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

Abstract

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.

Tensile Strength Statistics and Fracture Mechanism of Ultrahigh Molecular Weight Polyethylene Fibers: On the Weibull Distribution

“…Schwartz et al 35 also studied the influence of strain rate and gauge length on fiber properties based on the Weibull model, and their research made a great contribution to the application of the Weibull model in the field of UHMWPE. With the support of the "weakest link" theory, we speculated that the UHMWPE fiber monofilaments with flexible macromolecular chains meet the Weibull distribution, which has been proved by Boiko et al, 31,32 but it does not mean that the fiber bundles will also meet the Weibull distribution. 36,37 This is important, especially when the filament bundle is the main application.…”

“…With the support of the “weakest link” theory, we speculated that the UHMWPE fiber monofilaments with flexible macromolecular chains meet the Weibull distribution, which has been proved by Boiko et al, , but it does not mean that the fiber bundles will also meet the Weibull distribution. , This is important, especially when the filament bundle is the main application.…”

“…The Weibull distribution is based on the “weakest link” theory . If the strength distribution of the fiber conforms to the Weibull function, it means that its fracture is affected by random defects, which may be surface cracks, interface defects, , chain entanglement, and end points . In addition, for brittle materials, on the one hand, fracture is difficult to predict, and crack propagation rarely occurs; on the other hand, the strength of fiber materials is very discrete, and unexpected fractures are easy to occur when the average value is used to describe the strength properties of the fiber.…”

“…At present, many studies have extended the application of Weibull distribution to natural fiber materials, such as wool, spider silks, and plant fibers . In the field of chemical fibers, Boiko et al ,− used the Weibull model in several studies to analyze fiber, spinning solvent, sample types (monofilament or multifilament), and mechanical properties (strength, modulus, strain). The studies involved materials such as UHMWPE fiber, polyamide6, and polypropylene.…”