Fatigue strength and the Marin factors

This is a static copy of the chapter for search engines. The interactive version has animated figures, check questions, and buttons that load the example into the calculator.

Fatigue data comes from small, polished, perfectly loaded laboratory specimens. Your shaft is none of those things. The Marin approach takes the laboratory endurance limit and multiplies it down by a factor for each way in which reality is worse.

S_e = k_a·k_b·k_c·k_d·k_e·k_f·S′_e

S′_e — the laboratory value

For steels, a good estimate from the tensile strength alone:

S′_e = 0.5·S_ut (S_ut ≤ 1400 MPa), S′_e = 700 MPa above that

The cap matters: past about 1400 MPa the fatigue limit stops following the strength. This is the second reason not to solve a fatigue problem by ordering a stronger steel.

k_a — surface finish

Fatigue cracks start at the surface, so how the surface was made matters enormously.

k_a = a·S_ut^b

Finish	a (MPa)	b	k_a at 600 MPa
ground	1.58	−0.085	0.91
machined / cold-drawn	4.51	−0.265	0.83
hot-rolled	57.7	−0.718	0.58
as-forged	272	−0.995	0.46

Note the trend: the stronger the steel, the more it is punished for a rough surface. A forged surface on a high-strength steel throws away most of what you paid for.

k_b — size

k_b = 1.24·d^−0.107 (2.8 ≤ d ≤ 51 mm), k_b = 1.51·d^−0.157 (51 < d ≤ 254 mm)

Bigger sections have more material at high stress and more chance of containing a defect. A 100 mm shaft has about 25 % less fatigue strength than a 10 mm one of the same steel. ShaftLab applies k_b section by section, using the local diameter — a step at ⌀30 and a step at ⌀80 do not share a k_b.

k_c, k_d, k_e, k_f

k_c — load type. Because bending and torsion are combined through von Mises here, k_c = 1 and the √3 in the von Mises expression does the work. A steady axial stress is divided by 0.85 instead, which is the same correction wearing a different hat.
k_d — temperature. Roughly 1.0 up to about 350 °C for steel, then it falls away.
k_e — reliability. The laboratory numbers are medians, i.e. 50 % reliability. For a real design pick 99 % (k_e = 0.814) or 99.9 % (0.753).
k_f — everything else: corrosion (which can halve it, and removes the endurance limit altogether), plating, decarburisation, and beneficial effects like shot peening or nitriding (k_f > 1).

⚠ In a corrosive environment steel has no true endurance limit — the S-N curve keeps falling. If your shaft runs wet, do not design for infinite life on these numbers; design for a finite life with a corrosion factor and inspect.

💡 Watch the numbers in panel 05 as you change the surface finish. Going from ground to as-forged on a 600 MPa steel roughly halves S_e — the same effect as doubling the load.