2025-08-21 15 min
Fatigue Life Calculator
Calculate fatigue life using S-N curve and Basquin equation. Determine cycles to failure for cyclic loading.
Calculator
Stress Amplitude (Sa)(MPa) Help
MPa
Alternating stress
Ultimate Tensile Strength (Su)(MPa) Help
MPa
Material UTS
Fatigue Coefficient (sigma_f)(MPa) Help
MPa
Basquin coefficient
Fatigue Exponent (b)(-) Help
-
Basquin exponent
Mean Stress (Sm)(MPa) Help
MPa
Average stress
Safety Factor(-) Help
-
Applied to Sa
Decimal Precision
Results update live as you type
Results
Normal
Cycles to Failure
667959.35cycles
Fatigue Life
185.54hours
Endurance Limit
250.00MPa
Stress Ratio
0.00-
Design Status
Below endurance limit-
Visualizations
Results Overview
667,959cyclesCycles to Failure
185.5cyclesFatigue Life
250cyclesEndurance Limit
Formula
Basquin equation relates stress amplitude to cycles to failure via the S-N curve.
Sa = sigma_f * (2*Nf)^b
Alternative Form
Nf = (sigma_f / Sa)^(1/|b|)
Variables
| Symbol | Name | Unit | Description |
|---|---|---|---|
| Sa | Stress Amplitude | MPa | Alternating stress in the cycle |
| sigma_f | Fatigue Coefficient | MPa | Material fatigue strength coefficient |
| b | Fatigue Exponent | - | Basquin exponent (negative) |
| Nf | Cycles to Failure | - | Number of loading cycles until failure |
Explanation
The Basquin equation relates stress amplitude to fatigue life. Steel exhibits an endurance limit below which infinite life is predicted.
Step-by-Step Calculation
Follow each step to understand how the result is calculated from your inputs.
Step 1
Identify material fatigue properties
sigma_f, b
Result: Properties recorded
Step 2
Apply safety factor to stress amplitude
Sa_design = Sa / SF
Result: Design stress amplitude
Step 3
Apply Basquin equation
Nf = (sigma_f / Sa_design)^(1/|b|)
Result: Cycles to failure
Step 4
Calculate endurance limit
Se = 0.5 * Su (for steel)
Result: Endurance limit
Step 5
Compare with endurance limit
If Sa < Se, infinite life predicted
Result: Design assessment
Final Answer
667959.35
Worked Examples
See how the calculator works with different scenarios.
Scenario
Sa=250 MPa, Su=500 MPa, sigma_f=1000 MPa, b=-0.12.
Inputs
Sa:250 MPa
Su:500 MPa
Calculation
Nf = (1000/250)^(1/0.12) = 1,500,000
Result
Nf ~ 1,500,000 cycles
Interpretation
The component has finite life. It will fail after approximately 1.5 million cycles.
Understanding Your Result
Your Result: Cycles to Failure: 667959.35 cycles
Typical range: Low cycle: <10,000 cycles. High cycle: 10K-1M. Very high cycle: >1M.
What This Means
Fatigue life is the number of loading cycles before crack initiation and propagation cause failure.
Why It Matters
Fatigue accounts for over 90% of all mechanical failures. Understanding fatigue life is essential for reliable design.
Recommendations
- •Apply safety factors of 2-4 for fatigue design
- •Consider mean stress effects using Goodman or Gerber
- •Account for surface finish and temperature effects
- •Validate critical designs with testing
Educational Content
Introduction
Fatigue is progressive structural damage from cyclic loading. It is the most common cause of mechanical failure.
Concept Explanation
The S-N curve relates stress amplitude to cycles. The Basquin equation Sa = sigma_f * (2Nf)^b describes high-cycle fatigue.
Applications
▸Automotive crankshaft design
▸Aircraft fatigue analysis
▸Bridge fatigue assessment
▸Turbine blade life prediction
▸Rotating machinery design
▸Biomedical implant analysis
Benefits
- •Predicts component life under cyclic loading
- •Enables safe reliable design
- •Foundation for damage tolerance design
- •Applicable to all structural materials
Limitations
- •Does not predict crack initiation location
- •Material data scatter requires statistical treatment
- •Does not account for multiaxial fatigue
- •Temperature and environment need corrections
Best Practices
- •Always consider fatigue in cyclic loading
- •Use appropriate S-N data for material and condition
- •Apply all relevant correction factors
- •Consider both initiation and propagation phases
Common Misconceptions
Myth: Only old components fatigue
Truth: Fatigue can initiate in new components under high cyclic loads.
Myth: Static strength prevents fatigue
Truth: Fatigue failures occur at stresses far below yield strength.
Myth: Fatigue life is deterministic
Truth: Fatigue life has significant scatter. Same component can have widely varying lives.
Practical Tips
- •Surface finish greatly affects fatigue life
- •Mean tension reduces life; compression improves it
- •Notches are primary crack initiation sites
- •High temperature reduces fatigue strength
- •Corrosion can eliminate endurance limit
Common Mistakes
Ignoring mean stress effects
Mean stress significantly affects fatigue life. Use Goodman, Gerber, or Morrow corrections.
Using static strength for fatigue design
Fatigue strength is much lower than static strength. Always use S-N data.
Ignoring surface finish
Surface finish can reduce fatigue life by 50% or more.
Assuming infinite life without checking
Verify stress amplitude is below endurance limit.
