A33 Failures due to cyclic fatigue

Topic

The insect wing is perhaps the structure most subject to cyclic fatigue—a phenomenon involving the accumulation of material damage under repeated loading, even when each individual load remains well below the material's yield strength. An insect wing undergoes millions of these flexion cycles during its lifespan; for instance, a fly living just thirty days—flapping its wings at two hundred cycles per second—accumulates around five hundred million flexion cycles before dying.

The relationship between the stress sustained by the material in each cycle and the number of fatigue cycles it can withstand before failure is described by the Wöhler curve: the greater the stress amplitude applied during each wing-flexion cycle, the fewer cycles the material can tolerate before failing due to fatigue.

However, insect wings rarely flap with a constant stress amplitude cycle after cycle; instead, the actual flight load varies continuously depending on the insect's speed and maneuvers. Miner's rule allows for the estimation of accumulated wing damage in such scenarios by summing the damage contribution of each individual cycle, even when stress amplitudes differ from one cycle to the next.

In addition to cycle amplitude, another factor affects accumulated wing damage: the mean stress around which each loading cycle oscillates. The Goodman diagram accounts for the effect of this mean stress on the wing's fatigue life: the higher the tensile component of the mean stress to which the wing is subjected, the shorter its fatigue life. Within the wing, it is the wing joints that bear the brunt of this damage: any sharp notch in a joint concentrates stress so intensely that the actual stress experienced by the material at that point can be three to five times greater than the nominal stress calculated without accounting for such concentration. This greatly amplified actual stress drastically shortens the joint's fatigue life because—according to the Wöhler curve—higher stress always implies fewer tolerable cycles before failure.

To counter this risk concentrated at the wing joints, insect wings have evolved specific microstructures within these joints that distribute damage rather than allowing it to concentrate at a single point, while also preventing any incipient cracks from propagating. Thanks to these microstructures, the insect wing is able to withstand the hundreds of millions of flexion cycles required during its lifespan, even though, without this defense, each individual joint would be the weakest point of the entire wing.

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