Stereological measurement and error estimates for three‐dimensional fiber orientation

Randy S. Bay, Charles L. Tucker

Research output: Contribution to journalArticlepeer-review


A method is presented for measuring three‐dimensional fiber orientation in fiber‐reinforced polymers and placing confidence limits on the results. The orientations of individual fibers are determined from the elliptical intersections between the cylindrical fibers and a polished section. This can be done using either manual digitization or automated image analysis. Volume averages for the sample are computed using an orientation‐dependent weighting function that corrects for the bias of an area‐based sample. Equations are developed for nonuniform fiber lengths, using both number‐average and weight‐average measures of orientation. Sources of systematic, measurement, and sampling error are discussed and equations for sampling error and the propagation of measurement error are derived. The results use a second‐rank tensor to characterize fiber orientation, but the error analysis can be applied to any type of orientation parameter. We implement the technique using manual digitization of optical micrographs. Our implementation accurately measures samples with known orientation, and produces identical results from two perpendicular sections of a glass fiber/nylon injection‐molded sample.

Original languageEnglish (US)
Pages (from-to)240-253
Number of pages14
JournalPolymer Engineering & Science
Issue number4
StatePublished - Feb 1992
Externally publishedYes

ASJC Scopus subject areas

  • General Chemistry
  • Polymers and Plastics
  • Materials Chemistry


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