Calculate material fatigue life under cyclic loading. Predict component lifespan with S-N curves and stress analysis.
Fatigue is the progressive and localized structural damage that occurs when a material is subjected to cyclic loading. The S-N curve (Stress-Number of cycles) represents the relationship between cyclic stress amplitude and the number of cycles to failure.
Key Concept: Materials have an endurance limit - a stress level below which the material can withstand an infinite number of cycles without failure. For steels, this is typically 40-50% of the ultimate tensile strength.
Stress Amplitude: Higher stress amplitudes result in shorter fatigue lives. The relationship is typically logarithmic.
Mean Stress: Non-zero mean stresses (R-ratio ≠ -1) affect fatigue life. Tensile mean stresses reduce fatigue life, while compressive mean stresses can increase it.
Surface Condition: Surface roughness, scratches, and notches act as stress concentrators, significantly reducing fatigue life.
Material Properties: Ultimate tensile strength, yield strength, and microstructure all influence fatigue behavior.
| Material | Ultimate Strength (MPa) | Yield Strength (MPa) | Endurance Limit (MPa) | Typical Applications |
|---|---|---|---|---|
| Carbon Steel (AISI 1045) | 585 | 450 | 240-290 | Shafts, gears, bolts |
| Stainless Steel (304) | 505 | 215 | 200-240 | Chemical equipment, food processing |
| Aluminum 6061-T6 | 310 | 275 | 90-110 | Aircraft parts, bicycle frames |
| Titanium Ti-6Al-4V | 950 | 880 | 450-550 | Aerospace, medical implants |
| Gray Cast Iron | 250 | - | 110-140 | Engine blocks, machine bases |
To enhance fatigue resistance in engineering components:
High-cycle fatigue occurs at lower stress levels where failure happens after more than 10,000 cycles. The material behavior is primarily elastic.
Low-cycle fatigue involves higher stress levels with significant plastic deformation, leading to failure in fewer than 10,000 cycles. Strain-life approaches are typically used for low-cycle fatigue analysis.
Mean stress significantly influences fatigue life. A tensile mean stress (R > 0) decreases fatigue life, while a compressive mean stress (R < 0) can increase it. Common models to account for mean stress effects include:
The endurance limit is the maximum stress amplitude that a material can withstand for an infinite number of cycles without failing. This concept is particularly important for:
For materials without a clear endurance limit, the fatigue strength at 10^7 or 5×10^8 cycles is often used as a practical endurance limit.
Fatigue life predictions have inherent uncertainties due to:
Typical accuracy ranges from a factor of 2 to 10 in life prediction. For critical applications, testing under actual service conditions is recommended.
Miner's Rule (also known as the Palmgren-Miner linear damage hypothesis) is used to estimate fatigue damage under variable amplitude loading. The rule states that damage accumulates linearly:
D = Σ(n_i / N_i)
Where:
While Miner's Rule is widely used due to its simplicity, it has limitations. It doesn't account for load sequence effects, and actual failure often occurs at D values different from 1 (typically between 0.7 and 2.2).