Fatigue Analysis

Stress-Life Method (S-N)

1. Application

   • High-cycle fatigue (N > 10^4 cycles)
   • Elastic stress conditions
   • Rotating machinery, vibration loading

2. S-N Curve Development

   S = A * N^b
   
   Where:
   S = stress amplitude
   N = cycles to failure
   A, b = material constants
   

3. Endurance Limit Modifiers

   Se = Se' * ka * kb * kc * kd * ke * kf
   
   Where:
   ka = surface factor
   kb = size factor
   kc = load factor
   kd = temperature factor
   ke = reliability factor
   kf = miscellaneous effects
   

Strain-Life Method (epsilon-N)

1. Application

   • Low-cycle fatigue (N < 10^4 cycles)
   • Plastic strain present
   • Notched components

2. Coffin-Manson Equation

   epsilon_a = (sigma_f'/E) * (2Nf)^b + epsilon_f' * (2Nf)^c
   
   Where:
   epsilon_a = strain amplitude
   sigma_f' = fatigue strength coefficient
   b = fatigue strength exponent
   epsilon_f' = fatigue ductility coefficient
   c = fatigue ductility exponent
   

3. Neuber's Rule for Notches

   (Kt * S)^2 / E = sigma * epsilon
   

Fracture Mechanics

1. Application

   • Damage tolerance analysis
   • Crack growth life prediction
   • Inspection interval determination

2. Paris Law

   da/dN = C * (delta_K)^m
   
   Where:
   da/dN = crack growth rate
   delta_K = stress intensity factor range
   C, m = material constants
   

3. Stress Intensity Factor

   K = beta * S * sqrt(pi * a)
   
   Where:
   beta = geometry factor
   S = remote stress
   a = crack length
   

Load Spectrum Development

1. Rainflow Cycle Counting

   • Extract cycles from complex load history
   • Identify cycle ranges and means
   • Generate cycle count matrix

2. Damage Summation

   D = sum(ni/Ni)
   
   Failure when D >= 1.0
   

3. Load Sequence Effects

   • Consider overload retardation
   • Evaluate block loading effects
   • Apply appropriate interaction models

Mean Stress Corrections

Process Integration

• ME-008: Fatigue Life Prediction

Input Schema

{
  "component": "string",
  "material": {
    "name": "string",
    "Su": "number (Pa)",
    "Sy": "number (Pa)",
    "Se_prime": "number (Pa)",
    "sigma_f_prime": "number (Pa)",
    "epsilon_f_prime": "number",
    "b": "number",
    "c": "number"
  },
  "loading": {
    "type": "constant_amplitude|spectrum",
    "stress_amplitude": "number (Pa)",
    "mean_stress": "number (Pa)",
    "spectrum_file": "string (if spectrum)"
  },
  "geometry": {
    "Kt": "number (stress concentration)",
    "surface_finish": "string",
    "size": "number (mm)"
  },
  "target_life": "number (cycles)",
  "reliability": "number (0-1)"
}

Output Schema

{
  "fatigue_life": {
    "predicted_cycles": "number",
    "safety_factor": "number",
    "critical_location": "string"
  },
  "damage_summary": {
    "total_damage": "number",
    "damage_by_range": "array"
  },
  "analysis_details": {
    "method_used": "string",
    "mean_stress_correction": "string",
    "modifying_factors": "object"
  },
  "recommendations": {
    "design_changes": "array",
    "inspection_interval": "number (if applicable)"
  }
}

Best Practices

1. Use appropriate method for expected life regime (HCF vs LCF)
2. Include all relevant modifying factors
3. Account for mean stress effects
4. Validate material properties from tested data
5. Consider multiaxial stress states for complex loading
6. Apply appropriate safety factors per industry standards

Integration Points

• Connects with FEA Structural for stress inputs
• Feeds into Test Planning for validation requirements
• Supports Material Selection for fatigue-resistant materials
• Integrates with Design Review for life certification