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Power Equation for Stress-Life

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A power relationship can be used to estimate the S–N (stress-life) curve for a steel:

S = 10CN b (for 103 < N < 106)

where the exponents, C and b, of the stress-life curve are determined from the endurance limit and the stress at 1000 cycles:

C  =  log10 (S1000)2 Se

b  =  – 1 3 log10 S1000 Se

When plotted on log-log coordinates, the result is linear.


Nomenclature

symbol	description
S	alternating stress, or stress amplitude
N	life, in number of cycles
Se = σN	endurance limit
Su = σu	ultimate stress, or ultimate strength
S1000	alternating stress for life of 1000 cycles

The power equation can be rewritten for life:

N = 10^–C/bS^1/b

also, going back to the original form, if substitutions are made using the correlations

S₁₀₀₀ ≈ 0.9*S_u    and    S_e ≈ 0.5*S_u

then,

S = 1.62S_uN  ^{– 0.085}

Note: These equations are only estimates.