Fatigue Life Estimator — S-N Curve

Estimate a modified endurance limit and a high-cycle fatigue life for steel under constant-amplitude, fully reversed loading. Enter stress amplitude, tensile strength and five modifying factors, then compare the result with the interactive S–N graph. This is an approximate steel model for preliminary assessment; material-specific fatigue data are needed for a design life prediction.

What is fatigue life?

Fatigue life is the total number of load cycles a part can take before a crack forms and grows enough to cause a break. The S-N curve is a chart that relates the stress level to how many cycles to failure, so you can estimate service life for a given set of real stresses.

Simple Explanation

Repeated bending can eventually break a paperclip. That illustrates cyclic damage, but severe paperclip bending involves plastic strain and is not the high-cycle elastic model used here. An S–N curve describes how stress amplitude relates to fatigue life under stated test conditions.

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S-N Curve and Fatigue Loading Diagram

Fatigue Life Calculator - S-N Curve

How to Use This Calculator

1. Enter the Alternating Stress (σₐ) and Ultimate Tensile Strength (Sut) for steel in the selected units. Use the same units for both stresses; the unit selector converts entered values.
2. Set the five modifying factors — surface, size, load, temperature and reliability — from suitable fatigue data. Each must be greater than zero and no greater than 1.
3. Use Try Example to load and calculate the worked example below.
4. Click Calculate to see your result.

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Mathematical Equations

Modified endurance limit

For this approximate steel model, stresses are converted to MPa internally:

S′_e = min(0.5 S_ut, 700 MPa)
S_e = k_a k_b k_c k_d k_e S′_e

S_ut is ultimate tensile strength. The five dimensionless factors account for surface condition, size, loading, temperature and reliability. Enter factors greater than zero and no greater than 1 for this reduction-factor model. They modify the endurance limit, not the applied stress.

Finite-life S–N segment

The curve joins an approximate stress of S_t = 0.9 S_ut at 1,000 cycles to the modified endurance limit S_e at 1,000,000 cycles. It is a straight line on log–log axes; its slope changes when the modifying factors change.

b = log₁₀(S_e/S_t) / 3
σ_a = S_t (N/1,000)^b
N = 1,000 (σ_a/S_t)^1/b

Here σ_a is stress amplitude and N counts complete cycles. The finite-life equation is used only when S_e < σ_a ≤ S_t. At or below S_e, the idealized curve has no finite-life intersection. Above S_t, the calculator reports that the loading is outside its high-cycle range.

How this relates to Basquin’s equation

With material-specific fatigue coefficients, Basquin’s equation is σ_a = σ′_f(2N)^b, so N = ½(σ_a/σ′_f)^1/b. The quantity 2N counts reversals, not complete cycles. This calculator uses the two-point approximation above rather than measured σ′_f and b for a particular alloy.

Worked Example — Try Example

Use σ_a = 300 MPa, S_ut = 800 MPa, k_a = 0.85, k_b = 0.90, k_c = 1, k_d = 1 and k_e = 0.95. These illustrative factors describe a reduced bending endurance limit; choose factors from data for your actual component.

• S′_e = 400 MPa.
• S_e = 0.85 × 0.90 × 1 × 1 × 0.95 × 400 = 290.7 MPa.
• S_t = 0.9 × 800 = 720 MPa; b ≈ −0.131296.
• N = 1,000 × (300/720)^1/b ≈ 786,750 cycles.

The interactive graph starts with the same example. Its “Combined factors” slider is the product k_c × k_d × k_e; here that product is 0.95. The form and graph have independent inputs but use the same equations.

Below the endurance limit

With S_ut = 600 MPa and all five factors equal to 1, S_e = 300 MPa. An amplitude of 200 MPa is below that plateau, so the model does not predict a finite failure cycle count. It does not establish an unlimited real service life.

Understanding Fatigue Life and S–N Curves

Repeated loading can initiate and grow fatigue cracks even when the peak stress is below the material’s yield strength. An S–N curve relates stress amplitude to the number of cycles reaching a specified fatigue-failure criterion. Its accuracy depends on material test data and how closely the test conditions match the component.

