Fatigue Life Estimator — S-N Curve

Mechanical parts often fail from repeated loading at stresses well below their yield strength. Predicting when that occurs isn't guesswork—it comes down to calculations. This Fatigue Life Estimator (S-N Curve) lets you determine a modified endurance limit and estimate cycles to failure based on alternating stress, tensile strength, and five straightforward modifier factors. It's important in applications like drivetrain components, aircraft structures, and actuator systems, where a missed fatigue estimate can lead to real-world failures. Below you'll find explanations for the Marin equation, Basquin's formula, a worked example, and an FAQ.

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

If you bend a paperclip back and forth, it won't snap on the first try. But if you keep at it, eventually it will break—no matter that you never pulled hard enough to straighten it. That's fatigue. The S-N curve is just a way of charting how many cycles at a given stress will cause that break.

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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 your material in MPa or psi.
2. Set the 5 modifying factors — Surface (kₐ), Size (kb), Load (kc), Temperature (kd), and Reliability (ke) — to match your real operating conditions.
3. Use the Try Example button to load a pre-filled steel shaft scenario if you want to see a working result first.
4. Click Calculate to see your result.

📹 Video Walkthrough — How to Use This Calculator

Mathematical Equations

Simple Example

Steel shaft with σₐ = 200 MPa, Sut = 600 MPa, all k-factors = 1.0:

• Se' = 0.5 × 600 = 300 MPa
• Se = 1.0 × 1.0 × 1.0 × 1.0 × 1.0 × 300 = 300 MPa
• σₐ (200 MPa) < Se (300 MPa) → Infinite life (> 10⁷ cycles)

Understanding Fatigue Life and S-N Curves

Fatigue failure is behind most unexpected breaks in mechanical parts—it's responsible for the majority of real-world failures. You need a practical way to estimate cycles to failure under repeated loads. The S-N curve and fatigue equations serve that purpose, using actual stress cycles and simple math instead of assumptions.

The Science Behind Fatigue Failure

Fatigue happens when a part gets loaded and unloaded many times, even at stresses well below the material's yield point. Cracks often start at stress risers or imperfections at the surface. Over time, the crack grows with each cycle until it finally fails.

The S-N curve plots the applied stress (amplitude) on the vertical and the log of cycles to failure along the horizontal. You'll see three basic regions on most S-N curves:

• Low Cycle Fatigue (LCF): High stresses, lower number of cycles (less than about 10⁴)
• High Cycle Fatigue (HCF): Moderate stresses, bigger cycle counts (~10⁴ to 10⁶)
• Infinite Life Region: Stresses below the endurance limit; parts can survive more than 10⁷ cycles so long as conditions don't change

Modifying Factors in Fatigue Analysis

Lab data usually overstates fatigue life compared to real world parts, mostly because test samples are smaller, smoother, and more carefully loaded. The analysis here applies simple modification factors to bring the calculation closer to field reality:

Surface Condition Factor (k_a)

Most fatigue cracks start at the surface. Polished samples hold up best (kₐ near 1.0); rough, as-forged parts drop as low as 0.4. With machined or peened surfaces, you see a wide range in between. The finish you get matters, especially in actuator rods or shafts.

Size Factor (k_b)

Larger parts tend to have lower fatigue strength since the odds of a flaw increase and the stress distribution isn't as favorable. For common shaft sizes, k_b can drop to 0.6, while small diameter parts get closer to 1.0.

Loading Factor (k_c)

The way the part is loaded affects fatigue. Pure axial loading usually gets k_c = 1.0. Bending is a bit harsher (about 0.9), and torsion is worse (around 0.58). Identify your real-world loading before setting this value.

Practical Applications and Real-World Examples

Suppose you're designing a connecting rod for an engine. It will see regularly-reversed loading at a few thousand RPM, racking up tens of millions of cycles per year. When you input typical values into the calculator:

Given Parameters:

• Alternating stress: 180 MPa
• Ultimate tensile strength: 600 MPa (decent steel)
• Surface factor k_a = 0.8 (machined)
• Size factor k_b = 0.85 (not tiny, not massive)
• Load factor k_c = 1.0 (tension/compression)
• Temperature factor k_d = 1.0 (ambient)
• Reliability factor k_e = 0.897 (90% reliability)

Calculation:

S_e' = 0.5 × 600 = 300 MPa
S_e = 0.8 × 0.85 × 1.0 × 1.0 × 0.897 × 300 = 183.2 MPa

With alternating stress (180 MPa) just under the endurance limit (183.2 MPa), you expect the part to last effectively forever (assuming simple, repeated cycles). Still, such a small margin leaves little room for mistakes or variable loads—reconsider the design if unplanned loads or surface finish could be worse.

Advanced Considerations for Linear Actuator Design

Fatigue in actuators isn't always straightforward. Loads might pulse, reverse, or vary with every cycle. Many actuators see millions of reversals in service:

• Lead Screw Fatigue: Screws take bending, not just tension. Watch alternating loads here.
• Housing Stress Concentrations: Bolt holes, shaft exits, or grooves can be fatigue hot spots.
• Bearing Fatigue: Bearings are their own category and take a different set of numbers to predict life.
• Gear Tooth Fatigue: In gear-driven systems, watch for root cracking in the teeth. It's often the limiting step.

Design Optimization Strategies

There are straightforward ways to improve fatigue life:

Stress Concentration Reduction

Adding fillets, rounding sharp changes, and generally smoothing out geometry helps a lot. Every notch increases local stress, so reduce them whenever possible and use these fatigue numbers to show the effect.

Surface Treatment

Processes like shot peening put compressive stresses at the surface. This can actually push k_a above 1.0 in rare cases. Hardening the surface also stops cracks from starting there.

Material Selection

Higher strength materials sometimes help, but don't count on tensile strength alone to solve fatigue issues. Look at the ratio of endurance limit to tensile strength (S_e/S_ut) for a clearer picture of real benefit.

Validation and Testing

No calculator replaces a real test for a mission-critical part. It's common to run accelerated fatigue tests at higher stress and then extrapolate to longer lives using the same basic formulas. This often uncovers failure modes you won't spot on paper.

Combining FEA (finite element analysis) with calculated S-N results can help spot risky locations before you even build a part. This approach is especially useful in actuators where load paths are complex and not always obvious.

Industry Standards and Safety Factors

Applying a safety factor is standard practice, especially in fatigue. Typical values run from 2 to 10, depending on how dangerous a failure would be, how well you know the loads, and how solid your material data is.

Standards like ASME and ISO provide guidelines here—review them for your application. In linear actuator assemblies, these references guide decisions for components meant to cycle millions of times without a surprise failure.

Frequently Asked Questions

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