🚀 Fatigue Life Calculator & Simulator
- Enter Tensile Strength & Fatigue Modification Factors: Set the tensile strength (Sut) of the mechanical component and adjust the surface finish (ka), size (kb), and reliability (kc) modification factors according to the Marin equation format.
- Enter Alternating & Mean Stress Amplitudes: Specify the mean stress (σm) and the sinusoidal alternating stress amplitude (σa) acting during rotation.
- Monitor Real-Time Rotating Shaft Stress Behavior: Analyze the shaft fatigue model animation on the left, where the shaft rotates at high speed, repeatedly applying tensile and compressive stresses.
- Analyze S-N Diagram & Diagnose Fatigue Failure Cycles: Obtain precise computation results on the log-scale S-N curve on the right, determining whether the current operating principal stress state lies within the infinite life region (over 10⁶ cycles) or will reach failure (finite life failure) after a specific number of repeated cycles.
📚 Read Detailed Explanation on Mechanical Component Endurance Limit & S-N Curve ▼
1. Mechanical Fatigue Failure & The Influence of Mean Stress
Even if the load applied to a mechanical structural member is much lower than the material's yield strength, repeated application thousands to millions of times over a long period can initiate and propagate localized micro-cracks, leading to sudden and complete failure. This phenomenon is called Fatigue Failure. In reality, more than 80% of all mechanical component failures are attributed to fatigue.
The presence of mean stress (σ_m) under alternating stress drastically reduces the material's fatigue resistance. Tensile mean stress causes stress concentration that opens up cracks, accelerating fatigue crack propagation, whereas compressive mean stress tends to close cracks, thereby extending fatigue life.
2. Goodman and Gerber Fatigue Correction Equations
The Modified Goodman relation and the Gerber relation are representative failure envelope models used to correct the alternating stress limit when mean stress is present.
- Modified Goodman Diagram: A geometric linear model that guides conservative, safe design. It is most widely adopted in practical strength evaluation for its conservative nature.
σ_a / S_e + σ_m / S_ut = 1 / FS - Gerber Envelope: A parabolic curve model that closely fits the average of experimental data.
σ_a / S_e + (σ_m / S_ut)² = 1 / FS
Here, Se is the actual Modified Endurance Limit, corrected by multiplying various environmental factors.
3. S-N Curve and Basquin's High-Cycle Life Equation
A graph plotting the relationship between stress amplitude and the number of cycles to failure (Cycles, N) on a logarithmic scale is called an S-N Curve (Stress-Life Curve). Ferrous materials exhibit a unique characteristic where an Endurance Limit (or Fatigue Limit) appears—a threshold below which the material can theoretically withstand infinite cycles (typically over 10⁶ to 10⁷ cycles) without failing.
In the finite life region (10³ to 10⁶ cycles), the fatigue life is approximated by Basquin's Equation.
σ_rev = a × N^b → N = (σ_rev / a)^(1/b)
Here, σ_rev is the Goodman equivalent fully reversed stress amplitude (excluding mean stress), and the exponent b and constant a are derived from the slope intersecting the strength at 10³ cycles (0.9 Sut) and the endurance limit (Se). This equation forms the foundation of mechanical design for components requiring guaranteed infinite life, such as railway axles, shafts, and fan blades.