ENDURANCE LIMIT REDUCTION FACTORS

Completing fatigue testing of R.R. Moore specimens provides the response of a material under ideal conditions. These

tests are made using a piece of raw material that is machined and then carefully polished. In practice, real parts may

have significantly less resistance to fatigue damage than the polished specimens used to determine the rotating bending

endurance limit (𝑆𝑒′). It is standard practice to account for material, manufacturing, environmental and design impacts

on fatigue life through reduction factors that are applied to the rotating bending endurance limit:

𝑆𝑒 = 𝑘𝑎𝑘𝑏𝑘𝑐𝑘𝑑𝑘𝑒𝑘𝑓𝑆𝑒′

where

𝑘𝑎 = depends on how the part is manufactured, resulting in different surface characteristics

𝑘𝑏 = depends on the size of the part

𝑘𝑐 = depends on the type of loading (axial, bending, torsion)

𝑘𝑑 = depends on the temperature where the part is placed in service

𝑘𝑒 = allows a designer to account for different levels of part reliability

𝑘𝑓 = accounts for a collection of other things that can reduce fatigue life (a reminder to consider other factors)

𝑆𝑒′ = endurance limit from an R.R. Moore test (rotating bending with carefully polished surface)

𝑆𝑒 = endurance limit corrected so that it can predict the fatigue resistance at a particular point in a real part

SURFACE CORRECTION FACTOR, 𝒌𝒂:

SIZE CORRECTION FACTOR, 𝒌𝒃:

Larger parts are generally more susceptible to failure than smaller parts. This makes sense if you think of a part as made

up of very small links of chain (like the grains that define the microstructure). A large part is more likely to fail since it is

made up of many more chain links, and it only takes one link (the weakest link) to cause failure. Here, the mode of

failure is the initiation of a small crack on the surface which eventually propagates to complete failure of the part.

The values above apply for rotating bending of a part with a circular cross section. For parts that are not rotating and for

situations when the cross section is not circular, we need to determine the cross sectional area of the part subjected to

at least 95% of the peak stress (only the highly stressed grains or chain links are susceptible to failure).

LOADING CORRECTION FACTOR, 𝒌𝒄:

The type of loading (bending, torsion, or axial loading) can have a dramatic impact on fatigue resistance for a given

alternating stress level. Since R.R. Moore specimens are tested under rotating bending, there is NO reduction factor for

bending.

Axial loading has no gradient, so all of the grains in the material are subjected to the peak stress. So, it makes sense that

the endurance limit (as determined using R.R. Moore specimens) should be reduced.

Torsional stresses also vary linearly from the axis of rotation to the outer fiber (similar to the way that bending stresses

vary linearly from the neutral axis to the outer fiber). But, the loading factor adopted is applied to account for the fact

that torsional stresses must be transformed to determine the effective normal stress (torsional stress induces a normal

stress at 45 degrees to the axis of rotation, and the tensile normal stress associated with this torsion drives crack

growth).

We can see where this 0.59 comes from by examining the von Mises effective stress when only a single torsional stress

component is present:

TEMPERATURE CORRECTION FACTOR, 𝒌𝒅:

The yield and ultimate strengths of a material drop off as temperature is increased. We will predict the reduction in the

fatigue resistance by determining the reduction in the ultimate strength and then using this reduced ultimate strength

to estimate the endurance limit at elevated temperature.

Table 6-4 shows the tensile strength reduction factors for 21 different carbon and allow steels. A relationship fit to that

data is provided below.

This factor of kd can be used along with 𝑆𝑒′ determined for room temperature (either estimated using the tensile

strength or determined experimentally).

RELIABILITY CORRECTION FACTOR, 𝒌𝒆:

A reliability factor of 1.0 is associated with a reliability of 50%. This means that half of the specimens would be expected

to have an endurance limit greater than the 𝑆𝑒′ determined experimentally or estimated from 𝑆𝑢𝑡, and half would be

expected to have an endurance limit less than 𝑆𝑒′ . If greater reliability is desired, we can use the reduction factors

provided in the table below.

Reliability (%) 𝒌𝒆

50 1

90 0.897

95 0.868

99 0.814

99.9 0.753

99.99 0.702

99.999 0.659

99.9999 0.620

RELIABILITY CORRECTION FACTOR, 𝒌𝒇:

A number of other factors can act to reduce the fatigue resistance of a part. These include tensile residual stresses,

corrosion, plating, metal spraying, the cyclic frequency and other factors. Factors that reduce fatigue resistance must be

accounted for when designing parts. Surface treatments such as shot peening can induce compressive residual stresses

and increase the fatigue resistance of a part (cracks don’t open and grow well in compressive stress fields).