A3 Fatigue in Polymers (Hysteresis Heating)

Topic

The viscous component of this polymer—quantified by the loss factor described in greater detail by another model in this set—dissipates a characteristic amount of energy during each applied loading cycle. Under cyclic loading, the polymer does not deform and recover along the exact same stress-strain curve in both directions; instead, it traces a hysteresis loop between the loading and unloading phases of each cycle, and the area enclosed within that loop represents the energy dissipated during that cycle. A higher loss factor for the polymer results in greater energy dissipation per cycle for a given cyclic load amplitude.

The repetition of this energy dissipation—cycle after cycle at the frequency of the applied load—generates heat within the polymer: each additional loading cycle dissipates the same amount of energy as the previous one, and the accumulation of this repeatedly dissipated energy over time constitutes the rate of heat generation. For a constant amount of energy dissipated per cycle, a higher cyclic loading frequency results in a higher rate of heat generation, because the same amount of energy is dissipated more frequently per unit of time. Consequently, in this model—characterized by its viscous component and the initial heat generation rate—that very rate of heat generation raises the polymer's local temperature (provided the heat generated exceeds the material's capacity to dissipate it into the surroundings) to the point of causing local softening; this can lead to failure before any crack propagates significantly. Thus, this hysteresis-induced thermal fatigue contrasts with the fatigue described by models for other material classes—such as metals—where the dominant failure mechanism is the progressive growth of a single fatigue crack rather than hysteresis heating. The fact that the polymer dissipates—cycle after cycle—significantly more energy through hysteresis than a metal does under identical loading cycles causes this hysteresis heating mechanism, which is negligible in metals, to become the dominant fatigue mechanism in the polymer.

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