PSI - Issue 33

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Evgeny Lomakin et al. / Procedia Structural Integrity 33 (2021) 809–817 Lomakin E.V., Fedulov B.N. / Structural Integrity Procedia 00 (2019) 000–000

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Fig. 2. Normalized limit loads Integrating over OM line of �� , we obtain limit load values shown in Fig.2. Limit loads obtained for different variants of angle cuts and the stress state sensitivity parameter C of plastic material’s properties . It is possible to see smooth decay of limit load values in case of increase of material parameter C for all angles of cuts . 3.2 Numerical solution In the previous sections, the analytical solution was obtained based on a rigid-plastic model of the material. The error of this approximation is quite difficult to estimate. To do this, we need to get an elastic-plastic solution, which is associated with certain difficulties. In fact, there is no reason to state that when the Young's modulus tends to infinity, the elastic-plastic solution will tend to a solution obtained using the rigid-plastic approach. It is obvious that the difference between the complete elastic-plastic and the used rigid-plastic solution scheme can significantly depend on the type of the problem, on the geometry and the degree of development of plastic processes in the deforming solid body. Anyway, in order to argue about the validity of the obtained solutions, it is necessary to obtain experimental data on real solid details or to perform numerical elastic-plastic solutions. To obtain numerical solution for the strip with V-shape cuts special subroutine realizing elastic-plastic behavior eq. (1) with linear sensitivity (2) for ABAQUS software was developed. Material properties with slight hardening were used. Elastic constants were chosen as E = 200000 , ν = 0 . 3 . Hardening behavior was modeled by changing parameter k in plasticity criterion (1) introducing dependence on equivalent plastic strain ε �� � � �ε� � � � � ε� � � � � dt , where � � � � -plastic strains. The chosen dependence �� �� � has the following form:

k (0 . 0000) = 200 , k (0 . 0009) = 220 , k (0 . 0022) = 225 , k (1 . 0000) = 226 .

Four nodes full integrated elements with plane strain formulations were used. Numerical mesh used for the analysis is shown in Fig. 3. Only one quarter of the geometry was modelled due to symmetry. There is a finer mesh in the model near concentrator. Fig 4 - 7 show results of numerical modelling: displacements, stress values, equivalent plastic strain and the invariants.