S N Curve
What are the axes on an S-N curve?
Cycles to failure N is plotted on the horizontal axis, and alternating stress amplitude S_a (or stress range) is plotted on the vertical axis, usually on logarithmic scales.
What is the stress ratio R in fatigue testing?
R is the ratio of minimum cyclic stress to maximum cyclic stress. Fully reversed loading corresponds to R = -1, while load-unload cycling without reversal gives R = 0.
Why do shop components sometimes fail below the design load?
Fatigue failure is driven by accumulated cyclic damage, stress concentrators, surface finish, geometry, residual stress, and vibration. These real-world modifiers shift the actual S-N behavior below the ideal lab curve, so nominal static load is not a reliable predictor.
An S-N curve, also called a Wöhler curve, plots cyclic stress amplitude against cycles to failure, commonly on log-log axes. It estimates how many load cycles a part can survive at a given stress level, or what stress level is allowable for a target life. It is the basis for fatigue-life prediction and cumulative damage methods such as Miner's Rule.
In CNC shops and fabrication cells, the S-N curve matters whenever hardware sees repeated loading rather than a single static load: rotating shafts, fixture clamps, welded brackets, machine frames, toolholders, robotic end-effectors, and press components. These parts experience vibration, bending, or alternating tension/compression over millions of cycles, so designers use the material's fatigue curve to match geometry and surface condition to the expected duty cycle. On the floor, fatigue validation compares actual service stress histories—spindle-induced vibration, cyclical clamping, slide actuation, oscillatory tooling loads—to the curve to estimate life. The curve is built from constant-amplitude test data and divided into low-cycle, finite-life, and high-cycle regions. For steels, modifiers for surface finish, size, load type, temperature, and reliability shift predictions away from the ideal lab curve, so machining quality and assembly detail directly affect fatigue life.
Surface damage from machining or fabrication: Tool marks, burrs, weld toe defects, and sharp transitions create local stress concentrators that initiate fatigue cracks far earlier than the nominal curve predicts. The part's real life drops below the S-N estimate.
Static strength substitution: A component can pass a single load test but fail under repeated bending or vibration because S-N behavior depends on cycles and stress amplitude, not just peak load. Fatigue strength, not yield strength, governs long-term survival.
Mismatched stress history: Constant-amplitude S-N data misleads when actual service involves variable loads, mean stress, overloads, or tension spikes. Without reducing the spectrum using a cumulative damage model like Miner's Rule, life predictions can be dangerously optimistic.