What is the shape of a bundle? An analysis of Rosen's fibrous composites experiments using the chain‐of‐bundles model

Abstract

In the 1960s, W. B. Rosen conducted some remarkable experiments on unidirectional fibrous composites that gave seminal insights into their failure under increasing tensile load. These insights led him to a grid system where the nodes in the grid were ineffective length fibers and to model the composite as something he called a chain‐of‐bundles model (i.e., a series system of parallel subsystems of horizontal nodes that he referred to as bundles), where the chain fails when one of the bundles fails. A load‐sharing rule was used to quantify how the load is borne among the nodes. Here, Rosen's experiments are analyzed to determine the shape of a bundle. The analysis suggests that the bundles are not horizontal collection of nodes but rather small rectangular grid systems of nodes where the load‐sharing between nodes is local in its form. In addition, a Gibbs measure representation for the joint distribution of binary random variables is given. This is used to show how the system reliability for a reliability structure can be obtained from the partition function for the Gibbs measure and to illustrate how to assess the risk of failure of a bundle in the chain‐of‐bundle model.

A Sketch of Some Stochastic Models and Analysis Methods for Fiber Bundle Failure under Increasing Tensile Load

“…Below is a summary of results from Sections 2 and 4 in Li et al (2018). In this formulation, let N = {1, .…”

“…The main finding of the analysis in Grego et al (see Figure 9 there) was that a Weibull with ρ = 5 and σ = 2 was a reasonable model for the lower tail of the component strength distribution of an ineffective length fiber. In Section 4.5, we discuss how Li et al (2018) use this information to see that a 4 × 4 grid is an appropriate size bundle to model Rosen's specimen data as a chainof-bundles model and to determine the Gibbs measure for the of this size. We also discuss their nonparametric estimation of the specimen breaking strength distribution for Rosen's 9 specimen breaking strengths.…”

“…On the other hand Hansen et al (2015)'s book is an excellent introduction to FBM's that is accessible to nonphysicists. The purpose of this sketch is not to give a comprehensive review of the literature (the latter two references and Li et al, 2018, are good sources to start this) but rather to sketch some research on load-sharing models and statistical analysis methods relevant for FBM's that have been overlooked by the physical science community. These are illustrated by summarizing the findings from Li et al (2018) regarding Rosen's Specimen A experiments and the necessary results needed for this.…”

Current Overview of Statistical Fiber Bundles Model and Its Application to Physics-based Reliability Analysis of Thin-film Dielectrics

“…This approach was used to determine the shape of a bundle in Li, Gleaton and Lynch (2019) where P bundle failed when there was a route/crack across bundle. This network model may also have implications for the reliability of certain types of nanosensors.…”