The Chain-of-Bundles Probability Model For the Strength of Fibrous Materials I: Analysis and Conjectures

Analytical results are discussed for the chain-of-bundles probability model for the strength of fibrous materials. Two load sharing rules are considered for failed and nonfailed fibers in a bundle. The first is the equal load sharing rule of classical analysis, and the second is a local load sharing rule which is more realistic for composite materials. A rather detailed discussion of past statistical analysis is given. From a careful study of previous results, several conjectures and key questions about the behavior of the strength are generated. Also, an exact analysis of failure is per formed so that the properties of the strength distribution can be studied. Difficulties of a general analysis are discussed in detail. The sequel will contain a thorough numerical investigation of the model with emphasis on studying the convergence of certain transformed distributions and on answering key questions raised in this study.