Loading assumptions

This estimator assumes constant-amplitude, fully reversed loading: the stress varies from −σ_a to +σ_a, with zero mean stress. The amplitude is half the stress range, not the full peak-to-peak range. A one-direction load that varies from zero to a maximum has a nonzero mean stress and needs a suitable mean-stress correction before using a fully reversed curve.

The 1,000-cycle and 1,000,000-cycle anchors are approximate steel reference points, not universal boundaries for every alloy or loading mode. Significant cyclic plasticity needs a strain-life analysis. Welded details, corrosive environments, variable-amplitude loading and multiaxial stresses need appropriate material and design methods rather than this simple curve.

Choosing modifying factors

• Surface, k_a: use data for the actual finish and material strength. A rough surface can lower endurance strength.
• Size, k_b: use a relation appropriate to the section and loading. Bending size corrections are not automatically applicable to axial loading.
• Load, k_c: the rotating-beam reference is bending, commonly assigned 1. Approximate Marin factors often use 0.85 for axial loading and 0.59 for torsion. A load factor alone does not validate the complete finite-life curve for a different stress state.
• Temperature, k_d: account for operating temperature using suitable material data. This tool accepts reduction factors only.
• Reliability, k_e: select from the fatigue-data convention you are using. This factor does not provide a confidence interval for the displayed life estimate.

Applying the result to an actuator mechanism

Start with the alternating stress at the location being assessed, including a suitable fatigue stress-concentration treatment. Actuator thrust alone is not a stress value: the section, load path, bending and local geometry matter. Check maximum stress and yielding separately. Bearings, gears, screws and welded joints can require their own fatigue-life methods, so this component estimate is not an actuator service-life rating.

Design checks and testing

Improve a fatigue-sensitive detail by reducing local stress, smoothing abrupt section changes or selecting a better-supported material and finish. Validate the load spectrum and inspect the effects of corrosion, temperature and manufacturing variation. Use the safety margins and fatigue method required by the applicable design standard; a stress safety factor and a life multiplier are not interchangeable. Safety-critical designs need qualified engineering review and appropriate testing.

Method references

• COMSOL: Stress-Life Models — Basquin notation and approximate steel S–N anchors.
• Union College: Fatigue Review II — steel specimen endurance estimates and modifying factors.

Frequently Asked Questions

What is the difference between fatigue life and static strength?

Static strength concerns a single loading event. Fatigue life concerns repeated stress cycles and a specified fatigue-failure criterion. A component can fail from fatigue at stresses below its yield strength, so both checks can be necessary.

How accurate is this fatigue-life estimate?

This is an approximate steel curve built from tensile strength and modifying factors, not a fit to test data for your alloy. It has no guaranteed error band. Use material-specific fatigue data and representative component tests when a life prediction is needed for design.

What does no finite life predicted mean?

The entered amplitude is at or below the modeled endurance plateau, so the idealized curve has no finite-life intersection. It does not guarantee unlimited service life. Corrosion, variable loading, mean stress, defects and other damage mechanisms can invalidate that assumption.

How do I choose the modifying factors?

Use a consistent fatigue reference and material data for the surface finish, section size, loading, temperature and reliability. All five factors must be greater than zero and no greater than 1 in this reduction-factor calculator. The graph combines the load, temperature and reliability factors into one product.

Can I use this calculator for aluminum or other materials?

No. The implemented endurance estimate and reference anchors are a steel approximation. Many aluminum alloys do not show an endurance plateau. Use an appropriate measured S–N curve or a material-specific fatigue method for other materials.

Does the calculator include mean stress or a safety factor?

No. It assumes fully reversed, constant-amplitude loading with zero mean stress. Apply a justified mean-stress treatment when needed, check yielding separately, and use the safety margins required by your design standard. Changing a modifying factor is not a substitute for those checks.

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