How is fatigue life calculated using the Basquin S-N curve?

Basquin's law states σa = σf'(2Nf)^b, so fatigue life is Nf = (1/2)·(σa/σf')^(1/b). The fatigue strength coefficient σf' is approximately 1.5·Su for steel, and the Basquin exponent b is typically −0.085. The modified endurance limit Se' = ka·kb·kc·Se accounts for surface finish (ka), size (kb), and reliability (kc) factors. If the stress amplitude falls below Se', infinite life is predicted.

What is the boundary between low-cycle fatigue (LCF) and high-cycle fatigue (HCF)?

The transition life Nt is the cycle count where the S-N curve intersects the modified endurance limit Se', typically between 10^5 and 10^7 cycles for steel. Below Nt is the LCF regime, dominated by large stress amplitudes and plastic strain; above Nt is HCF, where elastic strain governs. This tool displays Nt directly so you can identify which regime your operating stress falls in.

Does aluminum alloy have a fatigue endurance limit?

Aluminum alloys do not exhibit a true fatigue endurance limit. The S-N curve continues to decrease monotonically on a log-log scale even at very high cycle counts. For design purposes, a fatigue strength at a specified life (commonly 10^7 or 5×10^8 cycles) is used instead of an endurance limit. When the aluminum preset is selected in this tool, the flat endurance limit region is disabled to reflect this behavior.

How much does the stress ratio R affect fatigue life?

A positive stress ratio R (tensile mean stress) reduces fatigue life through the Goodman correction: the effective stress amplitude becomes σa_eff = σa / (1 − σm/Su), where σm = σa·(1+R)/(1−R). For example, at R = 0 (pulsating tension) versus R = −1 (fully reversed), with Su = 800 MPa, σa = 200 MPa, and σm = 200 MPa, the effective amplitude increases by a factor of ~1.33, significantly reducing predicted life.

S-N Curve Fatigue Life Estimation Tool — Free Online Calculator

Material Class

Material Strength

Ultimate Tensile Strength S_u 800 MPa

Endurance Limit S_e (recommended: 0.5·S_u) 400 MPa

Basquin Exponent b -0.085

Correction Factors

Surface Finish Factor k_a 0.80

Size Factor k_b 0.90

Reliability Factor k_c 0.90

Loading Conditions

Stress Amplitude σ_a 200 MPa

Stress Ratio R = σ_min/σ_max -1.0

Formulas

$S_e' = k_a k_b k_c S_e$
$\sigma_a = \sigma_f'\!(2N)^b$
$N_f = \tfrac{1}{2}\!\left(\dfrac{\sigma_a}{\sigma_f'}\right)^{1/b}$

Fatigue Life N_f

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cycles

Modified Endurance Limit S_e'

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MPa (ka·kb·kc·Se)

Safety Factor n = S_e'/σ_a

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safety factor

Transition Cycle N_t

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LCF / HCF boundary

1. S-N Diagram (Log-Log) — Basquin's Law + Endurance Limit + Operating Point

2. Correction Factor Effect: Original Curve (Dashed) vs. Modified (Solid)

3. Fatigue Life Scatter Band (±2σ)