What is an S-N curve and how is it used in fatigue analysis?

An S-N curve (Wohler curve) plots stress amplitude versus the number of cycles to failure on a log-log scale. It is used to predict the fatigue life of components under cyclic loading. The curve follows Basquin's equation: sigma_a = sigma'_f (2N)^b, where sigma'_f is the fatigue strength coefficient and b is the fatigue strength exponent.

What is the difference between Goodman, Soderberg, and Gerber criteria?

All three criteria account for mean stress effects on fatigue. Goodman uses a linear relationship between stress amplitude and mean stress (sigma_a/Se + sigma_m/Sut = 1/n). Soderberg is more conservative, replacing Sut with yield strength Sy. Gerber uses a parabolic relationship with (sigma_m/Sut)^2, which fits experimental data better for ductile materials.

How do Marin factors modify the endurance limit?

Marin factors adjust the laboratory endurance limit to real-world conditions: ka (surface finish: ground, machined, hot-rolled, forged), kb (size: larger parts have lower fatigue strength), kc (reliability: higher reliability requires lower allowable stress), kd (temperature: reduced strength above 450 deg C), and ke (stress concentration via Kf). The corrected endurance limit is Se = ka x kb x kc x kd x ke x Se'.

Fatigue Life Simulator

S-N Curve • Goodman Diagram • Marin Factors • Basquin Equation — Simulate • Explore • Practice • Quiz

Mode

Input Parameters

Material

Surface Finish

Mean Stress (σm) 100 MPa

Stress Amplitude (σa) 120 MPa

Diameter 30 mm

Temperature 25 °C

Reliability

Stress Concentration Kt 1.5

Notch Sensitivity q 0.8

Understanding Fatigue Life Analysis — S-N Curves, Goodman Diagrams & Endurance Limits

Fatigue failure is one of the most common causes of mechanical component failure in service, responsible for an estimated 80-90% of all structural failures. Unlike static overload, fatigue occurs under cyclic loading at stress levels well below the material's ultimate tensile strength. This free interactive fatigue life simulator lets you explore S-N curves, Goodman diagrams, Marin correction factors, and multiple mean-stress criteria to predict whether a component will survive its intended service life.

The S-N Curve and Basquin's Equation

The S-N curve (also called a Wohler curve) is the foundation of fatigue analysis. It plots stress amplitude on the vertical axis against the number of cycles to failure (N) on a logarithmic horizontal axis. In the high-cycle fatigue regime, this relationship follows Basquin's equation: σ_a = σ'_f (2N)^b, where σ'_f is the fatigue strength coefficient and b is the fatigue strength exponent (typically -0.05 to -0.15). For steels, an important feature is the endurance limit (Se') — a stress level below which the material can theoretically endure infinite cycles. For Sut ≤ 1400 MPa, Se' ≈ 0.5 × Sut.

Marin Correction Factors

The laboratory endurance limit must be corrected for real-world conditions using the Marin equation: Se = k_a × k_b × k_c × k_d × k_e × Se'. The surface factor (k_a) accounts for roughness — a forged surface may reduce fatigue strength by 50% compared to a polished specimen. The size factor (k_b) reflects that larger components have more potential crack initiation sites. Reliability (k_c), temperature (k_d), and miscellaneous factors including stress concentration (Kf) further modify the allowable endurance limit.

Mean Stress Effects: Goodman, Soderberg & Gerber

Most real-world loading involves a non-zero mean stress. The Goodman criterion (σ_a/Se + σ_m/Sut = 1/n) provides a linear, moderately conservative prediction. Soderberg replaces Sut with Sy for greater conservatism, while Gerber's parabola fits experimental data more accurately for ductile metals. This simulator plots all three criteria simultaneously, allowing direct comparison of safety factors for any operating condition.

Cumulative Damage and Miner's Rule

When components experience variable-amplitude loading, Miner's rule predicts failure when the cumulative damage fraction D = Σ(n_i/N_i) reaches 1.0. Each load level consumes a fraction of the total fatigue life. This simple linear damage model, while not perfect, remains the most widely used method in engineering practice for variable loading fatigue analysis.

Who Uses This Simulator?

This fatigue life simulator is designed for mechanical engineering students, design engineers, materials science students, and technical education instructors. It is ideal for learning fatigue analysis concepts, verifying hand calculations, exploring the effect of design parameters on component life, and preparing for examinations on machine design and strength of materials.

Explore Related Simulators

If you found this fatigue life simulator helpful, explore our Stress-Strain Diagram Trainer, Mohr's Circle Simulator, Stress Concentration Simulator, and Shaft Torsion Simulator for more hands-on practice.