Statistical Analysis of the Mechanical Behavior of High-Performance Polymers: Weibull’s or Gaussian Distributions?

Abstract

This work addresses the following problem: which of the statistical approaches, Weibull’s or Gaussian, is more appropriate to correctly describe the statistical distributions of the mechanical properties of the high-performance polymer materials of different sample types (single or multifilament oriented fibers) and chain architectures (ultra-high-molecular-weight polyethylene, polyamide 6, or polypropylene)? Along with the routine mechanical properties such as strength, strain at break, and Young’s modulus, an apparent viscoelastic modulus and an apparent strain at break found when differentiating the stress–strain curves have been considered for the first time. For this purpose, a large sample number (50 in each series) has been tested. It has been shown that the values of the Weibull’s modulus (m) characterizing the data scatter were dependent both on the chain architecture and the sample type for the five elastic, viscoelastic and fracture characteristics analyzed. The Weibull’s model has been found to be more correct as compared to the Gaussian one. The different statistical approaches used for the analysis of the large arrays of the data are important for a better understanding of the deformation and fracture mechanisms of quasi-brittle and quasi-ductile high-performance polymer materials.