Fatigue Life Calculator

S-N Curves and Fatigue Behavior

The S-N curve (also called Wohler curve) plots stress amplitude versus number of cycles to failure. For steels and many alloys, the curve shows:

• Low-cycle fatigue (LCF): Below ~10^3 cycles, plastic deformation dominates
• High-cycle fatigue (HCF): Between 10^3 and 10^6-10^7 cycles
• Endurance limit region: Beyond ~10^6 cycles for steels (horizontal asymptote)

The S-N relationship in the finite life region follows:

S = a * N^b (Basquin equation)

Endurance Limit Concept

The endurance limit (Se') is the stress amplitude below which a material can theoretically survive infinite cycles. For steels:

• Se' = 0.5 * Sut for Sut ≤ 1400 MPa (200 ksi)
• Se' = 700 MPa (100 ksi) for Sut > 1400 MPa

Aluminum and other non-ferrous metals typically do not exhibit a true endurance limit - the S-N curve continues to decline.

The modified endurance limit (Se) accounts for real-world conditions:

Se = ka * kb * kc * kd * ke * kf * Se'

Goodman Diagram and Mean Stress Effects

Real loading rarely involves pure alternating stress - there's usually a mean (static) component. The Goodman diagram plots alternating stress vs. mean stress to define safe operating regions:

• Goodman line: sigma_a/Se + sigma_m/Sut = 1 (conservative, widely used)
• Gerber parabola: sigma_a/Se + (sigma_m/Sut)^2 = 1 (more accurate for ductile metals)
• Soderberg line: sigma_a/Se + sigma_m/Sy = 1 (most conservative)
• Yield (Langer) line: sigma_a + sigma_m = Sy (static yield failure)

The safety factor is determined by how far the operating point is from the failure line.

Miner's Rule for Cumulative Damage

For variable amplitude loading, Palmgren-Miner's linear damage rule estimates cumulative fatigue damage:

D = sum(ni/Ni) = n1/N1 + n2/N2 + ... + nk/Nk

Where ni = cycles at stress level i, Ni = cycles to failure at that stress level. Failure occurs when D ≥ 1.

Correction Factors Explained

• Surface factor (ka): Accounts for surface finish. Polished surfaces have higher fatigue strength than rough surfaces. ka = a * Sut^b
• Size factor (kb): Larger parts have more potential crack initiation sites and stress gradients. For rotating round sections: kb = (d/7.62)^-0.107 for 8-250mm
• Load factor (kc): Accounts for loading type - bending (1.0), axial (0.85), torsion (0.59)
• Temperature factor (kd): High temperatures reduce fatigue strength. kd = 1.0 below 450C, decreases above
• Reliability factor (ke): S-N data is typically for 50% survival rate. Higher reliability requires lower allowable stress