PSI - Issue 33

M.P. Tretyakov et al. / Procedia Structural Integrity 33 (2021) 871–877 Author name / Structural Integrity Procedia 00 (2019) 000–0 0

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Fig. 1. Specified piecewise linear dependence characterizing the elastoplastic behavior of steel 40Cr with a section of nonlinear hardening and postcritical deformation.

Fig. 2. View of the design model of a cylindrical sample after discretization.

For the numerical solution of the problem, a geometric model of a cylindrical steel sample of the following dimensions was built: diameter of the working part d 0 = 12 mm; length of the working part l 0 = 60 mm; the radius of the transition from the working to the gripping parts R = 25 mm; diameter of gripping parts D = 20 mm; length of the gripping parts h = 25 mm. This sample geometry meets the requirements of GOST 1497-84 Metals. Tensile Test Methods. To select the degree of discretization of the computational domain, a multistep iterative procedure was carried out with an estimate of the convergence of the results in terms of the value of the maximum equivalent von Mises stresses. A breakdown into 8024 finite elements was chosen, which corresponded to the convergence condition. Discretization of the cylindrical sample was carried out on hexahedral 8-node finite elements SOLID185. The view of a cylindrical specimen after subdivision into a finite element mesh is shown in Figure 2. To solve the problem with a section of nonlinear hardening and softening, a model of multilinear kinematic hardening, independent of the strain rate, was used, which makes it possible to simulate material softening. In the calculations, the left side of the sample was fixed relative to the longitudinal direction (u x = 0), as well as from preventing rotation along the x axis. On the right side of the specimen, displacements u x = u 0 are specified, which corresponds to the “rigid” loading scheme. The elastoplastic problem was solved in several stages with a gradual increase in the value of the specified initial displacement u 0 . 3. Results and discussion When solving problems of modeling the formation of a neck in a sample, the literature provides two ways: changing the initial geometry (reducing the diameter of the working part) or underestimating the mechanical properties (Young's modulus or yield stress). As a result, it is possible to initiate plastic flow in a given area and to study how the development of localization of deformations occurs. In the case when the specified methods are not used in the problem, the localization of deformations in the form of a neck is not observed (as a rule, when the working part of the specimen is modeled without gripping areas, or double localization may occur (determined by symmetry, when the specimen with gripping parts is modeled). Figure 3 shows the results of solving the problem for a sample with a smooth working part. In this case, due to the appearance of an uneven complex stress state caused by the presence of transition areas from the working area of the sample to the gripping ones, two zones of localization of deformations are formed in the immediate vicinity of the transition areas.