BIZOMAT MAKEOS · Strength
Fatigue Life from the S-N Curve (Steel)
How many cycles will this steel part survive at this alternating stress?
Estimated cycles to failure for a fully reversed (or equivalent) alternating stress from a Basquin S-N line between 10³ cycles and the corrected endurance limit at 10⁶ cycles.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Alternating stress (fully reversed equivalent) | MPa | Alternating stress amplitude, including Kf; convert mean stress effects first (e.g. with the Goodman relation). |
| Tensile strength | MPa | Ultimate tensile strength. |
| Corrected endurance limit | MPa | Endurance limit corrected for surface, size, load, temperature and reliability. |
| Fatigue strength fraction at 10³ cycles | Fraction of Su reached at 1000 cycles (about 0.9 for steels below 500 MPa, falling for stronger steels). | |
| Required life | cycles | Number of cycles the part must survive. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Alternating stress (fully reversed equivalent)
- What it is
- The amplitude of the alternating stress (half the peak-to-peak range) at the critical point, already multiplied by the fatigue notch factor and converted to a fully reversed equivalent if there is a mean stress.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 100000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 300 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Life falls steeply as the stress amplitude rises; at or below the endurance limit it is taken as unlimited.
- Get it right
- Use the amplitude, not the full range; a stress swinging between +100 and −100 MPa has an amplitude of 100 MPa.
What this means: Tensile strength
- What it is
- The ultimate tensile strength of the steel from the certificate or specification. With the fraction below it fixes the top end of the S-N line at a thousand cycles.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 100000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 700 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use tensile strength, not yield strength.
What this means: Corrected endurance limit
- What it is
- The endurance limit of the part, meaning the stress it can withstand for a million cycles, after correction for surface finish, size, load type, temperature and reliability.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 100000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 250 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the corrected value for the part, not the polished test-specimen limit; the corrections usually lower it substantially.
What this means: Fatigue strength fraction at 10³ cycles
- What it is
- The fraction of tensile strength that the steel can withstand for a thousand cycles. It fixes the high-stress end of the S-N line and comes from fatigue data or your design text.
- Units and format
- Enter a plain number with no unit. The form accepts 0.5 to 1. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.9 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Type it as a fraction, not a percentage.
What this means: Required life
- What it is
- The number of load cycles the part must survive in service, from the design life and the number of cycles per hour, day or operation.
- Units and format
- Enter a number in cycles: cycles. The form accepts 1 cycles or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100000 cycles as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Count load cycles, not machine revolutions, unless each revolution is one cycle of stress.
Method and formulas
- Line through (10³, f Su) and (10⁶, Se) on log axes: σ = a N^b.
- a = (f Su)² ÷ Se; b = −(1/3) log₁₀(f Su ÷ Se).
- N = (σa ÷ a)^(1/b); below Se the life is taken as unlimited.
- Example: 300 MPa alternating in 700 MPa steel gives about 255,980 cycles.
Limitations
- Approximate S-N estimate for steels; scatter is large, so apply a life factor.
- Above about 10³ cycles only; low-cycle fatigue needs strain-life methods.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Estimate the life of a part loaded above its endurance limit
- Find the stress allowed for a required number of cycles
- Compare design options for limited-life parts
Who it is for
- Design engineers
- Structural and mechanical engineers
- Engineering students
What you get
- Estimated cycles to failure
- Stress allowed for the required life
- Basquin constants
Interpreting the result
- Fatigue life is very sensitive to stress: 10% less stress can mean several times more life.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 200–211, 358. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
Finite life and mixed loads
In Metal Fatigue by the Numbers
What it covers: How to estimate the life of a part stressed above its endurance limit from an S-N line, add up mixed loads with Miner's rule, and why averaging stresses hides the damage.
Method explained here · BIZOMAT original book
Fatigue under random loading
In Random Vibration by the Numbers
What it covers: From RMS stress to fatigue life: the S–N line, Miner's rule with three bands and with the Rayleigh distribution, and how the endurance limit assumption swings the predicted life.
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