Fatigue Life Analyzer

Calculate material fatigue life under cyclic loading. Predict component lifespan with S-N curves and stress analysis.

Basic Analysis
Advanced Analysis
Material Comparison
R = σ_min / σ_max
Enter multiple stress levels and corresponding cycles for spectrum loading analysis

Understanding Fatigue Life and S-N Curves

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.

Factors Affecting Fatigue Life

1

Stress Amplitude: Higher stress amplitudes result in shorter fatigue lives. The relationship is typically logarithmic.

2

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.

3

Surface Condition: Surface roughness, scratches, and notches act as stress concentrators, significantly reducing fatigue life.

4

Material Properties: Ultimate tensile strength, yield strength, and microstructure all influence fatigue behavior.

Common Material Properties

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

Fatigue Life Improvement Techniques

To enhance fatigue resistance in engineering components:

  • Shot peening: Introduces compressive residual stresses on the surface
  • Surface hardening: Methods like carburizing or nitriding increase surface hardness
  • Design optimization: Avoid sharp corners and stress concentrators
  • Material selection: Choose materials with higher endurance limits
  • Regular inspection: Detect cracks before they reach critical sizes

Frequently Asked Questions

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:

  • Goodman relation: Conservative approach for brittle materials
  • Gerber parabola: Better for ductile materials
  • Soderberg line: Most conservative, uses yield strength

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:

  • Designing components for infinite life (e.g., aircraft structures, rotating machinery)
  • Steels and titanium alloys typically exhibit a clear endurance limit
  • Aluminum and copper alloys do not have a distinct endurance limit - their S-N curves continue to decline

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:

  • Material variability: Even within the same material batch, properties can vary
  • Manufacturing processes: Surface finish, residual stresses, and heat treatment affect fatigue behavior
  • Loading conditions: Real-world loading is often more complex than laboratory tests
  • Environmental factors: Temperature, corrosion, and other factors influence fatigue

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:

  • D = Total damage (failure occurs when D ≥ 1)
  • n_i = Number of cycles at stress level i
  • N_i = Number of cycles to failure at stress level i

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).