Fatigue Life Simulator
S-N Curve • Goodman Diagram • Marin Factors • Basquin Equation — Simulate • Explore • Practice • Quiz
Input Parameters
1 Overview
The Fatigue Life Simulator predicts component fatigue behaviour using the S-N curve (Basquin’s equation), Goodman diagram, and Marin correction factors. It supports 6 materials, 4 surface finishes, adjustable stress concentration (Kt), notch sensitivity (q), reliability levels, and temperature effects. The simulator plots both the S-N curve and the Goodman/Soderberg/Gerber failure criteria simultaneously.
Fatigue failure accounts for an estimated 80–90% of all structural failures in service. Unlike static overload, fatigue occurs at stress levels well below the ultimate tensile strength under repeated cyclic loading. The endurance limit (Se) is the stress amplitude below which a steel component can theoretically survive infinite cycles. This simulator helps you understand how material, geometry, surface finish, and loading conditions affect Se and fatigue life.
2 Getting Started
The simulator opens in Simulate mode with Steel 1020, machined surface, σm = 100 MPa, σa = 120 MPa, 30 mm diameter, 25°C, 90% reliability, Kt = 1.5, and q = 0.8. The canvas displays two diagrams: the S-N curve (stress amplitude vs. cycles on log scale) and the Goodman diagram (σa vs. σm with Goodman, Soderberg, and Gerber lines).
Below the canvas, readout cards show the corrected endurance limit Se, individual Marin factors (ka through ke), predicted life in cycles, safety factors for each criterion, and the operating point on the Goodman diagram. Adjust any input slider or dropdown to see instant updates.
3 Simulate Mode
Select a Material from 6 options (Steel 1020, Steel 4140, Steel 4340, Al 6061-T6, Al 7075-T6, Ti-6Al-4V), each with specific Sut and Sy values. Choose a Surface Finish (Ground, Machined, Hot-rolled, Forged) to set the Marin surface factor ka.
Set the Mean Stress σm (0–500 MPa) and Stress Amplitude σa (10–500 MPa) using sliders. Adjust Diameter (5–150 mm) for the size factor kb, Temperature (20–700°C) for kd, Reliability (50–99.9%) for kc, and Stress Concentration Kt with Notch Sensitivity q for ke.
The corrected endurance limit is Se = ka × kb × kc × kd × ke × Se′, where Se′ = 0.5 × Sut for steels (capped at 700 MPa). The operating point (σm, σa) is plotted on the Goodman diagram — if it falls inside the safe region, the component has infinite life; if outside, the predicted number of cycles to failure is computed from the S-N curve.
4 Explore Mode
Explore mode presents concepts in four categories: Fundamentals (fatigue mechanism, crack initiation and propagation, endurance limit), S-N Curve (Basquin’s equation, low-cycle vs high-cycle fatigue, endurance limit for steels vs aluminium), Mean Stress (Goodman, Soderberg, Gerber criteria, comparison of conservatism), and Design Factors (Marin factors ka–ke, Miner’s rule for variable amplitude, safe-life vs damage-tolerance design).
Each concept includes a formula card and worked example. Pay special attention to the distinction between steels (which have a true endurance limit) and aluminium alloys (which do not — they continue to lose strength at higher cycles).
5 Practice & Quiz
Practice mode generates random fatigue problems. You might be asked to calculate the corrected endurance limit, find the Goodman safety factor, or predict cycles to failure. Enter your answer, click Check Answer, and review the step-by-step solution. Click Next Problem for another challenge. Your running score is tracked.
Quiz mode presents 5 multiple-choice questions covering S-N curve interpretation, mean stress effects, Marin factor application, and fatigue life prediction. After completing all questions, a detailed result panel shows your score with a star rating and per-question review.
6 Tips & Best Practices
- For steels with Sut ≤ 1400 MPa, the uncorrected endurance limit is Se′ ≈ 0.5 × Sut. Above 1400 MPa, cap Se′ at 700 MPa.
- The Goodman criterion (σa/Se + σm/Sut = 1/n) is the most commonly used mean-stress criterion in industry.
- Soderberg is more conservative (uses Sy instead of Sut), while Gerber fits experimental data better for ductile metals.
- Surface finish has a huge impact: a forged surface can reduce Se by 50% or more compared to a ground surface.
- The fatigue stress concentration factor Kf = 1 + q(Kt − 1). Lower notch sensitivity q reduces the effect of geometric stress raisers.
- Miner’s rule for variable amplitude: failure occurs when Σ(ni/Ni) = 1. Each stress level consumes a fraction of total life.
- Try increasing the temperature above 450°C and observe how kd drops sharply — high-temperature fatigue strength is significantly lower.
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: σa = 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 = ka × kb × kc × kd × ke × Se'. The surface factor (ka) accounts for roughness — a forged surface may reduce fatigue strength by 50% compared to a polished specimen. The size factor (kb) reflects that larger components have more potential crack initiation sites. Reliability (kc), temperature (kd), 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 (σa/Se + σm/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(ni/Ni) 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.