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Combined weakest link and random defect model for describing strength variability in fibres

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Abstract

A mathematical model which describes the strength variability along the length of a fibre was developed. The model is a combination of the modified weakest link and random defect models. This combined model describes very well the strength variability data of aramid fibres.

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Abbreviations

L :

Specimen length

F(s) :

Cumulative frequency distribution of link strengths

1 — F(s) :

Survival function of a link

F L(s):

Cumulative frequency distribution of strengths of a specimen of length L

1 — F L(s):

Survival function of a specimen of length L

s :

Strength variable

s 0 :

Fibre defect-free strength for a random defect or combined model

s 1, s 2...:

Fibre strength at the point of a defect

s 1′, s 2′ ...:

Strength a fibre must have at the location of the defect to have a strength of s at the location of the defect

λ:

Length of a hypothetical link in a weakest link model

ϱ2, ϱ2 ...:

Defect frequencies (mean number per unit length)

v 1, v 2 ...:

Defect severities, 0 ≦ v ≦ 1

ϱ(s):

Defect frequency distribution function defined in terms of the strength at the defect

ξ(v):

Defect frequency distribution function defined in terms of the defect severity

α, β :

Defect frequency distribution parameters (Equation 14)

a, b :

Weibull distribution parameters (Equation 4)

P(m) :

Probability that m defects will occur in a given specimen length

m :

Number of defects occurring

¯s :

Mean strength

CV :

Coefficient of variation of strength

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Authors and Affiliations

  1. Fibers Research Division, E. I. DuPont De Nemours & Co. Inc., 23261, Richmond, Virginia, USA

    W. F. Knoff

Authors
  1. W. F. Knoff
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Knoff, W.F. Combined weakest link and random defect model for describing strength variability in fibres. Journal of Materials Science 28, 931–941 (1993). https://doi.org/10.1007/BF00400876

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  • DOI: https://doi.org/10.1007/BF00400876

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