Session X22: Focus Session: Deformation and Fracture

8:00 AM–10:36 AM, Friday, March 9, 2007
Colorado Convention Center Room: 108

Sponsoring Units: GSNP DMP
Chair: Ian Robertson, University of Illinois at Urbana-Champaign

Abstract ID: BAPS.2007.MAR.X22.9

Abstract: X22.00009 : String breaking and the Petersburg Paradox

10:00 AM–10:12 AM

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  Jake Fontana
    (Liquid Crystal Institute, KSU)

  Peter Palffy-Muhoray
    (Liquid Crystal Institute, KSU)

The Petersburg Paradox(1) provides a simple paradigm for systems that show critical sensitivity to rare events. The breaking strength of filaments, yarns and strings is determined by the presence of defects. In a given sample, the largest defect determines the stress at which failure occurs, and since the defect distribution is a function of sample size, the breaking strength of strings depends on their length. Analogy with the Petersburg paradox suggests that the breaking strength should vary approximately linearly with the logarithm of the length. We have carried out experiments to measure the breaking strength of samples of polyester sewing thread and of monofilament fishing line ranging in length from \textit{1mm} to \textit{1km}. We describe our experiments, present the results, and, compare fits of our data to Weibull and mean field failure statistics and the predictions from analogy with the Petersburg Paradox. 1. I. Todhunter, \textit{A History of Mathematical Theory of Probability}, (Chelsea, New York, 1949)

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