Gaussian and Non-Gaussian Distributions of Fracture Properties in Tensile Stretching of High-Density Polyethylene

Tensile Strength Statistics of High-Performance Mono- and Multifilament Polymeric Materials: On the Validity of Normality

Recently, the statistical distributions of the mechanical properties, including tensile strength (σ), of several high-strength high-modulus oriented polymeric materials have been analyzed by employing the Weibull's and Gaussian statistical models. However, a more detailed comprehensive analysis of the distributions of the mechanical properties of these materials aimed to estimate the validity of normality by employing some other statistical approaches, is needed. In the present work, the σ statistical distributions of the seven high-strength oriented polymeric materials based on the polymers with three different chain architectures and conformations, ultra-high-molecular-weight polyethylene (UHMWPE), polyamide 6 (PA 6), and polypropylene (PP), each in the form of both single and multifilament fibers, have been investigated using graphical methods, such as the normal probability and quantile-quantile plots, and six selected formal normality tests, such as the Kolmogorov-Smirnov, Shapiro-Wilk, Lilliefors, Anderson-Darling, D'Agostino-K squared, and Chen-Shapiro tests. It has been found that the conformity of the σ distribution curves to the normal distribution, including the linearity of the normal probability plots, for the materials with lower strengths (σ < 1 GPa, quasi-ductile PA 6- and PP-based materials) is more correct as compared to those for the materials with markedly higher strengths (σ > 4 GPa, quasi-brittle UHMWPE-based materials). The impact of the sample type (single or multifilament fibers) on this behavior turned out to be negligible.

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

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.