Chapter 54. Why it is Necessary to Determine Each Fiber Diameter when Estimating the Parameters of the Distribution of Fiber Strengths

  1. Ersan Ustundag and
  2. Gary Fischman
  1. Edgar Lara-Curzio and
  2. Christiana M. Russ

Published Online: 26 MAR 2008

DOI: 10.1002/9780470294567.ch54

23rd Annual Conference on Composites, Advanced Ceramics, Materials, and Structures : A: Ceramic Engineering and Science Proceedings, Volume 20, Issue 3

23rd Annual Conference on Composites, Advanced Ceramics, Materials, and Structures : A: Ceramic Engineering and Science Proceedings, Volume 20, Issue 3

How to Cite

Lara-Curzio, E. and Russ, C. M. (1999) Why it is Necessary to Determine Each Fiber Diameter when Estimating the Parameters of the Distribution of Fiber Strengths, in 23rd Annual Conference on Composites, Advanced Ceramics, Materials, and Structures : A: Ceramic Engineering and Science Proceedings, Volume 20, Issue 3 (eds E. Ustundag and G. Fischman), John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9780470294567.ch54

Author Information

  1. Metals & Ceramics Division Oak Ridge National Laboratory Oak Ridge, TN 37831–6069

Publication History

  1. Published Online: 26 MAR 2008
  2. Published Print: 1 JAN 1999

ISBN Information

Print ISBN: 9780470375631

Online ISBN: 9780470294567

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Keywords:

  • diameters;
  • ceramic;
  • mechanical;
  • parameters;
  • mechanical properties

Summary

A Monte Carlo simulation was conducted to show that it is not appropriate to determine individual fiber strengths, and in turn, the parameters of the distribution of fiber strengths, by taking the ratio of the experimentally-determined breaking loads and the average cross-sectional area of the fibers. It is shown, for the case of fibers with strengths that are Weibull-distributed and with diameters that are Normal-distributed, that when individual fiber strengths are calculated using the average of the fibers cross-sectional area, the error in the estimation of the parameters of the strength distribution increases with the spread in the distribution of fiber diameters. It is shown that for values typical of some ceramic fibers, the Weibull modulus can be underestimated by as much as a factor of four.