Influence of the sample number for the prediction of the tensile strength of high tenacity viscose fibres using a two parameters Weibull distribution
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The objective of this work is to determine an adequate number of samples for an accurate prediction of tensile strength of fibres using a Weibull distribution. Theory will be compared to experimental results in order to know the effect of experimental errors on the theoretical expectations. The diameter and strength distribution of high tenacity viscose were evaluated. The chosen Weibull distribution was with two parameters. First, the best probability estimator for Weibull was determined using a random selection of experimental datas. Then, in order to be able to predict the number of sample knowing the variation of the Weibull modulus m, different relationship between the coefficient of variation of m and the number of sample n were tested. The relationship CV = 0.78/\(\sqrt n\) presented good agreement with experimental datas. The influence of the variation of m on the predicted value of strength was studied in order to determine an adequate number of sample to obtain limited variation of the predicted strength. The last part focus on experimental verification of the points previously developed. It was shown that it is possible to determine the influence of the variation of the Weibull modulus on the predicted strength. However, no correlation was found between the variations of the Weibull modulus and the error on the predicted strength.
KeywordsRegenerated cellulose High tenacity viscose Weibull distribution Tensile strength prediction
The authors acknowledge Carnot Institute “MICA” for financial funding. The authors would like to thank the French National Association of Research and Technology (ANRT) for funding the research through the Ph.D. Grant awarded to B.P. Revol. The authors would also like to thank the reviewers for their useful comments which helped in improving this work.
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Conflict of interest
The authors declare that they have no conflict of interest.
- Joffe R, Andersons J, Spārniņš E (2009) Applicability of Weibull strength distribution for cellulose fibers with highly non-linear behaviour. In: ICCM 17, Edinburgh: 17th international conference on composite material. Edinburgh, UK. IOM communications, LondonGoogle Scholar
- Kelly A, Macmillan NH (1986) Strong solids. Clarendon, OxfordGoogle Scholar
- Ritter J, Bandyopadhyay N, Jakus K (1981) Statistical reproducibility of the dynamic and static fatigue experiments. Bull Am Ceram Soc 60:798–806Google Scholar
- Weibull W (1939) A statistical theory of the strength of materials. Ingeniörsvetenskapsakademiens Handligar 151:1–45Google Scholar
- Weibull W (1951) A statistical distribution function of wide applicability. J Appl Mech 18:293–297Google Scholar