Statistical criteria for the limits of application of Hooke's law

Modern methods for studying the stress-strain state of solids use graphical methods based on a stress-strain curve to determine the transition from elastic deformation to plastic deformation. However, this approach is not formal and it is intended only for when stress is a function of strain in the one-dimensional case. Cases, when strain is a function of the stress, are also of practical importance. The purpose of the study is to develop formal rules for determining the limits of applicability of Hooke's law. The proposed analytical methods for determining the transition from elastic deformation to plastic deformation are based on consistent statistical sequential. In this article, quadratic forms are derived for calculating the point at which the type of an increasing monotonous numerical sequence changes from linear to non-linear type. With the help of these quadratic forms, statistical criteria (approximation-estimation tests) are constructed to determine the limits of applicability for Hooke's law. These boundaries are defined as Markov moments. The novelty of the results shows that it is possible to determine the yield point without visualizing the experimental data. The numerical example of the application of a parabolic approximation-estimation test is provided. From the results of this experiment, it can be concluded that the analytical determination of the limits of applicability of Hooke's law coincides with a visual assessment. Approximation-estimation tests provide an opportunity to determine the limits of applicability of Hooke's law analytically.