A1 Fatigue

Topic

Under a repeatedly applied cyclic load, this metal can fail progressively even when the load amplitude remains well below the static yield stress established by another model in this set; this progressive failure under cyclic loading—distinct from the static yielding that would occur under a sustained load of the same magnitude—constitutes fatigue in the metal. The repeated nature of this cyclic loading—even though individual cycles fall far below the static yield stress—eventually nucleates a fatigue crack at some point within the metal, a result that a single cycle of the same amplitude would never produce.

Once the fatigue crack has nucleated, the stress amplitude of the continuing cyclic load determines—according to Basquin's relation—how many load cycles the metal will withstand before failing due to fatigue (its fatigue life). A higher stress amplitude results in a shorter fatigue life, while a lower stress amplitude results in a longer fatigue life.

Once nucleated, the fatigue crack does not grow at a constant rate during each load cycle; instead, its growth is governed by the stress intensity factor range of each cycle, as described by Paris's Law: the greater the stress intensity factor range (between the minimum and maximum of each cycle), the further the fatigue crack advances during that cycle. A larger stress intensity factor range—whether due to higher load amplitude or because the crack has already grown sufficiently—results in a higher crack propagation rate, in accordance with Paris's Law. For this reason, the model—accounting for the cyclic loading and the initial fatigue crack—integrates Paris's Law across the entire course of crack growth, from the size at nucleation to the critical size at which the metal ultimately fractures, in order to determine the propagation life leading up to that final failure. While the Basquin relationship estimates the metal's total fatigue life based on stress amplitude—without distinguishing between the nucleation and propagation stages—this integration of Paris's Law specifically isolates the propagation stage once the fatigue crack has already formed. The fact that the critical crack size (at which final fracture occurs) depends on the metal's fracture toughness allows another model in this set to experimentally correlate that same toughness with Charpy test results for the metal. Furthermore, the fact that the fatigue behavior is dominated by a single crack—which nucleates, grows, and ultimately causes the part to fracture—clearly distinguishes it from the fatigue of composite materials, where progressive degradation under cyclic loading is governed by damage distributed across many points simultaneously, rather than by a single dominant crack.

ID:4440