Combined weakest link and random defect model for describing strength variability in fibres
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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.
KeywordsPolymer Mathematical Model Material Processing Combine Model Defect Model
Cumulative frequency distribution of link strengths
- 1 — F(s)
Survival function of a link
Cumulative frequency distribution of strengths of a specimen of length L
- 1 — FL(s)
Survival function of a specimen of length L
Fibre defect-free strength for a random defect or combined model
- s1, s2...
Fibre strength at the point of a defect
- s1′, s2′ ...
Strength a fibre must have at the location of the defect to have a strength of s at the location of the defect
Length of a hypothetical link in a weakest link model
- ϱ2, ϱ2 ...
Defect frequencies (mean number per unit length)
- v1, v2 ...
Defect severities, 0 ≦ v ≦ 1
Defect frequency distribution function defined in terms of the strength at the defect
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)
Probability that m defects will occur in a given specimen length
Number of defects occurring
Coefficient of variation of strength
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