Characterizing the cross-sectional geometry of thin, non-cylindrical, twisted fibres (spider silk)

Quantitative tensile property evaluation of fibres requires accurate cross-sectional area measurement at a location close to the point of failure. Laser diffraction was evaluated as a non-destructive technique for characterizing the cross-sectional geometry of translucent, non-cylindrical, and/or twisted fibres with thicknesses in the range 2-5 μm. Forcibly silked major ampullate fibres from Nephila clavipes spiders were used as specimens. Scanning electron microscopy was used to calibrate the extent to which laser diffraction over- or under-estimates fibre diameter. For the purpose of area measurement, elliptical or oval cross-sections can be treated as though they were circular. We demonstrate mathematically that the area can be obtained to within a few per cent of the true value, if (a) the circle is assigned an "equivalent diameter" equal to the average of at least four measurements of apparent diameter, (b) the apparent diameter measurements are taken at equal intervals of fibre rotation through a 180° range, and (c) the axial ratio of the cross-section is less than 1.5. The extent to which a non-cylindrical fibre is twisted can be deduced from the periodicity of bright and dark regions that alternate along the length of the fibre in reflected light. Values of cross-sectional ellipticity and area measured from a twisted fibre were smaller than the corresponding values obtained from a twist-free fibre. The apparent diameter of twist-free major ampullate fibre was found to be highly variable-by as much as ±20% relative to the mean within a 0.6 mm length. Therefore, local measurements of area, rather than a value derived from fibre denier, should be used in tensile property evaluation of this material.