Abstract

The macroscopic and phenomenological stress-strain curves of various natural and synthetic fibers have been analyzed without the need to consider microscopic mechanisms. A new concept involving the “average stress-strain curve” or contour line for fibrous materials was proposed and used to successfully analyze the extremely large data sets obtained for wool and PET (polyethylene terephthalate)-POY (partially oriented yarn) fibers. This new method is necessary to quantitatively analyze the mechanical properties of fibrous materials. Our method proved to be useful to eliminate the significant statistical fluctuations that are usually attributed to sample deviations of fibers. Based on the relationship between experimentally measured load-extension, the stress σf at each point during the entire process of strain development from 0 to εf was averaged. The need to truncate parts of the experimental data at fracture proved to be crucial. From a purely mathematical point of view, two averaging methods for stress under a given strain can be applied. One is to average based on sample size and the other based on sample size immediately before fracture. The physical bases of the two methods are proposed. This concept and method are expected to be extended to other types of materials to obtain their “average stress-strain curve”.

Keywords:Mechanical properties; Stress-strain curve; Fracture strength; Elongation at break; Wool; PET; POY