About spearmen’s factor of rank correlation for characteristics of durability of composite materials

Based on the results of tensile, compression, bending and interlayer shear tests on carbon fiber plastic samples made on the basis of unidirectional carbon fabric and an epoxy binder (reinforcement direction 0), as well as on the results of tensile and compression tests on fiberglass samples based on glass fabric and an epoxy binder, the coefficients were determined by Spearmen’s factor of rank correlation, and the corresponding empirical regression equations of strength characteristics for various stress ranges were obtained. It is shown that to assess the close relationship (correlation) of the strength characteristics of composite materials, the use of Spearmen’s factor of rank correlation coefficient is appropriate and effective in the case where the distribution of samples of experimental values is different from normal or compliance with the normal distribution law is questionable due to high scatters. At the same time, in contrast to the Pearson linear correlation coefficient, the Spearmen’s factor of rank correlation coefficient makes it possible to evaluate not only the linear relationship of characteristics, but nonlinear monotonic functional relationships that are characteristic of the strength characteristics of most structural composite materials. For the considered composite materials, the Spearmen’s factor of rank correlation coefficient was determined and the corresponding empirical dependencies and regression equations of strength characteristics were obtained for various stress ranges, which can be used in evaluation calculations of strength, in mathematical modeling and planning mechanical tests. Establishing statistically substantiated functional (both linear and nonlinear) dependencies between the main, including between the calculated strength characteristics, assessing the type and parameters of distributions of experimental values of the strength and elasticity characteristics of composite materials is one of the main tasks aimed at ensuring effective and safe operation of products and structures made of polymer composite materials.

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