MEC-06

Basquin S–N law

σa = σf' (2N)^b in high-cycle fatigue.

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FatigueBasquin 1910ASTM E466

Governing equation

\sigma_a=\sigma_f'(2N)^b

where

\sigma_f': Fatigue coefficient (MPa)
b: Basquin exponent (—)
N: Cycles to failure (cycles)
\sigma_a: Allowable amplitude (MPa)

Lecture brief

Historical brief

Machine design grew from Coulomb torsion and Hertz contact (1881) through Soderberg fatigue and the heat-engine cycle. The lab writes shaft, bearing, contact and thermodynamic limits in SI. This sheet (MEC-06 — Basquin S–N law) is the form associated with Basquin 1910 · ASTM E466. Working symbols: $\sigma_f'$ , $b$ , $N$ $\rightarrow$ $\sigma_a$ . Basquin observed that log stress versus log reversals is linear in the elastic-life regime, defining the fatigue strength coefficient and exponent.

Purpose

Purpose: compute

\sigma_a

from

\sigma_f'

b

N

in Mechanical via

\sigma_a=\sigma_f'(2N)^b

σa = σf' (2N)^b in high-cycle fatigue. Use it when a real mechanical question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

\sigma_f' = 900.000\,\mathrm{MPa}

b = -0.090\,\mathrm{—}

N = 1.000e+6\,\mathrm{cycles}

, the governing relation

\sigma_a=\sigma_f'(2N)^b

yields

\sigma_a = 243.865\,\mathrm{MPa}

. Fully reversed uniaxial, no mean stress. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Fatigue coefficient \sigma_f'900 MPaBasquin exponent b-0.09 —Cycles to failure N1000000 cycles

Outputs

Allowable amplitude \sigma_a243.865 MPa

Reading speed

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Narration of this film

Fully reversed uniaxial, no mean stress.

Basquin observed that log stress versus log reversals is linear in the elastic-life regime, defining the fatigue strength coefficient and exponent.

Reading speed

Watch on YouTube