Joseph Marin in 1962 in book Mechanical Behavior of Engineering Materials introduced factors that adjust endurance limit of rotating beam specimen to endurance limit or real structural part
\[S_e=k_a \cdot k_b \cdot k_c \cdot k_d \cdot k_e \cdot k_f \cdot S'_e\]
where
\(k_a\) - surface factor
\(k_b\) - size factor
\(k_c\) - loading factor
\(k_d\) - temperature factor
\(k_e\) - reliability factor
\(k_f\) - miscellaneous effect factor
\(k_a\) accounts that in lab specimen has mirror polished surface and in real life it's often worse. Flaws on surface where stresses are high impact fatigue endurance. Surface factor could be found in:
- Shigley's "Mechanical Engineering Design"
- Fundamentals of Machine design
- Johnson "Specifying a surface finish that wont fail in fatigue"
\(k_b\) accounts uneven stress distribution in rotating beam specimen. Higher diameter cylinder has, higher stress should be on the outer surface and lower fatigue endurance would be
For rotating cylinders:
\(k_b = 0.879d^{-0.107}\) for \(0.11 in \leq d \leq 2 in\)
\(k_b = 0.91d^{-0.157}\) for \(2 in < d \leq 10 in
or
\(k_b = 1.24 d^{-0.107}\) for \(2.79 mm \leq d \leq 51 mm\)
\(k_b = 1.51 d^{-0.157}\) for \(51 mm < d \leq 254 mm\)
For axial loading \(k_b = 1.0 \)
\(k_c\) accounts type of loading. Test are performed for bending condition. For other types correction is needed
- \(k_c=1.0\) - for bending
- \(k_c=0.7 - 0.9\) - for axial
- \(k_c=0.58\) - for torsion
\(k_d\) accounts temperature effect. Endurance strength decreases with increasing temperature. If temperature knock-down factor for tensile strength (S_ult) is available it should bu used as k_d. For steel approximation from Shigley could be used
\[k_d = 0.975 + (0.432 \cdot 10^{-3} ) /cdot T - (0.115 \cdot 10^{-5} ) \cdot T^2 + (0.104 \cdot 10^{-8} ) \cdot T^3 - (0.595 \cdot 10^{-12} ) \cdot T^4 \]
\(k_e\) accounts reliability
\(k_e\) accounts various factors:
- Residual stresses
- Plating
- Corrosion