Paris' law

Paris' law is an empirical relation that models fatigue crack growth rate as a power function of the range of stress intensity at a crack tip.

Stress-intensity factor: A fracture-mechanics quantity measuring the intensity of stress near a crack tip. Paris' law uses its range to represent the effect of cyclic loading.
Linear elastic fracture mechanics: The theory of crack behavior in materials whose response is predominantly elastic. It supplies the stress-intensity framework used by Paris' law.
Fatigue life prediction: The estimation of cycles or time until fatigue failure occurs. Integrating Paris' law estimates cycles spent in the crack-growth regime.
Paul C. Paris: An American engineer who developed the empirical fatigue crack-growth relation now known as Paris' law. His work established the power-law description of crack growth.
Fatigue crack growth: The progressive extension of a crack under repeated or fluctuating loads. Paris' law describes one regime of this broader process.
Stress intensity: A measure of the elastic stress field near a crack tip. The law's independent variable is derived from stress intensity.
Damage tolerance: An engineering approach that permits flaws while ensuring they remain detectable and safe before failure. Paris-law estimates help set inspection intervals for growing cracks.
Paris–Erdogan equation: A power-law equation relating fatigue crack growth per cycle to the range of stress intensity. The equation's name records Paris and Fatigue? Actually Erdogan's contribution to its development.
Crack-growth exponent: The exponent that determines how strongly crack-growth rate responds to stress-intensity-factor range. Its value sets the curvature and sensitivity of the Paris-law relation.
Load ratio: The ratio of minimum to maximum load, or corresponding stress, in a loading cycle. Crack growth at a given range can vary with this cycle parameter.

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