The Poisson-Weibull Flaw Model for Brittle Fiber Strength

Howard M. Taylor
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Howard M. Taylor: University of Delaware, Department of Mathematical Sciences

A chapter in Extreme Value Theory and Applications, 1994, pp 43-59 from Springer

Abstract: Abstract The Weibull distribution with rate parameter α > 0 and shape paramenter σ > 0 is given by $$W(x;\alpha ,\sigma ) = 1\; - \;\exp \{ - \sigma {x^\sigma }\} \;,\;for\;x\; \geqslant \;0.$$ . The tensile strength S(t) of a single fiber of length t is often assumed to follow a Weibull distribution of the form W(x; αt, σ), where a and a are material constants. The explicit appearance of the length t in the rate parameter is an expression of a weakest-link size effect in which the fiber strength is viewed as the minimum strength of independent sections.

Keywords: Weibull Distribution; Flaw Model; Compete Risk Model; Weibull Plot; Weibull Shape Parameter (search for similar items in EconPapers)
Date: 1994
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4613-3638-9_3

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DOI: 10.1007/978-1-4613-3638-9_3

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