Deformation and strength of silica fibers in three-point bending in consideration of nonlinear elasticity of glass

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

“…In this strain range, the onset of the local fracture processes (chain scission, interfibrillar slipping) is expected. Hence, this mechanical property ‘approaches’ the fracture properties such as σ and ε b for which the Weibull’s model works properly [ 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 ]. On the other hand, the E 1 value characterizes the very beginning of the sample deformation.…”

“…This behavior is due to the formation and development of surface microcracks at the final stages of orientational drawing, the so-called kink bands, which are initiators of the most intense crack growth at the deformation stages preceding the sample failure [ 1 , 2 ]. For this reason, in order to correctly estimate the average values of σ , E , and strain at break ( ε b ), σ av , E av , and ε av , which are important characteristics playing a key role in choosing the most appropriate fields for material applications, the number of identical samples to be tested should be increased markedly, from the generally accepted about five [ 5 , 6 , 7 , 8 ] to some dozens, or even hundreds [ 2 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 ]. In this case, the statistical distributions of mechanical properties can also be analyzed, and additional information obtained, for instance, on their conformity to a certain theoretical model (e.g., Gaussian [ 23 ], Weibull’s [ 9 , 10 , 11 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 ]).…”

“…For this reason, in order to correctly estimate the average values of σ , E , and strain at break ( ε b ), σ av , E av , and ε av , which are important characteristics playing a key role in choosing the most appropriate fields for material applications, the number of identical samples to be tested should be increased markedly, from the generally accepted about five [ 5 , 6 , 7 , 8 ] to some dozens, or even hundreds [ 2 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 ]. In this case, the statistical distributions of mechanical properties can also be analyzed, and additional information obtained, for instance, on their conformity to a certain theoretical model (e.g., Gaussian [ 23 ], Weibull’s [ 9 , 10 , 11 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 ]). It can be helpful for a better understanding of the deformation and fracture mechanisms of materials and for making a more proper recommendation about their practical use.…”

Evolution of Statistical Strength during the Contact of Amorphous Polymer Specimens below the Glass Transition Temperature: Influence of Chain Length

“…In turn, learning the most correct form of this distribution can give complementary useful information aimed at in-depth analysis of the deformation and fracture mechanisms in materials of various chemical origins. Indeed, on one hand, for the materials characterized by both extremely high ( σ > 1 GPa [ 5 , 6 , 7 ], both organic and inorganic fibers) and extremely low strengths ( σ < 1 MPa [ 8 , 9 , 10 , 11 ], weak polymer–polymer interfaces), i.e., for the materials drastically differing in the σ value, by 3 orders of magnitude, the σ statistical distributions have been found to follow the same distribution form: the Weibull distribution [ 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 ]. In this case, one observes a linear plot in the specific coordinates lnln [1/(1 − P j )] = f(ln σ ), where P j is the cumulative probability of failure.…”

“…It is important to note that the validity of a given distribution type implies a certain mechanism of deformation or fracture. For instance, if the Weibull distribution for σ holds [ 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 ], it indicates that the fracture process is dominated by the presence of surface cracks and their propagation across the sample cross-section [ 6 ]. By contrast, if the Gaussian model is most correct, it suggests that the deformation or fracture process is controlled by many factors which are independent and equally weighted [ 21 , 22 , 23 ].…”