Deterministic method to calculate the strength of cotton yarns
Abstract
The strength of cotton yarns as fibrous materials is determined from experiments with sufficient reliability. In addition, there are theoretical and empirical formulas for calculating the strength of cotton yarns. On the example of A.N. Soloviov's formula, it is shown that the structure of cotton yarn and the process of its strain under stretching to breakage are based on approximate assumptions and idealizations. A physically and mathematically substantiated deterministic method for determining the strength of cotton yarn is proposed. The proposed method is based on a formula derived from a physically nonlinear law of yarn strain, developed on the basis of an analysis of the results of serial experiments on stretching the yarn to breakage. The results of calculations by the deterministic method are compared with the results of experiments for three types of cotton yarns, produced by different technological methods. The results of the comparisons showed good agreement between the calculated and experimental data. This confirms the reliability of the proposed deterministic method.