A2 Fiber Fracture and Bundle Strength

Topic

The strength of an individual fiber within this bundle is not a single value but follows a Weibull distribution; much like the strength of a monolithic ceramic—already established in another model in this set—the strength of each fiber varies according to this distribution because each contains internal defects whose size and location cannot be predicted beforehand. Because these defects are unpredictable, fiber strength cannot be described by a single value but must instead be characterized by that same Weibull distribution. To describe this variability, the model employs the same Weibull distribution used for the same purpose in the model describing the brittle fracture of the monolithic ceramic.

However, this Weibull distribution for the individual fiber is not fixed; the length-scale effect—also adopted from the monolithic ceramic's brittle fracture model—modifies the fiber's expected strength based on its length. A longer fiber contains a greater number of potential internal defects along its length, resulting in lower expected strength; conversely, a shorter fiber contains fewer potential defects, resulting in higher expected strength.

The fact that each individual fiber in the bundle possesses its own strength—distributed according to Weibull and modified by length—determines the strength of the entire fiber bundle, in accordance with Daniels' theory: when a fiber in the bundle breaks, the load it was carrying does not vanish but is redistributed among the neighboring fibers that have not yet failed. This redistribution of load among the surviving fibers means that each individual break increases the load borne by the remaining fibers, until the number of broken fibers reaches a point where the remaining ones can no longer support the redistributed load. The strength of the entire fiber bundle is precisely the load at which this collective failure occurs.

For this reason, the model—which incorporates the distributed strength of the individual fiber—determines the strength of the entire bundle through a combination of three elements: the Weibull distribution and the length-scale effect (both adapted from the model describing brittle fracture in monolithic ceramics), and the load redistribution among surviving fibers (as described by Daniels' theory).

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