PSI - Issue 33

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

875

Fig. 3. Fields of distribution of equivalent stresses at the last step of loading a smooth specimen.

Further in the work, in order to initiate the localization of deformations and the formation of a "neck" in the center of the working part of the sample, the initial reduction in diameter by 0.05 mm is laid, which is less than 1 % in relation to the nominal diameter. This deviation of the diameter of the working part of the specimen meets the geometric tolerances in the manufacture of specimens for testing. According to the results of solving the problem for point 5 (Table 3), it can be seen that the localization of plastic deformations begins to develop in the working part of the sample and a neck is formed in the central zone of the working part. The value of the maximum relative transverse constriction in the test section δmax increased to 6.9 %. The distribution fields of equivalent stresses (a) and equivalent deformations (b) are shown in Figure 4.

a

b

Fig. 4. Fields of distribution of equivalent stresses (a) and equivalent deformations (b) after calculation for point 5 (Table 3).

The obtained calculation data show that, starting from the solution of the problem for the fifth point corresponding to the ultimate strength of the material, the process of localization of deformations and the formation of a "neck" in the working part of the sample is observed. At all subsequent stages of postcritical deformation, the localization of deformations progresses and the “neck” in the working part of the specimen progresses. At the last stage of postcritical deformation, the value of the maximum relative transverse contraction δmax was 75.9%. The distribution fields of equivalent stresses (a) and equivalent deformations (b) are shown in Figure 5. Figure 5 (a) shows that the maximum stress values arise in the peripheral zones of the working part of the specimen, and in the neck zone the stresses are lower, since the material in the neck is at the stage of postcritical deformation. The maximum deformations are observed in the localization zone (Figure 5, b). To analyze the obtained simulation results, as well as to compare them with experimental data, Figure 6 shows the dependences of the conditional stresses σ on the value of the applied displacement ux obtained in test (1), the simulation data for the sample of the initial smooth geometry (2) and the sample with the initial narrowing of the working part (3). Figure 7 shows an image of the initial shape of the sample in an undeformed state (transparent contour) and the final geometry after calculation (blue contour).