Statistical elastic and fracture mechanical properties of quasi-brittle and ductile amorphous polymers

The main goal of this work was to elucidate, for the first time, the applicability of Gaussian and Weibull statistical models to describe the distributions of the mechanical properties of quasi-brittle and ductile amorphous polymers and miscible blends thereof characterizing by tensile strength of common materials of order of 10–100 MPa. For this purpose, the distributions of tensile strength ( σ ), strain at break ( ε ), and Young’s modulus ( E ) of polystyrene (PS), poly(2,6-dimethyl-1,4-phenylene oxide) (PPO), and two miscible blends thereof with different PS/PPO weight ratios (3/1 and 1/1) have been analyzed using the Gaussian and Weibull statistical models. It has been shown that the applicability of a chosen theoretical model to correctly describe the statistical distribution of a measured mechanical property was dependent on the property analyzed ( σ , ε , or E ), the sample brittleness [quasi-brittle PS ( ε = 3%) and PS/PPO blends ( ε = 4–5%) or ductile PPO ( ε = 20%)], and the PPO content in the test samples. Scatter of the experimental data of σ , ε , and E for the four polymer systems investigated has been characterized with the Weibull modulus ( m ) calculated from the plots constructed in specific coordinates “loglog(function of fracture probability) − log(property).” The calculated values of m for PS, PPO, and PS/PPO blends have been compared with those reported in the literature for ultra-high-strength materials of various natures ( σ > 1 GPa) and low-strength polymer–polymer interfaces ( σ