Question

a rotating bending test was conducted on a steel coupon with the thinnest diameter at 8.15mm

	load(kg)	number of cycles
test 1	22.5	30750
test 2	23.5	4750
test 3	29.7	5000

a) explain and describe the rotating bending test

b) Describe the stress cycle that was used;

Answer 1

a) I guess 'Rotating bending fatigue testing' and 'Rotating beam fatigue test' are one and the same. As beams are designed for bending, it has same meaning.

The sample are acted upon by bending moment. Under the action of bending moment, the upper part of the sample is under tensile stresses and lower part is under compressive stresses. And the central part of beam will be subjected to zero stresses. At the same time the sample is rotated, accordingly positions of the maximum tensile and compressive stresses will vary during one revolution of the sample.

The amplitude of these stress is given by:

Stress = (Bending moment)*y/(area moment of inertia of beam cross-section)

Here y is distance of neutral axis to the outer surface.

We can increase or decrease the stress amplitude by increasing or decreasing the bending moment. During the test, number of revolution of sample before the first crack appears is recorded for different stress amplitude. Using this data, S-N curve is plotted, which is also known as Wohler diagram on logarithmic scale. From this curve we can get endurance limit which is the maximum amplitude of reversed stress the specimen can sustain for maximum number of cycle without fatigue failure. For steel specimen, 10⁶ number of cycles are taken as maximum number of cycles. One thing you should notice that endurance limit is not property of material. It depends on lot of factors such as surface finish of material, size and shape of specimen. I hope this will be helpful. You can refer some of design books for more information on the rotating beam fatigue testing. But it will talk in design perspective.

b)

The stress cycle counting technique breaks down the variable amplitude loading into a series of constant amplitude stress cycles, as shown in Table 7.2. Each one of these constant amplitude stress cycles is then considered in turn, together with the appropriate design S–N curve, Figure 7.20.

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Figure 7.20. Using the design S–N curve to calculate the damage from each stress range in the variable amplitude stress spectrum.

For the first constant amplitude stress range, Δσ1 the allowable number of cycles is N1. The number of cycles actually applied at this stress range, determined by the cycle counting technique is n1. We assume therefore that only a proportion of the total life is exhausted at this level of stress range, and that the fraction of life used is equal to n1/N1. This process is repeated for the second stress range, Δσ2, and establish that the proportion of life used is n2/N2, where N2 corresponds to the design life at a stress range Δσ2. We can therefore build up a table of the damage associated with each part of the fatigue stress spectrum as an acceptable design, the total of all the fractions of life must be less than one.