The Chain-of-Bundles Probability Model for the Strength of Fibrous Materials II: A Numerical Study of Convergence

Abstract

A thorough numerical investigation is conducted for the chain-of- bundles probability model. The emphasis is on studying the convergence of certain transformed distributions. Strong numerical evidence of con vergence is presented in support of a weakest link transformation for scal ing to large fibrous materials. Also, exact results are graphed for small bundles. The numerical results are discussed in light of the key questions and conjectures raised in the preceding paper of this series. For practical purposes the Weibull distribution may be used to represent the strength distribution of fibrous materials. The associated shape and scale parameter values for the fibrous material agree extremely well with those that are experimentally observed, as is shown in a specific example. The variability in strength is substantially reduced in passing from a single fiber to the fibrous material, but for customary specimen sizes, the median strength of the fibrous material is somewhat less than that of the fiber.