.   Since reliability = 1 - probability of failure, this serves as a illustrative measure of reliability.


The S_N (Wohler) plotted values are mean values based on a number of tests resulting in loads at failure.   The strength values are mean values implying a 50% survival rate.  To enable determination of design strength values with a higher survival rate i.e upwards then the indicated strength values must be reduced..This involves the use of the Reliability factor determined by statistical adjustment of the 50% value S'n.....Put simply , "increasing the factor of safety results in lower risk of failure "
Using the standard normal cumulative distribution and assuming an 8 % standard deviation for both the stress and strength, an analytic expression for cr may be deduced.   This expression results in the values given in the table below..

Reliability Cr
0,5 1
0,9 0,897
0,95 0,868
0,99 0,814
0,999 0,753
0,9999 0,702
0,99999 0,659
0,999999 0,620
C m = Miscellaneous Factor

This factor is a general factor to allow for various factors which are not easily quantifiable.   These factors may include the influence of: corrosion, electrolytic plating (metallic coatings), metal spraying, cyclic frequency, fretting corrosion (due to microscopic motions of tightly fitted parts), and radiation effects on materials.   When corrosion, for example, is combined with cyclic loading, failure is likely to be more accelerated and the endurance limit lower than expected from separate estimates of the two factors.   The reason for this is that corrosion and stressing occur not only at the same time but also interact with one another.   As another example, in regions where bearing loads exist, the risk of fretting corrosion occurring is higher than at other locations of a component.   As a result, the value of Cm should be lower in these locations than at others.   Hence, in a particular situation actual fatigue data may not be applicable and an estimate of Cm must be included in the design and material selection process.

Shot peening, cold rolling, case hardening and nitriding can improve the fatigue strength and reduce the effect of stress concentrations.

Fatigue Links
  1. Efatigue.com... Excellent Source of Fatigue data. (Based on US materials )

Fatigue Index

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