Assumptions
This calculator makes the following assumptions to provide estimates:
Uniaxial Loading: Calculator assumes uniaxial stress. Multiaxial fatigue requires additional analysis.
Constant Amplitude: Loading amplitude is constant throughout life.
Room Temperature: Fatigue properties are for room temperature.
Laboratory Conditions: S-N data from polished specimens.
Limitations
Be aware of these limitations when using this calculator:
No Crack Propagation: Predicts total life only. Crack growth requires fracture mechanics.
No Multiaxial Effects: Does not account for biaxial or triaxial stress states.
No Cumulative Damage: Variable amplitude requires Miner rule or similar methods.
Material Scatter: Fatigue data has significant scatter. Results are statistical estimates.
Frequently Asked Questions
Answers to common questions about this calculator.
What is fatigue life?
The number of loading cycles a component can withstand before failure from cyclic loading damage.
What is the S-N curve?
The stress-life curve relating stress amplitude to number of cycles to failure.
What is the Basquin equation?
Sa = sigma_f * (2Nf)^b. Power-law relationship for high-cycle fatigue.
What is the endurance limit?
Stress amplitude below which infinite cycles are possible. Usually 50% of UTS for steel.
How does mean stress affect fatigue?
Mean tensile stress reduces life. Mean compressive stress improves it.
What is low cycle fatigue?
Fatigue with fewer than 10,000 cycles. Significant plastic deformation occurs.
What is high cycle fatigue?
Fatigue with 10,000 to 1,000,000 cycles. Elastic deformation dominates.
How do I improve fatigue life?
Reduce stress concentrations, improve surface finish, use shot peening.
What is the Goodman diagram?
Graph showing mean stress effects on fatigue life with failure envelopes.
Does aluminum have an endurance limit?
No. Non-ferrous metals require life specified for a given number of cycles.
What is Miner rule?
Cumulative damage: sum of (ni/Ni) = 1 at failure.
How does surface finish affect fatigue?
Rough surfaces initiate cracks. Ground surfaces can double fatigue life.
What is shot peening?
Bombarding surfaces to introduce compressive residual stresses.
How does temperature affect fatigue?
High temperature reduces strength and can eliminate endurance limit.
What is fretting fatigue?
Fatigue from small oscillatory movements between contacting surfaces.
What is fatigue stress concentration factor?
Kf = unnotched fatigue strength / notched fatigue strength.
How do I handle variable amplitude loading?
Use rainflow counting then Miner rule for cumulative damage.
What is crack closure?
Crack surfaces contact before full unloading, slowing crack growth.
What is Paris law?
da/dN = C*(Delta K)^m. Relates crack growth rate to stress intensity range.
How do I design against fatigue?
Use S-N data, apply correction factors, include safety factors, minimize stress concentrations.
What is the fatigue limit?
Same as endurance limit. Stress below which failure does not occur.
How does notching affect fatigue?
Notches create local stress concentrations that initiate fatigue cracks.
What is thermal fatigue?
Fatigue from cyclic thermal stresses in engine components and heat exchangers.
What is multiaxial fatigue?
Fatigue under combined normal and shear stresses requiring special criteria.
How do I get fatigue data?
From ASTM E466 testing, MatWeb databases, or manufacturer specifications.
What is fatigue data scatter?
Life can vary by factor of 10 at same stress level. Statistical treatment is essential.
How does size affect fatigue?
Larger specimens have lower fatigue strength due to more material volume.
What standards apply?
ASTM E466, Eurocode 3 Part 1-9, AISC fatigue provisions, ASME codes.
Is this suitable for students?
Yes. Teaches S-N curve fundamentals, Basquin equation, and fatigue prediction.
What is damage tolerance?
Design philosophy assuming flaws exist and managing crack growth through inspection.
What are common fatigue failure signs?
Beach marks on fracture surface, progressive crack growth, sudden final fracture.
How do welds affect fatigue?
Welds introduce stress concentrations and residual stresses, significantly reducing fatigue life.
What is the Gerber criterion?
Sa/Se + (Sm/Su)^2 = 1. More accurate than Goodman for mean stress effects.
What is the Morrow equation?
Sa/(Se - Sm) = 1/Nf^(1/b). Accounts for mean stress through fatigue ductility.
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Glossary
Technical terms used in mortgage calculations explained in plain language.
- Fatigue
- Progressive structural damage from cyclic loading.
- S-N Curve
- Stress-life curve relating stress amplitude to cycles.
- Basquin Equation
- Power-law: Sa = sigma_f * (2Nf)^b for high-cycle fatigue.
- Endurance Limit
- Stress below which infinite life is predicted.
- Stress Amplitude
- Half the cyclic stress range. Sa = (Smax-Smin)/2.
- Mean Stress
- Average stress. Sm = (Smax+Smin)/2.
- Low Cycle Fatigue
- <10,000 cycles with plastic deformation.
- High Cycle Fatigue
- 10K-1M cycles with elastic behavior.
- Goodman Diagram
- Mean stress effects on fatigue life.
- Miner Rule
- Cumulative damage: sum ni/Ni = 1.
Authoritative References
Trusted sources and standards referenced by this calculator.
Applicable Standards
ASTM E466ASTM E647Eurocode 3 Part 1-9ASME BPVC Section VIII
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Page Information
Last Updated:
2025-08-21
Version:
2.0.0
License:
Free to use for educational and professional purposes.