During testing, the top of the R.R. Moore specimen will be in compression, and the bottom will be in tension due to the

bending stresses. As the specimen rotates, a point on the top (which is in compression) will rotate around to the bottom,

causing the stress state at the point to change sinusoidally from compression to tension, resulting in a stress history like

the one shown below.

A given stress amplitude will cause failure after a number of cycles. Here, the stress amplitude that will cause failure

after N cycles is called the fatigue strength, Sf.

If we repeat a number of fatigue tests and plot Sf and N pairs on a graph, we obtain the well-known S-N plot.

𝑆𝑒′ is called the ENDURANCE LIMIT. Stresses below this value are predicted to never cause failure.

𝑆𝑓1 is the fatigue strength corresponding to a life of N1 cycles. Likewise, 𝑆𝑓2 is the fatigue strength corresponding to a life

of N2 cycles.

The plot above is typical for steels where 1,000,000 cycles is typically taken as the number of cycles corresponding to

infinite life.

PROPERTIES FOR STEELS

The following empirical relationships have resulted from many experiments on different types of steel.

When tensile strengths are not available, another relationship that is sometimes used to estimate the rotating bending

endurance limit is …

For the endurance limits above, we most often assume that 𝑆𝑒′ corresponds to 1,000,000 cycles (or 106 cycles).

We know that a log-log plot of stress amplitude (S) and lifetime (N) is effective in making sense of fatigue behavior which

inherently involves a large amount of scatter. A log-log plot for the high cycle fatigue range (above 1,000 cycles) is

provided below:

EXAMPLE

An ANSI 4130 steel specimen, water quenched and tempered so that it has a tensile strength of 150 ksi, is subjected to a

standard rotating bending test. Estimate the fatigue life for a fatigue strength of 100 ksi. A fatigue strength of 100 ksi

would correspond to the situation where a point on the outer surface of the R.R. Moore specimen (at the center)

undergos a sinusoidal stress history where the stress varies from -100 ksi to 100 ksi.

a. Since we don’t have specific fatigue properties yet, we will need to use the empirical relationship presented in

the notes to estimate the endurance limit.

b. Since we don’t have specific fatigue properties, we will need to use the empirical relationship in the notes to

estimate the fatigue strength at 1,000 cycles.

c. These two data points define the log S versus log N plot. We can find the constants that define the slope and

intercept of the line on the S-N plot.

d. We can now estimate the fatigue life corresponding to a stress amplitude of 100 ksi.

DISCUSSION: An alternating stress of 100 ksi is estimated to cause failure in 14,100 cycles. Please note that there will

likely be significant scatter in the life for a given stress level … this is just an estimate based on the response that is

typical for steels with this tensile strength. The fatigue strength / life data point falls between the fatigue strength at 103

cycles (119.6 ksi) and the endurance limit of 75 ksi at 106 cycles.