Modeling of Cyclic Elastoplastic Deformation During Material Testing for Bending

Abstract

In the strength calculations of structural elements for the characterization of the stress state in dangerous concentration zones (thread sections, various recesses, change of shaft diameters, holes, keyways, cracks) nominal stresses are used, which are determined without taking into account the influence of the concentrator, or local conditional stresses, which are calculated under the assumption of elastic deformation as multiplication of nominal stresses and theoretical concentration coefficient. In reality, when the structures are overloaded and often under the standard modes of variable loading, three-dimensional inhomogeneous fields of the main local stresses and elastoplastic deformations arise in the concentration zones, which are changed with increasing number of loads as a result of cyclic instability of materials. To determine the stresses and elastoplastic deformations of the load-bearing elements of structures under a simple (proportional or close to it) single loading, a comparatively well-developed theory of small elastoplastic deformations in the formulation of A. A. Il'yushin is widely used. With respect to variable proportional loading, the deformation theory of plasticity has been developed and experimentally substantiated not to the full extent largely due to the lack of modern test equipment, available experimental techniques and the limited experimental results characterizing the regularities of cyclic elastoplastic deformation of a wide range of structural materials in a wide range of the number of loads characteristic for load-bearing elements of structures. In connection with this, the relatively simple methodology presented in this paper, the available equipment and the results of experimental and analytical modeling of the regularities of cyclic elastoplastic deformation during testing of the material for bending are of scientific and practical importance for improving the methods for estimating the fatigue strength and durability of load-bearing structural elements.