Question

Suppose you have a 4340 steel plate in fully reversed axial loading, with an axial load varying from 15000 lbf to -15000 lbf. The plate is 1⁄4” thick, 2” high, and 5” long. A hole is in the center of the plate, and is 1/4“ in diameter. The stress concentration factor chart is in the Quiz 3 References. The fully adjusted endurance limit was found to be Se = 25 ksi.​

The fatigue strength fraction f is 0.76. The notch sensitivity is 0.95.

What is the life in cycles of this bar?

References Fully Reversed Loading Fatigue:

https://d3c33hcgiwev3.cloudfront.net/_b812cd169fbe57b00756e256731aa4a3_Quiz-3--References-Fully-Reversed-Loading-Fatigue-.pdf?Expires=1593993600&Signature=c5lXDSj-l8Sa7aUp1pCxY88L-MSbdEMoEUYl-YZMNvdU11UqQ-2vZAPYcuzbYmwZt28RMIoSf~KHf-5h6nZgUc89eqWDtLRmffjmk1wjAgll8Vgnuhza-m3ni5~IjL9utiaQrGCmoFZBEr8FzNyHi1629kpKoMAL4FHW7TRLG5g_&Key-Pair-Id=APKAJLTNE6QMUY6HBC5A

Answer 1

I am using the graph that you have attached so values that I assumed i mentioned in the bracket and remaining values I have taken from the data that you have given.

Solve for the reverse axial loading -

Corrected endurance strength is given by -

Where

Load correction factor = 0.85 (For axial loading)

Surface finish factor = 1

Size factor = 1 (For axial loading)

q = Notch seneitivity = 0.95

Stress concentration factor -

Where Theoretical stress concentration factor.

K = Fatigue strength factor = 0.76

Notch sensitivity q =

Notch sensitivity shows that to what extent the sensitivity of the material to fracture is affected because of the presence of a notch, an abrupt change in cross-section, crack etc.

Kf = Actual stress concentration factor.

Plate dimension -

d (Hole dia) = 0.25 inch

H (Height) = 2 inch

So d/H = 0.125

Kt = 2.6 (From given graph)

Therefore,

For reversible loading maximum and minimum load is given -

Where e = Thickness = 0.25 in

H = Height = 2 in

d = Dia of hole = 0.25 in

Amplitude stress is given as -

Mean stress =

For steel -

Genralised S-N curve for steel is given as -

N = Cycles to failure.

Log-Log scale -

The straight line before line i.e. parallel to x-axis shows finite life cycle region but line i.e. parallel to x-axis shows infinite life cycle.

Now,

Therefore,

by using straight-line equation -

If you still have any doubt or answer does not match, please ask in the comment section so that I will look into it.